From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
On 5 Jun 2018, at 03:34, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
The difference is perhaps most easily captured in the use of the word
"exists". If we say that there "exists" an integer between 2 and 4,
then that could be called mathematical existence.
You can do that.
And that is all that is necessary for mathematics to be used in the
rest of science.
Yes, but in metaphysics, we need to put all cart on the table, and
eventually, with computationalism, we cannot make sense of anything
more than elementary arithmetic for an ontological basic existence,
the one which has to be assumed. (Or any Turing equivalent machinery).
It is only when you go beyond this concept of mathematical existence
and use the word in the same way as we would say that the moon
"exists", that you run into trouble.
On the contrary, there will be indeed a integers in between 2 and 4.
But the moon will get only a phenomenal existence. It will definitely
not have the same sense as the arithmetical ExP(x), but the moon will
only be “observable”, and that will be a modal existence, actually
like []<>Ex[]<>P(x), with [] and <> a material modality (I have given
three examples of them).
You agree, then, that the meaning of the word "exists" in "the moon
exists" is different from its meaning in "there exists an integer >2 and
<4". That is probably all we need. You claim that the first meaning
("the moon exists") is secondary to the meaning in arithmetical
existence. But that is no more than your assertion. You want to say that
the moon's existence is derivative -- depending ultimately on
arithmetical realism. On the other hand, I say that the mode of
existence of the moon is primary, and arithmetic is totally derivable
from a few axioms invented by human creatures, who share their existence
with the moon.
You want to claim that arithmetical existence is simpler than physical
existence. But that is clearly false because you cannot derive physics
from arithmetic, but I can derive arithmetic from physics -- humans did
it as soon as they learned to count! Claiming that the derivation of
physics from arithmetic is "a work in progress", so I have no right to
criticize computationalism because that work is not completed, is
nothing more than special pleading based on unwarranted and unevidenced
assumptions.
Physics is clearly simpler than arithmetic because it "exists" without
any further work -- arithmetic requires the existence of a conscious
mind, and minds have not yet evolved in computationalism.
Bruce
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