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".

Many years ago while rummaging in a used book store I decided to buy "Human Evolution Coloring Book", I wanted to learn more about evolution. I learned all about how the hand evolved from the fin?-or was it the gills?-of fish. I looked in vain for a description of how my reasoning ability evolved from the fish.

"Philosophy in The Flesh" by George Lakoff, linguist, and Mark Johnson, philosopher, that I discovered at my local community college library several months ago finally helped me understand this, which since Darwin must be an obvious connection.

Darwin's theory declares that human capacity grows out of animal capacity but until I discovered this book PTF no one had given me any idea how this is possible. I studied a little philosophy but it never made much sense to me how pure reason with a dichotomy of mind and body could be inherited from tadpoles.

In the last three decades linguists, neuroscientists, philosophers, and others utilizing the scientific method of empirical study have organized a new cognitive theory that is described in this book. I shall call this Metaphor Theory even though no one in this book gives the theory a name. These ?'cognitive scientists' from many differing domains of knowledge speak of themselves as experimentalists. And the theory goes unnamed. I call the theory metaphor theory and I think that this theory will one day become the first paradigm of a new cognitive science.

We normally think of metaphors as merely linguistic means to associate an unknown with a known. ?'Understand is grasp' is one common metaphor ?'more is up' is another. The woods are full of such common metaphors and these metaphors are much more than meet the uninitiated eye.

Metaphor theory claims that almost all cognitive action takes place unconsciously. Metaphors, as we commonly know them, are conscious phenomena but metaphors are more importantly unconscious happenings in tadpoles and in humans. All creatures with neural capacity categorize, conceptualize, and infer; the principal characteristics of reasoning. Here in metaphors we see how human reason is connected to tadpole existence.

A standard technique for checking out new ideas is to create computer models of the idea and subject that model to simulated conditions to determine if the model behaves as does the reality. Such modeling techniques are used constantly in projecting behavior of meteorological parameters.

Neural computer models have shown that the types of operations required to perceive and move in space require the very same type of capability associated with reasoning. That is, neural models capable of doing all of the things that a body must be able to do when perceiving and moving can also perform the same kinds of actions associated with reasoning, i.e. inferring, categorizing, and conceiving.


Throughout our life we constantly make judgments about such abstract matters as difference, importance, difficulty, and morality, and we have subjective experiences such as affection, desire, love, intimacy and achievement. 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.

"When we conceptualize understanding an idea (subjective experience) in terms of grasping an object (sensorimotor experience) and failing to understand an idea as having it go right by us or over our heads" we are using a sensorimotor experience as the metaphor for the subjective experience. The metaphor ?'understand is grasp' results from our conflating a sensorimotor happening with a later subjective experience.

Metaphor is a standard means we have of understanding an unknown by association with a known. When we analyze the metaphor ?'bad is stinky' we will find: we are making a subjective judgment wherein the olfactory sensation becomes the source of the judgment. ?'This movie stinks' is a subjective judgment and it is made in this manner because a sensorimotor experience is the structure for making this judgment.

Why is the premise "A straight line is the shortest distance between two points" self-evident. It is because this is one of the first things an infant learns and it is verified and reinforced constantly throughout life by our sensorimotor experiences. The metaphor ?'more is up' is not so pervasive in our experience but its rationale is similar.

If we recognize metaphor as a means to associate something new with something old, something known with something unknown, we can begin to understand what CS is proposing in this revolutionary theory. CS is presenting a theory based upon empirical evidence gathered by the combined effort of linguists, philosophers, and neural physicists that metaphor is a very necessary element of our ability to reason as we do.

We normally think of metaphor as a tool of language whereby one can enlighten another by making an association of an unknown with a known. CS is making a much more radical use of metaphor.

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.

Shapless

It has been awhile since I have studied logic but I think your first paragraph is a beautiful example of a circular argument. I would say to this statement that the reason it is obviously true is because experience has shown us over and over that it is true.

As we have experiences we develop metaphors?-mental spaces containing the structure of experience?-and these metaphors are mapped from one mental space to another and thus become the foundation for the structure in the new mental space. Example: an infant's first experience is the warmth and security when first held and then perhaps each time held feels the same sensation plus additional sensations. Perhaps also along the way this structure is mapped into a mental space containing the abstract concept of affection thus this structure of warmth and security become part of the "DNA" of a new mental space. That is why affection is warmth is so easy for all of us to recognize as ?'truth'.

If you have not seen my attempt to define metaphor I will include that post.


Metaphors

Throughout our life we constantly make judgments about such abstract matters as difference, importance, difficulty, and morality, and we have subjective experiences such as affection, desire, love, intimacy and achievement. 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.

"When we conceptualize understanding an idea (subjective experience) in terms of grasping an object (sensorimotor experience) and failing to understand an idea as having it go right by us or over our heads" we are using a sensorimotor experience as the metaphor for the subjective experience. The metaphor ?'understand is grasp' results from our conflating a sensorimotor happening with a later subjective experience.

Metaphor is a standard means we have of understanding an unknown by association with a known. When we analyze the metaphor ?'bad is stinky' we will find: we are making a subjective judgment wherein the olfactory sensation becomes the source of the judgment. ?'This movie stinks' is a subjective judgment and it is made in this manner because a sensorimotor experience is the structure for making this judgment.

Why is the premise "A straight line is the shortest distance between two points" self-evident. It is because this is one of the first things an infant learns and it is verified and reinforced constantly throughout life by our sensorimotor experiences. The metaphor ?'more is up' is not so pervasive in our experience but its rationale is similar.

If we recognize metaphor as a means to associate something new with something old, something known with something unknown, we can begin to understand what CS is proposing in this revolutionary theory. CS is presenting a theory based upon empirical evidence gathered by the combined effort of linguists, philosophers, and neural physicists that metaphor is a very necessary element of our ability to reason as we do.

We normally think of metaphor as a tool of language whereby one can enlighten another by making an association of an unknown with a known. CS is making a much more radical use of metaphor.

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 think we are not using words that the other understands.

If we use words with this meaning:
Premise?-a proposition antecedently supposed or proved as a basis of argument or inference
Axiom?-a self-evident truth

Question?-how can we accept any proposition as an axiom? Because everyone agrees that it is self-evident. Why is it self evident? We ?'feel' that it is true. Our ?'gut' tells us it is true. Cognitive science as defined in "Philosophy in the Flesh" claims that experience creates a mental space with the neural structure acquired in an experience. This structure is mapped into another mental space at some other time and becomes the foundation for a new concept.

When a person constantly discovers that a straight line is the shortest distance between two points then that becomes a ?'fact' that the person ?'feels' is true. The neural structure of the experience is mapped into the concept of the ?'straight line' and thus we understand how this gut feeling is possible.

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.