On 3/1/2015 4:00 PM, LizR wrote:
On 2 March 2015 at 12:08, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>>
wrote:
Until you reflect that logic is just about relations between concepts we
made up -
so maybe "logically necessary" isn't so necessary after all. I find it
interesting
that a lot of "logically necessary" truths were contradicted by quantum
mechanics:
Nothing can be in two places at the same time. Two things can't be in the
same
place at the same time. The truths of arithmetic seem to me to be the same way.
The number of letter in "this" word plus the number of letters in "that" word is 10
because each has 5 letters. Or is it only 5: t h i s a ? It depends on
how you
conceptualize "letters"; are they marks on the paper or are those marks on
tokens of
the Platonic letters?
The truths you mention were hypotheses about the nature of the universe. I don't think
QM contradicted any arithmetical truths (if there are such things). It just showed that
some intuitions about the nature of the universe we inhabit were wrong.
Sure. But maybe our intuitions about counting are wrong too - at least insofar as they
apply to the world.
I don't agree with your "truths of arithmetic seem to be the same way" argument. At
least, not as stated - the example with the letters is merely a matter of what you're
counting - are you counting the total number of letters, or only how many different
letters there are? You get two different results depending on which of those you choose,
but you get the same result every time for a given choice.
You don't see the "No true counting" fallacy analogous to "No true Scotsman"? There are
twelve people on our high school basketball team and six people on our tennis team. When
they have a banquet do I have to set 18 places?
In other words, there's no space for contingency once you've properly defined the
problem. Which means that the truth of the matter does in fact appear to be logically
necessary, unlike the "truths" about the nature of the universe (well, until a better
contradictory example comes along - any ideas?)
Right, the necessary truth is a truth in Platonia, a world entirely defined by
us.
Brent
As far as the laws of mathematics refer to reality, they are not
certain, and as far as they are certain, they do not refer to
reality.
-- Albert Einstein
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