On Feb 7, 4:06 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 06 Feb 2011, at 22:20, 1Z wrote:
On Feb 5, 7:43 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
Computationalism needs Church thesis which needs AR (Arithmetical
Nope, just AT (arithmetic truth).
Actually, comp needs only, for the ontology, the quite tiny
As I have stated many times, it doesn;t matter in the least
how many or few immaterial objects you attribute existence to.
It's like saying pixies exist, but only a few
It is always better to make a theory precise.
The theory that some precise number of pixies exist is just
as wrong as the theory that some indeterminate number exists.
Mathematical anti realists hold that *no* mathematical
objects exist. And they still accept CT and all the rest.
Please don't put metaphysics where there is only
Believing in what is not proven is religion. I can
argue for anti realism.
I argue in favor of nothing.
You argue that some subset of mathematics has immaterial existence.
That's philosophy. You force me to be
explicit on this; I do science. I am a logician, and I show that
rational agent believing in comp believe that ... etc. I don't know
about the truth.
(saying yes to the admittedly betting doctor).
Saying yes to the doctor will not guarantee your
immaterial existence if there is no immaterial existence.
But there is immaterial existence.
To be fair, that's an unargued claim, not an argument.
I recall you that I say in the
ontological context that something exist if Ex (bla-bla-bla x) is
in the standard model of arithmetic.
Utterly wrong. In the *mathematical* context something
exists if there is a true backwards-E statement asserting
it, but the whole point of anti realism is that that is merely
game playing and does NOT imply RITSIAR ontological existence.
I use the standard meaning of
existence of numbers, etc.
As I have told you many times, there is no standard meaning.
AR/Platonism is a separate assumption to yes Dr.
I have drop out AR. You need AR (in which everyone believes except
ultrafinitists and the bad faith philosophers) to understand the term
"digital" used by the doctor.
No you don't. Mathematical anti realists can understand "digital
<And with comp,
it is math, indeed, even (full, above Sigma_1 arithmetic.
Arithmetical realism is what you need to apply the excluded
computer science and in arithmetic.
The excluded middle is a much of a formal rule as
anthing else. Formalists can apply it, so it is compatible
with anti realism.
The theory admits a formal study. You don't act like a formalist at
all. The term "Formalism" makes not an atom of sense without
Formalism is a major variety kind of anti realism.
In philosophy arithmetical realism is the weaker
of all possible realism, except again for the ultrafinitists.
The weakest kind is NONE WHATSOEVER....no pixies. Zip. Nada.
If you are formalist and anti realist on the numbers you are in
or, once and for all, just replace numbers by the
following formal expression 0, s(0), s(s(0)), etc. + the axioms I
sent to Andrew, etc.
Yep. Formalism says you have rules, and you manipulate them
and certain things seem to move around a change, and we
call those sets and numbers....and they don't really exist.
When you switch off your PC there is no more Supermario,
and when you stop doing maths there are no more numbers.
AUDA provides more than a formalism,
I don;t mean "a formalism"=" a mechanisable system for applying rules"
I mean "formalism"="the claim that mathematics is a game played
various sets of rules and is not 'about' any real entity".
I have pointed out the distinction to you many times
it provides an arithmetisation,
which is a *weakening* of formalism, made possible by AR. Gödel
already exploited this.
To understand the fundamental
consequences of Church thesis you need to accept that some program
computes function despite we have no means to know if it is total
partial, or that a program will stop or not.
And I can accept that by positing LEM as a formal rule. I don;t
have to posit an immaterial Plato's heaven
I make clear that the immaterial Plato Heaven for the machine is just
the truth of arithmletical proposition.
Truth is not existence.
It is an non arithmetical
notion, union of the entire Kleene-Mostowki arithmetical hierarchy,
and well know non controversal mathematical object in the field of
Sighh.to anti-realists, all immaterial existence is controversial
I use the "immaterial Plato heaven" terminology, either as poetical
Well, it isn;t material since matter is some sort of iluusion within
it, according to you
or as a point in the arithmetical representation of some
term in Plotinus theory.
I explained this already to you, but you keep adding metaphysical
stuff which don't exist.
It's metaphyscial already. I exist , and you say I am a programme
that is not running on a physcial platform. That adds up to
a statement about existence. You are making a statement
about me, so you are making a statement about existence.
You conclusion is ontological, so it either comes from
an ontological premise or it is a non sequitur.
Only ultrafinitist denies AR.
Wrong. Anti realists deny it. I have pointed this out many
times. You think the only debate is about the minimal
set of mathematical objects, and that is not the only debate. Anti
can accept a maximal set of objects, with the proviso that their
existence is fictive and not real existence
I am agnostic on all notion of existence.
All, except my own
consciousness here and now.
You keep insisting that some subset of arithmetic exists!!!!
I suggest a theory, and derive
consequences in that theory.
AR+, the idea that we don't need more than AR, in this setting,
consequence of the math. From 'outside' the tiny effective
sigma_1 complete set is enough. from inside, even mathematicalism
not enough (it is more 'theologicalism').
The ontological status of
objects is a area of contention in metaphysics, and not
proven by mathematics itself.
With comp, you don't need more than the part on which almost
agrees: arithmetical realism.
Anti realists do not agee on the real existence of any
part. There are no pixies at all, not just a few pixies.
If you believe in prime numbers,
I don't. No pixies means no pixies.
and if you are patient and good
willing, I can explain that there are all universal numbers, and why
assuming comp that's enough and that's necessary to solve the white
rabbit problem. And that postulating physical laws miss the
epistemological existence of the qualia.
The basic ontology is not important. If you take less than a
system (like numbers, combinators, ...) you don't have enough for
comp, if you take more you miss the qualia.
No problem with a formalist interpretation of all this. Actually
formalize at the meta-level what the machine can uderstand to be non
formalisable (like consciousness).
The engineers, the scientists, most
Except for Thorgny Tholerus I never met an ultrafinitist. You don't
have to decide if numbers are idea of the mind or sort of angel in
Plato Heaven. With comp the very idea of number will itself be a
number, a sort of second order number, relative to universes
ULtrafinitism has nothing to do with it. For formalists
no number exists. They have no prejudice about any kind,
If comp is false because, according to you 7 does not exist, then it
is your problem.
I never said that. The whole point is that comp and AR are *separate*
assumptions. The one is *not* a corollary of the other
I told you that I am working in a theory, which is neutral on those
question. Formalist have normally less problem with a tiny sigma_1
arithmetic than with the real or complex numbers.
Anti realist formalists, and any other kind of anti realists
DO NOT ACCEPT THE REAL EXISTENCE OF ANY MATHS AT ALL.
I just don't believe you don't believe in seven.
Well, I don't. And I have been having the same argument with you
for years, and you really need to stop thinking in your box.
'immaterial' with 'inexistent'.
If you don't believe in seven, do you still believe in the formal
expression s(s(s(s(s(s(s(0))))))) ?
I believe in the pixels I am looking at..which are material. But that
is the existence of pixels, not of numbers or sets.
And you cannot refute an argument by anticipating a refutation.
you have a refutation of MGA you should present it.
See Colin Klein;s refutation of Maudlin's Olympia.
We have already discussed this and Colin Klein does not touch the
movie graph argument.
Then you had better stop saying the MGA and Olympia are equivalent
The movie graph *argument*, is not attacked by Klein. Klein attacks
the Olympia *argument*.
When I say that Olympia and MGA are equivalent, I am talking about
conclusion, not about the arguments leading to the conclusion.
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