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Originally Posted by Ken G
That is a different meaning for "objective" than the one I use, and it is also not the one that defines objectivity in science. The problem with your definition is that it is circular-- if you look at your use of "rational" and "sufficently informed", you find that you have to define "rational" as "agreeing with the consensus". Also, "suffciently informed" must mean "educated about the consensus". It's all based on consensus.
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I can be educated about a "consensus" -- for example, a political or moral consensus -- without agreeing with it. I can think of several instances where this happens, and I'm sure everyone else can think of their own examples (though I still feel the word "consensus" is not appropriate for what you're talking about there). Typically, when I disagree with a
majority view (not the same as consensus) that's because reason leads me to a different conclusion.
Quote:
Originally Posted by Ken G
Logic defines its own concept of consistency.
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I thought you said natural selection did...
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Originally Posted by Ken G
A different form of logic could be just as consistent to its own rules-- and be totally useless in practice.
But this is a perfect example. There is nothing wrong with asserting 2+2=5 in a universe where any time you merge two sets of two objects, a fifth object mysteriously appears. There is nothing "irrational" about 2+2=5, unless you have experience in our world. It is purely a familiarity that 2+2=4.
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2+2=5 would imply that 0=1 (nothing is the same as something)... Could it really be just in our world that this is absurd?
Define me another one where it isn't absurd.
Quote:
Originally Posted by Ken G
There is no difficulty imagining how a universe that we consider illogical could exist, indeed I would claim there is ample evidence that our own universe is illogical in esoteric ways. That's why actual life often requires the use of a "fuzzier" form of logic than is axiomatized by first-order logic. For example, we think we can easily tell if a set does not contain itself, and we think that we can describe the set of all sets with some particular attribute, but formal logic cannot axiomatize the set of all sets that do not contain themselves (Betrand Russell's crisis). Formal logic fails us, we just can't handle this seemingly real set.
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Regardless of whether mathematics can prove anything, one thing I think we can all agree on is that imagination proves nothing. For instance, and by the way, the set of all sets is not an object in our universe. It's just something we imagined naively with our minds at one time, but as it turns out it's not a particularly logical idea.
But I wasn't asking you to
imagine an illogical universe; that's too easy. I'd like to see you define it in concrete terms, constructively. Build a model of it.
As for Bertrand's paradoxes and whatnot, Goedel argues that they are not failures of mathematics, but rather the dead ends of an overambitious project of formal logic. But I'm not talking about formal, symbolic logic here. When I use the words "logic", "reason", or "rational", I mean the plain principles of self-consistency which we all understand and apply in our everyday lives.
Quote:
Originally Posted by Ken G
Indeed, it may even be argued that our universe is illogical in ways with everyday applications. The universe appears to do things which are random, and our best theory says it may be inherently random. How does a logical universe do random things, what does that mean? The alternative is even worse, that our universe does not do random things, because then everything is deterministic and therefore predetermined. The fully inclusive third possibility is that the universe is neither determined, nor random, but that some inscrutable agent decides how seemingly random events come out. Logic dictates it has to be one of the three, but the inscrutability of the third option means it is outside of logic, and the first two seem impossible. So logic leads us to the conclusion that our universe cannot be completely ruled by logic. I'd call that an illogical universe.
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That's a particularly weak argument. There is nothing about randomness which makes it illogical.
The randomness in modern science is not illogical; it's the determinism of classical physics that was naive.
(A good example of a fake "contradiction/paradox" that turns out to be no more than a simple misunderstanding born of false expectations.)
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Originally Posted by Ken G
But that's irrelevant. Whether it turned out to be useful or not had nothing to do with any of his proofs or axiom choices-- it supports my point. The mathematical rigor of his work stood entirely on its own, the "truth" (as in provability) of his work is completely independent from whether or not it ever made contact with the objective world.
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To the contrary, the fact that pure mathematics has frequently turned out to be right about the physical world
when it wasn't even trying to is strong empirical evidence that it is not arbitrary, but rather intimately bound to reality.
Quote:
Originally Posted by Ken G
Happens all the time. Newtonian mechanics, for example, applied to a hydrogen atom. The mathematics disagrees with the empirical result.
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Quite bluntly, it was not Newton's mathematics that failed him in that case, but his physics.