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On Jan 19, 2014, at 11:51 PM, meekerdb <meeke...@verizon.net> wrote:

On 1/19/2014 3:41 PM, Jason Resch wrote:On Jan 19, 2014, at 3:31 PM, meekerdb <meeke...@verizon.net> wrote:On 1/19/2014 9:45 AM, Bruno Marchal wrote:But why should that imply *existence*.It does not. Unless we believe in the axioms, which is the casefor elementary arithmetic.But what does "believe in the axioms" mean. Do we really believewe can *always* add one more? I find it doubtful. It's just agood model for most countable things. So I can believe the axiomsimply the theorems and that "17 is prime" is a theorem, but Idon't think that commits me to any existence in the normal senseof "THAT exists".Axioms are a human invention which only approach the truth that wasalready there. Our picking some axioms to believe in changesnothing.You seem not to appreciate that this dissipates the one essentialadvantage of mathematical monism: we understand mathematics(because, I say, we invent it).

`I would say we understand some things about sine mathematical objects`

`because we can simulate them in our mind (or on computers) and learn`

`their properties.`

For example, the general shape of the Mandelbrot set.

But if it's a mere human invention trying to model the Platonic dingand sich then PA may not be the real arithmetic.

`It certainly isn't, as it leaves inaccessible an infinite number of`

`true statements. However, when it can prove something, like that a`

`certain Turing machine halts at a certain step, we find it is in`

`agreement with other axiomatic systems and reality.`

And there will have to be some magic math stuff that makesthe real arithmetic really real.

`I thought we were talking about truth not reality, though perhaps the`

`two are related. The Sanskrit word for truth also means that which`

`exists.`

`So what makes 2+2=4 true? I don't know, I suppose you might say`

`"magic".`

Jason

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