notes-books-kant prolegomena to any future metaphysics intermediate1

These are the more literal notes. Please see Self:notes-books-kant_prolegomena_to_any_future_metaphysics_intermediate2 for a more summarized version.

Copyright 2007 Bayle Shanks released under the Creative Commons Sharealike NC 2.0 license.

This should go without saying when i post notes on a book, particularly on something that i understand as little as philosophy, but: i'm probably misinterpreting some things and so some of this is probably wrong.

Note that most statements found on this page are my interpretation of what Kant says, not statements about what I personally believe. Indeed, when I say "I" below, I am usually speaking as Kant, except in my aside, and in my footnotes.

Some of my interpretations are close to Kant's phrasings. Not quoting something does not mean that I claim credit for coming up with a totally different, better phrasing, it means only that I do not assert that it is exactly what Kant (as translated) said.

Even when I quote Kant (double quotes), I make very liberal use of ellipsis (...). Sometimes I even skip over things that slightly change the meaning, such as qualifications that I consider unnecessary.

I want to note somewhere that a friend has suggested that Kant provides a blueprint for the mind of a rational being (my words, not his), and, as a student of cognitive studies, this is my primary interest in reading Kant.

Kant. Prolegomena to any future metaphysics. Translated and edited by Gary Hatfield. Revised edition. Cambridge Texts in the History of Philosophy.


The main question of this book is: is metaphysics possible?

Hume and the concept of Cause

I got to thinking about this stuff after reading David Hume. Hume studied the the connection of cause and effect.

Defn "cause": If A causes B, then if A is posited, B necessarily must also be posited.

Hume asked if the connection of cause and effect between two events can be deduced a priori using reason. His answer was no. Everyone misunderstood Hume. People thought he was arguing that we should give up thinking in terms of cause and effect, which he was not. Hume agreed that, when thinking about the physical world, cause and effect is indispensible. Hume's question was just, is the connection between cause and effect an a priori concept borne of pure reason?

Hume's argument was that the connection between cause and effect contains necessity. If you can conceive of two different things A and B, then it doesn't make sense to say a priori that just because A is, B must necessarily also be.

Hume then concluded that the concept of the connection of cause and effect has nothing to do with a priori pure reason, and is really just an a posteriori observation. I say, rather, that the concept of cause, considered in general, is in fact a priori.

In terms of method, I don't agree with philosophers who want to appeal to "ordinary common sense" to decide what is correct philosophy. Common sense is great for everyday life, but when you are debating people with different points of view, you need to use rigor. Hume's opponents said that cause and effect are real just because common sense says it is so. By contrast, I aim to give a rigorous ground for my views.

I have come to the conclusion that there are also other concepts which, similar to the concept of cause and effect, which are a priori. In the Critique of Pure Reason, I prove a formal deduction of these concepts. I also rigorously determine the boundaries of correct a priori reasoning.

What this book is

I have written this Prolegomena as an prologue to the Critique of Pure Reason. The Critique is difficult to read and so I thought it would be helpful to have an overview of it. The Prolegonmena gives the plan for the work that is actually carried out in the Critique. However, please look at this work as only preparatory exercises for reading the Critique.

In the Critique, I have attempted to completely describe the boundaries of the domain of pure reason. Because pure reason is such an isolated domain, there is nothing outside of it that could correct our judgement within it. Therefore, the validity and use of each part depends on the relation in which it stands to the others within reason itself. And so I think a Critique of Pure Reason must be entirely complete to be convincing, and that in the domain of this faculty one must determine and settle either all or nothing.

Even if you don't agree with my solution to the problem of how metaphysics can exist, this Prolegomena will still be useful because it certainly shows that the question of whether and how metaphysics can exist must be answered.


"reason": a faculty

"the understanding": a faculty

"a posteriori": reasoning that make use of things which are given in experience

"a priori": reasoning that is not a posteriori; "has an inner truth independent of all experience". Often Kant puts "a priori" after a noun phrase where I would have put it before (as a modifier of the noun phrase); for example, at once place later on he says that such-and-such can consist only of "judgements a priori", whereas I think the normal usage nowdays is to say "a priori judgements".

"pure": synonym for a priori

"pure reason": the faculty of a priori reasoning

"apodictic": an apodictic statement is one that is irresistibly convincing (i.e. any reasonable person will be convinced of it)

"science": an area of study which is irresistably convincing

"natural science": an area of study including both what we today would call "science", i.e. the deduction of natural laws from a posteriori experimentation, and also what we today would call part of philosophy, i.e. a priori reasoning about concepts used for the interpretation of the world. This is a little confusing because Kant says that there are parts of natural science which are necessarily true and which can be taken as a priori. He doesn't mean physical laws which we deduce from experimentation, though, he means various deductions that we would today call "philosophy" rather than "science".

Preamble on the distinguishing feature of all metaphysical cognition

1: On the sources of metaphysics

By definition, the source of metaphysical cognition cannot be empirical, and must therefore be a priori.

What's the difference between metaphysics and mathematics? The reader is referred to pp. 712 f. of the Critique of Pure Reason.

2: On the type of cognition that can alone be called metaphysical

On the distinction between synthetic and analytic judgements in general

Propositions are usually either analytic, or synthetic, or explicative.

defn Explicative propositions: propositions that merely re-explain without adding any new content.

defn Analytic judgements: "say nothing in the predicate except what was thought already in the concept of the subject, though not so clearly nor with the same consciousness".

The common principal of all analytic judgements is the principal of contradiction. For example, the definition of "body" is "something with extension", and from this you can derive "every body is extended" and also "no body is unextended". Another example: the definition of gold (actually, he says "the concept of gold") includes that gold is a body, is yellow, and is a metal. So you can say "gold is a yellow metal" and this is an analytic judgement. The second example shows that analytic judgements may concern themselves with empirical concepts.

defn Synthetic judgements: those which require a principal other than the principal of contradiction.

So, if you make a (content-ful) judgement that isn't analytic, then that judgement is synthetic. This isn't to say that synthetic judgements can contradict analytic ones; they have to be consistent with analytic judgements, but they go further.

Note that synthetic propositions might still be necessarily true.

Aside from Bayle

I know of at least two ways to interpret Kant's analytic/synthetic distinction. Part of this discussion will follow Wikipedia (;; 13 August 2007) Before giving the alternate interpretations, let's restate Kant's definition of the terms:

analytic proposition (according to Kant acc. to wikipedia): a proposition whose predicate concept is contained in its subject concept

synthetic proposition (acc. to Kant acc. to wikipedia): a proposition whose predicate concept is not contained in its subject concept

Interpretation #1 (the logical positivist interpretation)

The first way, which I tend to agree with, is that what Kant meant was this (ignoring explicative propositions):

analytic proposition: a proposition whose truth depends solely on the meaning of its terms

synthetic proposition: a proposition which is not an analytic proposition

A very similar definition would be:

analytic proposition: a proposition that is true by definition

synthetic proposition: a proposition which is not an analytic proposition

Note that under this interpretation, a mathematical proof (a deduction using accepted formal rules of logic, once the axioms are taken as given) is analytic. Such a deduction is necessarily true just because of the formal definitions of things, given the axioms.

But Kant says that mathematics is not analytic1. How can that be? Under this interpretation, we read that as meaning that the choice of axioms, and in that, relation of mathematical concepts to the real world, goes beyond analytic. For instance, the decision that space is 3 dimensional (which is involved in choosing axioms for the mathematics of space) is a synthetic one. We could do formal mathematics with different axioms, but they wouldn't describe actual space.

Interpretation #2 (my friend's interpretation)

A friend of mine has a different interpretation. In this interpretation, synthetic is when the representation (a representation is here thought of as a data structure) of the conclusion of the theorem is different from the representation of the premises. Therefore it's not the case that the conclusion of the theorem says nothing "except what was thought already in the concept of the [premises]". So, in hir interpretation, a formal proof need not be analytic. An example of something analytic is when you start with one representation, and then present just a restricted part of the same representation; for instance, if gold is defined as "yellow metal", then you can say, "gold is yellow".

Under this interpretation, a formal deduction might be considered synthetic even if the axioms are taken as given, if the conclusion of the proof is put into a different representation than the premises.

Why there are multiple interpretations

The Wikipedia page is helpful here.

Wikipedia says that "One common criticism is that Kant's notion of 'conceptual containment' is highly metaphorical, and thus unclear." Wikipedia goes on to say that, "the logical positivists drew a new distinction, and, inheriting the terms from Kant, christened it the "analytic/synthetic distinction."

However, my friend presents an interpretation of the terms that is quite different from the logical positivists', yet still consistent with Kant's definition.

Therefore I conclude that Kant's definition is indeed underspecified, due, as Wikipedia suggests, to its metaphorical nature (specifically, the notion of "conceptual containment"; Kant's definition uses the notion of "what was thought already in the concept of the subject", but since he hasn't defined (at least not prior to this definition in the text of the prolegomena) the terms "thought", "concept", or what it means for a thought to be "in" a concept). This metaphorical nature permits multiple very different interpretations to be consistent with Kant's words.

Luckily, although Kant states that the distinction between analytic and synthetic is essential for metaphysics, in my opinion very few of the arguments in the Prolegomena require the reader to make use of this concept. So the reader may continue onward without pausing to take firm stance on this issue.

I note that as a matter of hermeneutics, my friend proposes that the way such interpretation questions should be resolved is to choose whichever interpretations allows Kant not to contradict himself or make any errors.

Not to bias the reader's choice of interpretation of Kant, but merely to inform the reader of how the term is commonly used today, the current usage of the term is given by Wikipedia as "Analytic propositions are those which are true simply in virtue of their meaning while synthetic propositions are not." (i.e. the first of the definitions that Wikipedia says were put forward by the logical positivists).

Types of synthetic judgments

There are three types of synthetic judgements:

Properly metaphysical judgements are simply defined as those metaphysical judgements which are not analytic.

3: Note on the general division of judgements into analytic and synthetic

Another example of a judgement that is synthetic (although Kant doesn't say whether or not he agrees with it) is the principal of sufficient reason.


judgements: i dunno, but at the beginning of "On the distinction between synthetic and analytic judgements in general", he says that "metaphysical cognition must contain nothing but judgements a priori", so I guess a body of knowledge is made of judgements.

"principal of sufficient reason": "The principal of sufficient reason proposes that some sort of explanation must exist for everything" (

General question of the Prolegomena: Is metaphysics possible at all?


If there were a book or body of knowledge on the topic of metaphysics that argued from pure reason and was irresistibly convincing, then that would serve as an existence proof that metaphysics is possible. But since we don't have such a book, we'll have to consider the question by other methods.

The highest aim of metaphysics is "knowledge of a supreme being and a future life, proven from principals of pure reason".

What has been done so far? Many analytic metaphysical propositions have been derived. But the synthetic propositions which have been presented (for instance, the principal of sufficient reason) have not been "proved a priori" 2

Although we must not assume that metaphysics is possible, we do know that at least some a priori synthetic judgements exist. There are a priori synthetic judgments in mathematics (see above) and also in the philosophy of nature.


problematic: i think that by this he means that some concept has the status that we don't even know if it's possible or not. We can't just use the phrase "a possible concept" because maybe later we'll prove that it's impossible. So instead of calling it "a possible concept", he calls it a "problematic" concept. Not sure about this though.

General question: how is cognition from pure reason possible?


OK, actually, everyone can see how a priori analytic judgements 3 are possible 4. So really we just want to show that a priori synthetic judgements are possible.

So the question is really just:

How are a priori synthetic propositions possible?

"Transcendental philosophy" is the complete solution of this problem. Transcendental philosophy precedes metaphysics because its task is to settle the possibility of metaphysics in the first place.

We're going to divide the question into four parts and apply the analytic method:

  1. How is pure mathematics possible?
  2. How is pure natural science possible?
  3. How is metaphysics in general possible?
  4. How is metaphysics as science possible?

The main transcendental question, first part: how is pure mathematics possible?


To review, mathematics gives us a priori synthetic judgements which are certain. How?


We find that mathematics "must present its concept beforehand __in intuition__ and indeed a priori, consequently in an intuition that is not empirical but pure... in the place of which philosophy can content itself with discursive judgements from mere concepts, and can indeed exemplify its apodictic teachings through intuition but can never derive them from it."

Mathematics "must be grounded in some pure intutition or other, in which it can present, or, as one calls it, construct all of its concepts in concreto yet a priori".

So "if we could discover this pure intuition and its possibility" then we're set because it would explain how a priori synthetic judgements are possible in mathematics.


Now, we can form some concepts a priori, without our being in an immediate relation to an object (namely, those that contain only the thinking of an object in general). Examples: the concept of magnitude, of cause. But even these still require, in order to provide them with signification and sense, a certain use in concreto, i.e. application to some intuition or other, by which an object for them is given to us.

But not intuitions:

An intuition is a representation.

An intuition requires the immediate presence of an object.

"It therefore seems impossible originally to intuit a priori, since then the intutition would have to occur without an object being present..."


Well, so we have some kind of intuition that we can get without the presence of any external object. What do we have left? We have ourselves ("the subject"). So, the intuition must contain nothing except something about the subject. There's only one thing it could contain; "the form of sensibility, which in me as subject precedes all actual impressions through which I am affected by objects. For I can know a priori that the objects of the senses can be intuited only in accordance with this form of sensibility.



Note that our a priori intuition of the form of sensibility only gives us information about how objects appear to us (i.e. are perceived through our senses), not how objects are in and of themselves. So we still don't have any a priori knowledge about objects in and of themselves. But we do have some a priori knowledge about what kinds of appearences it is possible for us to experience.

"Now space and time are the intuitions upon which pure mathematics bases all its cognitions and judgements..."


"...for mathemtics must first exhibit all of its concepts in intuition..."


"... and pure mathematics is pure intuition - "


"that is, it must first construct them, failing which (since mathematics cannot proceed analytically, namely, through the analysis of concepts, but only synthetically) it is impossible for it to advance a step, that is, as long as it lacks pure intuition, in which alone the material for synthetic judgements a priori can be given".

"Geometry bases itself on the pure intuition of space. Even arithmetic forms its concepts of numbers through successive addition of units in time, but above all pure mechanics can form its concepts of motion only by means of the representation of time. Both representations" (space and time, I think), "are, however, merely intuitions...from the very fact of that they are pure intuitions a prioi, they prove that they are mere forms of our sensibility that must precede all empirical intutition (i.e. the perception of actual objects)"


To summarize the last few sections:

"The problem of the present section is therefore solved."

"Pure mathematics, as synthetic cognition a priori, is possible only because it refers to no other objects than mere objects of the senses, the empirical intuition of which is based on a pure and indeed a priori intuition (of space and time), and can be so based because this pure intuition is nothing but the mere form of sensibility, which precedes the actual appearance of objects, since it is fact first makes this appearance possible."

"This faculty of intuiting a priori does not, however, concern the matter of appearance - i.e. , that which is sensation in the appearance, for that constitutes the empirical - but only the form of appearance, space and time."



"the usual and avoidably necessary procedure of the geometers. All proofs of the thoroughgoing equality of two given figures (that one can in all parts be put in the place of the other) ultimately come down to this: that they are congruent with one another; which plainly is nothing other than a synthetic propostion based upon immediate intuition; and this intuition must be... a priori"

"That... space... has three dimensions.... can, however, by no means be proven from concepts, but rests immediately upon intuition, and indeed on pure a priori intuition..."

"...that we can require that a line should be drawn to infinity... or that a series of alterations (e.g. spaces traversed through motion) should be continued to infinity, presupposed a representation of space and time that can only inhere in intuition, that is, insofar as the latter is not in itself bounded by anything; for this could never be concluded by concepts."


A paradox that supports my idea that space and time are not "actual qualities attaching to things in themselves" but are rather "mere forms of our sensory intuition".

"If two things are fully the same (in all determinations belonging to magnitude and quality) in all the parts of each that can always be cognized by itself alone, it should indeed then follow that one, in all cases and respects, can be put in the place of the other, without this exchange causing the least recognizable difference."

But consider two objects which are mirror-images of each other, for instance, my left hand and my right hand, or my ear and its image in the mirror. But you can't switch these things. A left-handed glove won't fit the right hand. "...there are no inner differences here that any understanding could merely think; and yet the differences are inner as far as the senses teach.."

Therefore, "These objects are surely not representations of things as they are in themselves, and as the pure understanding would cognize them; rather, they are sensory intuitions, i.e. appearances, whose possibility rests of the relation of certain things, unknown in themselves, to something else, namely our sensibility. Now, space is the form of outer intuition of this sensibility, and the inner determination of any space is possible only through the determination of the outer relation to the whole space of which the space is a part (the relation to outer sense); that is, the part is possible only through the whole, which never occurs with things in themselves as objects of the understanding alone, but does occur with mere appearances. We can therefore make the difference between similar and equal but nonetheless incongruent things (e.g. oppositely spiralled snails) intelligible through no concept alone, but only through the relation to right-hand and left-hand, which refers immediately to intutition"


Note 1 (Kant's note, not my note)

"Pure mathematics... can have objective reality only under the....condition that it refers merely to objects of the senses..." but "...our sensory representation is..." not "... a representation of things in themselves, but only of the way in which they appear to us".

Taking the example of geometry, this doesn't mean that geometry is mere poetic "phantasy", but rather that geometry is "valid necessarily for space and consequently for everything that may be found in space, because space is nothing other than the form of all outer appearances, under which alone objects of the senses can be given to us."

Of course, if our senses "had to represent objects as they are in themselves" then geometry wouldn't be very helpful ("would be credited with no objective validity"), because we'd have no a priori proof that our experiences would agree with geometry ("it is simply not to be seen how things would have to agree necessarily with the image that we form of them by ourselves and in advance").

It's silly that some mathematicians worry that perhaps "a line in nature might indeed be composed of physical points, consequently that true space in objects might be composed of simple parts, notwithstanding that the space which the geometer holds in thought can by no means be composed of such things". Because, this space in thought itself makes possible physical space, i.e. the extension of matter; ... this space is by no means a property of things in themselves but representations of our sensory intuition; and that, since space as the geometer thinks it is precisely the form of sensory intution which we find in ourselves a priori and which contains the ground of the possibility of all outer appearances (with respect to their form), these appearances must of necessity...harmonize with the propositions of the geometer, which he extracts not from any fabricated concepts, but from the subjective foundation of all outer appearances, namely sensibility itself"


"In this and in no other way can the geometer be secured, regarding the indubitable objective reality of his propositions...."

Note 2 (Kant's note, not my note)

Is my theory idealism? "Idealism consists of the claim that there are none other than thinking beings; the other things that we believe we perceive in intuition are only representations in thinking beings, to which in fact no object existing outside these beings corresponds".

"I say in opposition: There are things given to us as objects of our senses existing outside us, yet we know nothing of them as they may be in themselves, but are acquainted only with their appearances, that is, with the representations that they produce in us because they affect our senses."


"Accordingly, I by all means avow that there are bodies outside us, that is, things which, though completely unknown to us as to what they may be in themselves, we know though the representations which their influence on our sensibility provides for us, and to which we give the name of a body - which word merely signifies the appearance of this object that is unknown to us but is nonetheless real"

This is the opposite of idealism!

People already accept that things like color and taste don't belong to things in and of themselves, but only to their appearances. I'm just saying that "the remaining qualities of bodies, which are called primarias" are the same, for example, "extension, place, and more generally space along with everything that depends on it (impenetrability or materiality, shape, etc)". In fact, I say that all of the "properties that make up the intuition of a body" belong only to its appearance.

But I'm not saying that things don't exist, like idealists do, I'm just saying that we can't know them as they are in themselves, but rather we can access them only through the senses.

How could I be less idealist? I've already said that "the representation of space is perfectly in accordance with the relation that our sensibility has to objects" -- perhaps you'd like me to also say that the representation of space is even "fully similar to the object"; but I don't think that makes sense, any more than the assertion that "the sensation of red is similar to the property of cinnabar that excites this sensation in me".

Note 3 (Kant's note, not my note)

Now, some people will say that I'm saying that the sensible world is an illusion. I'm not saying that; in fact I'm saying that the sensible world is our only way of relating to objects outside ourselves. It's true that appearances may seem misleading; for example, planets look like they travel progressively and retrogressively. This doesn't mean that their appearance is a meaningless "illusion", though, it just means that you have to futher interpret the data that you get from the senses.

Even if you consider space to be something "real", outside of ourselves, the planets still seem to travel retrogressively sometimes. So you see, this so-called "illusion" happens whether we consider space to be "real", or whether just part of the "form of sensibility". So it isn't an argument against considering it a "form of sensibility".

Btw, another way to state the problem with considering space as "really real" ("inhering in things themselves") is that you mistakenly consider space to be "universally valid" when really it is just "a condition of the intuition of things (attaching merely to my subject, and surely valid for all objects of the senses, hence for all merely possible experience)". The error is that you referred space to to "the things in themselves and did not restrict it to conditions of experience".

So, my theory certainly doesn't render the sensible world an illusion. In fact, my doctrine is the only means for proving that geometry has an a priori basis and so is not "self-produced brain phantoms, to which no object at all corresponds...", that is, for proving that geometry is NOT an illusion!

People will call my theory idealism because I call it "transcendental idealism", and they'll think it's like Descartes empirical idealism or what I call Berkeley's "visionary" idealism. Descartes thought that people were free to deny the existence of the material world. Berkeley asserted idealism as above (that there were no actual objects outside thinking beings, and that what we think are objects are merely representations).

But as I said, I don't doubt the existence of things. All I claim is that "appearences", including space and time, are not things, but merely "representations", and also that they are not "determinations that belong to things in themselves".

I thought that the "transcendental" in "trancendental idealism" would serve to prevent me being confused with Descartes' or Berkeley's idealism. The way that I use the word "transcendental", it "never signifies a relation of our cognition to things, but only to __the faculty of cognition__" (his italics).

But maybe I should call it "critical idealism" instead 12

Btw, while we're talking about idealism, I think that the naive theory, which considers space and time as inhering in things themselves, is reverse idealist. Because, just like Berkeley's "visionary" idealism makes actual things into mere representations, the naive theory makes mere representations (space and time) into things. So maybe we could call the naive theory "dreaming idealism".

So there, everyone is idealist BUT me. Humpf.

The main transcendental question, second part: how is natural science possible?


One meaning of the word "nature" is "the existence of things, insofar as that existence is determined according to universal laws".

"If nature meant the existence of things __in themselves__, we would never be able to cognize it, either a priori or a posteriori." (his italics)

"Not a priori, for how are we to know what pertains to things in themselves, inasmuch as this can never come about throught the analysis of our concepts (analytical propositions), since I do not want to know what may be contained in my concept of a thing (for that belongs to its logical essence), but what would be added to this concept in the actuality of a thing, and what the thing itself would be determined by in its existence apart from my concept".

"My understanding, and the conditions under which alone it can connect the determinations of things in their existence, prescribes no rule to the things themselves; these do not have to conform to my understanding, but my understanding would have to conform to them; they would therefore have to be given to me in advance so that these determinations could be drawn from them, but then they would not be cognized a priori".

"Such cognition of the nature of things in themselves would also be impossible a posteriori. For if experience were supposed to teach me __laws__ to which the existence of things is subject, then these laws, insofar as they relate to things in themselves, would have to apply to them __necessarily__ even apart from my experience. Now experience teaches me what there is and how it is, but never that it necessarily must be so and not otherwise. Therefore it can never teach me the nature of things in themselves."


But nevertheless there are actually universal a priori laws of nature. I don't mean things like the laws of physics which have been discovered by experiment. I mean things like "that substance remains and persists, that everything that happens always previously is determined by a cause according to constant laws, and so on".


There's a second meaning for the word "nature", "namely one that determines the __object__, whereas in the above meaning it only signified the __conformity to law__ of the determinations of the existence of things in general. Nature considered __materialiter__ (footnote: Materiality is Latin for "materially." In Kant's usage (ultimately derived from scholastic Aristotelianism), "matter" and "material" need not refer specifically to the physical matter of which objects are composed; here he uses the term to refer to the totality of objects of experience (see also 36) by contrast with the (merely 'formal') general laws governing those objects (as discussed in 15, 17)) is the __sum total of all objects of experience__."

If something cannot be an object of an experience, then we can't say anything about it, so we won't consider such things.

defn? in concreto: in any example of a possible experience

defn (sorta) hyperphysical: "Cognition of that which cannot be an object of experience"


"The __formal__ in nature in this narrower meaning is therefore the conformity to law of all objects of experience, and, insofar as this conformity is cognized a priori, the __necessary__ conformity to law of those objects."

But we aren't going to consider the of objects in themselves, just the laws of those objects which are of a possible experience. So of course the laws that we come up with might have to do more with the nature of experience than the nature of objects themselves (we can't tell the difference, since we can never know anything about objects which aren't objects of a possible experience).

So the following two phrasings13 are equivalent: 1) 'we are investigating universal laws about the nature of objects (but only as objects of a possible experience)' 2) 'we are investigating universal laws about the nature of experience (and its relationship to objects)'


But I prefer the second phrasing, because the first phrasing is perilously close to, "we are investigating universal laws about the nature of objects", so people might get confused and think we are talking about objects in themselves.

So, we can say that we are investigating, "the subjective laws under which alone a cognition of things through experience is possible". And if we want to say something along the lines of 'everything must have a cause', but restricted to objects of a possible experience, then instead of saying something like, "everything (of which which experience shows that it happens) must have a cause", we'll say something like, "A judgement of perception can never be considered as valid for experience without the law, that if an event if perceived then it is always referred to something preceding from which it follows according to a universal rule".

from our investigation of the a priori universal rules of possible experience, we will "determine nature as the whole object of all possible experience"


"... all judgements of experience are empirical, i.e. have their basis in the immediate perception of the senses; nonetheless the reverse is not the case, that all empirical judgements are therefore judgements of experience; rather, beyond what is given in sensory intuition, special concepts must yet be added, which have their origin completely a priori in the pure understanding, and under which every perception first can be subsumed and then, by means of the same concepts, transformed into experience."

we'll sometimes call these special concepts categories, and sometimes we'll call them 'pure concepts of the understanding'.

defn judgements of experience: Empirical judgements, insofar as they have objective validity

defn judgements of perception: Empirical judgements that are only subjectively valid

judgements of perception do not require a pure concept of the understanding, but only the logical connection of perceptions in a thinking subject

judgements of experience require, in addition to the representations of sensory intuition, categories, which are what make the judgement of experience objectively valid.

a judgement is said to be objective if and only if it is necessarily, universally valid.

"All of our judgements are at first mere judgements of perception; they hold only for us, i.e. for our subject, and only afterwards do we give them a new relation, namely to an object, and intend that the judgement should also be valid at all times for us and for everyone else; for if a judgement agrees with an object, then all judgements of the same object must also agree with one another, and hence the objective validity of a judhement of experience signifies nothing other than its necessary universal validity."

"...objective, i.e., as expressing not merely a relation of a perception to a subject, but a property of an object"


"Objective validity" = "necessary universal validity" (where 'universal' = 'for everyone') (we say "objective validity" even though we don't know the object in itself)

Through a judgement of objective validity "we cognize the object (even if it otherwise remains unknown as it may be in itself) by means of the universally valid and necessary connection of the given perceptions; and since this is the case for all objects of the senses, judgements of experience will not derive their objective validity from the immediate cognition of the object (for this is impossible), but merely from the condition for the universal validity of objective judgement, which, as has been said, never rests on empirical, or indeed snesory conditions at all, but on a pure concept of the understanding."

If "through the concept of the understanding the connection of the representations which it provides to our sensibility is determined as universally valid, then the object is determined through this relation, and the judgement is objective."

For example: "the sugar is sweet" is judgement of perception. It is a subjectively valid judgement. Making this judgment does not imply "that I should find it so at every time, or that everyone else should find it just as I do..."; "the sugar is sweet" expresses only a relation of a sensation to a subject (namely myself), and only in my present state of perception. "The sugar is sweet" is not expected to be valid for the object.

By contrast, 'the air is elastic' can be a judgement of experience14. "What experience teaches me under certain circumsances, it must teach me at every time and teach everyone else as well, and its validity is not limited to the subject or its state at that time." Therefore such a judgement is "objectively valid".

"...if I say, 'the air is elastic', then this judgement is to begin with only a judgement of perception; I relate two sensation in my senses only to one another. If I want it to be called a judgement of experience, I then require that this connection be subject to a condition that makes it universally valid. I want therefore that I, at every time, and also everyone else, would necessarily have to conjoin the same perceptions under the same circumstances".



Now we will "...analyze experience in general..." in order to see "...what is contained in this product of the senses and the understanding, and how the judgement of experience is itself possible."

"Perception"16 is "...the intuition of which I am conscious...".

'Perception' is an ability of the faculty of the senses. 'Judging' is an ability of the faculty of the understanding.

There are two types of judging: 1) "when i merely compare the perceptions and conjoin them in a consciousness of my state" (judgement of perception) 2) "when I conjoin them in a consciousness in general" (judgement of experience)

(1) is "is merely a connection of perceptions within my mental state, without reference to the object"

"Hence for experience it is not, as is commonly imagined, sufficient to compare perceptions and to connect them in one consciousness by means of judging; from that there arises no universal validity and necessity of the judgement, on account of which alone it can be objectively valid and so can be experience."


In order for a judgement of experience can occur, certain other judgements must occur beforehand18. Namely, "the given intutition must be subsumed under a concept that determines the form of judging in general with respect to the intuition, connects the empirical consciousness of the latter in a consciousness in general, and thereby furnishes empirical judgements with universal validity; a concept of this kind is a category, which does nothing but simply determine for an intuition the mode in general in which it can serve for judging".

For instance, in order to make the judgement "the air expands the balloon19" as a judgement of experience, you must invoke the concept of cause; then "the concept of air serves, with respect to expansion, in the relation of the antecedent to the consequent in a hypothetical judgement". So the concept of cause determines the mode in which the intuition (of blowing into the balloon and it blowing up) serves for judging.

In other words, all we perceived was that we blew into the balloon and then the balloon inflated. To say that our breath __caused__ the expansion of the balloon is adding something. We say that the concept of cause "determined the mode" in which the intuitions of, (a) blowing into the balloon, and (b) the balloon expanding "serve" in the judgement of experience. Specifically, (a) is the antecedent and (b) is the consequent in a hypothetical judgement20

"This expansion is thereby represented not as belonging merely to my perception of the air in my state of perception or in several of my states or in the state of others, but as __necessarily__ belonging to it, and the judgement: the air is elastic, becomes universally valid and thereby for the first time a judgement of experience, because certain judgments occur beforehand, which subsume the intuition of the air under the concept of cause and effect, and thereby determine the perceptions not merely with respect to each other in my subject, but with respect to the form of judging in general (here, the hypothetical), and in this way make the empirical judgement universally valid" (his italics)

"To have a more easily understood example, consider the following: If the sub shines on the stone, it becomes warm. This judgment is a mere judgment of perception and contains no necessity, however often I and others also have perceived this; the perceptions are only usually found so conjoined. But if I say: the sun __warms__ the stone, then beyond the perception is added the understanding's concept of cause, which connects __necessarily__ the concept of sunshine with that of heat, and the synthetic judgment becomes necessarily universally valid, hence objective, and changes from a perception into experience" (his italics)

All synthetic judgments which are objectively valid consist not merely of intuitions that have merely been connected in a judgment through comparison; rather, a pure concept of the understanding has always been added, "...under which these concepts had been subsumed..."

"Even the judgments of pure mathematics in its simplest axioms are not exempt from this condition. The principle: a straight line is the shortest line between two points, presupposed that the line has been subsumed under the concept of magnitude, which certainly is no mere intuition, but has its seat solely in the understanding and serves to determine the intuition (of the line) with respect to such judgments as may be passed on it as regards the quantity of these judgments, namely plurality, since through such jedgments it is understood that in a given intuition a homogeneous plurality is contained."

"plurality (__judicia plurativa__) (kant's footnote: so I would prefer those judgments to be called, which are called particularia in logic. For the latter expression already contains the thought that they are not universal. If, however, I commence from unity (in singular judgments) and then continue on to the totality, I still cannot mix in any reference to the totality; I think only a plurality without totality, not the exception to the latter (translator's footnote: Kant't point is that a collection of singular judgments that covers all of the individuals in a domain neither explicitly refers to the collected totality of such individuals (as a totality), not explicitly denies the universality of its extension (a denial that would be suggested by called such judgements 'particular'); it refers to a plurality, i.e., to more than one individual, but it leaves undetermined whether or not it covers all of the individuals in the domain). This is necessary, if the logical moments are to be placed under the pure concepts of the understanding; in logical usage things can remain as they were.)"



here's a table with "that which belongs to judgments in general, and the various moments of the understanding therein". Each of these "pure concepts of the understanding" corresponds to one of the "moments".

(all tables have four sections, arranged spatially as:

 2       3

even though i'll write then in columns)

"Logical table of judgements:

1. According to quantity Universal Particular Singular

2. According to quality Affirmative Negative Infinite

3. According to relation Categorical Hypothetical Disjunctive

4. According to modality Problematic Assertoric Apodictic "

"Trancendental table of concepts of the understanding:

1. According to quantity Unity (measure) Plurality (magnitude) Totality (the whole)

2. According to quality Reality Negation Limitation

3. According to relation Substance Cause Community

4. According to modality Possibility Existence Necessity "

"Pure physiological (translator's note: physiologische: used to mean 'pertaining to the investigation of nature', an older meaning that is consistent with its etymology) table of universal principals of natural science:

1. Axioms of intuition 2. Anticipations of perception 3. Analogies of experience 4. Postulates of empiricial thinking in general "


"....the discussion here is not about the genesis of experience, but about that which lies in experience."

So "experience consists of intuitions, which belong to sensibility, and of judgments, which..." belong to the understanding.

The "judgments that the understanding forms solely from sensory intuitions" are not judgements of experience. The judgments that the understanding forms solely from sensory intuitions "...only connect perceptions as they are given in sensory intuition...".

The judgements of experience "...are supposed to say what experience in general contains...", not just what mere perception, "...whose validity is merely subjective...", contains.

The judgment of experience must still add something that "..determines the synthetic judgment as necessary, and thereby as universally valid...", "...beyond the snesory intuition and its logical connection (in accordance with which the intuition has been rendered universal through comparison in a judgment)...". And this something has gotta be "...that concept which represents the intuition as in itself determined with respect to one form of judgment rather than the others, i.e., a concept of that synthetic unity of intuitions which can be represented only through a given logical function of judgments."


the business of the senses is to intuit

the business of the understanding is to think

To think is to unite representations in a consciousness. Thinking is the same as judging or as relating representations to judgments in general.

This unification either arises merely relative to the subject and is contingent and subjective, or it occurs without condition and is necessary and objective.

Judgments are either subjective, if representations are related to one consciousness in one subject alone and are united in it, or they are objective, if they are united in a consciousness in general, i.e., are united necessarily therein.

The logical moments of all judgments are so many possible ways of uniting representations in a consciousness. If, however, the very same mmoments serve as concepts, they are concepts of the __necessary__ unification of these representations in a sconsciousness, and so are principles of objectively valid judgments.

This unification in a consciousness is either analytic, through identity, or synthetic, through combination and addition of various representations with one another. experience consists in the synthetic connection of appearances (perceptions) in a consciousness, insofar as this connection is necesary.

Therefore categories are those under which all perceptions must first be subsumed before they can serve in judgments of experience, in which the synthetic units of perceptions is represented as necessary and universally valid. (Kant's footnote: But how does this proposition: that judgments of experience are supposed to contain necessity in the synthesis of perceptions, square with my proposition, urged many times above: that experience, as a posteriori cognition, can provide merely contingent judgments? If I say: Experience teaches me something, I always mean only the perception that is in it - e.g., that upon illumination of the stone by the sun, warmth always follows - and hence the proposition from experience is, so far, always contingent. That this warming flollows necessarily from illumination by the sun is indeed contained in the judgment of experience (in virtue of the concept of cause), but I do not learn it from experience; rather, conversely, experience is first generated through this addition of a concept of the understanding (of cause) to the perception. Concerning how the perception may come by this addition, the Critique must be consulted, in the section on transcendental judgment, pp. 137 ff (A 137-47/ B 176-87))" (his italics)


"Judgments, insofar as they are regarded merely as the condition for the unification of given representations in a consciousness, are rules."

"Now since, with respect to the possibility of all experience, if merely the form of thinking is considered in the experience, no conditions on judgments of experience are above those that bring the appearances (according to the varying form of their intuition) under pure concepts of the understanding (which make the empirical judgment objectively valid), these conditions are therefore the a priori principles of possible experience.

Now the principals of possible experience are, at the same time, universal laws of nature that can be cognized a priori. And so the problem that lies in our second question, presently before us: __How is pure natural science possible?__ is solved."

"For the systemization that is required for the form of a science is here found to perfection, since beyond the aforementioned formal conditions of all judgements in general, hence of all rules whatsoever furnished by logic, no others are possible, and these form a logical system; but the concepts based thereon, which contain the a priori conditions for all synthetic and necessary judgments, for that very reason form a transcendental system; finally, the principals by means of which all appearances are subsumed under these concepts form a physiological system, i.e., a system of nature, which precedes all empirical cognition of nature and first makes it possible, and can therefore be called the true universal and pure natural science."


The 1st of the physiological principles (the 1st entry in the 3rd table above) may be stated: "All appearances are, as regards their intuition, extensive magnitudes".

That is, this principle subsumes all appearances, as intuitions in space and time, under the concept of __magnitude__ and is to that extent a principle for the application of mathematics to experience.

(Kant's note: The three subsequent sections could be difficult to understand properly, if one does not have at hand what the Critique says about principles as well; but they might have the advantage of making it easier to survey the general features of such principals and to attend to the main points (translator's note: In reading the next three sections, the obscurity will be reduced by keeping in mind that Kant is discussing the Tables in Part 21. Here he relates the first two entries in the Physiological Table (Axioms and Anticipations) to the category of magnitude (respectively, extensive magnitude, and intensive magnitude or degree). In the 'A' edition of the Critique, the two corresponding propositions read: Axiom, 'All appearances are, as regards their intuition, extensive magnitudes" (A 162); and Anticipation, "In all appearances the sensation, and the __real__ that corresponds to it in the object (realitas phaenomenon), has an intensive magnitude, i.e., a degree (A 166).))

The 2nd entry in that table may be stated:

 "In all appearances the sensation, and the __real__ that corresponds to it in the object (realitas phaenomenon), has an intensive magnitude, i.e., a degree"

This does not subsume the properly empirical - namely sensation, which signifies the real in intuitions - directly under the concept of __magnitude__, since sensation is no intuition __containing__ space or time, although it does place the object corresponding to it in both.

Between reality (sensory representation) and nothing, i.e., a complete emptiness of intuition in time, a difference that has a magnitude, for indeed between every given degree of light and darkness, ..., even smaller degrees can be thought, just as between consciousness and unconsciousness (psychological darkness) ever smaller degrees occur; therefore no perception is possible that would show a complete absence, e.g., no psychological darkness is possible that could not be regarded as a consciousness that is merely outweighed by another, stronger one, and so it is in all cases of sensation. Therefore all sensations, ... have degrees - which is the second application of mathematics (__mathesis intensorum__) to natural science.

Sensations form the proper quality of empirical representations (appearances).


Dynamical categories

The determination of the relation of appearances or of whether they exist (3rd entry in the table) is not mathematical but dynamical.

As we have seen before, in order to make this determination objectively valid (hence fit for experience), we must subject it to a category.

If the determination at hand is whether something exists, the corresponding category is the concept of substance, which, as a concept of the thing itself, underlies all determination of existence.

If the determination at hand is the relation of appearances in a temporal sequence, i.e., an event, then the appearances must either be subsumed:

These principles are the actual laws of nature, which can be called dynamical.

the physiological theory of method

Finally, we might wish to make determinations about the agreement and connection of appearances, to put it another way, about the relation not so much of the appearances among themselves in experience, but of their relation to experience in general.

If we relate the agreement of appearances with the formal conditions that the understanding cognizes, the corresponding category is possibility.

If we determine the connection of appearances with the material of the senses and perception, the corresponding category is existence.

If we unite both possibility and existence in one concept, the corresponding category is necessity.

So, the physiological theory of method concerns the distinction of truth and hypotheses, and the boundaries of the reliability of the latter.


The third table of principles is awesome because, since I derived it through a formal derivation using only bare reason, "one can be certain there are no more such principles".

I note that the principle by which the table was derived is that of the faculty for judging in general (which constitutes the essence of experience with respect to the understanding).

Note that, because of the way that the derivation was done, the categories are valid only when they contain only the conditions of possible experience in general. Another way to say this is that only as objects of experience are all things necessarily subject a priori to the conditions of the categories.

Hence, the following statements are not warranted:

No one can prove statements like those, because such a synthetic connection out of mere concepts, in which all relation to sensory intuition on the one hand and all connection of such intuition in a possible experience on the other is lacking, is utterly impossible.

Another way to say what I'm saying in this section is that the principles of the categories do not directly constrain appearances and their relation, but only to the possibility of experience. That is, the principles of the categories refer to the objectively and universally valid synthetic propositions through which judgments of experience are distinguished from mere judgments of perception.

Appearances constitute the matter of experience, but not the form.

To go over the proof for the principal of the first entry again:

"The appearances, as mere intuitions __that fill a part of space and time__, are subject to the concept of magnitude, which synthetically unifies the manifold of intuitions a priori according to rules"

To go over the proof for the principal of the second entry again:

"Because the real in the appearances must have a degree, insofar as perception contains, beyond intuition, sensation as well, between which and nothing, i.e., the complete disappearance of sensation, a transition always occurs by diminution, insofar, that as, as sensation itself __fills no part of space and time__ (Kant's footnote: warmth, light, etc. are just as great {(according to degree) in a small space as in a large one; jast as the inner representations (pain, consciousness in general) are not smaller according to degree whether they last a short of a long time. Hence the magnitude here is just as great in a point and in an instant as in every space and time however large. Degrees are therefore magnitudes, not, however, in intuition, but in accordance with mere sensation, or indeed with the magnitude of the ground of an intuition, and can be assessed as magnitudes only through the relation of 1 to 0, i.e., in that every sensation can proceed in a certain time to vanish through infinite intermediate degrees, or to grow from nothing to a determinate sensation through infinite moments of accretion (Quantitas qualitatis est gradus (translator's note: 'the magnitude of quality is degree')), but yet the transition to sensation from empty time or space is possible only in time, with the consequence that although sensation, as the quality of empirical intuition with respect to that by which sensation differes specifically from other sensations, can never be cognized a priori, it nonetheless can, in a possible experience in general, as the magnitude of perception, be distinguished intensively from every other sensation of the same kind."

I remind you that the first and second entries make possible and determine "...the application of mathematics to nature, with respect to the sensory intuition whereby nature is given to us."

Unlike the principles for applying mathematics to natural science in general, the principles under the third entry (Analogies of experience) do not concern the generation of intuitions.

Rather, the principles under the third entry concern the connection of the existence of intuitions together in one experience, and since this connection can be nothing other than the determination of existence in time according to necessary laws, under which alone the connection is objectively valid and therefore is experience.

It follows that the proof does not refer to synthetic unity in the connection __of things__ in themselves, but of __perceptions__, and of these indeed not with respect to their content, but to the determination of time and to the relation of existence in time in accordance with universal laws.

These universal laws contain therefore the necessity of the determination of existence in time in general (hence a priori according to a rule of the understanding), if the empirical determination in relative time is to be objectively valid, and therefore to be experience.


Now we can "...dispose thoroughly of the Humean doubt."

"He rightly affirmed: that we in no way have insight through reason into the possibility of casuality, i.e., the possibility of relating the existence of one thing to the existence of some other thing that would necessarily be posited through the first one."

I add to this that we have just as little insight into:

"Nonetheless, I am very far from taking these concepts to be merely borrowed from experience, and from taking the necessity represented in them to be falsely imputed and a mere illusion through which long habit deludes us..." rather, I've proved that "...they and the principles taken from them..." can be deduced a priori and are objectively correct, "... though of course only with respect to experience".


So, I do not have the least concept of such a connection of things in themselves, how they can exist as substances or act as causes or stand in community with others (as parts of a real whole).

And I can still less think such properties of appearances as appearances (for these concepts do not contain what lies in appearances, but what the understanding alone must think)

But in understanding and in judging in general, we have a concept, "...that representations belong in one kind of judgment as subject in relation to predicate, in another as ground in relation to consequent, and in a third as parts that together make up a whole possible experience.

"... the above-mentioned moments, i.e., that it belonged under the concept of substance, or of cause, or (in relation to other substances) under the concept of community..."

(and he reiterates that this stuff applies not to things in themselves, but only to objects of possible experience)


An attempt at the problem of the concept of cause:

By means of logic, we have a priori: the form of a conditioned judgment in general, that is, the use of a given cognition as ground and another as consequent.

Let's suppose that a rule of relation is found in perception, and that that rule says this: that a certain appearance is constantly followed by another (though not the reverse).

Now this is a case for me to use hypothetical judgment and, e.g., to say: If a body is illuminated by the sun for long enough, then it becomes warm. Here there is of course not yet a necessity of connection, hence not yet the concept of cause. That proposition is merely a subjective connection of perceptions.

If the proposition is to be a proposition of experience, then it must be regarded as necessarily and universally valid. A proposition of that sort would be: the sun through its light is the cause of the warmth.

Experience can be an objectively valid cognition of appearances and their sequence in time only insofar as the antecedent appearance can be conjoined with the subsequent one according to the rule of hypothetical judgments.

The empirical rule "If a body is illuminated by the sun for long enough, then it becomes warm" is now regarded as a law ("The sun through its light is the cause of the warmth") ....I therefore have quite good insight into the concept of cause, as a concept that necessarily belongs to the mere form of experience.

But I have no insight at all into the possibility of a thing in general as a cause, because the concept of cause indicated a condition that in no way attaches to things, but only to experience.


"....the pure concepts of the understanding have no significance at all if they depart from objects of experience and want to be referred to things in themselves (noumena) (translator's note: Noumena ... meaning 'intelligible object'.... In Part 32 he contrasts noumena with phaenomena, ... appearances). They serve as it were only to spell out appearances, so that they can be read as experience..."

An attempt to apply the pure concepts of the understanding to things in themselves would result in "...arbitrary conjoinings without objective reality whose possibility cannot be cognized a pirori and whose relation to objects cannot, through any example, be confirmed or even be made intelligible, since all examples can be taken only from some possible experience or other and hence the objects of these concepts can be met with nowhere else but in a possible experience."

"This complete solution of the Humean problem, though coming out contrary to the surmise of the originator, thus restores to the pure concepts of the understanding their a priori origin, and to the universal laws of nature their validity as laws of the understanding, but in such a way that restricts their use to experience only...."

It's not that, "...they are derived from experience, but that experience is derived from them, a completely reversed type of connection that never occurred to Hume."

"... both pure mathematics and pure natural science can never refer to anything more than mere appearances, and they can only represent either that which makes experience in general possible, or that which, being derived from these principles, must always be able to be represented in some possible experience or other."


Many a person might claim that simply through common sense, s/he already, not merely suspected, but had known and understood, that:

With all of our reason we can never get beyond the field of experiences.

Therefore this person would claim that the rigorous work presented here is superfluous. But if you question such a person on hir rational principles, s/he must admit that among them there are many that s/he has not drawn from experience, which are therefore independent of it and valid a priori - how and on what grounds will s/he then realized that it is unwarranted to make use of these principles outside of all possible experience?


"Already from the earliest days of philosophy, apart from the sensible beings or appearances (phaenomena) that constitute the sensible world, investigators of pure reason have thought of special intelligible beings (noumena), which were supposed to form an intelligible world; and they have granted reality to the intelligible beings alone, because they took appearance and illusion to be one and the same thing (which may well be excused in an as yet uncultivated age).

In fact, if we view the objects of the senses as mere appearances, as is fitting, then we thereby admit at the very same time that a thing in itself underlies them, although we are not acquainted with this thing as it may be constituted in itself, but only with its appearance, i.e., with the way in which our senses are affected by this unknown something. Therefore the understanding, just by the fact that it accepts appearances, also admits to the existence of things in themselves, and to that extent we can say that the representation of such beings as underlie the appearances, hence of mere intelligible beings, is not merely permitted but also inevitable.

Our critical deduction in no way excludes things of such kind (noumena), but rather restricts the principles of aesthetic (translator's note: 'aesthetic'.... meaning quite generally things pertaining to, and limited to, the senses by comparison with the intellect) in such a way that they are not supposed to extend to all things, whereby everything would be transformed into mere appearance, but are to be valid only for objects of a possible experience. "

"Hence intelligible beings are therefore allowed only with the enforcement of this rule, which brooks no exception whatsoever: that we do not know and cannot know anything determinate about these intelligible beings at all, because our pure concepts of the understanding as well as our pure intuitions refer to nothing but objects of possible experience, hence to mere being of sense, and that as soon as one departs from the latter, not the least significance remains for those concepts."


"There is in fact something insidious in our pure concepts of the understanding, as regards enticement toward a transcendent use; for so I call that use which goes out beyond all possible experience. It is not only that our concepts of substance, of force, of action, of reality, etc, are ... independent of experience, likewise contain no sensory appearance ...., and so ... seem to refer to things in themselves (noumena); but also, ..., that they contain in themselves a necessity of determination which experience never equals. The concept of cause contains a rule, according to which from one state of affairs another follows with necessity; but experience can only show us that from one state of things another state often, or, at best, commonly, follows, and it can therefore furnish neither strict universality nor necessity (and so forth)."

So, "the concepts of the understanding appear to have much more significance and content than they would if their entire vocation were exhausted by mere use in experience...." and so we try to find other uses for them which are illegitimate.


"Two .... investigations were therefore needed, which were carried out in the Critique , pp. 137 ff and 235 ff (translator's note: On the Schematism of the Pure Concepts of the Understanding (A 137 ff / B 176 ff); On the Basis of the Distinction of All Objects in General into Phaenomena and Noumena (A 235 ff / B 294 ff))."

The first showed that "... the senses do not supply pure concepts of the understanding in concreto, but only the schema for their use, and that the object appropriate to this schema is found only in experience (as the product of the understanding from materials of sensibility)."

"In the second investigation (Critique, p. 235) it is shown: that notwithstanding the independence of our pure concepts of the understanding and principles ... outside the field of experience nothing at all can be thought by means of them, because they can do nothing but ... determine the logical form of judgment with respect to given intuitions; but since beyond the field of sensibility there is no intuition at all, .... there are no means through which they can be exhibited in concreto, and so all such noumena, together with their aggregate - an intelligible world - are nothing but representations of a problem, whose object is in itself perfectly possible, but whose solution, given the nature of our understanding, is completely impossible, since our understanding is no faculty of intuition but only of the connection of given intuitions in an experience; and experience therefore has to contain all the objects for our concepts, whereas apart from it all concepts will be without significance, since no intuition can be put under them."


The understanding can easily exceed its bounds; it starts by considering the pure concepts that dwell within itself prior to all experience; all it has to do in order to daydream is to remove the constraints that pure concepts always have their application in experience; and, "what is to hinder it from doing so, since the understanding has quite freely taken its principles from within itself?". And then folly results, where people make all sorts of unsupportable claims about things in themselves.

Practically speaking, people won't stop doing this if we just tell them that it's very difficult to make supported claims about things in themselves. Peple won't stop trying until we prove that it's __impossible__ to do so, as I have.

36: How is nature itself possible?

"This question, which is the highest point that transcendental philosophy can ever reach, and up to which, as its boundary and completion, it must be taken, actually contains two questions.

First: How is nature possible in general in the __material__ sense, namely, according to intuition, as the sum total of appearances; how are space, time, and that which fills them both, the object of sensation, possible in general? The answer is: by means of the constitution of our sensibility, in accordance with which our sensibility is affected in its characteristic way by objects that are in themselves unknown to it and that are wholly distinct from said appearances. This answer is, in the book itself, given the the Trancendental Aesthetic (translator's note: ... the first part of the Trancendental Doctrine of Elements), but here in the Prolegomena through the solution of the first main question.

Second: How is nature possible in the __formal__ sense, as the sume total of the rules to which all appearances must be subject if they are to be thought as connected in one experience? The answer..." is "... it is possible only by means of the constitution of our understanding, in accordance with which all these representations of sensibility are necessarily referred to one consciousness, and through which, first, the characteristic manner of our thinking, namely by means of rules, is possible, and then, by means of these rules, experience is possible - which is to be wholly distinguished from insight into objects in themselves. This answer is, in the book itself, given in the Transcendental Logic, but here in the Prolegomena, in the course of solving the second main question"

The a priori universal laws of nature, "... are not rules of analytic cognition, but are genuine synthetic amplificiations of cognition..."

Agreement between the principles of possible experience and the laws of the possibility of nature can come about from only three causes:

(1) "...these laws are taken from nature by means of experience" (2) "...nature is derived from these laws of the possibility of experience in general and is fully identical with the mere universal lawfulness of experience." (3) "...a spirit who can neither err nor deceive originally implanted these natural laws in us."

(1) is self-contradictory because by definition, universal laws of nature must be priori.

(3) doesn't give us a criterion for distinguishing correct propositions from incorrect ones, since obviously people have incorrect notions about metaphysics also, and how are we supposed to distinguish those ideas that the spirit of truth has put into us from the other ones?

So only (2) is left.

We must distinguish empirical laws of nature from pure or universal laws of nature. The former presuppose particular perceptions, the latter do not. The latter "...contain merely the conditions for the necessary unification of ... perceptions in one experience...". With respect to universal laws of nature, nature and possible experience are identical.


Next I'm going to give an example which is supposed to show that "laws which we discover in objects of sensory intuition, especially if these laws have been cognized as necessary, are already held by us to be such as have been put there by the understanding, although they are otherwise in all respects like the laws of nature that we attribute to experience."


"If one considers the properties of the circle by which this figure unifies in a universal rule at once so many arbitrary determinations of the space within it, one cannot refraqin from ascribing a nature to this geometric thing. Thus, in particular, two lines that intersect each other and also the circle (translator's note: Kant specifies below that each line is a chord...) ... partition each ofther in a regular manner such that the rectangle from the parts of one line is equal to that from the other. Now I ask, 'Does this law lie in the circle, or does it lie in the understanding?' i.e., does this figure, independent of the understanding, contain the basis for this law in itself, or does the understanding, since it has itself constructed the figure in accordance with its concepts (namely, the equality of the radii), at the same time insert into it the law that chords cut one another in geometrical proportion? If one traces the proofs of this law, one sson sees that it can be derived only from the condition on which the understanding based the construction of this figure, namely, the equality of the radii. If we now example upon this concept so as to follow up still further the unity of the manifold properties of geometrical figures under common laws, and we consider the circle as a conic section, which is therefore subject to the very same fundamental conditions of construction as other conic sections, we then find that all chords that intersect within these latter (within the ellipse, the parabola, and the hyperbola) always do so in such a way that the rectanges from their parts are not indeed equal, but always stand to one another in equal proportions. If from there we go still further, namely to the fundamental doctrines of physical astronomy, there appears a physical law of reciprocal attraction, extending to all material nature, the rule of which is that these attractions decrease inversely with the square of the distance from each point of attraction, exactly as the spherical surfaces into which this force spreads itself increase, something that seems to reside as necessary in the nature of the things themselves and which therefore is customarily presented as cognizable a priori. As simple as are the sources of this law - in that they rest merely on the relation of spherical surfaces with different radii - the consequence thereform is nonetheless so excellent with respect to the variety and regularity of its agreement that not only does it follow that all possible orbits of the celestial bodies are conic sections, but also that their mutual relations are such that no other law of attraction save that of the inverse square of the distances can be conceived of as suitable for a system of the world."

"Here then is nature that rests on laws that the understanding cognizes a priori, and indeed chiefly from universal principles of the determination of space. Now I ask: do these laws of nature lie in space, and does the understanding learn them in that it merely seeks to investigate the wealth of meaning that lies in space, or do they lie in the understanding and in the way in which it determines space in accordance with the conditions of the synthetic unity toward which its concepts are one and all directed? Space is something so uniform, and so indeterminate with respect to all specific properties, that certainly no one will look for a stock of natural laws within it. By contrast, that which determines space into the figure of a circle, a cone, or a sphere is the understanding, insofar as it contains the basis for the unity of the construction of these figures. The bare universal form of intuition called space is therefore certainly the substratum of all intuitions determinable upon particular objects, and, admittedly, the condition for the possibility and variety of those intuitions lies in this space; but the unity of the objects is determined solely through the understanding, and indeed according to conditions that result in its own nature; and so the understanding is the origin of the unversal order of nature, in that it comprehends all appearances under its own laws and thereby first brings about experience a priori (With respect to its form), in virtue of which everything that is to be cognized only through experience is necessarily subject to its laws."

"...the understanding, since it makes experience possible, at the same time makes it that the sensible world is either not an object of experience at all, or else is nature."

39: Appendix to pure natural science; On the system of categories

Previously, philosophers have given an aggregate of categories, but now I have systemitized this. Because of this, I can show that my enumeration of the categories isn't missing any of them, and doesn't have any extraneous ones.

To find the categories in aggregate is easy enough: "To pick out from ordinary cognition the concepts that are not based on any particular experience and yet are present in all cognition from experience (for which they constitute ... the form of connection)...." can be done by a procedure similar to examining a language and enumerating rules of grammar. However, compiling an aggregate in this manner doesn't let you "...give a reason why any given language should have preceisely this and no other formal constitution..." or to say for sure that you are not missing some grammar rules, or that every rule is really a fundamental rule.

"Aristotle had compiled ten such pure elementary concepts under the name of categories (Kant's footnote: Substantia, Qualitas, Quantitas, Relatio, Actio, Passio, Quando, Ubi, Situs, Habitus (translator's footnote: substance, quality, quantity, relation, action, affection, time, place, position, state; see Aristotle, Categories, Chapter 4)). To these, which were also called predicaments, he later felt compelled to append five post-predicaments (Kant's footnote: oppositum, prius, simul, motus, habere (translator's footnote: opposition, priority, simultaneity, motion, possession)), some of which (like prius, simul, motus) are indeed already found in the former;..." but this mere aggregation can serve only as a hint to future inquirers, because it is not an idea worked out according to rules.

During my "investigation of the pure elements of human cognition... I first succeeded ... to distinguish and separate with reliability the pure elementary concepts of sensibility (space and time) from those of the understanding. By this means the 7th, 8th, and 9th categories were now excluded from the above list. The others could be of no use to me, " because they were just an aggregate, not a derivation based on a principle.

"In order... to discover such a principal, I cast about for an act of the understanding that contains all the rest and that differentiates itself only through various modifications or moments in order to bring the multiplicity of representation under the unity of thinking in general; and there I found that this act of the understanding consists in judging. Here lay before me now, already finished though not yet wholly free of defects, the work of the logicians, through which I was put in the position to present a complete table of pure functions of the understanding, which were however undetermined with respect to every object. Finally, I related these functions of judging to objects in general, or rather to the condition for determining judgments as objectively valid, and there arouse pure concepts of the understanding, about which I could have no doubt that precisely these ... neither more nor fewer, can make up our entire cognition of things out of the bare understanding. As was proper, I called them __categories__, after their ancient name, whereby I reserved for myself to append in full, under the name of __predictables__, all the concepts derivable from them - whether by connecting them with one another, or with the pure form of appearance (space and time), or with its matter, provided the latter is not determined empirically (the object of sensation in general)...."

The great thing about my system of categories is that "...through it the true signification of the pure concepts of the understanding and the condition of their use could be exactly determined. For here it became apparent that the pure concepts of the understanding are, of themselves, nothing by logical functions, but that as such they do not constitute the least concept of an object in itself but rather need sensory intuition as a basis, and even then they serve only to determine empirical judgments - which are otherwise undetermined and indifferent with respect to all the functions of judging - with respect to those functions, so as to procure universal validity for these judgments..."

"All sorts of nice notes can be made on a laid-out table of categories, such as: 1. that the third arises from the first and second, conjoined into one concept, 2. that in those for quantity and quality there is merely a progression from Unity to Totality, or from something to nothing (for this purpose the categories of quality must stand thus: Reality, Limitation, full Negation), without correlata or opposita, while those of relation and modality carry the latter with them, 3. that, just as in the __logical table__, categorical judgments underlie all the others, so the category of substance underlies all concepts of real things, 4. that, just as modality in a judgment is not a separate predicate, so too the modal concepts do not add a determination to things, and so on. Considerations such as these all have their great utility. If beyond this all the __predictables__ are enumerated -- they can be extracted fairly completely from any good ontology (e.g. Baumgarten's (translator's note: ontology was the first major division of Baumgarten's Metaphysica)) - and if they are ordered in classes under the categories (in which one must not neglect to add as complete an analysis as possible of all these concepts), then a solely analytical part of metaphysics will arise, which as yet contains no synthetic propositions whatsoever and could precede the second (synthetic) part, and, through its determiniteness and completeness, might not only have utility, but beyond that, in virtue of its systematicity, a certain beauty."

I've also made a table of "concepts of reflection", which, although other authors mingle them with the categories, are actually "...only concepts of the mere comparison of already given concepts" (i.e. the categories). "translator's note: In the appendix to the Trancendental Analytic, On the Amphiboly of the Concepts of Reflection (A 260-8 / B 316-28), Kant provides a fourfold division of 'concepts of reflection' which pertain to judgment itself (identity/difference, agreement/opposition, inner/outer, and determinable/determination or matter/form)."

Another reason it's helpful to have systemically derived the table of categories is that, once you do so, you realize that there are some other things, the trancendental concepts of reason, which can be put into their own table. The trancendental concepts of reason "...have a completely different nature and origin than the concepts of the understanding (so that the table must also have a different form)....". Other metaphysicians have tended to erroneously mix together the categories and the trancendental concepts of reason (because it's only due to the systemization of the categories that you realize that the trancendental concepts of reason don't fit).


"logical moments" or "moments of the understanding": maybe he means "modes" instead of "moments"?

"intuition": so, i think "intuition" is the cause of a sensation in the exterior world, whereas the "sensation" is the percept. not sure though. but intuitions do have extent in time and space, whereas sensations don't.

"ground of X": cause of X

"rhapsody": the first time this appears, in Part 39, the translator explains essentially that it means something 'stitched together' which might be just a part of a larger work.

The Main Transcendental Question, Third Part: How is metaphysics in general possible?


Pure mathematics and pure nature science don't need, for their own sake, the metaphysical deductions that we have presented in the previous two chapters. Math is supported by its own evidence. Nature science, "... though arising from pure sources of the understanding, is nonetheless supported from experience and thoroughgoing confirmation by it - experience being a witness that natural science cannot fully renounce and dispense with, because, as philosophy (translator's note: the word 'philosophy' is here used broadly (as was normal in Kant's time) to include nature science or 'natural philosophy' as one of its branches...) despite all its certainty it can never rival mathematics.

So those metaphysical deductions are only necessary for metaphysics.

"Apart from concepts of nature, which always find their application in experience, metaphysics is further concerned with pure concepts of reason that are never given in any possible experience whatsoever, hence ... whose objective reality ... and with asssertions truth or falsity cannot be confirmed ... by any experience; and this part of metaphysics is ... that which forms its essential end, toward which all the rest is only a means..."

The third question, which we consider here, concerns the "core and characteristic feature of metaphysics, namely, the preoccupation of reason simply with itself, and that acquaintance with objects which is presumed to arise immediately from reason's brooding over its own concepts without its either needing mediation from experience for such an acquaintance, or being able to acheive such an acquaintance through experience at all."

"Without a solution to this question reason will never be satisfied with itself. The use in experience to which reason limits the pure understanding does not entirely fulfill reason's own vocation. Each individual experience is only a part of the whole sphere of the domain of experience, but the __absolute totality of all possible experience__ is not itself an experience, and yet is still a necessary problem for reason, for the mere representation of which reason needs concepts entirely different from the pure concepts of the understanding, whose use is only __immanent__, i.e., refers to experience insofar as experience can be given, whereas the concepts of reason extend to the completeness, i.e. the collectivel unity of the whole of possible experience, and in that way exceed any given experience and become __transcendent__." (his italics)

"... just as the understanding needed the __categories__ for experience, reason contains in itself the basis for __ideas__, by which I mean necessary concepts whose object nevertheless __cannot__ be given in any experience." (his italics)

"Since all illusion consists in taking the subjective basis of a judgment to be objective, pure reason's knowledge of itself in its transcendent (overreaching) use will be the only prevention against the errors in which reason falls if it misconstrues its vocation and, in transcendent fashion, refers to the object in itself that which concerns only its own subject and the guidance of that subject in every use that is immanent."


It's very important to keep the "...__ideas__, i.e., of pure concepts of reason..." separate form the categories, the "...pure concepts of the understanding...".


Since what relates to pure reason's __ideas__ can never be given in experience, and also the __theses__ produced by the transcendent cognitions of reason can never be confirmed or refuted through experience, only pure reason itself is in a position to detect any errors that we may make when we think of these things. So we gotta be careful.


I thought it was important to derive the categories according to a system, and so I tried to do the same thing for the ideas.

"Since I had found the origin of the categories in the four logical functions of all judgments of the understanding, it was completely natural to look for the irigin of the ideas in the three functions of syllogisms (translator's note: i.e. inferences of reason); for once such pure concepts of reason (transcendental ideas) have been granted, then, if they are not to be taken for innate, they could indeed be found nowhere else except in this very act of reason, which, insofar as it relates merely to form, constitutes the logical in syllogisms, but, insofar as it represents the judgments of the understanding as determined with respect to one or another a priori form, constitutes the transcendental concepts of pure reason."

"The formal distinction of syllogism necessitates their division into categorical, hypothetical, and disjunctive."

Therefore the concepts of reason based thereupon contain:

Each of these gives rise to a dialectic, but each in its own way, so all this provides the basis for dividing the entire dialectic of pure reason into:

"...through which derivation it is rendered completely certain that all claims of pure reason are represented here in full, and not one can be missing, since the faculty of reason itself, whence they all originate, is thereby fully surveyed."


"...the ideas of reason are not, like the categories, helpful to us in some way in using the understanding with respect to experience, but are completely dispensable with respect to such use, nay, are contrary to and obstructive of the maxims for the cognition of nature through reason, although they are sitill quite necessary in another respect, yet to be determined (translator's footnote: Examples of 'maxims of reason' or 'maxims of speculative reason' are given in the Critique in the Regulative Use of the Ideas of Pure Reason, at A 666-8 / B 694-6, and include 'principles' of homogeneity or aggregation, of variety or division into species and of affinity or continuity of forms (also, A 658 / B 686). Kant says that the ideas of reason are regulative with respect to the use of the understanding in experience, and he gives the term 'maxims' to the so-called principles that guide such use. In mentioning a further respect in which it is necessary to use the ideas of reason, we may suppose that Kant is speaking of their use in practical or moral reasoning.)."

" explaining the appearances of the soul, we can be completely indifferent to whether it is a simple substance or not; ...." for whether or not something is simple isn't "sensorily intelligible" in any possible experience / intelligible in concreto / a cause of any appearances, hence the concept of simple cannot cannot "... serve as a principal of explanation of that which supplies inner or outer experience."

"Just as little can the cosmological ideas of the beginning of the world or the eternity of the world (a parte ante (translator's note: 'up until now', literally, 'on the side of the previous')) be used to explain any event in the world itself."

"Finally, in accordance with a correct maxim of natural philosophy, we must refrain from all explanations of the organizations of nature drawn from the will of a supreme being..."

So you can see that the pure ideas of reason "...have a completely different determination of their use..." from the categories.

"Nevertheless our laborious analytic of the understanding (translator's note: Kant refers to the Transcendental Analytic in the Critique, which included the Deduction...) would have been entirely superfluous, if our aim had been directed toward nothing other than mere cognition of nature insofar as such cognition can be given in experience; for reason conducts its affairs in both mathmetics and natural science quite safely and quite well, even without any such subtle deduction."

"The solution to this question is as follows: Pure reason does not, among its ideas, have in view particular objects that might lie beyond the field of experience, but it merely demands completeness in the use of the understanding in the connection of experience. This completeness can, however, only be a completeness of principles, but not of intuitions and objects. Nonetheless, in order to represent these principles determinately, reason conceives of them as the cognition of an object, cognition of which is completely determined with respect to these rules - though the object is only an idea - so as to bring cognition through the understanding as close as possible to the completeness that this idea signifies."

45: Preliminary remark to the Dialectic of Pure Reason

"We have shown above (partpart 33, 34): that the purity of the categories from all admixture with sensory determinations can mislead reason into extending their use entirely beyond all experience to things in themselves; and yet, because the categories are themselves unable to find any intuition that could provide them with significance and sense __in concreto__, they cannot in and of themselves provide any determinate concept of anything at all, though they can indeed, as mere logical functions, represent a thing in general. Now hyperbolic objects of htis kind are what are called noumena or pure beings of the understanding (better: beings of thought) - such as, e.g., __substance__, but which is thought __without persistence__ in time, or a __cause__, which would however __not__ act __in time__, and so on - because such predicates are attributed to these objects as serve only to make the lawfulness of experience possible, and yet they are nonetheless deprived of all the conditions of intuition under which alone experience is possible, as a result of which the above concepts again lose all significance."

"There is, however, no danger that the understanding will of itself wantonly stray beyond its boundaries into the field of mere beings of thought, without being urged by alien laws. But if reason, which can never be fully satisfied with any use of the rules of the understanding in experience because such use is always still conditioned, requires completion of this chain of conditions, then the understanding is driven out of its circle, in order partly to represent the objects of experience in a series stretching so far that no experience can comprise the likes of it, partly (in order to complete the series) even to look for __noumena__ entirely outside said experience to which reason can attach the chain and in that way, independent at last of the conditions of experience, nonetheless can make its hold complete. These then are the transcendental ideas, which, although in accordance with the true but hidden end of natureal determination of our reason they may be aimed not at overreaching concepts but merely at the unbounded expansion of the use of concepts in experience, may nonetheless, through an inevitable illusion, elicit from the understanding a __transcendent__ use, which, though deceitful, nonetheless cannot be curbed by any resolve to stay within the bounds of experience, but only through scientific instruction and hard work." (his italics)

46 1. Psychological ideas (Critique, pp. 341 ff)

(translator's note: A 341-405, Of the Paralogisms of Pure Reason; largely replaced by B 399-432)

defn "the substantial itself" = "true subject" = that which remains after all accidents (as predicates) have been removed

It has long been observed that the substantial itself is unknown to us. The substantial itself is only an idea.

There's no way around that, and we should accept it. But human understanding want to cognize the substantial itself determinately, like an object that is given.

We want this because "Pure reason demands that for each predicate of a thing we should seek its appropriate subject, but that for this subject, which is in turn necessarily only a predicate, we shold seek its subject again, and so forth to infinity (or as far as we get). But from this it follows that we should take nothing that we can attain for a final subject, and that the substantial itself could never be thought by our every-so-deeply-penetrating understanding, even if the whole of nature were laid bare before it; for the specific nature of our understanding consists in thinking everything discursively, i.e., though concepts, hence through more predicates, among which the absolute subject must therefore always be absent. Consequently, all real properties by which we cognize bodies are mere accidents for which we lack a subject - even impenetrability, which must always be conceived only as the effect of a force."

What about our consciousness of ourselves, is this an absolute subject?

"It does appear that we have something substantial in the consciousness of our self (the thinking subject), and indeed have it in immediate intuition; for all the predicates of inner sense are referred to the $I$ as subject, and this $I$ cannot again be thought of as predicate of some other subject. It therefore appears that in this case completeness in referring the given concepts to a subject as predicates is not a mere idea, but that the object, namely the __absolute subject__ itself, is given in experience."

"But this expectation is disappointed. For the $I$ is not a concept (Kant's note: If the representation of apperception, the $I$, were a concept through which anything might be thought, it could then be used as a predicate for other things, or contain such predicates in itself. But it is nothing more than a feeling of an existence without the least concept, and is only a representation of that to which all thinking stands in relation (relatione accidentis (translator's note: 'relation of accident' ('Accidents' are modes or properties of a substance, to which they are related as their substrate - an unknown substrate, Kant argues)) at all, but only a designation of the object of inner sense insofar as we do not further cognize it through any predicate; hence although it cannot itself be the predicate of any other thing, just as little can it be a determinate concept of an absolute subject, but as in all the other cases it can only be the referring of inner appearances to their unknown subject. Nevertheless, through a wholly natural misunderstanding, this idea (which, as a regulartive principle, serves perfectly well to destroy completely all materialistic explanations of the inner appearances of our soul) (translator's note: the original has an asterisk here, with no corresponding note) gives rise to a seemingly plausible argument for inferring the nature of our thinking being from this presumed cognition of the substantial in it, inasmuch as knowledge of its nature falls completely outside the sum total of experience."


"This thinking self (the soul), as the ultimate subject of thinking, which cannot itself be represented as the predicate of another thing, may now indeed be called substance: but this concept .... remains ... empty and without any consequences, if persistence (as that which renders the concept of substances fertile within experience) cannot be proven of it."

To prove this, you'd have to prove "... from the concept of a subject that does not exist as the predicate of another thing, that the existence of that subject is persistent throughout, and that it can never come into being nor pass away, either in itself or through any natural cause."

But "Synthetic a priori propositions of this type can never be proven in themselves, but only in relation to things as objects of a possible experience.".

So "Persistence ... can never be proven from the concept of a substance as a thing in itself, but only for the purposes of experience." I proved this in the First Analogy of Experience (Critique ... (translator's note: A 182-9 ... B 224-32))".


"If ... we want to infer the persistence of the soul from the concept of the soul as substance, this can be valid ... only for the purpose of possible experience, and not of the soul as a thing in itself ... beyond all possible experience ... life is the subjective condition of all our possible experience; consequently, only the persistence of the soul during life can be inferred..."


Consider the proposition that:

Necessarily, our outer perceptions correspond to something real outside us

"This also can never be proven as a connection of things in themselves, but can well be proven for the purpose of experience. That is ... to say: it can be proven that there is something outside us of an empirical kind, and hence as appearance in space;..."

"Outside me empirically is that which is intuited in space; and"

"because this space, together with all the appearances it contains, belongs to those representations whose connection according to laws of experience proves their objective truth, ... it follows that I am, by means of outer appearances, .... conscious of the reality of bodies as outer appearances in space..." at least, i am concious of this

in the same way that i am conscious of the existence of my soul in time;

because, 'the reality of my soul (as an object of inner sense)' is proven only by 'the connection of the appearances of the inner sense'.

Because I cognize my soul only as an object of inner sense through the appearances constituting an inner state; my soul's being as it is in itself, which underlies these appearances, is unknown to me.

Contrast this view to the view of Cartesian idealism (material idealism). Cartesian idealism asks whether experience carries with itself sure criteria to distinguish it from imagination. Cartesian idealism presupposes space and time as conditions for the existence of objects and merely asks whether the objects of the outer senses are actually to be found in the space in which we put them while awake, in the way that the object of inner sense, the soul, actually is in time.

Cartestian idealism distinguishes only outer experience from dream, and lawfulness as a criterion of the truth of the former from the ... latter.

Using my philosophy, by contrast, the doubt can be easily removed, just as we always remove it in ordinary life by investigating the connection of appearances in both space and time according to unversal laws of experience, and if the representation of outer things consistently agrees therewith, we cannot doubt that those things should not constitute truthful experience.

The key step (in my philosophy) to removing this doubt is that, appearances are considered as appearances only in accordance with their connection within experience.

It is just as secure an experience that bodies exist outside us (in space) as that I myself exist in accordance with the representation of inner sense (in time) - for the concept: __outside us__, signifies only existence in space.

The I in the proposition __I am__ does not signify merely the object of inner intuition (in time) but also the subject of consciousness.

Similarly, body does not signify merely outer intuition (in space) but also the thing __in itself__ that underlies this appearance.

Therefore the question of whether bodies (as appearances of outer sense) exist __outside my thought__ as bodies in nature can without hesitation be answered negatively; but here matters do not stand otherwise for the question of whether I myself __as an appearance of inner sense__ (the soul according to empirical psychology) exist in time outside my power of representation, for this question must also be answered negatively. In this way everything is, when reduced to its true signification, conclusive and certain.

Although I've called it "transcendental idealism", you might refer to my philosophy as "formal idealism", because the answer to those questions is negative.

So, as we have seen, my philosophy actually destroys material idealism. For if space is nothing but a form of my sensibility, then it is, as a representation in me, juast as real as I am myself, and the only question remaining concerns the empirical truth of the appearances in this space.

But if you accept material idealism, and assume rather that space and the appearances are something existing outside us, then all the criteria of experience can never, outside our perception, prove the reality of these objects outside us.

Metaphysicians of history often try to infer the soul's "...necessary continuation after the death of a human being (principally because the simplicity of this substance, which had been inferred from the indivisibility of consciousness, saved it from destruction through dissolution)." Their error is to think this principal can be valid outside the realm of possible experience.

50: Cosmological ideas (Critique...)

(translator's note: A 405-567 / B 432-595, The Antimony of Pure Reason)

"I call this idea cosmological because it always finds its object only in the sensible world and needs no other world than that whose object is an object for the senses, and so, thus far, is immanent and not transcendent, and therefore, up to this point, is not yet an idea; by contrast, to think of the soul as a simple substance already amounts to thinking of it as an object (the simple) the likes of which cannot be represented at all to the senses. Notwithstanding all that, the cosmological idea expands the connection of the conditioned with its condition (be it mathematical or dynamical) so greatly that experience can never match it..."


By the way, this will provide a good example of the usefulness of a system of categories. There are only 4 such transcendent ideas, as many as there are classes of categories. In each idea, they refer only to the absolute completeness of the series of conditions for a given conditioned.

"In accordance with these cosmological ideas there are also only four kinds of dialectical assertions of pure reason, which show themselves to be dialectical because for each assertion a contradictory one stands in opposition in accordance with equally plausible principles of pure reason..."

table (written, as usual, with the following layout: 1 2 3 4

1. Thesis: The world has, as to time and space __a beginning (a boundary)__. Antithesis: The world is, as to time and space, __infinite__.

2. Thesis: Everything in the world is constituted out of the __simple__. Antithesis: There is nothing simple, but everything is __composite__.

3. Thesis: There exist in the world causes through __freedom__. Antithesis: There is no freedom, but everything is __nature__.

4. Thesis: In the series of causes in the world there is a __necessary being__. Antithesis: There is nothing necessary in this series, but in it __everything is contingent__.


"If ... we think of the appearances of the sensible world as things in themselves..." then both the theses and the antithesis in the above table can be proved.


Two mutually contradicting propositions cannot both be false. If they seem to be, then we must have assumed something impossible.


"... the first two antimonies I call mathematical because they concern adding together or dividing up the homogeneous". They are both false.

"...experience as a distinct way of cognizing objects that is granted to human beings alone..."

It's invalid to talk about things in themselves in space and time, we can only talk about objects of possible experience as being in space and time. " is not possible to have experience either of __infinite__ space of infinitely flowing time, or of a __bounding__ of the world by an empty space or by an earlier, empty time; these are only ideas. Therefore the magnitude of the world, determined one way or the other, must lie in itself, apart from all experience. But this contradicts the concept of a sensible world, which is merely a sum total of appearance, whose existence and connection takes place only in representation, namely in experience, since it is not a thing in itself, but is itself nothing but a kind of representation. From this it follows that, since the concept of a sensible world existing for itself is self-contradictory, any solution to this problem as to its magnitude will always be false..."

"The same holds for the second antinomy, which concerns dividing up the appearances. For these appearances are mere representation, and the parts exist only in the representation of them, hence in the dividing, i.e., in a possible experience in which they are given, and the dividing therefore proceeds only as far as possible experience reaches. To assume that an appearance, e.g., of a body, contains within itself, before all experience, all of the parts to which possible experience can ever attain, means: to give to a mere appearance, which can exist only in experience, at the same time an existence of its own previous to experience, which is to say: that mere representations are present before they are encountered in the representational power, which contradicts itself..." hence both thesis and antithesis 2 are false.


The first two antimonies were "mathematical", and the last two are "dynamical".

In the first two antimonies, the falsity of the presupposition was that something self-contradictory (namely, appearance as a thing in itself) would be represented as being unifiable in a concept. So, in the first two antimonies, both of the mutually opposing assertions were false.

In the last two antimonies, the falsity of the presupposition consists in this: that something that is unifiable is represented as contradictory. So, in the last two antimonies, the assertions, which are set in opposition to one another through mere misunderstanding, can both be true.

In the first two antimonies, mathematical combination necessarily presupposes the homogeneity of the things combined (in the concept of magnitude). If it is a question of the magnitude of something extended, all parts must be homogeneous among themselves and with the whole.

In contrast, in the last two antimonies, dynamical connection does not require this. In the connection of cause and effect homogeneity is allowed, but is not required; for the concept of causality (whereby through one thing, something completely different from it is posited) at least does not require it.

If, in the last two antimonies, the objects of the sensible world were taken for things in themselves, and the previously stated natural laws for things in themselves, contradiction could again not be avoided.... But if natural necessity is referred only to appearances and freedom only to things in themselves, then no contradiction arises...

Within appearance, every effect is an event, or something that happens in time. By the universal law of nature, an effect must be preceded by a determination of the casuality of its cause (a state of the cause) from which the effect follows in accordance with a constant law. But this determination of the cause to causality must also be something __that occurs or takes place__; the cause must have __begun__ to __act__, for otherwise no sequence in time could be thought between it and the effect. Both the effect and the causality of the cause would have always existed. Therefore the __determination__ of the cause __to act__ must also have arisen among the appearances, and so it must, like its effect, be an event, which again must have its cause, and so on, and hence natural necessity must be the condition in accordance with which efficient causes are determined.

By contrast, if freedom were a property of certain causes of appearances, then that freedom must, in relation to the appearances as events, be a faculty of starting those events __from itself (sponte)__ (translator's note: 'spontaneously'), i.e., without the causality of the cause itself having to begin, and hence without need for any other ground to determine its beginning.

But then __the cause__, as to its causality, would not have to be subject to temporal determinations of its state.

That is to say, the cause would __not__ have to be __appearance__ at all, i.e., would have to be taken for a thing in itself, and only the __effects__ would have to be taken for __appearances__ (Kant's footnote: The idea of freedom has its place solely in the relation of the __intellectual__, as cause, to the __appearance__, as effect. Therefore we cannot bestow freedom upon matter, in consideration of the unceasing activity by which it fills its space, even though this activity occurs through an inner principal. We can just as little find any concept of freedom to fit a purely intelligible being, e.g., God, insofar as his action is immanent. For his action, although independent of causes determining it from outside, nevertheless is determined in his eternal reason, hence in the divine __nature__. Only if __something__ should __begin__ through an action, hence the effect be found in the time series, and so in the sensible world (e.g., the beginning of the world), does the question arise of whether the causality of the cause must itself also have a beginning or whether the cause can originate an effect without its causality itself having a beginning. In the first case the concept of this causality is a concept of natural necessity, in the second of freedom. For the reader will see that, since I have explained freedom as the faculty to begin an event by oneself, I have exactly hit that concept which is the problem of metaphysics.)

If this sort of influence of intelligible beings on appearances can be thought without contradiction, then natural necessity will indeed attach to every connection of cause and effect in the sensible world, and yet that cause which is itself not an appearance (though it underlies appearance) will still be entitled to freedom, and therefore nature and freedom will be attribiutable without contradiction to the very same thing, but in different respects, in the one case as appearance, in the other as a thing in itself.

We have in us a faculty that not only stands in connection with its subjectively determining grounds, which are the natural causes of its actions - and thus far is the faculty of a being which itself belongs to appearances - but that also is related to objective grounds that are mere ideas, insofar as these ideas can determine this faculty, a connection that is expressed by __ought__. This faculty is called __reason__, and insofar as we are considering a being (the human being) solely as regards this objectively determinable reason, this being cannot be considered as a being of the senses; rather, the aforesaid property is the peroperty of a thing in itself.

The possibility of that property - namely, how the __ought__, which has never yet happened, can determine the activity of this being and can be the cause of actions whose effect is an appearance in the sensible world - we cannot comprehend at all.

Yet the causality of reason with respect to effects in the sensible world would nonetheless be freedom, insofar as __objective grounds__, which are themselves ideas, are taken to be determining with respect to that casuality. For the action of that causality would in that case not depend on any subjective, hence also not on any temporal conditions, and would therefore also not depend on the natural law that serves to determine those conditions, because grounds of reason provide the rule for actions universally, from principles, without influence from the circumstances of time or place.

What I adduce here counts only as an example, for intelligibility, and does not belong necessarily to our question, which must be decided from mere concepts independently of properties that we find in the actual world.

I can now say without contradiction: all actions of rational beings, insofar as they are appearances (are encountered in some experience or other), are subject to natural necessity; but the very same actions, with respect only to the rational subject and its faculty of acting in accordance with bare reason, are free.

What, then, is required for natural necessity? Nothing more than the determinability of every event in the sensible world according to constant laws, and therefore a relation to a cause within appearance; whereby the underlying thing in itself and its causality remain unknown. This might be termed "the law of nature".

Theorem: the law of nature is consistent with both of the following cases:

Case 1: the rational being is a cause of effects in the sensible world through reason and hence through freedom.

Case 2: the rational being does not determine such effects through rational grounds.


Case 1: The action takes place according to maxims whose effect within appearance will always conform to constant laws. However, reason is the cause of these natural laws and is therefore free.

Case 2: The action does not take place according to principles of reason, then it is subject to the empirical laws of sensibility, and in both cases the effects are connected according to constant laws; but we require nothing more for natural necessity, and indeed know nothing more of it. However, the effects flow according to mere natural laws of sensibility, because reason exercises no influence on them; but, because of this, reason is not itself determined by sensibility (which is impossible), and it is therefore also free in this case.


Note that the key here was to use things in themselves as determining grounds.

"In this way practical freedom - namely, that freedom in which reason has causality in accordance with objective determining grounds - is rescued, without natural necessity suffering the least harm..."

This can also help elucidate what we have had to say about transcendental freedom and its unification with natural necessity (in the same subject, but not taken in one and the same respect). For, as regards trancendental freedom, any beginning of an action of a a being out of objective causes is always, with respect to these determining grounds, __a first beginning__, although the same action is, in the series of appearances, only __a subalternate beginning__ ... so that in rational beings (or in general in any beings, provided that their causality is determined in them as things in themselves) one can conceive of a faculty for beginning a series of states spontaneously without falling into contradiction with the laws of nature. For the relation of an action to the objective grounds of reason is not a temporal relation; here, that which determines the causality does not precede the action as regards time, ... but rather they represent determining causes21 as things in themselves, which are not subject to temporal conditions."

The 4th antimony is disposed of in a similar manner to the 3rd. "For if only the __cause in the appearances__ is distinguished from the __cause of the appearances__ insofar as the latter cause can be thought of as a __thing in itself__, then these two propositions can ... exist side by side, as follows: that there occurs no cause of the sensible world (in accordance with similar laws of causality) whose existence is absolutely necessary, as also on the other side: that this world is nonetheless connected with a necessary being as its cause (but of another kind and according to another law)..."


Once the reader sees that indeed there are these 4 pairs of seemingly contradictory propositions, and that only by my theory can the seeming contradiction be resolved, they will be futher motivated to give my theory a fair hearing.

55: III. Theological idea (Critique ...)

(translator's note: A 571-83 / B 599-611, On the Trancendental Ideal, and the subsequent discussion in A 642 / B 670)

"The 3rd trancendental idea ... provides material for the most important among all the uses of reason..." Although here as ever there is danger of confusing ourselves if we try to say we know anything about things in themselves beyond experience. "Here reason does not, as with the psychological and the cosmological idea, start from experience and become seduced by the ascending sequence of grounds into aspiring, if possible, to absolute completeness in their series, but instead breaks off entirely from experience and descends from bare concepts of what would constitute the absolute completeness of a thing in general - and so by means of the idea of a supremely perfect first being - to determination of the possibility, hence the reality, of all other things;..." Here we presuppose a being with the goal of "... comprehensibility in the connection, ordering, and unity of ... experience".

Because we're not starting with experience and working up, it's not as easy to become confused and to try to misapply concepts transcendently. So I won't bother to talk more about the 3rd trancendental idea here -- just read the relevant section of the Critique if you want to read about it.



notable quotes

Kant agrees that, even given everything he says here, we don't know what the actual data structure of concepts is / the rules for when it can be inferred that an appearance falls under a concept:

"The concept of dog signifies a rule according to which my imagination can specify the figure of a four-footed animal in general, without being restricted to any one particular shape presented to me by experience, or even to any possible image that I can exhibit in concreto. This schematism of our understanding with respect to the appearances and their bare form is a hidden art in the depths of the human soul, whose true operations are difficult ever to divine from nature and place unveiled before our eyes." (Analytic of Principles, Critique of Pure Reason, A 141 and B 181)

Kant makes no claim that he can say why our cognition works the way it does:

4:318 (Part 36)

"But how this characteristic property of our sensibility itself may be possible, or that of our understanding and of the necessary apperception othat underlies it and all thinking, cannot be further solved and answered, because we always have need of them in turn for all answering and for all thinking of objects."


1. Some examples of his reasoning. 4:268-269: "That the straight line between two points is the shortest is a synthetic proposition. For my concept of the straight contains nothing of magnitude, but only a quality. The concept of the shortest is therefore wholly an addition and cannot be extracted by any analysis from the concept of the straight line. Intuition must therefore be made use of here, by means of which alone the synthesis is possible."

"Some other fundamental propositions that geometers presuppose are indeed actually analytic and rest on the principal of contradiction; however, they serve only, like identical propositions, as links in the chain of method and not as principles: e.g., a=a, the whole is equal to itself, or (a+b)>a, i.e. the whole is greater than its part. And indeed even these, although they are valid from the concepts alone, are admitted into mathematics only because they can be exhibited in intuition."

2. i think he is using the word 'proof' not to mean a proof using the axiomatic method, but to mean the giving of an irresistable argument.

3. math-style deductions following definitions; this interpretation is disputed though

4. seems to me that math-style deductions following definitions are easy to see why they are possible: note that automated theorem provers exist :)

5. First, I note that I added "What do we have left? We have ourselves ("the subject"). So, the intuition must contain nothing except something about the subject."; Kant doesn't say that, he just starts out with something irrelevant, then points out for the third(?) time that a priori things have to happen before an object is presented, and then finally says, so there's only one choice: the form of sensibility is the only type of intuition that can happen without an object.

Well, first, I don't see why the form of sensibility is only type of intuition that can happen without an object. As my inserted text makes clear, it seems to me that the line of reasoning is: to be a priori we can't have an object; without an object we still have ourselves (the subject); so we can still use intuitions about ourselves; and the form of sensibility concerns only ourselves, so we can use it. But this doesn't say that there aren't other types of intuitions which also concern only ourselves.

Again, it's hard to know what Kant would say to this, because he doesn't actually explain why "the form of sensibility" is the only way for intuition to be valid even without an object, he just asserts it (although he probably didn't notice that he was making a bald assertion, because that sentence starts with a "therefore" phrase).

My second problem with this is that it's not clear to me that we do in fact have access to an intuition whose content is "the form of sensibility". It's clear that that we don't have complete access to the workings of our mind. So it cannot be assumed without proof that we have access to any specific information about how our mind works. Yet here Kant seems to assume that we have some access to "the form of sensibility". Although, in his defence, he does present some evidence (although not irresistable proof); the evidence is that our ideas about space and time, such as that space is three-dimensional, do seem to hold up in practice. As he later shows, we have no reason to believe that space (much less 3D space) is "actually" "out there" in reality. This leaves us with two options; we can say that somehow we noticed that our sensory observations accord with a 3D space, that is, that our idea of 3D space is a posteriori, or we can say that there is some a priori reason for us to think in terms of 3D space. Kant chooses the latter, and saying that this a priori reason is that we have special access to the "form of sensibility", that is, that we can somehow know from introspection that the way our mind works is such that we can know that we will never perceive an experience that doesn't fit into the paradigm of 3D space. Because of this a priori knowledge, we make mathematical statements like "the space that we live in is 3D". Now for the evidence: these statements turn out to be useful. This lends support to his theory that we (correctly) determined that our minds were such that we would never perceive a non-3D (or non-spatial) reality.

And, also in his defence, my current opinion is that, in fact, the reason we perceive 3D space really is that "the form of sensiblity" contains the 3D spatial paradigm. Our brains seem to be hardwired for spatial perception: the visual system contains topographic maps; also, when we imagine things rotating, it takes longer to imagine them as the angle of rotation increases. But this is my opinion based on contingent facts, not an irresistable proof as Kant seems to want (and think he has). So, while I bet that he's right here, I don't think he's proved it, as he claims.

But in summary, I have two doubts at this juncture: (1) i doubt that "the form of sensibility" is necessarily the only thing that we can intuit "a priori", (2) i doubt that we actually can intuit "the form of sensibility".

6. huh? what about modern algebra? number theory? mathematical logic? i think there are large areas of mathematics which have nothing to do with space and time (although you can restate much of them in terms of space and time; still, I don't think space and time are essential or necessary for them).

7. i still don't understand what he means by this

8. at this point i present some notes from elsewhere regarding what Kant seems to mean by "pure mathematics". By "pure" he means just that it is a priori. And I should write down something he says over and over about mathematics; he says in Part 2, "the essential feature of pure mathematical cognition, differentiating it from all other a priori cognition, is that it must throughout proceed __not from concepts__, but always and only through the construction of concepts (Critique, p. 713). Because pure mathematical cognition, in its propositions, must therefore go beyond the concept to that which is contained in the intuition corresponding to it, its propositions can and must never arise through the analysis of conepts, i.e. analytically, and so are one and all synthetic." What does he mean to "construct" a concept? I may as well quote the part from Critique of Pure Reason p. 713: "Philosophical cognition is cognition through reason from concepts; mathematical cognition is cognition through reason from the construction of concepts. But to construct a concept means: to exhibit a priori the intuition corresponding to it. For the construction of a concept, then , a nonempirical intuition is required, which therefore, as intutition, is an individual object, but which, as the construction of a concept (a general representation), must nonetheless express (in the representation) universal validity for all possible intutitions belonging under that same concept. Thus I construct a triangle by exhibiting the object that corresponds to this concept, either through bare imagination in pure intuition, or else (in accordance with imaginiation) on paper in empirical intuition, but in either case fully a priori, without having to borrow the pattern for the object from one or another experience. This single sketched-out figure is empirical, and yet it nonetheless serves to express the concept without prejudice to the generality of the concept, because in connection with this empirical intuition only the act of the construction of the concept is looked to, for which many determinations, e.g., of size, sides, and angles, are equivalend, and so these differences, which do not alter the concept of the triange, are abstracted from .... give the concept of a triangle to a philospher and have him find out, in his manner, how the sum of its angle may be related to the right angle. He has then nothing but hte concept of a figure that is enclosed in three straight lines, and the concept of the same number of angles in that figure. Let him now contemplate this concept for as long as he wants, he will ascertain nothing new. He can analyze and clarify the concept of a straight line, or of an angle, or of the number three, but he cannot come upon any other properties, which simply are not to be found in these concepts. But let the geometer take up this question. He begins forthwith to construct a triangle. Because he know that two right angles taken together amount to exactly as much as all the adjacent angles taken together that can be erected form a point on a straight line, he therefore extends one side of his triangle and gets two adjacent angles, which are equal to two right angles taken together. Of these two angles, he now divides the exterior one by erecting a line parallel to the opposite side of the triangle, and he sees that here an exteriori adjacent angle is produced that is equal to an interior angle, and so on. In this way, through a chain of inferences, always led by intuition, he arrives at a fully evidence and (at the same time) universal solution to the question."

and the next paragraph in the main text also..,

9. not sure that i agree with this section

10. i think he is saying that people worry that physical space is not continuous, and he is saying, who cares, perceptual space is (or more broadly: if physics can be explained by a theory that utilizes the mathematics of discrete space, nevertheless our cognitions will think of this as being embedded in a continuous space). it's possible that he's saying that in fact the mathematics of discrete space will never be the simplest theory, even for explaining very specialized and weird circumstances such as quantum physics, and we can know this a priori because of our special access to "the form of sensibility", and that "the form of sensiblity" somehow forces this to be the case, but it seems unlikely to me that he would want to assume that we can learn constraints on the laws of physics by introspection, so i don't think this is what he means.

but note that i still have doubt that we have this special a priori access that allows us to know things about the "form of sensibility". Do we really have an a priori proof that space (existing as part of the form of sensibility) is continuous? I doubt it. So, I doubt that continous geometry has "objective validity" in his terms (i.e. that we know a priori that a necessary condition of our experience is continuous space).

11. then how is he sure that they exist outside of any thinking being?

12. oh yeah that'll make a big difference -- not! imo if you don't want people thinking its idealism you shouldn't use the word 'idealism'

13. I reversed the ordering of the two phrasings.

14. actually Kant doesn't explicitly give an example of a judgement of experience, but I think this is the example that he meant to give; but it's a little confusing because 'the air is elastic' can also be a judgement of perception, depending on whether you are talking about just immediately perceiving that the air is elastic, or whether you are asserting that as a property of the object

15. and of course if we tried to implement this in a computer we would quickly encounter the generalization problem; that is, since every two sets of circumstances, considered in their entirely, are different, how do we know when circumstances are sufficiently "the same" to force the conjoining of the perceptions? the simple answer is to require all judgements of experience contain within their statement a complete specification of the premises for when conditions are the same; that is, an "operalization", to use a term from psychology, or equivalently, a recipe for performing the measurements necessary to measure the predicates that are being talked about. But a complaint with that is that, in everyday life, if you hear someone making an objective assertion (like, if someone says, "when you hit a drum hard, it makes a loud sound"), and you ask them to formally operationalize it, they will probably give you an incorrect formalization with 'bugs' in it -- suggesting that their cognition didn't really have such a precise set of premises attached.

16. I'm guessing he means the faculty of perception, not an individual percept

17. OK, I disagree with that. It seems to me that the way the word "experience" is usually used is that experience happens when sensations enter your consciousness (i.e. when there are qualia). Whether or not one makes judgements about how these sensations relate to objects outside oneself seems to be irrelevant to the question of whether an experience has happened. For example, one can imagine a drug-addled or crazy person who has a "hallucinatory" experience of unconnected sensations without having the mental capacity to relate these things to any stable reality. If one asked this person to describe the experience (afterwards when they were sane), of course they wouldn't come up with much; but they might say something like, "i saw blueness, and i felt pain". One might argue that in this case, they made a judgement of the existence of "blueness" and "pain" as objects outside themselves, and so there was a judgement of type (2); but if so, then what is left for Kant to have meant by a judgement of type (1)? And also, one could argue that the qualia happened during the insanity, but then when the person became sane they interpreted their memories using judgements of type (2) (how could they have memories of insanity? Minsky's "k-lines" perhaps; maybe some preconscious neurological mechanism makes it so that, when they think about taking the drug that made them insane, this triggers a partial return to the state of insanity which is associated with that memory in a content-addressable way, and this partial return causes them to re-experience the sensations of blueness and pain; so you see, no reasoned narrative or symbolic encoding of history is necessary for memory of unprocessed sensations to be possible).

So, I disagree that Kant's usage of the word "experience" corresponds to everyone else's. And I will go forward treating this word as if he had made up a new word, KantExperience?, which has no prior definition.

Which is not to say that KantExperience? is useless or uninteresting or unrelated to concepts that other people talk about. I think Kant's "experience" might denote what I would call, "an element suitable for inclusion within a rational narrative of subjective experience". Or perhaps, "narrative event" or more generally, "narrative atom". So I don't think Kant's word "experience" is about qualia, but rather about narration.

18. Kant doesn't seem to provide a name for these "certain judgements", at least not yet.

19. Kant didn't say anything about a balloon, he doesn't even explicitly give the example, he just starts talking about air expanding

20. I don't understand yet if the "hypothetical" is another word for "using the concept of cause" or if it's something else -- if something else then this sentence should be amended to add something about cause being involved.

21. note: as my friend pointed out, this is causality based on the notion of logical implication, in contrast to one based on a series of physical effects going forward through time