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.
This is where the careless use of the word 'truth' can lead to poor
reasoning. Propositions can be true or false, axioms are neither.
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.
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.
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. In the MGA you simply argue
that you cannot believe that the recording is conscious, 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.
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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