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.
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
your philosophical stance! I am not alone is noticing this! (See the
linked passage here
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."
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
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
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
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!
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