Logical Absolutes

[polymath257]

But they don’t come from anywhere. They just are.

This is what they call "brute facts" in philosophy. "Why are things this way? They just are." 

Isaac Newton changed the way science works by changing his metaphysical approach to looking at the world. Before Newton, people weren't satisfied with the "it's just that way" explanation. But Newton announced that he couldn't say what gravity is or why it acted that way, only that he could describe how it acts. And that's been how science works ever since. With lots and lots of "it just does" included. 

Galileo was less willing to do this. So for example he rejected the idea that the moon causes the tides, despite abundant evidence, because he couldn't explain how distant objects could act on each other, and he wasn't satisfied with "they just do." 

But "they just do" is not an explanation. "They do because they do." It's basically giving up, and saying that no answer can be given. But not everyone is willing to do that. Obviously a lot of people will reject any attempt to go beyond "they just do", because it can't be done through science. It's metaphysics. But if they want to work on it I don't see why that's bad.

I think it goes farther than that. When you answer why something happens, you are resorting to some type of *more* fundamental rules for your explanation. But that means that the *most* fundamental rules 'just are'. There can be no explanation because any explanation would have to be in terms of more fundamental rules.

And that is the role many people (rightly or wrongly) assign to logic: they see it as having some of the most fundamental rules. So to ask where the rules of logic 'come from', in that system, is to ask for something that is impossible.

Now, it may well be that logic is NOT at the 'most fundamental' level. In which case, there *would* be an explanation for logic, but maybe NOT for that more fundamental set of rules and truths.

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Does it 'reflect a metaphysical truth' to say that a certain chess position allows mate in 3 moves? Because, when it comes down to it, mathematical 'truths' are in the same category as that statement.

Since the rules of chess are made by people, here you're making a case for Intelligent Design.

And I am saying that the rules of math, just like the rules of language, are made by people to help us make sense of the world around us. So, no, I am NOT making a case for ID. i am saying that a language we made up to help us understand the world and its regularities can be used, sometimes surprisingly, to understand the world and its regularities.

Of course, this ignores the large parts of mathematics that (at least currently) don't seem to correspond to anything in the real world whatsoever.

But, even in the case of 2+2=4, the only reason we can reasonably use it is that we live in a certain temperature range and deal with objects that are often fairly solid.

But, for example, if you take 2 quarts of water and 2 quarts of alcohol, you will NOT get 4 quarts of mixture. The formal, mathematical system does not yield valid predictions in that case.

Alternatively, if you want to deal with subatomic particles and their interactions, it is quite common for, say, two protons to collide and produce many protons, many pions, and many other particles. Again, a simple 1+1=2 simply does not describe the actualities of what happens physically.

The way I see it is that mathematics is a language we have made. Some aspects of that language are useful for modeling some aspects of the world around us. Some are not. And even those aspects that are useful are not universally useful. Whether any particular piece of mathematics applies to the 'real world' is a matter of observation and testing.

Oh, and I *am* a mathematician. I have been a research mathematician for the last 35 years.

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Are the laws of logic, math, and nature not somehow part of reality? I'm pretty sure they're real. 

Are the rules of English real or not? i see the rules of logic and math being similar.

The laws of nature are a bit harder. I see them more as 'our best description so far'.