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... then Bruno and Stathis ask for the difference 
between yours and their definition... Which you respond with a contradiction 
to say platonism is false... 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.

> 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.

Quentin

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