Gabriel Syme

Hi, first time poster, long time reader. I have a question that I have just been dying to ask: Things like the Law of Contradiction [!((a==b)&&(a!=))], that are so fundamental to logic as we know it, well, are they really proven, somehow, or are they simply 'self-evident.' I have read a few philosophical texts lately for school and find myself mostly in line with Humian (sp.?) empiricism, so I doubt most everything. If you really are out there, you'll respond with a cogent, and truly ingenious point.

Thanks in advance... <img src="graemlins/notworthy.gif" border="0" alt="[Not Worthy]" /> <img src="graemlins/notworthy.gif" border="0" alt="[Not Worthy]" /> <img src="graemlins/notworthy.gif" border="0" alt="[Not Worthy]" />

--sr--

tyrrho

Don't know about cogent or ingenious, but there are a bunch of different answers:

empirical: "I've never seen a case where something is A and !A."

semantic: "I've defined A and !A so they can't both be true."

theological: "(insert appropriate verse here) implies that something can't be A and !A."

(and my favorite)
pragmatic: We can't have a decent argument unless we both agree that something can't be A and !A, so let's move on to something we disagree about.

I'm sure there are more. Anybody?

[ February 08, 2002: Message edited by: tyrrho ]</p>

jpbrooks

What sort of "proof" are you looking for? The fundamental axioms of logic cannot be denied without employing them in the process of the denial, but whether that observation could be considered a "proof" depends on one's definition of "proof".

(If you have further questions or comments, I have to leave soon, but I'll be back later tonight or early tomorrow morning hopefully.)

[ February 08, 2002: Message edited by: jpbrooks ]</p>

PJPSYCO

Logic is an extension of communication, and communication works of definition.

The basic idea behind evcerything is Universal Definition.

A=A true
A=notA false

This gives us the basis of universal definition, an object(ideas can be false) must have one and only one defintion, and that defintion can not be subject to change.
So, if A=B, and A=C, and B=notC then A=notA false.

For example, if I say point to the bowl, and you point to the plate, you are false because the bowl and the plate are distinct objects by their defintion.

bd-from-kg

sr:

It amazes me that this question keeps coming up. The laws of logic are neither proven nor self-evident; they are definitions.

Let’s start at the beginning. So far as logic is concerned, “true” is simply an undefined primitive.

To say that A is “false” is to deny that it is “true”.

To say ‘not A’ is to say that A is “false”. Given this definition, to say “A and not A” is simply to use the word “not” incorrectly. One is affirming and denying A at the same time.

Here’s what “and” means: If A and B are true, then A is true; moreover, if A and B are true, then B is true. To say “A and B, but not B” is to misunderstand the meaning of “and”.

Here’s what “imply” means: If A implies B and A is true, then B is true. Thus to say that A implies B and A is true, but B is false, is simply to misunderstand the meaning of “imply”.

Here’s what “all” means: “If all X are Y, then any particular X is Y.” Thus to say that all men are mortal and Socrates is a particular man, but Socrates is not mortal, is simply to misunderstand the meaning of “all”.

One could go through all logical terms in this fashion, and at the end of the day we would have all of the fundamental “laws of logic”.

A key point here is that most logical terms are connectives, and their definitions are simply instructions as to when it is appropriate to use them to “connect” things. They can’t really be defined in the way that nouns like “egg” or “unicorn” can. The only meaningful definitions are instructions as to when they may be properly used. And these instructions are called the “laws of logic”. Obviously these laws could be different. That would just mean that we were using different definitions for these words.

Vorkosigan

The foundations, and many of the laws of Logic, are built into us. See this <a href="http://www.psych.ucsb.edu/research/cep/primer.html" target="_blank">Primer on Evolutionary Psychology</a>

Be sure to read the second half.

Michael

Francois Tremblay

Little problem : you said "prove". As you must know, it is impossible to "prove" metaphysics, since proof requires a method of proof. However you can validate it.

The answer is because logic is a corollary of the axiom of identity (i.e. that all existants have definite attributes). In fact, "A is A" is nothing but a re-definition of identity. Likewise, the fact that contradictions cannot exist is deduced from identity.

Hope that helps.


PS turtonm, you committed the Naturalistic Fallacy. That a proposition is inborn is not a validation of that proposition.

[ February 08, 2002: Message edited by: Franc28 ]</p>

bd-from-kg

Franc28:

Once again you’ve managed to leave me completely baffled.

The distinction here escapes me. By “validating” the laws of logic, I assume you mean showing or verifying that they’re valid. Supposing that you could do this, how would that differ from “proving” them?

(My position, by the way, is that metaphysical axioms can neither be proved nor validated, but that the laws of logic are not metaphysical axioms.)

??? In what sense is logic a corollary of the axiom of identity?

Actually it doesn’t. In the first place contradictions do exist. For example: “My sister is male.” I suppose that you mean that contradictions aren’t true. But doesn’t that follow pretty immediately from the mere fact that they’re contradictions? And how is the supposed fact that, say, “A and A -&gt; B, but not B” cannot exist deduced from identity?

So far as I can see turtonm did not commit the Naturalistic fallacy or any other. sr was asking about the fundamental nature or status of the laws of logic: for example, whether they’re proved or self-evident. Turtonm’s answer, I gather, is that they’re not capable of proof, and seem self-evident only because of the way our minds (or if you prefer, brains) are structured, which in turn is the result of evolution. He didn’t claim to be demonstrating that they’re valid. I don’t agree with this answer, but that’s beside the point.

Clutch

bd, I think this is a case where understanding Franc's statement is made easier by knowing that he recommended a primer on Rand as a good introduction to philosophy. So, not real surprising that 'A=A' is written on stone tablets for him.

I agree that the role of axioms as definitions is weirdly overlooked in these discussions.

My two cents, it's also important to understand the origins of the very notion of proof in pictorial Euclidean geometry. That's the source of the idea that an axiom derives a sort of primitive justification from its immediate recognizability as a perfectly general principle. I mean, how do you prove that between any two points a straight line can be constructed? But at the same time, it's not just something you decide on a whim to take as primitive! You just think of the Euclidean plane, and you're supposed to see its generality -- "clearly and distinctly", as it were...

Francois Tremblay

Nice ad hominem, which only goes to prove my point that one who doesn't understand the axioms can't understand anything profoundly. Thank you.

[ February 09, 2002: Message edited by: Franc28 ]</p>