Where Does Logic (Formal) Come From

Coberst,

If you really want a discussion why not open a thread asking your central question. "Is logic healthy for us ?". You could then expand your title by briefly stating what you meant by "health".

Cognitive science claims that the manner in which we conceptualize and reason about these matters are determined, to one extinct or another, by sensorimotor domains of experience. CS claims that, in many cases, early experiences of normal mundane manipulations of objects become the prototypes from which these later concrete and abstract judgments are made.CS is claiming that the neural structure of sensorimotor experience is mapped onto the mental space for another experience that is not sensorimotor but subjective and that this neural mapping, which is unconscious and automatic, serves as part of the "DNA" of the subjective experience. The sensorimotor experience serves the role of an axiom for the subjective experience.

You answered your own question: this premise is self-evident because it is precisely that--a premise. It is something that is assumed to be true for the sake of an argument or a discourse; in this case, it is axiomatically assumed so that we can build a system of geometry upon it. Its "self-evidence" is part of its very definition. It was not deemed true because it matched experience; it was MADE true because it provided a useful basis for a system of mathematics.

Its conception had nothing to do with sense-experience, in other words, and it seems rather extravagant to claim that this mathematical axiom is one of the first things an infant learns. An infant learns how to get from Point A to Point B, certainly, but unless your hypothetical infant is a child prodigy it probably won't learn to apply a vocabulary of geometry to this until elementary school.

These cognitive science theories you speak of are attractive, but it might be helpful to keep in mind that they're good for explaining some kinds of knowledge but not others. You mentioned "judgment," for example, and that seems like a useful place to apply cognitive science. But like any theory, this one is ruined when you try to make it apply to everything in sight. The one thing that Kantian rationalism has going for it, in my opinion, is that it provides a more convincing picture of where mathematics comes from. That would be my response to your claim that "ideas associated with Idealism" be discouraged--quite a sweeping statement (unless you can be specific about which ideas you have in mind). CS is good for judgments, bad for mathematical knowledge; rationalism is good for mathematical knowledge, bad for judgments.

Intellectuals in general might do well to learn how to take the best parts of each theory rather than trying to find the one that explains everything. A theory that explains everything explains nothing.

Cognitive science claims that the manner in which we conceptualize and reason about these matters are determined, to one extinct or another, by sensorimotor domains of experience. CS claims that, in many cases, early experiences of normal mundane manipulations of objects become the prototypes from which these later concrete and abstract judgments are made.CS is claiming that the neural structure of sensorimotor experience is mapped onto the mental space for another experience that is not sensorimotor but subjective and that this neural mapping, which is unconscious and automatic, serves as part of the "DNA" of the subjective experience. The sensorimotor experience serves the role of an axiom for the subjective experience.

Yes, it might be worth brushing up on logic because my point was that premises are supposed to be circular. That's what makes them premises. Mathematics is chock full of 'em, which is why cognitive science is a poor explanation for mathematical knowledge. Premises are ideas that cannot be proven but, if assumed to be true, serve well as foundational axioms for systems of logic.

To put it another way, mathematical premises are not shown (or verified, via experience) to be true; they are defined as true because, when you get right down to it, you have to take it on faith that some things are true before you can operate within a logical system.

Again, the metaphor theory is attractive and, I imagine, lots of fun to wield; but, as with any theory, don't let it do your thinking for you. When you find yourself undermining the very definition of "premise," you're not really talking about logic anymore, which is what your topic claims to address.

I guess what I find unconvincing is the leap from the first statement to the next. I understand that you're offering "metaphor theory" precisely to explain this leap. My skepticism stems from what strikes me as a too vague and generalized treatment of mathematics and mathematical knowledge, which is a very specific kind of knowledge. I do not believe that our mathematical knowledge comes from sensory experience--especially geometry, which is by its nature built on abstractions and has no existence in the real world, and thus cannot be something empirically experienced. (Trying finding examples of the mathematical definitions of "line" and "point" in the real world.)

More specifically, what I find unconvincing is the implication that our mathematical knowledge derives from our experience in a neat, causal relation. I don't think it's as tidy as all that. That may be the way Euclid did it when he tried to systemetize geometry, but I don't think that's how it is learned now. I am more persuaded by a linguistic view: the experience of moving from one place to another develops independently of this mathematical knowledge, and the geometry behind it is, later, a system of vocabulary we apply to it. An infant can perceive a "here" and "there," and even how to get from one to the other; but I don't think we conceive of space in terms of lines and points until we learn the vocabulary to do so. I would not describe that learning as a "reinforcement" of prior experience; it is nothing less than a configuring of it--I'll go so far as to say effecting it. In short, when it comes to mathematics, I think knowledge has more to do with epistemology than empiricism.

This theory is as much a speculation as anyone else's, of course. You pays your money and takes your chances, as they say.

Shapless


Your statement "I think knowledge has more to do with epistemology than empiricism" caught my eye perhaps because it seems that is true by definition as I understand the words. Also the statement "This theory is as much a speculation as anyone else's, of course." "Speculation" seems inappropriate for this theory. A great deal of empirical research by respected scientists goes into forming this theory. I think that you error in dismissing this as "speculation".

I have posted this info about cognitive science for the purpose of arousing the curiosity of the reader sufficiently that the reader will study the theory and understand it. We all must make judgements as to the worth of a matter for study and you have decided that it is not worth the effort. I think you are mistaken and perhaps you will later see more about this theory and will change your mind.