I devoted chapters to fuzzy logics and the liar paradox, and
have showed some very original ways to approach problems like
these. I also created a more sophisticated version called
a Time-Space Liar paradox to study the original in more
detail. I also discuss these in terms of fuzzy logics. Further,
the problem is that like other functions that oscillate, there
seems to be "functions" in logic that oscillate. This infinite
oscillation is connected most simply to the trigonometric functions
they are related to exponentials via the sqrt(-1), which in turn
relates to infinite oscillation in more surprising ways which can
be incorporated into logic and specifically might have a bearing
on quantum physics. I did not have time to pursue this last part
in more detail but I did show some pointers in what I thought
intuitively to be direction that logic should pursue.
I will point out some intriguing things below.
ca314159@bestweb.net wrote:
>
> In article <383481b5.22773510@news.prosurfr.com>,
> jsavard@snooze.freenet.eZdZmonton.aZb.cZa (John Savard) wrote:
> > ca314159@bestweb.net wrote, in part:
> >
> > >Given that
> >
> > > 1) A and B are complementary
> > > 2) A and B are both true XOR A and B are both false
> >
> > >then, that 1) contradicts 2) is the essence of Simpson's Paradox.
> >
> > >We can make an arbitrary determination that "A is True"
> > >to resolve that paradox, but this choice is arbitrary as we could
> > >equally have chosen to make the determination that
> > >"B is True". Regardless of the choice we can then instantly
> > >determine the complementary variables state as "anti-correlated".
> >
> > Given (1) and (2), A is not true, and A is not false.
> >
> > Since (1) and (2) have caused A and B to be self-referential
> > statements, the law of the excluded middle no longer applies to them.
the original form of the liar paradox seems to be the woman and the
alligator (see the Paradoxicon by Faletta, and also my book mentioned
above).
An alligator seizes a child playing by the Nile. The mother implores
the alligator not to eat the child. The alligator says "OK, I will
take pity on you. If you guess what I will do correctly, I will let it
go. If you get it wrong I will have it for lunch."
The mother says; "Ok. You will eat my child. That is my guess. Now if
you eat it, I will be right, so you can't eat it and have to let it
go".
The alligator says "No, I can't let it go. If I let go, then your
guess will be wrong, so then I must eat it."
In this case, the truth itself is dependent on the very act of
assigning a truth value to the act, and is easier to see. (more detail
in my book.)
The "problem" in logic is that in the liar paradox, this act that
changes the truth value is the act of assigning a truth value to
the proposition. The Time-Space liar paradox I created shows this
explicitly.
> > either A and B are lacking in
> > concrete meaning, or the "givens" are themselves false. You are
> > missing whatever part it has that makes it really paradoxical, if any.
> >
> > Quantum-mechanically, a particle can have a state such that "A has
> > spin up" is neither true nor false, but subject to a probability
> > distribution. But once A is observed, if B is observed later, B may
> > have its own probability distribution, or it may correlate with A in
> > some fashion. But it can't, after observation, be both spin up and
> > spin down, either.
I created some 4-valued logics to fiddle with problems of this type.
For example, one has T, F and B (both, true and false), B' and the other
has T,F and N (neither false nor true), N'. These can be made to
collapse
to the standard T/F logic.
The spin is unknown before the measurement so the statement "it has
spin up or down" is neither true nor false, and then it collapses to
the T/F as as soon as the measurement is made.
OR the spin could actually be oscillating and that is what makes
the state unknowable. When the measurement is made then it catches
the spin at that particular moment.
> So, measuring a single spin-up particle collapses
> both its PD in the space-like domain and its PDF in the
> time-like domain and all the other states are then "false"
> (in this case there is only one other state in the binary
> state-space of up and down spins, so that the spin-down
> state is instantly "false" when the spin-up state is
> measured as "true")
-- Sincerely, M. Hubey hubeyh@mail.montclair.edu http://www.csam.montclair.edu/~hubey
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