Stathis Papaioannou wrote:
> Brent Meeker writes:
>>>Empirical science is universe-specific: eg., any culture, no matter how
>>>bizarre its psychology compared to ours, would work out that sodium
>>>reacts exothermically with water in a universe similar to our own, but
>>>not in a universe where physical laws and fundamental constants are
>>>very different from what we are familiar with.
>>>Mathematical and logical truths, on the other hand, are true in all possible
>>But this is really ciruclar because we define "possible" in terms of obeying
>>rules of logic and reason. I don't say we're wrong to do so - it's the best
>>can do. But it doesn't prove anything. I think the concept of logic,
>>mathematics, and truth are all in our head and only consequently in the world.
> Isn't this like saying that a physical object must be perceived iin order to
> exist? We define physical phenomena in terms of the effect they have on our
> senses or scientific instruments, but we assume that they are still "there"
> they are not being observed.
I don't see the analogy with defining "possible worlds" as those obeying some
logic and then saying that logic is a prior or analytic because it obtains in
all possible worlds. I agree that "logically possible" is broader than what we
think is "nomologically possible".
>>>The lack of contingency on cultural, psychological or physical
>>>factors makes these truths fundamentally different; whether you call
>>>them perfect, analytic or necessary truths is a matter of taste.
>>If you directly perceived Hilbert space vectors, which QM tells us describe
>>world, would you count different objects? I think these truths are
>>on how we see the world. I think there's a good argument that any being that
>>both intelligent and evolved will have the same mathematics - that's the jist
> If we lived in a world where whenever two objects were put together, a third
> magically appeared, would that mean that
> (a) 1+1=3, because we would think that 1+1=3
> (b) 1+1=2, but we would mistakenly think 1+1=3
I say (a), but someone might still invent Peano arithmetic in which 1+1=2. It
would be called "non-standard" arithmetic and only a few, ill regarded
mathematicians would study it. :-)
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