Bayle Shanks's website: notes-philosophy-logic-aristotleVsKantVsModernFormalLogic

aristotle and modern logic apparently disagree on what to do about 'vacuous implication'. My friend Ruadhan found a pdf or ppt from course notes once that explained this but i lost it (i think these notes also talked about squares of opposition, maybe).
kant has affirmative, negative, infinite, modern formal logic just has affirmative and negative (although perhaps modern formal logic's negative is kant's infinite? i forgot)
kant has universal, particular, singular, modern formal logic would say that universal (forall quantifier) can be formed from particular (exists quantifier) via negation and vice versa
kant has apodictic, problematic, assertoric, modern formal logic would probably say that problematic is just the negation of apodictic

mb what i am calling 'modern formal logic' is due to Frege?

" (3) But there is a third reason for the popularity of symbolic logic among philosophers, which is more substantial, for it involves a very important difference in philosophical belief. The old, Aristotelian logic was often scorned by 20th century philosophers because it rests on two commonsensical but unfashionable philosophical presuppositions. The technical names for them are “epistemological realism” and “metaphysical realism.” These two positions were held by the vast majority of all philosophers for over 2000 years (roughly, from Socrates to the 18th century) and are still held by most ordinary people today, since they seem so commonsensical, but they were not held by many of the influential philosophers of the past three centuries. (The following summary should not scare off beginners; it is much more abstract and theoretical than most of the rest of this book.) The first of these two presuppositions, “epistemological realism,” is the belief that the object of human reason, when reason is working naturally and rightly, is objective reality as it really is; that human reason can know objective reality, and can sometimes know it with certainty; that when we say “two apples plus two apples must always be four apples,” or that “apples grow on trees,” we are saying something true about the universe, not just about how we think or about how we choose to use symbols and words. Today many philosophers are skeptical of this belief, and call it naïve, largely because of two 18th century “Enlightenment” philosophers, Hume and Kant. Hume inherited from his predecessor Locke the fatal assumption that the immediate object of human knowledge is our own ideas rather than objective reality. Locke naïvely assumed that we could know that these ideas “corresponded” to objective reality, somewhat like photographs; but it is difficult to see how we can be sure any photograph accurately corresponds to the real object of which it is a photograph if the only things we can ever know directly are photographs and not real objects. Hume drew the logical conclusion of skepticism from Locke’s premise. Once he limited the objects of knowledge to our own ideas, Hume then distinguished two kinds of propositions expressing these ideas: what he called “matters of fact” and “relations of ideas.” What Hume called “relations of ideas” are essentially what Kant later called “analytic propositions” and what logicians now call “tautologies”: propositions that are true by definition, true only because their predicate merely repeats all or part of their subject (e.g. “Trees are trees” or “Unicorns are not non-unicorns” or “Unmarried men are men”). What Hume called “matters of fact” are essentially what Kant called “synthetic propositions,” propositions whose predicate adds some new information to the subject (like “No Englishman is 25 feet tall” or “Some trees never shed their leaves”); and these “matters of fact,” according to Hume, could be known only by sense observation. Thus they were always particular (e.g. “These two men are bald”) rather than universal (e.g. “All men are mortal”), for we do not sense universals (like “all men”), only particulars (like “these two men”). Common sense says that we can be certain of some universal truths, e.g., that all men are mortal, and therefore that Socrates is mortal because he is a man. But according to Hume we cannot be certain of universal truths like “all men are mortal” because the only way we can come to know them is by generalizing from particular sense experiences (this man is mortal, and that man is mortal, etc.); and we cannot sense all men, only some, so our generalization can only be probable. Hume argued that particular facts deduced from these only-probable general principles could never be known or predicted with certainty. If it is only probably true that all men are mortal, then it is only probably true that Socrates is mortal. The fact that we have seen the sun rise millions of times does not prove that it will necessarily rise tomorrow. Hume’s “bottom line” conclusion from this analysis is skepticism: there is no certain knowledge of objective reality (“matters of fact”), only of our own ideas (“relations of ideas”). We have only probable knowledge of objective reality. Even scientific knowledge, Hume thought, was only probable, not certain, because science assumes the principle of causality, and this principle, according to Hume, is only a subjective association of ideas in our minds. Because we have seen a “constant conjunction” of birds and eggs, because we have seen eggs follow birds so often, we naturally assume that the bird is the cause of the egg. But we do not see causality itself, the causal relation itself between the bird and the egg. And we certainly do not see (with our eyes) the universal “principle of causality.” So Hume concluded that we do not really have the knowledge of objective reality that we naturally think we have. We must be skeptics, if we are only Humean beings. Kant accepted most of Hume’s analysis but said, in effect, “I Kant accept your skeptical conclusion.” He avoided this conclusion by claiming that human knowledge does not fail to do its job because its job is not to conform to objective reality (or “things-in-themselves,” as he called it), i.e. to correspond to it or copy it. Rather, knowledge constructs or forms reality as an artist constructs or forms a work of art. The knowing subject determines the known object rather than vice versa. Human knowledge does its job very well, but its job is not to learn what is, but to make what is, to form it and structure it and impose meanings on it. (Kant distinguished three such levels of imposed meanings: the two “forms of apperception”: time and space; twelve abstract logical “categories” such as causality, necessity, and relation; and the three “ideas of pure reason”: God, self, and world.) Thus the world of experience is formed by our knowing it rather than our knowledge being formed by the world. Kant called this idea his “Copernican Revolution in philosophy.” It is sometimes called “epistemological idealism” or “Kantian idealism,” to distinguish it from epistemological realism. (“Epistemology” is that division of philosophy which studies human knowing. The term “epistemological idealism” is sometimes is used in a different way, to mean the belief that ideas rather than objective reality are the objects of our knowledge; in that sense, Locke and Hume are epistemological idealists too. But if we use “epistemological idealism” to mean the belief that the human idea (or knowing, or consciousness) determines its object rather than being determined by it, then Kant is the first epistemological idealist.) The “bottom line” for logic is that if you agree with either Hume or Kant, logic becomes the mere manipulation of our symbols, not the principles for a true orderly knowledge of an ordered world. For instance, according to epistemological idealism, general “categories” like “relation” or “quality” or “cause” or “time” are only mental classifications we make, not real features of the world that we discover. In such a logic, “genus” and “species” mean something very different than in Aristotelian logic: they mean only any larger class and smaller sub-class that we mentally construct. But for Aristotle a “genus” is the general or common part of a thing’s real essential nature (e.g. “animal” is man’s genus), and a “species” is the whole essence (e.g. “rational animal” is man’s species). (See Chapter III, Sections 2 and 3.) Another place where modern symbolic logic merely manipulates mental symbols while traditional Aristotelian logic expresses insight into objective reality is the interpretation of a conditional (or “hypothetical”) proposition such as “If it rains, I will get wet.” Aristotelian logic, like common sense, interprets this proposition as an insight into real causality: the rain causes me to get wet. I am predicting the effect from the cause. But symbolic logic does not allow this commonsensical, realistic interpretation. It is skeptical of the “naïve” assumption of epistemological realism, that we can know real things like real causality; and this produces the radically anti-commonsensical (or, as they say so euphemistically, “counter-intuitive”) “problem of material implication” (see page 23). Besides epistemological realism, Aristotelian logic also implicitly assumes metaphysical realism. (Metaphysics is that division of philosophy which investigates what reality is; epistemology is that division of philosophy which investigates what knowing is.) Epistemological realism contends that the object of intelligence is reality. Metaphysical realism contends that reality is intelligible; that it includes a real order; that when we say “man is a rational animal,” e.g., we are not imposing an order on a reality that is really random or chaotic or unknowable; that we are expressing our discovery of order, not our creation of order; that “categories” like “man” or “animal” or “thing” or “attribute” are taken from reality into our language and thought, not imposed on reality from our language and thought. Metaphysical realism naturally goes with epistemological realism. Technically, metaphysical realism is the belief that universal concepts correspond to reality; that things really have common natures; that “universals” such as “human nature” are real and that we can know them. There are two forms of metaphysical realism: Plato thought that these universals were real things in themselves, while Aristotle thought, more commonsensically, that they were real aspects of things which we mentally abstracted from things. (See Chapter II, Section 3, “The Problem of Universals.”) The opposite of realism is “nominalism,” the belief that universals are only man-made nomini (names). William of Ockham (1285–1349) is the philosopher who is usually credited (or debited) with being the founder of nominalism. Aristotelian logic assumes both epistemological realism and metaphysical realism because it begins with the “first act of the mind,” the act of understanding a universal, or a nature, or an essence (such as the nature of “apple” or “man”). These universals, or essences, are known by concepts and expressed by what logic calls “terms.” Then two of these universal terms are related as subjects and predicates of propositions (e.g. “Apples are fruits,” or “Man is mortal”). “Aristotle never intended his logic to be a merely formal calculus [like mathematics]. He tied logic to his ontology [metaphysics]: thinking in concepts presupposes that the world is formed of stable species” (J. Lenoble, La notion de l’experience, Paris, 1930, p. 35). Symbolic logic is a set of symbols and rules for manipulating them, without needing to know their meaning and content, or their relationship to the real world, their “truth” in the traditional, commonsensical sense of “truth.” A computer can do symbolic logic. It is quantitative (digital), not qualitative. It is reducible to mathematics. The new logic is sometimes called “propositional logic” as well as “mathematical logic” or “symbolic logic” because it begins with propositions, not terms. For terms (like “man” or “apple”) express universals, or essences, or natures; and this implicitly assumes metaphysical realism (that universals are real) and epistemological realism (that we can know them as they really are)." -- Peter Kreeft, Socratic Logic

see also http://plato.stanford.edu/entries/square/ , Aristotle's square of opposition.