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 
>>>worlds. 
>>
>>But this is really ciruclar because we define "possible" in terms of obeying 
>>our 
>>rules of logic and reason.  I don't say we're wrong to do so - it's the best 
>>we 
>>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" 
> when 
> 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 
>>the 
>>world, would you count different objects?  I think these truths are 
>>contingent 
>>on how we see the world.  I think there's a good argument that any being that 
>>is 
>>both intelligent and evolved will have the same mathematics - that's the jist 
>>of 
>>Cooper's book.
> 
> 
> If we lived in a world where whenever two objects were put together, a third 
> one 
> 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.  :-)

Brent Meeker

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