Re: FOL/Intuitionistic logic versus NAFL. Part 1. Failure of non-contradiction

On Nov 12, 8:47 am, "R. Srinivasan" <sradh...@xxxxxxxxxx> wrote:
Here T* is a NAFL theory that, like T, is held in the human mind and
proves all the axioms of T. Further, T* could change with time, i.e.,
the human mind could choose different theories for T* (i.e., different
interpretations of T) at different times, and different human minds
could choose different theories for T* at any given time.. E.g. I
could take T*=T+P today, while another individual could take T*=T+~P.
Tomorrow I could change my mind and take T*=T+~P irrespective of what
another individual chooses. T* is chosen by the free will of the human
mind.

But the point is, this is oversimplified from birth. If all that is
really
true then there is simply no such thing as T*. INSTEAD, there is a
TERNARY FUNCTION *, with THREE arguments, a mind m, a theory T,
and a time t, such that AmTt[ *(mTt) = <what you have been calling
T*>].

Your account raises the immediate *philosophical* problem
here involving "perdurantism". I am quoting this from the
Wikipedia article but you need to begin by picking a side.

Perdurantists break into two distinct sub-groups. The former are 'worm
theorists'. They believe that a persisting object is composed of the
various temporal parts that it has. So all persisting objects are four-
dimensional 'worms' that stretch across space-time, and that you are
mistaken in believing that chairs, mountains and people are actually
three-dimensional. This is to be contrasted to a more recent twist
called 'stage theory'. Stage theorists take you to be identical with a
particular temporal part at any given time. So, in a manner of
speaking, I only exist for an instantaneous period of time. However
there are other temporal parts at other times which I am related to in
a certain way (Sider talks of 'modal counterpart relations', whilst
Hawley talks of 'non-Humean relations') such that when I say that I
was a child, or that I will be an OAP, these things are true because I
am related to a temporal part that is a child (that exists in the
past) or a temporal part that is an OAP (that exists in the future).
Stage theorists are sometimes called 'exdurantists'.

My point is, abstract objects are generally considered completely
outside this debate.
Abstract objects take no note whatsoever of time; a symbol is always
the same symbol, irrespective of time.
Time simply is not meaningful as applied to an abstract string, such
as "abc". "abc" does not need a human
mind, or a time-continuum, in order to exist. T, IN CONTRAST to T*,
was historically/previously considered an abstract object. T*, by
contrast, since *you* are defining it, is something whose abstraction-
status is yet underdetermined.
You have to engage on THIS SUBpoint BEFORE you go pontificating about
your superstructure.

The NAFL model of T resides temporarily in the human mind and is
generated by that particular T* which the human mind specifies, in the
following sense. Only propositions provable/refutable in T* are
assigned the truth values "True"/"False" in the NAFL model of T.

How many different NAFL models of T might there be? Doesn't every
different
T*, in every different mind at every different time, offer a
potentially DIFFERENT
NAFL model of T? Why is there even any need to distinguish between a
NAFL
model of T and the-NAFL-model-of-T-generated-by-T*? Could we have two
different
T*'s generating the same NAFL model of T?
Given that all rich T's are going to have non-isomorphic models, does
it
*ever* even make *any* sense to speak of *the* NAFL model of T?
Won't NAFL allow T to have many different models?

The above is the truth definition for formal propostions in the
language of NAFL theories. There are absolute (Platonic) truths in
NAFL, but these are truths *about* NAFL theories and cannot be
formalized in the language of NAFL theories. For example, "T is
consistent" and "P is undecidable in T" are propostiions about NAFL
theories that are taken to have absolute (classical) truth values,
i.e., these propositons are either true or false without any reference
to NAFL theories and independently of the human mind.

So these classically true statements cannot be formalized/asserted by
NAFL theories?
That is a good reason to ashcan the whole paradigm right there.
Please!

Before gettting to the failure of the law of non-contradiction, let me
address an objection raised by George, who does not like the fact that
T, T* and the NAFL model are all (temporarily) resident in the human
mind. He asks why this should be the case. Note that there is no
unique value of T*, given some theory T. It is the human mind that
"fixes" T* (temporarily) and hence fixes the truth values for
undecidable propostions of T. I am asserting that there is no
objective criterion for fixing T* other than the free will of the
human mind and that is what NAFL is all about. In other words, if all
human beings are wiped out, there is simply no "truth" for formal
propositons of NAFL theories.

Well, that is a serious weakness. You have got to be clear about the
realm you are in. "If al human beings were wiped out" is kind of
stupid
anyway.

The theories themselves exist in an
abolute sense (independently of the human mind),

Oh, bull***. That is PRECISELY what you JUST denied!

but only the human
mind can "interpret" theories according to NAFL. The NAFL models for
NAFL theories will not exist without human beings.

OK, fine, I get it.
Theories are abstract.
Models are concrete.
But that is not as big a difference as you think.
In the classical paradigm, theories are abstract in the language of
your choice,
but models are abstract in ZFC. My point is, there remains, in both
cases,
a distinction of levels. That is all that is really needed. One
could still come up
with a formal language for talking about your held-in-mind-models of
NAFL theories.
The fact that they are held in human minds IS *not* IMPORTANT!


Another objection of George is that T* is a time-dependent variable
and should not be given the name of a constant. OK, but it is
something like the velocity of light "c" or other physical "constants"
which are taken to be "fixed" at a given instant, but could have
different values over a period of time.

Oh, bull***. Physical constants DO NOT have different values
over a period of time. That's WHY they're CALLED *constants* --
because they ARE *constant*!
More to the point, c *isn't* a physical constant.
c is a THEORETICAL constant in the current THEORY of physics.
As such, its SYNTACTIC status as a constant is NOT in doubt.
You have to speak coherent language, man.


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