On 11/3/2012 8:19 AM, Bruno Marchal wrote:


On 03 Nov 2012, at 12:43, Stephen P. King wrote:

On 11/3/2012 5:39 AM, Bruno Marchal wrote:
[BM] All this makes sense only because such truth does not depend on us and on our theories.

[SPK] No, that is an incoherent statement as it pretends to be meaningful in the absence of any means to evaluate its meaningfulness.

That is arithmetical realism. A statement like Church thesis and comp makes no sense at all without it. I have never heard about someone not believing in arithmetical realism. It is really basic. To pretend that arithmetical realism is false already needs arithmetical realism.
Dear Bruno,

You have now heard of someone like that! Church's thesis and comp make sense to me without AR, I don't pretend that I am the only mind and that it is because my thoughts can agree with those of other minds that there is something "real" to all of us. You still do not see thecrypto-solipsism <http://books.google.com/books?id=k_xYkhHiXbwC&pg=PA254&lpg=PA254&dq=crypto-solipsism&source=bl&ots=nUEID3Dj1a&sig=zBQ3_9dxB6nHe2EVQ3o2iJ_VZG0&hl=en&sa=X&ei=6gCVUMLUG4yk8gTXrIDICA&ved=0CE0Q6AEwBw#v=onepage&q=crypto-solipsism&f=false>of your philosophical stance! I am not alone is noticing this! (See the linked passage here <http://books.google.com/books?id=k_xYkhHiXbwC&pg=PA254&lpg=PA254&dq=crypto-solipsism&source=bl&ots=nUEID3Dj1a&sig=zBQ3_9dxB6nHe2EVQ3o2iJ_VZG0&hl=en&sa=X&ei=6gCVUMLUG4yk8gTXrIDICA&ved=0CE0Q6AEwBw#v=onepage&q=crypto-solipsism&f=false> for a discussion) David Deutsch has a long discussion of this problem in his book/The Fabric of Reality/.

At http://en.wikipedia.org/wiki/Talk%3AThe_Fabric_of_Reality , I found the following:

"Philosophers keep getting tangled up trying to prove scientific theories using pure logic alone, without any basis of facts. Viewing them as explanations instead brings many advantages, such as the ability to choose the simplest theory that fits the evidence. As an example, he demolishes Solipsism. Solipsism is generally supposed to be irrefutable, on the grounds that if everything is a dream, then so are the results of any test one could do. Deutsch refutes that by taking the theory seriously (as he says) and thinking out the ramifications. How is it that everything (specifically all fields of science) forms a consistent whole, even things one does not yet know? How do other, imaginary people know things that you do not? How can they have skills that you cannot equal? The end result is that you have a theory which includes all the complexity of the apparent world, plus an additional notion that it is the dream of a single entity. Thus it is actually a more complicated theory, not a simpler one."

    Sound familiar?

I don't see anything relevant for our (unclear) issue.

    Umm, must I put the quote in different words for you?

    Here is what Google translator gives us:

"Les philosophes garder s'empêtrer essayer de prouver les théories scientifiques utilisant la logique pure seul, sans aucune base de faits. Les considérant comme des explications provoque au contraire de nombreux avantages, comme la possibilité de choisir la théorie la plus simple qui s'adapte à la preuve. A titre d'exemple, il démolit solipsisme. Le solipsisme est généralement censé être irréfutable, au motif que si tout est un rêve, alors si sont les résultats d'un test qu'on pourrait faire. Deutsch réfute que, en prenant au sérieux la théorie (comme il dit) et de la pensée sur les ramifications. Comment se fait-il que tout (en particulier tous les domaines de la science) constitue un ensemble cohérent, même des choses qu'on ne sait pas encore? Comment puis-autres, des personnages imaginaires savoir des choses que vous n'avez pas? Comment peuvent-ils avoir des compétences que vous pouvez ne pas correspondre? Le résultat final est que vous avez une théorie qui comprend toute la complexité du monde apparent, plus une notion supplémentaire qui est le rêve d'une seule et même entité. Ainsi, il est en fait une théorie plus compliquée, pas un système plus simple."




Realism is not a single theory, there are many forms of realism <http://plato.stanford.edu/entries/realism/>. You seem to have a "naive realist" view of numbers, in that we can apprehend them directly or at least that the properties of numbers are innate and yet are apprehended directly.

I said innate for numbers, with the logic and their laws. I don't say innate for humans in the usual psychological sense. You are digressing.

Why is it different for numbers? What makes numbers "special"? You claim that numbers have dreams and other crypto-psychological claims, so why not?




I see this theory as nonsensical

Mee too, but this is not related to arithmetical realism.

OK, can you see how my critique of AR works? I claim that AR assumes too much; that it assumes innate properties without any explanation of how the definite of the properties of numbers obtains. We can assume safely that numbers have definite properties because we can consult each other and ask questions: "Hey John, is 43 Prime?", "My table of prime numbers has a 43 in it so it must be prime!", "OK!, 43 is Prime!".

But this narrative does not work in Platonia or any independent realm simply because the supporting structure of verification does not exist there! If we are to add the scaffolding of a structure on which truth and any other mathematical property supervenes, then we have to answer to Occam and explain why are we multiplying entities beyond necessity! So, what do we do? We accept that truth is contextual, that it is contingent - not on any one mind, not even some universal mind, but it is contingent on the mutual agreement between many minds.


as it offers no explanation as to how properties of numbers match up with those of our thoughts about numbers.

Comp makes that clear, as the reality is arithmetical, or equivalent.

Yes, but note my definition of "Reality": that which is incontrovertible for some collection of inter-communicative entities.




Umm, maybe you think that by equating the dreams of numbers to our inner thoughts, you can avoid this problem.

This follows from comp. I have not chosen this.

    You chose AR and a restricted definition of universality...


OK. Nice Move! But we are left empty handed when it comes time to explain thoughts of change and the problem of arithmetic bodies.

I am just formulating the problem, and solve a part of it.

    OK! Let's go forward!


--
Onward!

Stephen

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