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Re: A priori and empirical knowledge

Continuation: Nevertheless, xyz, I want to return to your earlier statements. You said: "In the first place, we have the a priori basis of mathematical knowledge, which entirely conflicts with this thesis [Empiricism]. In the second place, we have the method of necessarily truth-preserving deductive proof and logical demonstration, which once again conflicts with the inductive nature of empirical inferences and conclusions." What I object to here is your belief that purely analytic / apriori knowledge is possible. This is a commonly held view nowadays, since Kant, but it is false, untenable. You say: "The reason I bring this up is that it is often parroted that knowledge must be based upon empirical observation or "the empirical evidence". However, it remains open to question to what extent such dogmatic assertions are really true. You can prove the irrationality of the square root of 2 without ever leaving your arm chair, and no one would assert that this proof doesn't constitute a valid piece of knowledge." Here again, you are affirming the possibility of purely apriori mathematical knowledge, forgetting that the concepts involved in this proof are all ultimately based on experience. The rational insights that produce the proof are only the last links in a long chain. Again: "People are more inclined to say that we couldn't arrive at valid conclusions about the world without the justification of experience. Really? Nothing is simultaneously red all over and green all over. There; I came to a valid conclusion about the world without ever leaving my arm chair." Here, you think the law of non-contradiction can by itself produce knowledge. You forget that your statement would be incomprehensible to you or anyone who had not first empirically come to the concepts of "red, green, all over, is, nothing, and", not to mention "world, arm-chair, etc." You can't just ignore these antecedents in your thinking. So, whereas you do not take the extreme empiricism position that knowledge can come from empirical physical data alone, you do take the opposite extreme and think that knowledge can come from rational insight alone. This is the point of contention between us.

Something about you (optional) logician-philosopher

Re: A priori and empirical knowledge

I was somewhat hesitant to continue the discussion. I mean no offense, but I feel like the discussion turned out being rather protracted and confusing. I somewhat regret starting it, due to the confusion it ended up leading to. You are correct in that I do accept (a priori) analytic knowledge. For example, I do accept the sentence (e.g. "All bachelors are unmarried") as an analytic truth; I do accept that you can understand this proposition strictly by virtue of the meaning of the terms involved. In other words, I do accept that there are certain truths of reason that are self-evident, and intuitively graspable. I do not deny, of course, that in order to grasp certain truths of reason, one must look at dots of ink on a piece of paper, for instance. In order to understand the proposition "all bachelors are unmarried", one must of course be able to read the words on the page; but I do not believe that this has any bearing on the justification of the proposition as a priori knowledge. You are correct that this is the essential point where we disagree. Whether this means that I am going to the "opposite extreme", I am not so sure. In any case, I enjoyed the discussion even if it did lead to a rather significant amount of confusion.

Re: A priori and empirical knowledge

Permit me to reply to your two last points. Concerning "bachelors are unmarried men", please look here: http://www.thelogician.net/6_reflect/6_Book_2/6b_chapter_02.htm The proposition "bachelors are unmarried men" may appear in people's minds in one of two ways. Either (1) we arrived empirically at the idea that "there are unmarried men" and then decided to attach a name to this phenomenon, viz. "bachelor"; or (2) we found texts about "unmarried men", and other texts about "bachelors" and eventually realized from context that the two terms are equivalent. In case (1) although the new name being attached is a conventional act, there is no added knowledge, and it is ridiculous to speak of "analysis", not to mention that "unmarried men" is a concept based on experience (of men, of the social institution of marriage). In case (2) the tying together of two separate threads is not an "analytic" equation but an inductive act based on observation of contexts of use, and understanding of these contexts depends on experience of course. Try doing all that with the content-less "C are BA" - is even this analytic truth? As regards, taking into consideration the perception of "words on the page" as you put it - this relates to mathematical proofs. Many mathematical proofs are based on the manipulation of symbolic objects (whether as ink on paper or dots on a computer screen or in mental imagination). The behavior of these symbolic objects are effectively the empirical basis of the mathematical principles. The fact that physical objects like apples or mental objects like imagined apples are not used, but symbols like a, b, c changes nothing to the empiricism involved. Without the visualization of something there is no mathematical proof. So it cannot be said to be purely analytical, i.e. purely based on rational insight, without any content whatsoever. Similarly in logic - the laws of thought have no meaning if not "applied" to something more concrete. Even spoken in terms of symbols (as in "A is A") their meaning proceeds form the concrete percepts involved (A, is). As I said before, to ignore some elements of one's own discourse, and try to formulate philosophical, logical or mathematical ideas without taking into account ALL its constituents, is idiocy.

Something about you (optional) logician-philosopher

Re: A priori and empirical knowledge

Interesting discussion! So is there any merit in the "Analytic-synthetic" distinction?

https://en.wikipedia.org/wiki/Analytic–synthetic_distinction

According to Kant,a proposition whose predicate concept is contained in its subject concept is analytic, and a proposition whose predicate concept is not contained in its subject concept but related, is synthetic. The term "related" seems a bit vague here - related in what way?

an example of an analytic proposition is: All bachelors are unmarried
an example of a synthetic proposition is: All bachelors are alone

But both subjects here refer to the meaning of "bachelor", and the so-called synthetic proposition can be deduced from the analytic one.

To me it all seems like much ado about nothing.

Re: A priori and empirical knowledge

Hi McCoy - there's no such thing as purely analytic propositions (i.e. not based on experience) - all are synthetic to some extent (i.e. based on experience). Kant was a brainy guy, but in many ways also confused. If you have not read my little book "A short critique of Kant's unreason," I recommend it.
My main website is having tech problems right now, but you can read it here: http://tl-archive.net/6_reflect/6_Book_2/6_book_2.htm