Freethought & Rationalism Archive

NialScorva · 05-30-2002, 09:30 PM

Keep in mind that while Kant built extravagent structures around the notions of a priori, a posteriori, sythetic, and analytic statements, a lot has been argued. For example, David Hume presented the empirical fork, lumping all possible statements into the categories of analytic a priori (mathematics and logic) and synthetic a posteriori (empirical claims). Kant argued with that there existed synthetic a priori statements. My personal opinion, though incomplete and very possibly wrong, is that Kant did based upon his reaction to Hume's Enquiry rather than to his Treatise, which is a fuller argument. In addition, the existence of sythetic a priori is almost required for arguing for transcendentals.

I think a severe blow to the analytic a priori and sythetic a posteriori distinction was made by Wittgenstein, driven home by Quine later. Wittgenstein argued that logic and mathematics in and of themself don't reveal anything about the world that is not contained in the initial axioms themself. In addition, he refers to the mystical nature of anything transcendent to language; that which is transcendent to the language that expresses it cannot be said in it. Possibly not the first time it was said, but definately a clear showing that our language is artificial and though it models reality, it is *not* reality. He did this in a very formal manner, showing not just that natural languages such as english are incapable of transcending their own boundaries, but that formal mathematics were as well.

Later in his life, he returned to address that over-formalization, revising his strict formalism into the notion of language games for informal langauge. This is where I think Quine really hits hard, by readdressing what is transcendent to these language games: the raw empirical experience itself. So now it's come full circle, from Hume's matching ideas to their antecendent impression, to the critical shift of matching the impression to it's generated ideas. It's a subtle difference, but important.

Under the earlier empricists, "1+1=2" is purely a synthetic a priori statement. However, it is a statement made within game, and within that game it is a tautological statement. That particular language game does not allow there to be falsehoods. The statement quickly becomes sythetic a posteriori if we say "one ball plus one ball makes two balls" or "one mound of pudding plus one mound of puddng makes two mounds of pudding". Once the abstracts are tied to concretes, then the objective vs subjective debate begins. Does "plus" mean put the mounds of pudding side by side, or together?

Quine argues that the abstracts are made from repeated learning of concretes, IOW, the learning of language itself is a a posteriori process. Hume argued much the same 300 years before, and developmental psychology is inclined to agree. What does this mean for the analytic a priori vs synthetic a posteriori?

My thought is that the distinction is abstract itself, and as such, based upon the combined experience of the individual. What does it imply that the ability to distinguish analytic a priori statements is only available through a posteriori experience? Does the notion of analytic a priori have a place when the foundation that it's built on is based upon empirical notions?

NialScorva · 05-30-2002, 11:03 PM

Fun link of the day:

<a href="http://www.ditext.com/quine/quine.html" target="_blank">Quine's Two Dogmas of Empiricism</a>

Ierrellus · 05-31-2002, 04:32 AM

A lighted 1/3 of a sulfer match plus darkness inside a gas tank 2/3 full= 1 blown up automobile.

Ierrellus

[ May 31, 2002: Message edited by: Ierrellus ]

WJ · 05-31-2002, 05:23 AM

Very, very, enriching discussion, everyone(s)! Nail expressed that which I was unable to say earlier which I'll pose as a somewhat redundant question: How do tautologies, when *applied* to a some thing, impart a truth on its very nature? To that end, Kim, please share your thoughts about the limitations of 'shoehorning' what I'll call 'apriori objective truths' into what can be known about reality (or the nature of a thing).

I realize there will be dead ends and as other's have suggested Kant already explored the limitations of what can be known about reality, but as Nail suggested, it is interesting then to see how subjectivism/objectivism somehow emerges from such 'investigations' of a 'percieved' truth(s).

Perhaps too, as Max alluded, what [should]comprises truth value? Is ones man's junk another man's jewel?

Again, please feel free to explore any of these 'dichotomous' rules of thought, if you will.

I will go back to the engineering example as a quick recap thus far: I can create a wood beam from using an apriori truth which in turn imparts *part of* its nature. (Of course, in this example, we know that wood already exists. So we are not really uncovering any true novelty; we're just using a tautology as a tool.)

As another thought or metaphor, maybe in a strange way, .9999 exists because the world is somehow incomplete by our levels of understanding-logic? And that makes me wonder whether math is purely our own construct, or whether its essence of truth has its own independent existence that we discovered/uncovered thru physics. If its our own construct, I would have less faith/hope in objectivism and more hope is subjectivism. If it can be proven it has an independent existence, then logic wins and the nature of the world can someday be known. James? Anyone?

Walrus

James Still · 05-31-2002, 08:25 AM

Quote:

I think a severe blow to the analytic a priori and sythetic a posteriori distinction was made by Wittgenstein, driven home by Quine later. Wittgenstein argued that logic and mathematics in and of themself don't reveal anything about the world that is not contained in the initial axioms themself. In addition, he refers to the mystical nature of anything transcendent to language; that which is transcendent to the language that expresses it cannot be said in it. Possibly not the first time it was said, but definately a clear showing that our language is artificial and though it models reality, it is *not* reality. He did this in a very formal manner, showing not just that natural languages such as english are incapable of transcending their own boundaries, but that formal mathematics were as well.

Yes, you've put it very well. I had the Tractatus in mind when I said that a priori analytics contained no truth values (no correspondence to reality). And as we all know Wittgenstein suggests that we remain silent about those ideas that go beyond language. But if William James is correct, we can't help it when it comes to religion. Our imagination runs wild and speculations quickly become facts as they are passed from generation to generation. Sorry off topic.

Quote:

Later in his life, he returned to address that over-formalization, revising his strict formalism into the notion of language games for informal langauge. This is where I think Quine really hits hard, by readdressing what is transcendent to these language games: the raw empirical experience itself. So now it's come full circle, from Hume's matching ideas to their antecendent impression, to the critical shift of matching the impression to it's generated ideas. It's a subtle difference, but important.

I've never thought about a connection between W./Quine back to Hume again and I'm not sure I fully agree. Do you mean to say that Hume's skepticism of knowledge is akin to Wittgenstein's view that knowledge is agreement in language? I do agree that Wittgenstein's contribution to our understanding of how concepts are sustained in language-games was important. It is also largely ignored outside of a narrow circle in philosophy. But it's important I think to understand what W. meant by the language-game to see that what we regard as real (an existent) or an idea (a subsistent) will be revealed not by some extralinguistic measure, but by how we speak about the thing in the language-games that sustain it. I've written a long essay about certainty, belief-formation and language-games but I'm not sure if I want to share it with others yet. But you've got me thinking about it again.

Quote:

Under the earlier empricists, "1+1=2" is purely a synthetic a priori statement. However, it is a statement made within game, and within that game it is a tautological statement. That particular language game does not allow there to be falsehoods.

This gets right to the core of the problem that started this whole discussion. To ask, "Is 1/3 + 2/3 = 1 an objective truth, or is it a subjective truth?" is to be bewitched by language. And we all have to fight that sort of sorcery because it is powerful. The problem I think is in that tricky word "truth" because we want it to mean "something that is the case today, yesterday, tomorrow, forever, and even in the absence of human beings or the universe." In other words we seek extralinguistic foundations upon which to anchor such sentences because we can't stand the fact that truth and falsity is determined by the logic within the game itself. Yes, I very much agree with what you're saying here.

Quote:

Quine argues that the abstracts are made from repeated learning of concretes, IOW, the learning of language itself is a a posteriori process. Hume argued much the same 300 years before, and developmental psychology is inclined to agree. What does this mean for the analytic a priori vs synthetic a posteriori?

My thought is that the distinction is abstract itself, and as such, based upon the combined experience of the individual. What does it imply that the ability to distinguish analytic a priori statements is only available through a posteriori experience? Does the notion of analytic a priori have a place when the foundation that it's built on is based upon empirical notions?

Of course, analytics are supposed to be transcendental and inform our experiences. And I agree with your interpretation of Wittgenstein but there are some who take a Kantian approach to him, arguing that his various cryptic remarks on transcendent objects were meant to be taken literally rather than as subsistent objects within language. I don't think Wittgenstein will end the debate between the realists and the conceptualists anytime soon.

sotzo · 05-31-2002, 09:08 AM

Hi Bookman!

There are actually useful mathematics that are noncommutative (the associative property is the one that goes a+(b+c)=(a+b)+c)) -- the commutative property is a useful construct, but there exist equally "valid" (by which I mean useful and descriptive) mathematics which don't require it as an axiom.

The question is not whether or not an axiom is "useful" or "descriptive" in certain areas of mathematics. The question is whether or not in areas where it is "useful" or "descriptive" the axiom is true. Thus far, neither Devil nor anyone else has answered how it could be that the associative property could be falsified. The response has been that as an axiom it is true insofar as it is defined as "true". If that is the case, however, it should be possible to redefine the associative property. To my knowledge, an attempt to do so would lead to nonsense, which points in the direction of the existence of objective truth. (And yes, I'm a theist.)

By the way, I appreciate you correcting me on my definition of the associative property! Thanks!

sotzo · 05-31-2002, 09:12 AM

Hello CardinalMan:

Thanks for the link. I will check it out and get back to you with questions I'm sure I'll have!

By the way, which branch(es) of math do you study?

Cheers
jkb

Bookman · 05-31-2002, 09:46 AM

Quote:

Originally posted by sotzo:
If that is the case, however, it should be possible to redefine the associative[sic] property. To my knowledge, an attempt to do so would lead to nonsense, which points in the direction of the existence of objective truth. (And yes, I'm a theist.)

I didn't express myself very well before. There are well-behaved formal systems which are non-commutative. In other words one can "redefine the commutative property*" and the result is not nonsense.

I'm not sure what your background in mathematics is; in my course of study, I did not examine these ideas until the third year of my bachelor's program when I took my first class in abstract algebra.

Bookman

* I'm not comfortable with this phrasing, however. I might express it as: One can choose axioms which yield valid formal systems in which the commutative property does not hold.

James Still · 05-31-2002, 09:54 AM

Quote:

Originally posted by sotzo:
The question is not whether or not an axiom is "useful" or "descriptive" in certain areas of mathematics. The question is whether or not in areas where it is "useful" or "descriptive" the axiom is true. Thus far, neither Devil nor anyone else has answered how it could be that the associative property could be falsified. The response has been that as an axiom it is true insofar as it is defined as "true". If that is the case, however, it should be possible to redefine the associative property. To my knowledge, an attempt to do so would lead to nonsense, which points in the direction of the existence of objective truth. (And yes, I'm a theist.)

Hi sotzo. I quite agree that redefining the associative property leads to nonsense. But can we really say then that this leads to objective truth? I don't think so. As Nialscorva and I have mentioned, the reason the redefinition is nonsense is not because it fails to cohere with something "out there" somewhere but rather because it violates the logic of the language of mathematics itself. It's like my earlier example:

(1) All bachelors are unmarried men.

What would it mean to falsify this sentence? I don't think that question makes sense. Should I take a survey of unmarried men and ask them if they are not bachelors, looking for a counter-example that might render the proposition false? We all know that would be absurd. I cannot falsify it because it is tautological by definition just like the associative property of numbers. But it seems to me that we wouldn't say that the reason unmarried men are bachelors is because there is an objective truth that makes it so. We would say that our logic in using the word "bachelor" makes it true that all such men are unmarried.

"We feel that even when all possible scientific questions are answered, the problems of our life have not even begun to be touched." -Ludwig Wittgenstein

[Edited to add quote...]

[ May 31, 2002: Message edited by: James Still ]

NialScorva · 05-31-2002, 12:20 PM

James,

I'm gonna take my response to another thread, I'm interested in discussing it, but don't want to pull this thread off track.

05-31-2002, 04:32 AM	#33
Ierrellus Veteran Member Join Date: Mar 2002 Location: Canton, Ohio Posts: 2,082	A lighted 1/3 of a sulfer match plus darkness inside a gas tank 2/3 full= 1 blown up automobile. Ierrellus [ May 31, 2002: Message edited by: Ierrellus ]</p>

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05-30-2002, 09:30 PM	#31
NialScorva Veteran Member Join Date: Jan 2001 Location: Median strip of DC beltway Posts: 1,888	Keep in mind that while Kant built extravagent structures around the notions of a priori, a posteriori, sythetic, and analytic statements, a lot has been argued. For example, David Hume presented the empirical fork, lumping all possible statements into the categories of analytic a priori (mathematics and logic) and synthetic a posteriori (empirical claims). Kant argued with that there existed synthetic a priori statements. My personal opinion, though incomplete and very possibly wrong, is that Kant did based upon his reaction to Hume's Enquiry rather than to his Treatise, which is a fuller argument. In addition, the existence of sythetic a priori is almost required for arguing for transcendentals. I think a severe blow to the analytic a priori and sythetic a posteriori distinction was made by Wittgenstein, driven home by Quine later. Wittgenstein argued that logic and mathematics in and of themself don't reveal anything about the world that is not contained in the initial axioms themself. In addition, he refers to the mystical nature of anything transcendent to language; that which is transcendent to the language that expresses it cannot be said in it. Possibly not the first time it was said, but definately a clear showing that our language is artificial and though it models reality, it is not reality. He did this in a very formal manner, showing not just that natural languages such as english are incapable of transcending their own boundaries, but that formal mathematics were as well. Later in his life, he returned to address that over-formalization, revising his strict formalism into the notion of language games for informal langauge. This is where I think Quine really hits hard, by readdressing what is transcendent to these language games: the raw empirical experience itself. So now it's come full circle, from Hume's matching ideas to their antecendent impression, to the critical shift of matching the impression to it's generated ideas. It's a subtle difference, but important. Under the earlier empricists, "1+1=2" is purely a synthetic a priori statement. However, it is a statement made within game, and within that game it is a tautological statement. That particular language game does not allow there to be falsehoods. The statement quickly becomes sythetic a posteriori if we say "one ball plus one ball makes two balls" or "one mound of pudding plus one mound of puddng makes two mounds of pudding". Once the abstracts are tied to concretes, then the objective vs subjective debate begins. Does "plus" mean put the mounds of pudding side by side, or together? Quine argues that the abstracts are made from repeated learning of concretes, IOW, the learning of language itself is a a posteriori process. Hume argued much the same 300 years before, and developmental psychology is inclined to agree. What does this mean for the analytic a priori vs synthetic a posteriori? My thought is that the distinction is abstract itself, and as such, based upon the combined experience of the individual. What does it imply that the ability to distinguish analytic a priori statements is only available through a posteriori experience? Does the notion of analytic a priori have a place when the foundation that it's built on is based upon empirical notions?

05-30-2002, 11:03 PM	#32
NialScorva Veteran Member Join Date: Jan 2001 Location: Median strip of DC beltway Posts: 1,888	Fun link of the day: <a href="http://www.ditext.com/quine/quine.html" target="_blank">Quine's Two Dogmas of Empiricism</a>

05-31-2002, 05:23 AM	#34
WJ Senior Member Join Date: Feb 2002 Posts: 812	Very, very, enriching discussion, everyone(s)! Nail expressed that which I was unable to say earlier which I'll pose as a somewhat redundant question: How do tautologies, when applied to a some thing, impart a truth on its very nature? To that end, Kim, please share your thoughts about the limitations of 'shoehorning' what I'll call 'apriori objective truths' into what can be known about reality (or the nature of a thing). I realize there will be dead ends and as other's have suggested Kant already explored the limitations of what can be known about reality, but as Nail suggested, it is interesting then to see how subjectivism/objectivism somehow emerges from such 'investigations' of a 'percieved' truth(s). Perhaps too, as Max alluded, what [should]comprises truth value? Is ones man's junk another man's jewel? Again, please feel free to explore any of these 'dichotomous' rules of thought, if you will. I will go back to the engineering example as a quick recap thus far: I can create a wood beam from using an apriori truth which in turn imparts part of its nature. (Of course, in this example, we know that wood already exists. So we are not really uncovering any true novelty; we're just using a tautology as a tool.) As another thought or metaphor, maybe in a strange way, .9999 exists because the world is somehow incomplete by our levels of understanding-logic? And that makes me wonder whether math is purely our own construct, or whether its essence of truth has its own independent existence that we discovered/uncovered thru physics. If its our own construct, I would have less faith/hope in objectivism and more hope is subjectivism. If it can be proven it has an independent existence, then logic wins and the nature of the world can someday be known. James? Anyone? Walrus

05-31-2002, 09:08 AM	#36
sotzo Regular Member Join Date: May 2001 Location: Lakeland, FL, USA Posts: 102	Hi Bookman! There are actually useful mathematics that are noncommutative (the associative property is the one that goes a+(b+c)=(a+b)+c)) -- the commutative property is a useful construct, but there exist equally "valid" (by which I mean useful and descriptive) mathematics which don't require it as an axiom. The question is not whether or not an axiom is "useful" or "descriptive" in certain areas of mathematics. The question is whether or not in areas where it is "useful" or "descriptive" the axiom is true. Thus far, neither Devil nor anyone else has answered how it could be that the associative property could be falsified. The response has been that as an axiom it is true insofar as it is defined as "true". If that is the case, however, it should be possible to redefine the associative property. To my knowledge, an attempt to do so would lead to nonsense, which points in the direction of the existence of objective truth. (And yes, I'm a theist.) By the way, I appreciate you correcting me on my definition of the associative property! Thanks!

05-31-2002, 09:12 AM	#37
sotzo Regular Member Join Date: May 2001 Location: Lakeland, FL, USA Posts: 102	Hello CardinalMan: Thanks for the link. I will check it out and get back to you with questions I'm sure I'll have! By the way, which branch(es) of math do you study? Cheers jkb

05-31-2002, 12:20 PM	#40
NialScorva Veteran Member Join Date: Jan 2001 Location: Median strip of DC beltway Posts: 1,888	James, I'm gonna take my response to another thread, I'm interested in discussing it, but don't want to pull this thread off track.

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