This speculation is not grounded in fact;
nor in known theory;
nor even in hallucination.
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?
***
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.
This may sound dumb, but what if there is somthing we can’t even metareason
about? I mean, you can’t physicaly reson about resoning about it. Anyway,
maybe we can’t understand "twisted logic" because our mind uses "twisted
logic". But wait! That wouldn’t be logical!
DSM <dsm002_DEATH_TO_SPAMME…@bigfoot.com> wrote in article
<383070A2.6…@bigfoot.com>…
- Hide quoted text — Show quoted text -
> This speculation is not grounded in fact;
> nor in known theory;
> nor even in hallucination.
> 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?
> ***
> 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.
Don’t feel the need to apologize for the question, as it has been one
which philosphers have debated for many centuries. Back then though,
the question would be phrased something like: "Can God break the Laws of
Logic?"
Take Modus Ponens for example: given two propositions:
1. If A is true, then B is true.
2. A is true
The Laws of logic require that proposition #3:
3. B is true
to hold true if #1 and #2 are true. Now, could God, or some conceivable
universe, violate Modus Ponens and have propositions #1 and #2 true but
#3 be false? I believe Kant and DesCartes argued no, God could not do
this (assuming the existence of God, I am of this opinion as well).
Other philosophers and theologicians have argued just as strongly that
God is outside the boundaries of logic, and that yes he could. You
probably heard of the corollary questions like "Can God create a
mountain so big that he couldn’t lift it?" or even more directly "Can
God find something he can’t do?"
In Metalogic and Metamathematics of course, you can easily create formal
systems excluding Modus Ponens, or any other rule of inference. That is
to say, you can have a framework with different laws of logic than the
ones we normally use. You could even have inconsistent rules of
inference if you want (such as AxAF[Fx->~Fx]). Generally though, such
systems are not very interesting, since they usually prove everything is
both true and false. Loosely, you would normally want to include the
minimal set of axioms and rules of inference to be able to prove as many
things as possible "that are ‘true’" without making all the "false" ones
‘true’ as well. Godel proved of course that it was impossible to prove
or disprove *every* proposition unless you were already inconsistent, so
you are always left with undecidables (but that is another story).
Asking philosophical questions like this are not at all out of place on
And you might even inspire some interesting discussion.
this board. If we have room for questions from professionals, novices,
cranks, eccentrics and the rest, certainly we can find room for yours.
Jonathan Hoyle
The laws of logic do not possess a factual existence of their own. They are
fictitious entities created by the human mind to describe a consistent method
of abstraction. People could, if they wanted, associate other rules with the
phrase "laws of logic", but it would by no means change "correct reasoning" —
i.e. the new laws of logic, if inconsistent with the old ones, would yield
invalid conclusions, while the old ones would unfailingly yield valid
conclusions — since the phrase "correct reasoning" is merely a tautology for
the consistent method of abstraction that the laws of logic currently describe.
The only way to replace the laws of logic with laws inconsistent with those
currently employed and to yield valid conclusions is to both redefine "laws of
logic" and "valid conclusions", which is a exercise of no earthly value.
There is no part of our universe or any other that operates with a different
set of logical principles, nor indeed is there even a universe that operates
with the set of logical principles with which we are accustomed. The universe
simply is, and operates as it does. It is the human mind that has the capacity
to abstract experience and manipulate those abstractions (by which I mean
pattern matching on a database of abstract "properties"), and only in such a
context does "logic" even make sense.
Our minds are not capable of comprehending many things (such as the true nature
of time or experience) — particularly, we cannot comprehend anything unique in
this world, since it is only by understanding one object’s relationship to
another that we can "make sense" of it, and those things that are unique cannot
be so correlated. But this inability to comprehend has nothing to do with
logic, but everything to do with our base of experience.
So in short, your conception of logic is not correct (pun not intended), so
your questions do not make sense.
–
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.
DSM <dsm002_DEATH_TO_SPAMME…@bigfoot.com> wrote in message
news:383070A2.67B4@bigfoot.com…
- Hide quoted text — Show quoted text -
> This speculation is not grounded in fact;
> nor in known theory;
> nor even in hallucination.
> 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?
> ***
> 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.
In article <80q4q8$23m…@newssvr04-int.news.prodigy.com>, "John A. De
Goes" <jdegoesREMOVET…@prodigy.net> wrote:
> There is no part of our universe or any other that operates with a different
> set of logical principles, nor indeed is there even a universe that operates
> with the set of logical principles with which we are accustomed. The universe
> simply is, and operates as it does. It is the human mind that has the capacity
> to abstract experience and manipulate those abstractions (by which I mean
> pattern matching on a database of abstract "properties"), and only in such a
> context does "logic" even make sense.
Really?
You mean that gravitation is only a human abstraction and does not really
exist?
> Our minds are not capable of comprehending many things (such as the true
nature
> of time or experience) — particularly, we cannot comprehend anything
unique in
> this world, since it is only by understanding one object’s relationship to
> another that we can "make sense" of it,
I claim I can comprehend unique things. For example: 2 is the unique
even prime. I comprehend that completely.
Steve L
In article <383070A2.6…@bigfoot.com>,
dsm002_DEATH_TO_SPAMME…@bigfoot.com 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.)
At least that’s what I understood of it.
Steve L
Steve Leibel wrote:
> In article <80q4q8$23m…@newssvr04-int.news.prodigy.com>, "John A. De
> Goes" <jdegoesREMOVET…@prodigy.net> wrote:
> > There is no part of our universe or any other that operates with a different
> > set of logical principles, nor indeed is there even a universe that operates
> > with the set of logical principles with which we are accustomed. The universe
> > simply is, and operates as it does. It is the human mind that has the capacity
> > to abstract experience and manipulate those abstractions (by which I mean
> > pattern matching on a database of abstract "properties"), and only in such a
> > context does "logic" even make sense.
Just about every little hamlet on Earth operates with a different
of logic principles. It’s better just to tell the universe to
shut up in a while, and learn something about logic.
Walter Fisher wrote:
> The Laws of Logic are merely convenient mental tools we use to describe and
> manipulate our environment, just like mathematics or language.
Forgive me for stating my question so vaguely.
By "laws of logic" I did not mean any form of human thought directed to
make
convenient sense of our operating environment.
I was discussing the "Platonic forms" – type thing,
in other words, whatever it is about our universe that causes 2+2 to
equal 4,
and so on.
Humans with no awareness of or belief in
the laws of physics and mathematics nevertheless
live lives which are governed by these universal principles.
What I meant was, can (for example), through some devilish manipulation
of the Universe’s basic structure, 1+1 be made to equal 3? Could
causality
be violated?
In a short story by SF author Greg Egan, the protagonists discover a
region of numerical space where the (commutative law?) does not hold
true!
Imagine, perhaps for some values of X and Y X+Y <> Y+X. Ridiculous?
They try to prevent a corporation from stealing the secret and
exploiting the anomaly to play the stock market.
If you could break down causality, you could build a number of
interesting
and highly useful contraptions.
Consider the "time radio".
It is a classic SF gadget: A device allowing the transmission of
information
into the past (presumably to a waiting receiver.) This immediately
implies
causality violation. Now, think of the following "problem": you receive
a
transmission from yourself, then decide not to send it on the scheduled
day.
There are two "possibilities" for a solution:
(is this the right word for a non-existent phenomenon?)
1. You discover an elegant proof of the absense of free will, namely
that you find
yourself sending the message despite not having originally intended to
do it. All
seems perfectly normal except for this fact.
2. The message is received from a "parallel universe", in which ALL IS
THE SAME except
for the fact that you sent the message when you were supposed to.
3. You become the discoverer of a Distorted Logical Law.
Could the inhabitants of a universe deform its "Platonic forms?"
Perhaps this is as likely as canned sardines opening their container
from the inside-out.
Nevertheless, let us speculate.
LEIBEL
Really?
You mean that gravitation is only a human abstraction and does not really
exist?
DE GOES
Is gravity logic? No. Therefore I did not say or imply that gravity is only a
human abstraction and does not really exist.
LEIBEL
I claim I can comprehend unique things. For example: 2 is the unique even
prime. I comprehend that completely.
DE GOES
Everything is *relatively* unique to something else (that is, each entity
possesses at least one property that other entities do not). I would never deny
that. But few things in this world are *absolutely* unique — that is, few
things share extremely few or no other properties with anything else in the
realm of our experience. The number 2 is not such an entity, for among other
things, it is an integer, and hence shares all the attributes required for a
thing to be an integer (which are many and apply to a great many entities, such
as all elements in the set of integers or reals).
In general, if you can precisely communicate the full meaning of a concept to
someone who has not "experienced" that concept, then the concept is not
absolutely unique, for in the very act of communicating the idea, words are
employed, and words derive their meaning solely from association and
correlation.
One can precisely and fully communicate the idea of the number 2 to any being
of complexity sufficient to handle abstraction. But on the other hand,
communicating the experience of passing through time or the sensation of
redness to a being devoid of either would be impossible. These are the things
that we cannot form correlations with, and hence, the things that we cannot
comprehend (i.e. see clearly in relation to many other things). They are the
great mysteries of the universe that boggle our minds because we lack the
necessary conceptual framework.
–
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.
In article <01bf2fae$e8b42bc0$0300a8c0@Josh’sroom>,
Josh <mccartney…@geocities.com> wrote:
>This may sound dumb, but what if there is something we can’t even metareason
>about?
Then we’re screwed. Simple as that.
We’re learning a lot about what we can see and reason about. When you find
some of that other stuff, post it here.
Mark Folsom
DSM <dsm002_DEATH_TO_SPAMME…@bigfoot.com> wrote in message
news:383070A2.67B4@bigfoot.com…
- Hide quoted text — Show quoted text -
> This speculation is not grounded in fact;
> nor in known theory;
> nor even in hallucination.
> 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?
> ***
> 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.
In article <383070A2.6…@bigfoot.com>, DSM <dsm002_DEATH_TO_SPAMMERS_@b
igfoot.com> writes
…
>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.
So don’t!
–
Jeremy Boden
The Laws of Logic are merely convenient mental tools we use to describe and
manipulate our environment, just like mathematics or language. Just as you
can use "imaginary" number systems (like "i" which stand for the square root
of -1) in mathematics, you can use different logic systems, such as Boolean
Logic (computer programming) or even Polish Logic (pun intended).
If you go to an insane asylum, all laws of logic have even been suspended
and the residents don’t just keel over dead.
However, most humans find it advantageous to use our "standard logic" system
because it is most closely related to objective reality as we perceive it
and because it achieves the desired results in the most efficacious manner.
I am not an expert in the field of "logic"; I am just trying to apply
"Common Sense" to your question.
-
Walter
dum vivimus, vivamus! (Horace)
http://www.rationality.net
e-mail responses: delete x in return address (anti-spam)
—
DSM <dsm002_DEATH_TO_SPAMME…@bigfoot.com> wrote in message
news:383070A2.67B4@bigfoot.com…
> This speculation is not grounded in fact;
> nor in known theory;
> nor even in hallucination.
> 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?
snip
In article <383070A2.6…@bigfoot.com>, DSM <dsm002_DEATH_TO_SPAMMERS_@b
igfoot.com> writes
>This speculation is not grounded in fact;
>nor in known theory;
>nor even in hallucination.
>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?
The laws of two valued Aristotelian logic are simple rephrasing, or
tautology, and cannot be changed. But there are major departures from
them.
Firstly when we consider infinite mathematical structures we find
undecidable propositions. That is propositions which can be taken as
true, and for which the converse can also be taken as true.
Secondly we can consider many valued logics. You can get popular books
on "Fuzzy thinking". This is a respectable branch of mathematics with
real applications in computer programming. Fuzzy logic is an example of
a "many valued logic" in which uncertain propositions are given truth
values other than 0 or 1. There are a number of different many valued
logics, using different schemes for calculating truth values for
propositions, and with differing levels of applicability.
One of the motivations for many valued logic was the Heisenberg
uncertainty principle, the recognition that uncertainty is now a feature
of measurement. Quantum logic can be regarded as the correct many valued
logic for the interpretation of uncertainty in measurement.
–
Charles Francis
char…@clef.demon.co.uk
In article <383070A2.6…@bigfoot.com>, dsm002_DEATH_TO_SPAMME…@bigfoot.com wrote:
>This speculation is not grounded in fact;
>nor in known theory;
>nor even in hallucination.
>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
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.
Seth Russell
- Hide quoted text — Show quoted text -
DSM wrote:
> This speculation is not grounded in fact;
> nor in known theory;
> nor even in hallucination.
> 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?
> ***
> 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.
Seth Russell wrote:
> 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.
On Tue, 16 Nov 1999 10:23:07 GMT, ger…@indigo.ie (Gerry Quinn)
wrote:
>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
Seth Russell <s…@halcyon.com> wrote in message
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
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. 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.
–
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.
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?
- 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)
Eddie Corns <ed…@holyrood.ed.ac.uk> wrote in message
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.
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> >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" wrote:
> 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
Steve Leibel wrote:
> 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
karl malbrain wrote:
> You mean, like insect life???
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