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Posted by Harvey on July 27, 2001 17:42:33 UTC

Aurino,

Let me again summarize and reply to your arguments as Iunderstand them being stated:

1. Truth as being consistent statements is the only definition of truth worth considering: 'But if you think about it, that's the only definition of truth worth worrying about. Everything else is just an opinion.'

I don't agree. Where do the axioms of math come from? They come from observation and convention. If those observations and agreements are pure opinion, then that means the theorems are also opinion. Just because they are 'self-consistent' provides no reliable definition of truth since the term self-consistent is tautological (in the worst kind of way). For example, "Q:why is X+1=1+X?, A: Bcz it is consistent with our deductions of this premise. Q: Why is it consistent? A: Because when we apply these concepts they are consistent." In other words, you cannot justify a consistent approach (i.e., the coherence definition of truth) without using the coherence definition in your definition (aka tautology).

On the other hand, we can use the correspondence theory of truth by saying that it is true that I am typing if I see that I am typing. If asked why is X+1=1+X, I can say that if I *apply* this principle in the world (say with counting apples), I see that this algorithm corresponds the same (i.e., 1+10 apples corresponds visually as 10+1 apples). Now, I'm not saying that correspondence theory doesn't also have philosophical problems, but only that it can answer questions such as why we say mathematics is useful. It is useful because its usefulness corresponds with our experience of it being useful. You can't say that with a coherence theory of truth (it is useful because it is consistent doesn't say anything at all, it merely describes what mathematics is constructed to do - be consistent with axioms, other theorems, etc...).

2. Dick doesn't acknowledge GR: 'I don't think we're talking about the same person here. I have no idea why you would say that.'

I'm just going back to discussions I've had with Dick at Counterbalance. He has something against Einstein's GR theory. You might ask him about it. Evidently he couldn't obtain GR with his mathematical model so he has rejected it - at least partially.

3. Philosophy of math is pure opinion: 'Your opinion against his opinion, right? Opinions are like noses, everybody's got one. Most discussions on these forums are little more than my-nose-is-more-beautiful-than-your-nose kind of argument. It can be fun but it never leads anywhere.'

Listen to this very important statement: every thing uttered in any form is opinion. Math is an opinion. So, is physics. So, is the statement that the sun is over our head. Now, there are some opinions which we say fall in the category of fact. But, this is only a human category since we have no means to validate if our human way of looking at something is indeed as it is. Even math theorems would be seen doubtful if another set of theorems began to contradict that theorem starting tomorrow. Everything has the ability to be cast in doubt, so there is no statement that is infallible (even this one). The question is what statements are more expedient and worth treating with more gravity. We can decipher such statements by looking at their implications and self-consistency with the world. In the case of Alex's views on mathematics, I've already explored with him the ramifications of a mathematical order that has no axioms (or if it does those axioms are without basis to explain the world). So, each person must decide what is fact, what is probable, what is likely, etc. Fortunately for us humans we tend to buy into certain lines of reasoning over others, else the world would be in chaos.

4. There is a problem viewing science as a trail and error process: 'you still have the problem of how to determine which tries were successful and which ones failed. Your position is that right guesses promote survival, my position is that guesses that promote survival promote survival and nothing else, the "correctness" of a guess is a non-issue when it comes to evolution.'

Science is based on a few theories of truth. It uses the correspondence theory - probably more than any other. But, it also uses the coherence theory of truth with the usage of mathematics and principles of logic, and it also uses the pragmatist theories of truth (i.e., instrumentalism), and it uses Pierce's pragmaticist view of approximate truth (which is really the pure pragmatic view). There are others but they become more minor (e.g., truth is beautiful theories - I have no idea what those theories are called). These main four theories are weighed against each other and if every one gave the same weight to each there would be much less controversy in science. But, lucky us, when one theory is considered good, it usually is very good and has all the theories in its court (for example, GR is consistent, corresponding, instrumental, and most everyone has agreed upon it over the 85 years since its publication).

5. Physics is either built on axioms or else it is built on senses (opinion): 'I find it rather odd that you and Alex are so convinced that physics is tied up with math and yet refuse to accept its axiomatic character. Oh, math is built on axioms but physics is not, even though there isn't a single concept in physics which cannot be expressed with math. Isn't that strange?...Can't you see how that creates a fundamental problem? If you can't define empiricism, observation, experiment, in terms of math, how do you define them? In terms of your senses? Aren't you saying that the truth of physics rests on the reliability of your senses?'

Here is another test. Why not try to deduct the laws of physics with axioms of mathematics and see if you can predict the major achievements of physics over the next 20 years. If you don't see that as possible, as yourself why not. Aristotle was a pretty smart guy (maybe one of the smartest people of his time), but he couldn't do it even though he tried that approach. Science is by its nature an a posteriori/inductive approach to nature. It may someday have been formed completely as an a priori approach, but that is all going to be done with 20/20 hindsight.

6. Visual impressions of the world (e.g. there are stars) cannot be trusted to be universal among life form possibilities: 'Oh sure, and a particle is still a particle even when it looks like a wave, and a wave is still a wave when it looks like a particle.'

Let's doubt everything, even this statement. Now, what can you possibly say? Now, can someone doubt that? How about doubt that doubt? Where does irrationality start in such a scheme? You need to make certain solid assumptions (e.g., there are stars, we live on dry land, etc., etc.) before you can have any rational inquiry into the world. Yes, a factual ontology is impossible, but we can work within the confines of sound epistemological practice (e.g., science) to form ontological views of the world. Those views are philosophically certain, but for all practical purposes (FAPP) they are suitable for our understanding of the world.

Warm regards, Harv

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