On 15 Oct 2015, at 11:56, Bruce Kellett wrote:
On 15/10/2015 6:40 pm, Bruno Marchal wrote:
On 15 Oct 2015, at 00:48, Bruce Kellett wrote:
On 15/10/2015 2:10 am, Bruno Marchal wrote:
You talk like if I have claim knowing some truth. I do not. You
are doing philosophy of comp-theology. That
belongs to the field of philosophy of science, which is not my
expertise. You cannot use philosophy for making people doubting a
logical argument.
..........
of course if you doubt the truth of RA axioms, then I can't
explain.
Above you claim that you do not know some truth. So how do you
know the truth of the RA axioms?
By some truth, I meant some big metaphysical truth.
Then I do not *know* the truth of RA axioms, in any publicly
communicable way. I assume them, and that is not a problem, because
we all assume them when we do science.
No, you don't assume the truth of the RA axioms -- you assume that
these axioms are true statements about the particular field under
study, such as the properties of rocks in a field. The RA axioms are
not true statements if your field of study is drops of water or
clouds.
Of course. A theory is always about the particular, intended field of
study. but in this case, RA becomes the theory of everything. That is
the consequence of comp, by the UDA reasoning (even without step 8),
if you accept some form of Occam razor.
This is where the careless use of the word 'truth' can lead to poor
reasoning. Propositions can be true or false, axioms are neither.
No, but they are, or not, verified by the intended model of the
theory. As nobody have any problem with the usual intended model of
the arithmetical theories, this provides a clean notion of truth. That
notion of truth is known to be definable in informal or formal set
theories.
Of course, you are just being cavalier with your use of the word
'truth'. Axioms are not things which can be said to be either true
of false, at best they are only useful and productive, or not.
They are true or false in the standard model of arithmetic, that is
the mathematical structure (N, +, *).
Even PA can define what is true for any formula with a bounded
numer of quantifiers. What PA cannot do is to define the truth for
arbitrary formula, by Tarski Theorem.
When you claim that PA can define what is true for any bounded
formula, what you are actually saying is that some theorems can be
proved in PA.
Not at all. PA can proves its own incompleteness and so can know that
provability is different from truth. I mean literally that for the
formula F having a bounded number of quantifier, PA can define a
predicate T such that PA can prove A <-> T('A'). PA can prove that A
is actually equivalent with the truth of the formula represented with
Gödel number 'A'. That has nothing to do with provability.
Then if the axioms are true of the model under consideration, and
the rules of inference are truth-preserving, then the theorems are
true statements in that model.
If arithmetic is false, Church-Turing thesis makes no more sense.
You will have difficulties in defining
computable function from N to N.
See above. Arithmetic is neither true nor false, it is only useful
or not, depending on the context.
That is too vague. What do you mean by "Arithmetic"? "true" or
"false" apply only to arithmetical sentences. Then "true" means
"true in the standard model". That can be defined in analysis or
set theory (not in any arithmetical theory).
Right. 'true' and 'false' apply only to sentences (propositions) in
a particular model, not to axioms per se.
OK. But in number theory, like in set theory (and unlike in group or
ring theory), there is a notion of intended model. In group theory, we
like to study many different group at once. But in number theory, we
try to remains in the unique standard intended model. We have never
heard a mathematician saying that Wiles has proven Fermat theorem in
the standard model. We just say that Wiles has proven fermat theorem.
For number theory, only logicians studied and used the existence of
non standard models, motivated by question in logic, not in number
theory.
All proof of negative results are argument from incredulity.
Proving ~p is the same as proving p -> f.
This is just nonsense. An argument from incredulity is an argument
that claims that the difficulty of believing a conclusion
(incredulity) is a valid reason for rejecting the argument.
Proofs are things that happen in formal systems --
Formal proofs. But in science we don't use formal proofs. We reason
informally about them.
In our case (step 8) the "incredulity" just show that if we keep
materialism we have to accept non Turing emulable components in the
(generalized) brain playing a necessary role for consciousness to
proceed. It shows that you need a creationist-like God of the
argument to save a metaphysical commitment, despite there is no
evidence for it. It is a religious move, in the pejorative sense of
religious. You can as well add that you need a god to sustain that
primitive matter. It is a God-of-the-gap, and it is used to not
proceed in the formulation of a problem.
I do not accept this analysis of step 8.
That is so better than stopping at step 3. At least. Then step 8 is
far more subtle, and people tend to put too much in it.
In the MGA you simply argue that you cannot believe that the
recording is conscious,
That is obvious given that the recording does not make any precise
computation. But we might need to agree first on what is precisely a
computation.
and proceed to give some specious reasons for this belief. You do
not establish the points that you make above -- they are the
conclusions you wish to draw from your incredulity about the
possibility of a conscious recording. So you have not presented a
valid argument.
I gave different arguments. You are too much unclear here. I have not
much time now, but I think we should first agree on what is a
computation. It is difficult to explain as it needs a good
understanding of the difference between a computation and a
description of a computation, which is not so different from the
difference between the fact that 1+1=2 is true and the string "1+1=2".
Just slightly more subtle.
Another problem, for you, is that to make clearer your argument, you
should first explain what you mean by a recording, before showing me
how it computes, and why it computes the experience associated to the
Boolean graph (which as been filmed). Step 8 is used only to show that
the use of a small physical universe is a god-of-the-gap type of
argument, which can never been refuted logically (that is why it is a
waste of time to try to convince a creationist by logic alone).
Bruno
In fact, as established by earlier discussion, it is really by the
application of Occam's razor that you seek to demonstrate that non-
existence of primitive matter (whatever that is). Occam's razor is
not an valid rule of inference either. It is a rhetorical device --
not a truth-preserving principle of inference.
starting from axioms and following pre-defined rules of inference.
So the proof of ~p is simply a sound demonstration that ~p follows
from the axioms according to the rules of inference.
~p is an abbreviation of (p -> f). It assumes at the metalevel that
you are incredule of f. (that is consistent).
I think you had better refine your use of the word 'incredulity'. I
take it that (p -> f) is an attempt to formalize the conclusion that
p is false. But that is the case only if the axioms of your system
apply to the subject matter under consideration and that you have a
formal proof of ~p. As we agree, the axioms of RA do not apply to
all subject matters.
It is not a 'proof' that p is false. As I must stress again, truth
and falsity are not words that can be applied within the context
of axiomatic systems.
It can be applied only there, when we do science about it. It is
called "model theory" or semantic.
As non-logician do not know much of model theory, I spare them with
using it too much. I can do that because everyone agree with the
elementary arithmetical truth (except when doing bad philosophy).
If you have a real doubt that 17 is prime, you can't proceed. But
if you agree with such proposition, you should not have any
problem, neither in UDA nor in the translation in arithmetic.
I agree that 17 is prime in the normal system of arithmetic, given
the usual definition of a prime number. Whether the number 17 exists
in any useful sense depends on the subject matter under discussion.
The number 17 does not exist if the system under consideration (the
ontology of the model) is the number of elementary massless bosons;
in which system any statement about the 17 elementary massless
bosons would be necessarily false.
Bruce
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