Re: Incompleteness vs. Mechanical Reasoning

On Apr 6, 12:14 am, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:
Marshall <marshall.spi...@xxxxxxxxx> writes:
On Apr 5, 4:57 am, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:

Yeah, that would be a good point, if I had claimed that making
decisions is fundamentally about first-order reasoning.

When we decide what to do, we weigh competing reasons and select
accordingly.  This is pretty different than randomness.

If I were in an Aatu-like mood, I would ask you how you can be
sure that the perception of weighing competing reasons isn't
merely a purely subjective experience, a sensation that you,
a randomly-driven automaton, experience as a side-effect
of your existence.

I would say that I don't have any proof that my perceptions about how
I make choices are accurate at all.  But if our choices really are
primarily random, then we do not decide anything, since decisions are
reason-based.  

At least, that's how *I* interpret the term.

Our decisions can be made on the spur of the moment and we need not
even have any time to think about *why* we made such decisions. Let us
take an example of an individual X standing on the edge of a cliff.
Will X jump or not? X could make a decision with *no* reason for it,
at least, none that we human beings are capable of discerning. E.g. X
could have had a happy and successful life, etc. Then why did X jump?
The decision to jump could just be an axiomatic assertion in the mind
of X. E.g. one moment X is thinking, "I am not jumping because I am
happy and very successful in life", etc., etc. and the very next
moment, X has only one thought "I am jumping" and then jumps
simultaneously with the thought. Are you asserting that this scenario
is impossible? If so you have found a contradiction in the logic NAFL.

Here is how I would explain this phenomenon in NAFL. Let us say that X
has a theory T in mind and the propostion P that "X will jump" is
refutable in T for all the right reasons (X is successful in life, has
a happy family life, etc.). So the proposition P is false w.t. to T as
far as X is concerned, for X must be false in all intepretations of T
via its provability in T. So X makes a conscious decision not to jump.
But let us say that at some point of time, X's mind is blank (X has
only a theory T0 with the null set of extra-logical axioms in mind).
In wother words, X forgets all the right reasons for not jiumping (or
blanks them out of his mind). In the theory T0, P is neither provable
nor refutable. However, let us say that X has an interpretation T* of
T in mind that proves P. T* could just be T+P. In NAFL, provability of
P in T* is the only (temporary) "truth" that exists for P as far as X
is concerned. So effectively, at that point of time P is true w.r.to T
in X's mind and the only "reason" it is true is that X has added P to
T0 as an axiom out of free will. So X now has "X will jump" in mind,
and X jumps.

As far as NAFL is concerned, what X "really" or "actually" does is
outside the purview of logic. What counts for truth is the axiomatic
assertions made in the mind of X. So if X jumps while the whole world
(including X) has "X will not jump" in mind, that is beyond the reach
of logic as far as NAFL is concerned. Such a truth will forever have
to be metalogical from the NAFL ;point of view.So in a sense, as far
as NAFL is concerned, we human beings monitor "reality" at a
metalogical level, and then could (or could not), out of our free
will, choose to keep the axiomatic assertions made in our minds in
conformance with such a reality, which need not even exist for many
propostions (e.g. "infinite sets exist"). The logic is about axiomatic
assertions made in our minds and not about any reality that exists
independently of our minds.

Regards, RS
.

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