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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.
The main question of this book is: is metaphysics possible?
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.
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".
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.
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.
I know of at least two ways to interpret Kant's analytic/synthetic distinction. Part of this discussion will follow Wikipedia (http://en.wikipedia.org/wiki/Analytic-synthetic_distinction; http://en.wikipedia.org/w/index.php?title=Analytic-synthetic_distinction&oldid=150868325; 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
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.
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.
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).
There are three types of synthetic judgements:
Properly metaphysical judgements are simply defined as those metaphysical judgements which are not analytic.
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" (http://www.crossroads-cc.org/app/w_page.php?type=section&id=19).
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.
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:
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."
Examples.
"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"
"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...."
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".
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