> DSM wrote:

> > ***
> > Could some parts of the universe work according to logical laws
> > that are different from "ours"?

> Well, last week the estimable John Baez reported that logicians are
> looking into ways to make sense of axiomatic systems that are inconsistent
> (for some proposition P, you can prove both P and not P) yet not trivially
> so (somehow even though you have P and not P, you can’t from that infer
> the truth of every other proposition, as you normally could in regular
> "thought we learned some math in grad school, but evidently not" logic.)

This sounds like paraconsistent logic.  Normally, a logical system
operates under the "law" of the excluded middle: Every formula
in such a system is either true or false, and there is no third truth-
value to opt for.  In paraconsistent systems of logic, a formula
can be true or false, but it could also be true-and-false or neither-
true-nor-false; alternatively, a paraconsistent system employs the
truth-value "paradoxical".  As Leibel reports, one of the main objective
properties of paraconsistent logic is that it not be trivial–that is,
that it not prove every formula.  Two representative researchers in
this field are Bryson Brown and Graham Preist.

DSM wonders if there could be logical laws other than "ours".  What
then,
are *our* logical laws?  Brown and Preist are in a minority among
logicians, in that they don’t take the "law" of the excluded middle
to be necessary for the construction of a sound system of logic.  That
is, Brown and Preist (among others) have the view that paraconsistent
systems can have *models*, or to say this differently, that there are
parts of the universe for which paraconsistent logic is valid.  And
they are correct.  Nobody has a consistent belief-set.  Everybody
believes something which is inconsistent with something else they
believe.  Now, we could take this as motivation to improve the set
of our beliefs, but it is likely that human inconsistency is path-
logical, and unremediable.  Yet, in spite of our inconsistency, we
are able to balance our chequebooks, plan for the future and go to
moon.  So, clearly, our belief-sets are not trivial.  If we are
pathologically inconsistent, then classical logic (which respects
the law of the excluded middle, and which is what I think DSM is
referring to by "our logic") cannot instruct us about the logic of
human knowledge.  Perhaps paraconsistent logic can do this.  Classical
logic is more *agreeable to* our beliefs, but paraconsistent logic
is more *representative of* our beliefs.  So both of these systems
are "ours", albeit in different senses of that word.

James K

Yes … or even something that we have seen no example of yet.

> You’ve got a SUBJECTIVE/OBJECTIVE problem
> even greater than the `comprehensive solution to the paradoxes’ posters.  A
> BOLSHEVIK uses HISTORY as a guide. Karl M

You are quite possible correct.  I’ve done quite a bit of thinking about "my"
subjective/objective  "problem" … and i’m not sure i have it right yet.  But
we (from our subjective minds) make History as much as we are guided
by it.   So whether a proposition is True or not at any moment in History
from any particular point of view,  may not be the most important attitude
(association) to adapt towards it — especially when one is trying to create
something new.  And survival might depend on creating something new.

   Logic is great, survival is better
   Seth Russell

> The concepts of truth and falseness are necessary for the survival of any
> species that can abstract, manipulate abstractions, and then use the results to
> modify behavior.

Yes, an excellent strategy for survival, yet I do not have a measuring stick to
compare it to all strategies that might be.  Do you?

> Further, traditional logic has nothing to do with "human"
> attitudes towards propositions but everything to do with consistent abstract
> association, so it will be emerge naturally in any species whose patterns of
> abstract association are consistent over time.

I’m having a bit of a problem deriving a salient distinction between an "attitude
towards a proposition" and a "consistent abstract association".   Would you to
explicate the distinction that makes the difference to you?

   Seth Russell

news:80uvte$enp$1@scotsman.ed.ac.uk…

- Hide quoted text — Show quoted text -

> DSM <dsm002_DEATH_TO_SPAMME…@bigfoot.com> writes:

> >Under what circumstances could the laws of logic change?
> >What physical phenomena could cause such change, on a local
> >or Universe-Wide scale?

> Well, logic itself is an attempt to describe reality (under the assumption
> that matter/space/time consistently behaves in a certain way – ie
according to
> its own laws).  So the _laws_ of logic are any processes that can be used
to
> build consistent descriptions (logics) from an underlying axiomatic
system.
> So even if physics is different in different regions and gives rise to
> different logics, the laws of logic, which is basically constructing ever
> larger structures from unreducible (incompressible) sub-structures (or the
> other way if you prefer) , would be the same.

> The interesting thing really is whether physical laws are the same and
why.
> If all electrons for instance are _exactly_ identical (which wouldn’t be
> necessary to explain our current perception of the universe) how do they
know
> how to behave?

OBJECTIVELY they would behave exactly as if they were ACTUALLY all the SAME
electron.  OBJECTS are not SUBJECTS.

- Hide quoted text — Show quoted text -

> >What would be the consequences of such?
> >Is it even theoretically possible to predict this?

> >***
> >Could some parts of the universe work according to logical laws
> >that are different from "ours"? This is not an entirely ridiculous
> >query. We may have evolved in a region of space where logic-defying
> >anomalies (workable time travel, etc.) do not exist or are not
> >commonplace,
> >and therefore our brains are not equipped to think about them. This is
> >why
> >time travel – related violations of causality seem impossible. It is
> >probable
> >that they are possible, but we are physically incapable of reasoning
> >about
> >them.

> >In short, there may exist physical phenomena which are outside of the
> >human scope of reasoning; our minds are not capable of thinking properly
> >about them.

> I would argue that reasoning is basically traversing the search space
defined
> by an axiomatic system.  So all you’ve got to do is plug in every axiom
you
> can.  Whether you can hit on the relevant axioms is a limiting factor.
Also
> the search space is probably infinite so in practical terms we may not
find
> solutions even though in principle reasoning could find them.

That’s just called BRUTE FORCE.  When one DARES to use HISTORY as the guide,
you become a SUBJECT.  Karl M

–

John A. De Goes

 * View artificial life on your computer with free software from
http://pages.prodigy.net/jdegoes/bugsss.html.

 * Less than a nickel of every health care dollar is spent on medical research.
Visit http://www.researchamerica.org to learn what you can do.

Seth Russell <s…@halcyon.com> wrote in message

news:3831998B.C8ABDE9E@halcyon.com…

- Hide quoted text — Show quoted text -

> I don’t think you will find "the laws of logic" changing all that
> much with geography (in space or time).  Rather you will find
> them changing with the variety of life.  Traditional logic is all
> about our human  attitudes towards propositions – i.e. whether
> they are true or false.  Those attitudes seem to be  wired into
> our culture and they might even have some basis in our peculiar
> neurobiology.  But a different species of life could survive quite
> nicely with other attitudes towards other more interesting and
> diverse mental states; and could (and probably would) find our
> obsession with feelings of truth and falseness strangely irrelevant.

Well, logic itself is an attempt to describe reality (under the assumption
that matter/space/time consistently behaves in a certain way – ie according to
its own laws).  So the _laws_ of logic are any processes that can be used to
build consistent descriptions (logics) from an underlying axiomatic system.
So even if physics is different in different regions and gives rise to
different logics, the laws of logic, which is basically constructing ever
larger structures from unreducible (incompressible) sub-structures (or the
other way if you prefer) , would be the same.

The interesting thing really is whether physical laws are the same and why.
If all electrons for instance are _exactly_ identical (which wouldn’t be
necessary to explain our current perception of the universe) how do they know
how to behave?

- Hide quoted text — Show quoted text -

>What would be the consequences of such?
>Is it even theoretically possible to predict this?
>***
>Could some parts of the universe work according to logical laws
>that are different from "ours"? This is not an entirely ridiculous
>query. We may have evolved in a region of space where logic-defying
>anomalies (workable time travel, etc.) do not exist or are not
>commonplace,
>and therefore our brains are not equipped to think about them. This is
>why
>time travel – related violations of causality seem impossible. It is
>probable
>that they are possible, but we are physically incapable of reasoning
>about
>them.
>In short, there may exist physical phenomena which are outside of the
>human scope of reasoning; our minds are not capable of thinking properly
>about them.

I would argue that reasoning is basically traversing the search space defined
by an axiomatic system.  So all you’ve got to do is plug in every axiom you
can.  Whether you can hit on the relevant axioms is a limiting factor.  Also
the search space is probably infinite so in practical terms we may not find
solutions even though in principle reasoning could find them.

Ah well, the job I’ve been waiting on is finished so it’s time to go and feed
the cats.

Eddie
(Hmm, yes I know it’s all blethers – no need to tell me)

>In article <383070A2.6…@bigfoot.com>, dsm002_DEATH_TO_SPAMME…@bigfoot.com wrote:
(snip)
>>Under what circumstances could the laws of logic change?
>>What physical phenomena could cause such change, on a local
>>or Universe-Wide scale?
(snip)
>Seriously, logic – like mathematics – is essentially tautology.  There
>is no alternative.  Without logic, no meaningful statement is possible
>(some would perhaps argue for "Ommmmm…").

Hillary Putnam in a 1969 paper "Is Logic Emprical?" argued that logic
has an emprical component.  Just as geometry does not require that
parallel lines never meet, so also, logic bends but does not break
when confronted with the logic of quantum physics.

Reference: R.I.G. Hughes, The Structure and Interpretation of Quantum
Mechanics, pp. 178-217, Harvard University Press, 1989.

A search using the key words quantum logic yields an amazing catch.

John

news:3831998B.C8ABDE9E@halcyon.com…

> I don’t think you will find "the laws of logic" changing all that
> much with geography (in space or time).  Rather you will find
> them changing with the variety of life.  Traditional logic is all
> about our human  attitudes towards propositions – i.e. whether
> they are true or false.  Those attitudes seem to be  wired into
> our culture and they might even have some basis in our peculiar
> neurobiology.

Try the SURVIVAL of a small family group that NEEDS to know from its
children’s stories the difference between REALITY and FICTION.

> But a different species of life could survive quite
> nicely with other attitudes towards other more interesting and
> diverse mental states; and could (and probably would) find our
> obsession with feelings of truth and falseness strangely irrelevant.

You mean, like insect life???  You’ve got a SUBJECTIVE/OBJECTIVE problem
even greater than the `comprehensive solution to the paradoxes’ posters.  A
BOLSHEVIK uses HISTORY as a guide. Karl M

> I don’t think you will find "the laws of logic" changing all that
> much with geography (in space or time).  Rather you will find
> them changing with the variety of life.  Traditional logic is all
> about our human  attitudes towards propositions – i.e. whether
> they are true or false.  Those attitudes seem to be  wired into
> our culture and they might even have some basis in our peculiar
> neurobiology.  But a different species of life could survive quite
> nicely with other attitudes towards other more interesting and
> diverse mental states; and could (and probably would) find our
> obsession with feelings of truth and falseness strangely irrelevant.

  Humans themselves have periodically experimented
  with no logic, they tended to die off fast though.

>If this makes this post unwanted in your group, please forgive me
>for polluting your living space.

>Under what circumstances could the laws of logic change?
>What physical phenomena could cause such change, on a local
>or Universe-Wide scale?

>What would be the consequences of such?
>Is it even theoretically possible to predict this?

Postmodernism will be the new physics.

Seriously, logic – like mathematics – is essentially tautology.  There
is no alternative.  Without logic, no meaningful statement is possible
(some would perhaps argue for "Ommmmm…").

(BTW, Jack Vance wrote a short story once about the Earth passing
through a cloud of ‘negative probability’ or something.  When it left,
the last few rationalist survivors watched the previously successful
maniacs leap off cliffs etc.  Can’t remember the title, unfortunately.)

- Gerry Quinn