Quentin Anciaux wrote:
> Le Vendredi 18 Août 2006 14:21, 1Z a écrit :
> > Quentin Anciaux wrote:
> > > Hi,
> > >
> > > Le vendredi 18 août 2006 11:52, 1Z a écrit :
> > > > Stathis Papaioannou wrote:
> > > > > Peter Jones writes (quoting Bruno Marchal):
> > > > > > > Frankly I don't think so. Set platonism can be considered as a
> > > > > > > bold assumption, but number platonism, as I said you need a
> > > > > > > sophisticated form of finitism to doubt it. I recall it is just
> > > > > > > the belief that the propositions of elementary arithmetic are
> > > > > > > independent of you.
> > > > > >
> > > > > > Arithemtical Platonism is the belief that mathematical
> > > > > > structures *exist* independently of you,
> > > > > > not just that they are true independently of you.
> > > > >
> > > > > What's the difference?
> > > >
> > > > Things that exist are available for causal interaction. Numbers aren't.
> > >
> > > You were defining arithmetical platonism.... and now you define existing.
> > > Your two comments are contradictory.
> >
> > Not even remotely. I fact, what I have said can be written as two valid
> > syllogisms.
>
> Yes you were... You were denying the definition of Bruno (arithmetical
> realism) by giving yours
Firstly, that isn't *self* contradiciton.
Secondly, Bruno's approach is ambiguous. (If he clearly states
that AR is only about truth and not about existence, he can't claim
that
matter doesn't exist if COMP is true, because "matter doesn't exist"
is an existential statement and COMP (absent Platonism) isn't.
If he clearly states AR ia about existence, he can no longer
claim that COMP is his only premiss).
> ... then Bruno and Stathis ask for the difference
> between yours and their definition.
Defintion of what ? Existence ? Yes, I do have
a different definition.
> .. Which you respond with a contradiction
> to say platonism is false...
Platonism *is* false using my definitions. They must
be using a different defintion. That still doesn't
mean I am contradicting *myself*. I may be comtradicting other peopel:
well,
people are allowed to contradict each other.
> then either you were effectively contradicting
> yourself or you did not answer Stathis and Bruno question (it's one or the
> other).
> > Existence is availability for causal interaction
> > Numbers are not available for causal interaction
> > Numbers do not exist
>
> That's your definition of existence... this is your claim. Now a definition
> game will not resolve this problem obviously.
Then the problem cannot be solved at all, since there is no
other way of solving abstract problems. (All mathematical
problems are solved using definitions!)
Why, BTW, do you assume there is no way
of arriving at the correct definition ? Isn't that
what dictionaries are for.
> > Platonism is the claim that numbers exist
> > Numbers do not exist
> > Platonism is false
>
> Platonism does not claim number exist by your definition of existence hence
> your conclusion is ill based.
It isn't false if my definition of existence is the only defintion.
The ball is in the Platonists' court: they need to come
up with another definition of existence.
However, they presumably don't have one, or they would not be
asking me what "existence" means.
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Received on Fri Aug 18 2006 - 11:41:10 PDT