Kim o' the Concrete Jungle

Let's be careful here. I'm not trying to say that classical logic is wrong to employ the dichotomy. I'm only saying it's wrong to assume that the dichotomy represents some sort of absolute truth about the universe itself. All we really know about the true/false dichotomy is that it's something we must assume when we engage in logical argument.

Since we have formulated the system of logic ourselves and clearly set down all its rules, we can say, "this is true of logic" with a high degree of certitude. We might not be able to directly apprehend any "truth" about the universe beyond ourselves, but we are certainly able to tell if an argument is logical or not. This is the strength of all abstract systems.

But it is all too easy to assume that what happens to be true according to the syntax of an abstract system is also true of the universe outside of ourselves. We assumed that, because classical logic does not allow the coexistence of contradictory statements, that the universe itself would not allow apparent contradictions in its physical laws. Then the wave/partical question came along and blew that assumption out of the water.

You seem to be implying that "relative truth" means there is no real contradiction, even when two ideas appear to be contradictory. I agree this is probably a good way to think about it. And it leads us straight to the post-modern, relativistic idea that there are many possible models, and many possible truths, not all of which are going to be reconcilable, but which can all coexist.

I agree with you that it's sometimes difficult to come to an agreement about what words mean. I tend to think that 90% of such arguments are unnecessary; for, in the end, it only really matters that both sides are arguing about the same thing, and that the meanings of the key terms are not allowed to shift during the course of the argument. If, for example, some apologist wants to use some bizarre definition of the word "love", I'm happy to go along with that. I don't see much point in arguing about it. I am, however, going to hold him to his bizarre definition and not let him slip back into some more mundane meaning of the word.

John Page

Hi Kim!

This is not true. As you point out, it seems difficult to tell whether logic is logical! (Deliberate ironical dichotomy to point out common usage of the adjective "logical" to falsely give the impression of veracity.
It has to admit contradictory statements, otherwise one could not conclude that one is true and the other false. That this is the source of certain contradictions within logic is another story...... but here's a plug for the Contradictions and Dialetheism thread anyway.

Cheers, John

excreationist

Searle talked about this in one of his books where he looked at various theories about consciousness. In his chapter on Penrose, he said how Penrose pointed this out and used this as evidence that our brains are more than computers - i.e. they interact with quantum phenomena through microtubules or something. (According to Penrose)

I think an example Penrose and Searle used was something like this...

X goes from 1 to infinity. Is two times X ever odd?

The program would be....

x = 1
main loop:
if (x * 2) is odd -> stop; "it's odd!"
x = x + 1
goto main loop.

As long as the program doesn't come across an odd number, the program will keep going on forever.

When humans think about the answer to the question, their reasoning might go something like this:
1 odd
2 (2 * 1) even
3 odd
4 (2 * 2) even
5 odd
6 (2 * 3) even
7 odd
8 (2 * 4) even

And they see there is a pattern where the doubled numbers are always even.

Perhaps they have heard of the definition of "even" where it is defined as any number that 2 goes evenly into.

Every time X is multiplied by 2, 2 will go into the result since X was an integer. And since 2 goes evenly into the result, X doubled is always even. And even numbers are never odd, since numbers can only be odd OR even (not both). Therefore X doubled is never odd.

I think it involves us triggering associated memories and learnt patterns... e.g. that one about the definition of what an even number is. Our brain automatically triggers potentially relevant associations which are used to try and solve the problem we have given it.

Kim o' the Concrete Jungle

Hi John, maybe I didn't put those two statements as well as I could have. So I will try to clarify what I meant.

You can look at a logical syllogism and refer it back to the rules governing logical syllogisms, and with only a little trouble you can determine whether it follows those rules or not. That is what I was getting at, and that is why logic is a useful tool.

Of course, where you get into trouble is when you assume that because an argument is logical, it must say something about some "absolute truth" out there in the universe. It doesn't. And it doesn't because the only real justification we have for using logic is that it seems to be a good tool for checking the internal consistency of a model, and for drawing logical inferences.

If we want to test whether an idea about the universe is right (as far as we can determine such things), showing that it is logical might be a good start. But you would definitely have to follow it up with some kind of empirical test. If you can test an idea in a number of different ways, and if the test results are consistent to within a degree you find acceptable, then you can conclude the idea is "useful".

I prefer the word "useful" to the word "true". When you say a model is useful, you are not implying that it is perfect, or that it won't some day be surpassed by something even more useful (as has happened so many times in the physical sciences).

Yes, sorry. What I meant is that classical logic cannot find two contradictory and mutually exclusive statements to be both true. But there are some circumstances (particularly where we lack important contextual information) where we would need to conclude that both statements are true. And in such circumstances, classical logic will not help us.

The example that Edward de Bono provides in Parallel Thinking are these two statements:

(1) "The train leaves at four o'clock."

(2) "The train leaves at five o'clock."

Which statement is true? Both of them. There are two trains. The contextual information makes it clear that there is no contradiction, but if you didn't have the contextual information, you wouldn't know if the two statements were a real contradiction or only an apparent contradiction.

Either way, argument (logical or otherwise) would be of absolutely no use to anyone in this situation. Yet how many people would automatically assume that -- as per classical logic -- these statements could not both be true? And how many people would still get in an argument about it, when what they should be doing is empirically testing the two statements by, say, looking at the train time table?

Maybe someone some day will come up with some sort of comparitive logic system where there are three possible answers: (1) both statements are true; (2) both statements are false; (3) one statement is true and the other is false. And perhaps if you want to make it really sophisticated, you might also allow that one or both statements are irrelevant. (Hmm. Now that's got me thinking .)

John Page

Excre:

Yes, ultimately my mind seems to conclude that (according to my process of mind) I arrive at axioms or rules of thumb whereby one can make reliable statements such as:

"(According to the rules of mathematics) a number multiplied by 2 can never be odd (because the test of 'oddness' is when division by two results in a non-integer)" and

"(According to the rules by which computers operate) we cannot determine X, but (according to the process by which the mind operates) we can determine X, therefore we (think we) do not operate according to the same rules as computers."

Try this. Assuming the above conclusion "We (think we) do not operate according to the same rules as computers." is valid, and that computers operate using logical principles, humans do not think using logical principles (where logical principles are defined as the set of principles employed in computers.)

Do you think this is a) logical , b) reasonable, c) neither, d) don't know. I'm in the don't know category because I don't know how the human mind works therefore cannot make a logical [hee hee] conclusion.

Cheers, John

John Page

Hi Kim! No beefs with your post.
I think dealing with the abstract does create a lot of "non-issues" and liked your train example. It seems to me that judging facts in the "real" world produces a "truth of evidence" conclusion - and this is one of statistical probability or degree of fit in nature e.g. (I could have been fooled but) that object over there is a train. Thus, the equivalence of the object's qualities to those of a train has been satisfied in the truth teller's mind. Hence intersubjective agreement of what a train is etc.

Our mind uses the same kind of trick to fool itself into accepting the equivalence of what a symbol stands for. We all see and x, so when we see "x is x" we say this is true, it is a fact, irrespective of what x represents. Of course, this is nonsense and following your example if the x on the left is a train and the second is a horse the truthfulness goes away. Truth is, therefore, an assumption that two entities are equivalent for the purposes of the analysis carried out. I argue this is a property of all representational systems - they all make use of fictitious assumptions to beget useful tools.

For two entities to be absolutely identical in reality is nonsense, if they were identical we couldn't tell them apart. The LOI thus breeds logic, a useful tool that employs a fictitious concept.

Cheers, John

jpbrooks

(Or more generally, that the dichotomy is fundamental to communication.)

I tend to agree with you generally on this point. To assume that Logic dictates the nature of reality is to give assent to the (Rationalistic?) assumption that "rationality implies reality". However, to say that (we know that) the dichotomy does not represent some absolute truth about the universe is tantamount to assuming that it is true (rather than not true) that that the dichotomy does not represent some absolute truth about the universe.

Again, I generally agree. But can we really apply this fact to the origin and applicability to the universe of the abstract system as a whole?

True. But such a faulty assumption, as you correctly point out, is not an essential one in the inquiry into the nature of the universe anyway.

Yes, I agree with the Postmodern Relativists on that point.

Yes, you have a right to expect the apologist to be consistent in the use of his or her definitions.

Sorry for the brevity of my replies. I have to run.

excreationist

"humans do not think using (computer-style) logical principles"....

does that mean that no aspect of human thought is like a computer program's? I'd say that's false. If it means that human thought as a whole isn't just like the program I described, then that would be true.

The computer program to "solve" a logic problem I mentioned earlier used an "iterative" (x=1, x=2, x=3, etc) sequential program. But there are other kinds of logic... I think ours is a more parallel fuzzy kind - it can simultaneously try and look at higher-order patterns (the pattern of odd vs. even numbers in general) rather than be eternally limited to looking at specific cases, one at a time. e.g. x=1, x=2, x=3, x=4, x=5, etc.

John Page

HI excre! No it doesn't mean that, but its not what I posted - here "We (think we) do not operate according to the same rules as computers." No matter - we don't really know how we think yet - especially at the "higher" levels of consciousness. Oh yes, and there are many computer programs in existence that make different use of logical principles so we'd have to get down to specifics...

Cheers, John

excreationist

Yeah, Searle (in response to Penrose) was saying that computer programs could probably be made that work out if an infinite sequence is ever odd, etc -
But in traditional computer programs, the answer is non-computable [and Penrose's conclusion that our brain involves more than straight-forward physics (i.e. it also interacts with quantum phenomena - perhaps like a quantum computer)]
The traditional approach is more in line with traditional logic I think... to prove that no number in the sequence is odd, it involves looking at all of the numbers, and if any odd number is ever found, then the search is over. If the entire sequence is searched and no odd numbers exist, then we can logically say that there are no odd numbers there.
It's kind of like having a theory that "no unicorns exist (in the universe)" - to prove that theory you'd have to simultaneously check every part of the universe since one could be hiding somewhere. [And maybe one is invisible - that would make it even harder to find...]