John, List,
Richard Smyth has two monographs that deal squarely with these sorts of questions. I recommend both. In the Forms of Intuition, he reconstructs the central arguments in Kant's transcendental aesthetic of the Critique of Pure Reason. One of the salient points that Smyth makes is that Kant's distinctions between what is a priori and a posteriori, on the one hand, and the what is analytic and what is synthetic apply first and foremost to the classification of different sorts of cognitions. That is, neither distinction is used by Kant as a distinction between kinds of truths--as many 20th century analytic philosophers take the latter distinction (and sometimes even the former) to be. One obvious reason for thinking that philosophers like Goodman and Quine are using the distinction between the analytic and the synthetic in a very different way from Kant is that, on Kant's account, one and the same thing can be known in these two different ways. The same thing, I believe, is true for what is cognized a priori and what is cognized a posteriori. In geometry, for instance, if I draw the conclusion that the sum of the interior angles of a triangle is believed to be 180 degrees by measuring each angle with a protractor and then adding the numbers, then the cognition is a posteriori in character. If, on the other hand, the sum of the angles of a triangle are shown to be equal to two right angles by extending the base, constructing a parallel to the far side through the vertice where the base has been extended, and then proving the conclusion by opposite and adjacent angles, as is illustrated in the Elements, then the conclusion is known a priori. The key difference is that the conclusion of the former cognition, where the angles are measured with a protractor, can be generalized by induction and will hold only with some degree of probability for actual triangles as drawn on boards. The latter conclusion can be generalized to show that it holds necessarily for all idealized triangles in Euclidean space. It is these latter marks of having a universal and necessary character that Kant takes to be the hallmark of what is a priori as a cognition, inference, judgment, concept, element, etc. If an element in an a priori cognition is essential to the validity of that cognition, then the element is itself a priori in character. In an epilogue at the end of the work, Smyth draws out some of the implications of Kant's arguments in the transcendental aesthetic for better understanding the character of our cognitions in mathematical logic. This part of the discussion is, I think, very Peircean in inspiration and character. In Reading Peirce Reading, Smyth makes the point that Kant's division between what is known analytically and what is known a synthetically is, for Peirce, the fundamentally historical in character. What is, at one point in inquiry, known synthetically may, at a later point in inquiry, be known analytically. This can be seen in mathematics where something that is proven at an earlier synthetic stage of inquiry as a theorem may, at some later point, be treated by mathematicians as an axiom in a later development of the system. This point about geometry can, of course, also be applied to mathematical systems of logic. The upshot of Smyth's reconstruction of Peirce's account of what is cognized synthetically or analytically can be understood by thinking o the matter in light of a principle of continuity as applied to the growth of our cognitions over time. What, do you think, are the implications for applying the principle of continuity to the distinction between what is cognized a priori and a posteriori. Does the division have a timeless character, or does it have historical character that is indexed to our state of information at a given time and the growth of our understanding over time? Yours, Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: John F Sowa <[email protected]> Sent: Sunday, April 7, 2019 12:29:40 PM To: [email protected] Subject: Re: [PEIRCE-L] Phaneroscopy and logic On 4/7/2019 1:59 PM, Jeffrey Brian Downard wrote: > As an example of an /a priori/ element in moral cognition, consider > the role of the /feeling/ of respect in deliberation about the what is > required as a matter of duty. As an example of an a priori element in > aesthetic judgment, consider the condition of seeking harmony in the > experience of the beautiful. As an example of an /a priori/ element in > mathematical cognition, consider the role of the intuition of the whole > of ideal space in geometrical reasoning. > > In each case, I tend to think that Peirce agrees with Kant that these > are /a priori/ and not merely /a posteriori/ elements in our practical, > aesthetic and mathematical cognition. That's an interesting argument. But I recall something Peirce said about that issue (but it would require quite a bit of search to find exactly where). He said that Kant's Critik drV was his basic training in philosophy (when he was 16). But he diverged from Kant about what is a priori. Peirce admitted that there are probably some innate tendencies and preferences that determine value judgments. But experience (i.e., informal phaneroscopy) is essential to develop the details. John
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