On 18 Feb 2011, at 12:53, 1Z wrote:

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On Feb 18, 9:48 am, Bruno Marchal <marc...@ulb.ac.be> wrote:Hi, What do you mean by Platonia? The kind of Platonia in Tegmark or in Peter's (1Z) post does not make sense for mathematicians. Even if you are using a theory like Quine's NF, which allows mathematical universes, you still have nomathematical description of the whole mathematical reality. Tegmarkisnaïve about this. *Arithmetical* platonia can be said to exist, at least in the sense that you can prove it to exist in models of acceptable set theories, like ZF. It is just the structure (N, +, x). It is used in all papers in physics, math and logic, including Pratt ...Used as a formalism. It is not the case that everyone who uses arithmetic is a Platonist

`I did not say that, even with platonism restricted to arithmetical`

`realism, except for those using classical arithmetic or models of PA`

`in ZF, etc. To believe in (N,+,x) you need a stronger realism than`

`arithmetical realism, which says nothing about infinite sets.`

`And I am still waiting for you to explain me what *is* formalism`

`without using arithmetical realism or equivalent.`

`Let me answer to you. To be able to use a formalism, you need to`

`define what are the well-formed sentences; for this you need to define`

`them in the usual recursive way (or equivalent way) and this, together`

`with simple rules (like finding the first and second in a couple of`

`expressions) is ontologically as rich as sigma_1 realism.`

`Formalism, and all form of finitism which is a bit richer than`

`ultrafinitism, is entirely constructed (implicitly or explicitly) on`

`arithmetical realism. Gödel showed the deep "bisimulation" of`

`formalism and arithmetic.`

`With your use of the term Platonia, the theory I am working on, is`

`usually called finitism, and is usually considered as anti platonism.`

`This use is misleading because it is platonist, and even pythagorean,`

`in the sense of the neoplatonist.`

I think you are confusing people on the genuine issues, here. Bruno

Now, with computationalism, we don't even need such a mathematical arithmetical Platonia. We need only the idea that arithmetical truth (even a tiny effective part of it) is independent of you and me. Likein Plotinus, the ultimate being (arithmetical platonia) is not abeingitself (nor is matter!). So neither Platonia, nor even arithmetical Platonia needs to exist.Numbers needs to exist in some sense, and do exist in theories likeRAor PA, in the sense that such theories formally proves that Ex(x = sssssss0) for example. Just to be a bit precise. Bruno On 18 Feb 2011, at 02:49, Stephen Paul King wrote:Hi All,Question: Why must Platonia exist?Onward!Stephen“It is amazing what can be accomplished when nobody cares about who gets the credit.” Robert Yates-- You received this message because you are subscribed to the Google Groups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group athttp://groups.google.com/group/everything-list?hl=en .http://iridia.ulb.ac.be/~marchal/--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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