Bookman

I'm secure enough to admit that you totally lost me somewhere around "...synthetic apriori assumption/proposition...".

Can you dumb this down for me a bit?

Thanks,
Bookman

P.S. It's hard to convey on these boards but in this case I'm genuinely not being sarcastic. I really don't understand the question.

tronvillain

sotzo:
Ah, but it is possible to change a+b=b+a into either a+b<>b+a or a+b=a-b simply by convention. In the first case, simply replace "=" with "<>" in all cases. In the second case, a much more complex convention would be required, such as "what is on the right of an equals sign is written backwards with minus signs in the place of plus signs." Of course, only the first case is analagous to replacing "water" with "ret" but there is no reason one is any more or less a convention than the other.

James Still

Hey Bookman, rest assured that your ego is intact and secure because Kant's metaphysics is pretty difficult stuff for everyone. Simply put, Kant distinguished between analytical judgments and synthetic judgments. An analytic is something that is prior to experience (a priori) and the truth of the statement is contained in the subject itself:

(1) All bachelors are unmarried men.

This is an analytic proposition because you don't have to go around and take a survey of all unmarried men to find out their marital status. Just by reflecting upon the terms in the sentence you realize that it is true by definition. Kant would say that nothing new is added to the subject "bachelor" by predicating "unmarried" to it because the predication is contained with the subject itself. If you were to deny the predicate "unmarried" it would result in a contradiction of terms.

A synthetic proposition is one made after examining the evidence (a posteriori) and the truth of a synthetic is determined by this examination rather than just reflecting upon the terms:

(2) The ball is red.

No matter how hard you gaze at your navel you will not be able to say that the predicate of "redness" is contained within the subject (ball). You have to actually look at the ball to see if the proposition is true. But if you take away the predicate "redness" it doesn't result in a contradiction. A ball can be blue or yellow after all.

WJ is referring to a third Kantian possibility: the a priori synthetic, which Kant believed to be represented by the proposition:

(3) 7 + 5 = 12

He considered it prior to experience because numbers are ideas in our judgment rather than things out in the world. But he also said it was synthetic because it is not at all clear just by examining the terms that they are contained within the subject "12". The operator (+) and the two operands can fit into numerous permutations and be manipulated in several different ways. (For instance 5 is a relation between 3 and 2). It seems to be a linguistic (mathematical) rule that makes them work together in the equation rather than something a priori.

I should say at this point that this part of Kant's philosophy is very controversial and I admit that I don't fully understand where he's going with it. And I also admit that I understand WJ's point even less. If he agrees with Kant that mathematical equations are a priori synthetics and scientific experiments are a posteriori synthetics then he seems to be advancing a healthy empiricism of the sort Kant advocated.

WJ

Book!

(I'm certainly not an expert in physics as is obvious, but let me try to use my sense of logic or my layman's common sense to what I think you are asking.)

apriori=mathematical truth/axiom (universal?)
empiricism= aposteriori truth thru sense data

To design a wood beam I use a math formula to create part of its existence or properties, then I test it to see if it works. Conversely, if some thing's property/state cannot be physically tested, (like in thermodynamics the fact that water was boiling and leaves no physical evidence at some point in time), what method is used to make an 'objective' statement about its existing nature or future properties without physically witnessing, in this case, its boiling? Or in looking at a beam I know that a math formula was responsible for creating part of its existence. So I'm assuming here that a certain amount of objectivity (math) was instrumental in understanding its nature. And I can use this 'idea' of math any time I want to create a some thing.

So in that regard, this timeless universal 'metaphor' of truth (math) explained a certain amount of its nature. But if there is a some thing that's not verifiable, but still exists (like say consciousness) how objective can we be in surmising the truth abouts its nature?

I'm just thinking about methodology here. So when you say tautologies, when it is time to actually use them, it becomes part of a subjective/objective process when thinking about why the axiom itself works so well. I'm taking the lead from what zotso said in item 2.

Otherwise, I guess we're still back to what kind of truth does the metaphor really represent, when it is used within a given context.

Walrus

WJ

James!

Sorry we crossed. I think I understand what you are saying. Let me think about though and re-post. My initial reaction though is that a synthetic apriori, without taking its premise any further, is assumed to be true because we can't help assuming something to discover what it actually is. I know we're getting off topic from the idea of mathematics and existence, but if an assumpton is made without the ability to verify its truth value, my quandry is what should follow? I'll try to think of some better examples than the water boiling thing.

Like I say, I have no real aggenda, I want to see where this metaphor takes us when applying it to 'things in themselves'...

Thanks

Walrus

CardinalMan

There was a similar disscusion about this a while ago in the thread <a href="http://iidb.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=21&t=000408&p=" target="_blank">Counter arguments to mathematics as a descriptive language</a>. About two-thirds of the way down on that page, I posted about how the natual notion of "addition" for compiling baseball statistics or when playing with Rubik's cube differs from ordinary addition (and how in the case of the Rubik's Cube we do not have a+b = b+a).

I'm also in the process of writing some web pages about modern mathematics, and I elaborate on my previous post in a discussion about <a href="http://www.math.uiuc.edu/~mileti/algebra.html" target="_blank">Abstract Algebra</a>.

I'll be out of town until the middle of next week, so if you want to continue this discussion, give me a little while to get back to you.

CardinalMan

[ May 30, 2002: Message edited by: CardinalMan ]</p>

James Still

Kant relied exclusively on Newton's physics to say that time and space were transcendentally ideal and thus made our pure intuititions of the two elements possible. He also said that we can use those pure intuitions along with the categories of our experience to fashion a priori synthetic judgments. They are a priori because they derive from the pure intuitions and synthetic because they involve experiences within the world. But let's be clear about one thing: Einstein radically revised Newton's physics; thus, pulling the rug out from under Kant's suggestion that time and space are forms (ideals) of transcendental reality. We now know that time is not something fixed and ideal but rather a relation between bodies. Now perhaps this isn't fatal to Kant's metaphysics since you could say that it is our perception of these two elements that conditions our experience rather than their actual reality.

But my point is that using transcendental ideals as foundations for going beyond experience is fraught with danger. Yes can we assume that the mathematical truths of our construction are universal in scope. But the reason for that is because mathematics is a handy description of the phenomenal world's regularity and the relationships of its entities. Truth has nothing to do with it. These statements are tautological because they model what is already a given.) Thus, in my opinion the problem of verifying the truth value of mathematics turns out to be a pseudoproblem. The world "just is" and our experiences of it are such that we cannot go beyond that fact.

snatchbalance

WJ,

This is my philiosophy <a href="http://www.raveller.com/fools/" target="_blank">sb</a>. I've never read SK. I'll checkit out and get back to you.

This may be off the topic at hand, but I slept all through my class in diferential equations.

SB

[ May 30, 2002: Message edited by: snatchbalance ]</p>

Bookman

James,

I wonder what Kant would have made of Gödel? It would seem to me (from this brief introduction) that the incompleteness theorem wrecks any notion of trancendental ideals -- there will always be more axioms needed to extend the completeness of mathematics and in the absence of experience data we're forced to simply guess.

SB, nice page. It reminds me of <a href="http://www.amazon.com/exec/obidos/ASIN/1580083463/internetinfidelsA/" target="_blank">Crazy Wisdom</a> by Wes Nisker. I recommend it if you can get your hands on a copy.

Bookman

[ May 30, 2002: Message edited by: Bookman ]</p>

Kim o' the Concrete Jungle

To my mind, what this discussion mostly proves is that the whole objective/subjective dichotomy is not sufficient of itself to understand certain qualities of reality. In order to shoehorn mathematics into this dichotomy, one must resort to extremely difficult and convoluted arguments. This is one reason why I choose to cast things in a slightly different way (abstraction vs observed experience etc -- but I won't go into that here, since its not relevant to this thread).