On 4/6/2017 12:35 AM, Bruno Marchal wrote:
On 05 Apr 2017, at 20:46, Brent Meeker wrote:
On 4/5/2017 1:54 AM, Bruno Marchal wrote:
On 04 Apr 2017, at 16:47, David Nyman wrote:
I've been thinking about the Lucas/Penrose view of the purported
limitations of computation as the basis for human thought. I know
that Bruno has given a technical refutation of this position, but
I'm insufficiently competent in the relevant areas for this to be
intuitively convincing for me. So I've been musing on a more
personally intuitive explication, perhaps along the following lines.
The mis-step on the part of L/P, ISTM, is that they fail to
distinguish between categorically distinct 3p and 1p logics which,
properly understood, should in fact be seen as the stock-in-trade
of computationalism. The limitation they point to is inherent in
incompleteness - i.e. the fact that there are more (implied) truths
than proofs within the scope of any consistent (1p) formal system
of sufficient power. L/P point out that despite this we humans can
'see' the missing truths, despite the lack of a formal proof, and
hence it must follow that we have access to some non-algorithmic
method inaccessible to computation. What I think they're missing
here - because they're considering the *extrinsic or external* (3p)
logic to be exclusively definitive of what they mean by computation
- is the significance in this regard of the *intrinsic or internal*
(1p) logic. This is what Bruno summarises as Bp and p, or true,
justified belief, in terms of which perceptual objects are indeed
directly 'seen' or apprehended. Hence a computational subject will
have access not only to formal proof (3p) but also to direct
perceptual apprehension (1p). It is this latter which then
constitutes the 'seeing' of the truth that (literally) transcends
the capabilities of the 3p system considered in isolation.
I don't think so. It is not direct perceptual "seeing the truth"; it
is an inference in language and depends on language.
?
It is not an inference, but the recognition of a fact, like when a
smoke detector detect smoke.
But the fact that is "recognized" is that the Goedel sentence is (in
Goedel's language which he has encoded in arithmetic) says it cannot be
proven - and then one infers that the axiomatic system cannot be
completed. I don't see how any of this can even be considered without
language and inferences.
There is an implicit assumption of being awake, or not dreaming, but
still no inference, nor does it use language,
Who does proofs without language?
at least not necessarily. The smoke detector detects smoke through it
senses, and so believe in some representational sense that there is
smoke (the [](smoke)), and ... there is smoke (the p of []p & p).
Which is an instance of physical perception - not logical proof.
Brent
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