Philosophy

(Gwynn/31689) Pecc:

Gwynn@rss.iscabbs.com — Sun, 01 Jan 2012 20:11:00 -0600

Pecc:

No, I'm suggesting what Vanity said at the end, only a finite number of things
are actually true. And I submit that the way out isn't, screw paradox. To wit,
let's look at the liar. It's pretty clear, logically speaking, that it is in
fact the case that if the sentence is true, it's false, since a lie is a
falsehood, but if it's false, it's true, it was in fact a lie. You can't just
say, well that's wrong because then it breaks everything else! In other words,
I don't think you can deny that it is in fact a genuine paradox. I say the
solution is, you look at things the way you would any other thing.

P: Obama is not POTUS
Q: I own a horse
Either P or Q

OK, P isn't true, Obama is POTUS. Now what? It could still be true, I might own
a horse. Similarly, just as you say, nobody's getting stabbed by words,
actually. Same solution, you look at the actual situation and go, well logic
may tell us Q is true, but it turns out, Q doesn't actually obtain in the real
world, or fictional universe, or whatever. I don't think that breaks logic at
all, it just happens to be that the other disjunct isn't true, just like any
old disjunction, assuming we're dealing with things in our universe and not a
hypothetical world of logic.

Which brings me to my answer to your question. In one with unicorns, we know
we're dealing with a fictional universe, because we don't have unicorns. In 2,
well maybe your neighbor has a snowblower, or maybe she doesn't. We have to
figure that out one way or the other, if we're interested in its truth. But we
know we're dealing with a possibility in our universe. That brings us to three.

You haven't said, in some fictional universe, or, in some hypothetical
universe, or, this is a logic exercise so you're only allowed to consider
what's on the board, no outside information. So 3 too is about our universe,
and we know there's no king of France. Hence, there can be no bald king of
France either. So to sum up, in all cases, your three and a paradox, we have to
refer to whatever universe we're dealing with, whether that's ours, a fictional
universe, a logical world, Etc.

(Peccavimus/31688) ::rubs hands:: But you have fallen into my evil trap, Vanity! ...

Peccavimus@rss.iscabbs.com — Sun, 01 Jan 2012 19:49:00 -0600

::rubs hands::  But you have fallen into my evil trap, Vanity!  See, yes,
depending on the universe we select, unicorns do have wings.  And the statement
"unicorns do not have wings" presupposes a universe.  So:

P == unicorns have wings
~P == unicorns do not have wings

In making a proposition P (or its contrary, ~P), I am implying the existence of
a univere in which there are unicorns.  The hearer quite effortlessly
incorporates that presupposition.  We can say, then, that for each P

P > E U such that P xor ~P

Each P implies that there exists a universe U such that P xor ~P

Now, here's my trap: if I say

2)  My neighbor has a snowblower

aren't I also implying a universe U such that my neighbor either has or does
not have a snowblower?

or if I say

3)  The King of France is bald

aren't I implying a universe such that there is a king of France who either is
or is not bald?

Now, you incorporate 1) easily enough: (oh, I didn't mark it: 1) Unicorns don't
have wings) and you have no problem accepting a universe in which I have a
neighbor.  But if I say to a random person on the street -- well, a random
European on the street; I've used the example in class and had students unawar
that France has no king -- if I say to a random person on the street "The King
of France is bald," he or she might well say "There is no such universe such
that P or ~P, viz., that ther is a king of France who is or is not bald." 
Okay, he'll probably say "There is no king of France," but it amounts to the
same thing.

Now, the question that fascinates me is . . . why?  Why are (1) and (2) easily
accomodated, but (3) seems to trip us up?

We can make (3) acceptable, of course.  I can say "Louis' mistress looked upon
his gleaming pate, its periwig eskew in post-coital bliss, and thought, 'Well,
mon dieu, the king of France is bald!'"  Or I could say "His Imperial Aztec
Majesty, Lord of the Americas and Protector of the Faith of Quetzalcoatl-Christ
ran the razor over his tattoed scalp.  Finally, he thought, looking in the
mirror, the King of France is bald."  And if that's the first sentence of a
story you accomodate it: you say, I am in a universe now in which the king of
France is, apparently, a weird mixture of Aztec and Christian . . . okay. 
Without this kind of accomodation, there'd be no science fiction or fantasy at
all as a genre -- or, for that matter, no anecdotes.

But why do those get a pass, while "The King of France is bald" free of context
doesn't?  What is it in the context that gives us the power to accomodate those
universes?

And, a more ontological question, is there a universe that isn't simply
constructed from language, and if so, what is it like?

(Vanity/31687) "Unicorns don't have wings" perhaps is something that we really ...

Vanity@rss.iscabbs.com — Sun, 01 Jan 2012 19:01:00 -0600

   "Unicorns don't have wings" perhaps is something that we really can affirm a
truth value of, if we know what universe we are referring to.
   Statements about fiction are quite amenable to being characterized as true
or false, since the universe of most fictions is rather circumscribed and
(sometimes) self-consistent. Thus, if I ask, "Did the Wicked Queen poison Snow
White with an apple?" I should be able to get a definite "yes" or "no" answer,
as long as the respondent understands that the question is about truth-values
*within the Snow White universe*.  If I ask the question immediately after
telling someone the story, I can be pretty assured of getting a definite
answer, since we have jointly entered into that universe, in imagination, and
our discussion continues to take place within that universe, and the
truth-values we discuss are its truth-values.  However, if I ask the question
randomly and out of context, I can't assume that my respondent will follow me
obligingly into that universe, and she might well answer "No, because Snow
White never existed!"
   That's a simple case.  What, however, happens if the discussion crosses the
boundary between universes, and mingles fictional 'fact' with real-world fact?
What is the truth-value of the statement "The Wicked Queen is *really* Snow
White's mother, not her stepmother"?
   Now, one response is, like my previous respondent, that "The Wicked Queen
never existed, so she can't be anybody's mother *or* stepmother!"  And that's
fair enough.  And if I take as my universe only the most common version of the
Snow White story, the statement is obviously false.
   However, the statement is still true in a sense -- in the original story of
"Sneewittchen" collected by the Grimms, the Queen who tries to kill Snow White
is her own mother, who was jealous of her.  The Grimms changed the story
because they were worried about the moral effect it might have on children who
read it.  To evaluate the truth value 'correctly' -- i.e., as intended by the
speaker -- you need to cross back and forth between two different versions of
the Snow White universe, refer to the truth value of the proposition in both
universes (which is different), and return to our universe and judge between
those truth values according to criteria which are internal to neither universe
-- though the statement still ends up being framed as a proposition about the
Snow White universe *as if* it were a single thing.
   Likewise, if we define our universe -- let's say, the universe of the
_Unicorn Tapestries_, or for that matter the universe of the _D&D Monster
Manual_ -- we can affirm that unicorns are wingless.  On the other hand, there
are doubtless universes in which some unicorns have wings (tattoo artists seem
to specialize in them); and maybe there even are, or will be, universes in
which unicorns *must* have wings.  Regardless of the variation, with respect to
each universe we should be able to state definitively whether "Unicorns have
wings" is true or false, much more definitely, perhaps, than similar statements
in our exceedingly complex universe.  The problem arises when we try to
synthesize propositions about these other universes in terms of our own, where
their rules don't necessarily apply.
   There also arises a problem when the universe constructed by a work of
fiction or folklore or myth carries within itself a contradiction.  A writer
may, through carelessness or even by way of intention, state contradictory
facts about some event or character; or a later editor may conflate
contradictory stories into one.  Neither version has necessary authority to
supersede the other.  To take a well known if somewhat controversial example,
within the first two chapters of Genesis, God first makes man on the sixth day,
after bringing forth the birds out of the waters (Genesis 1:20-27); and then
again he makes man, and subsequently forms the beasts and birds out of the
earth (Genesis 2:15-19).  Within the Genesis Universe, it has to be true that
God both created man before *and* after the birds and beasts.  It's a flagrant
contradiction (at least, assuming each act of creation to be a unique
occurrence); but the Genesis universe doesn't instantaneously collapse from a
lapse of logic.  The damage is, as it were, contained; we overlook the
inconsistency, both by a kind of linguistic legerdemain (there are obvious
shifts in tone and structure from Genesis 1 to Genesis 2) but also because it
doesn't really impinge on what writers are pleased to call the narrative logic
of the story.
    On the other hand, some writers can intentionally play with such
inconsistencies.  I recall one story (somewhat indistinctly) in which, over
several iterations of a similar situation, three characters were, respectively,
husband, wife, and son;  father, daughter, and son; father, son, and
daughter-in-law -- and so forth, in varying combinations, with the details of
the situation varying.  Within this universe, making truth statements about the
relationships involved (e.g. "X is Y's mother") becomes precarious if not
impossible.  And yet, within whatever universe-internal logic allows these
contradictory truths, it is still not true that *anything* could be true,
because only a limited, finite number of things actually *are* true.

(Peccavimus/31686) Are you suggesting with your last sentence that the world does n...

Peccavimus@rss.iscabbs.com — Sun, 01 Jan 2012 16:28:00 -0600

Are you suggesting with your last sentence that the world does not obey logical
laws?

(Gwynn/31685) But unicorns don't have wings, by definition. But it does get at...

Gwynn@rss.iscabbs.com — Sun, 01 Jan 2012 16:18:00 -0600

But unicorns don't have wings, by definition. But it does get at an interesting
idea, related to Pecc's idea about metaphor. Do unicorns exist? Clearly they do
not, I can't go ride one, but clearly in some sense they do, you and I both
know perfectly well what a unicorn is, and why it doesn't have wings, because
that's Pegasus, of course! And I guess that's why paradox isn't a problem for
me, because to me, it looks like we're confusing two different things. Namely,
whatever constructed logic world we've made, and the world we live in.

(Giraffe/31684) >the number of day-to-day propositions we run into that have tra...

Giraffe@rss.iscabbs.com — Sun, 01 Jan 2012 15:55:00 -0600

>the number of day-to-day propositions we run into that have traditional binary
>logical truth value is vanishingly small

I question whether this proposition has a truth value.  :)

(Peccavimus/31683) Giraffe> Actually, I'd probably say that the number of day-to-d...

Peccavimus@rss.iscabbs.com — Sun, 01 Jan 2012 15:29:00 -0600

Giraffe>  Actually, I'd probably say that the number of day-to-day propositions
we run into that have traditional binary logical truth value is vanishingly
small, unless we do logic for a living.

Other than example sentences on here today, I'm not sure I've run into a single
one.  Oh, wait, no, when the woman at Caribou gave me the answer to the trivia
question, that had truth value.

(Peccavimus/31682) Well, there's a huge batch of propositions that don't have tru...

Peccavimus@rss.iscabbs.com — Sun, 01 Jan 2012 15:22:00 -0600

Well, there's a huge batch of propositions that don't *have* truth value,
either because they're essentially meaningless ("Colorless green ideas sleep
furiously"), or because they're context dependent ("That's my new car."), or of
course because they're not really propositions at all ("Good morning.")

And of course imperative and questions don't have truth value.

The most interesting case, to me, is metaphor, in which the semantic content is
untrue while the pragmatic meaning may be true.  "She's a tiger in the bedroom"
isn't true: she's a person, not a tiger, no matter where she is.  But it may
very well be true if you give her a few drinks and blow in her ear.

One older definition of metaphor is that a metaphor is a statement that is
literally and obviously false, forcing the hearer to draw an implicature or
assume that the speaker is a lunatic.  (I should have said "explanation," not
"definition" above)

Lakoff isn't terribly fond of that Gricean approach to metaphor, though, but
then he kind of sweeps the role of logic in language into the dustpin with a
pushbroom (which, interestingly, is both meaningless -- logic isn't a thing you
can sweep -- and metaphoric -- even if it were he wouldn't have swept it away .
.. . and I didn't realize that when I wrote it).

My absolute favorite proposition to contemplate is something I read in a comic.
I don't remember the joke or the punchline, and don't care, because the
sentence itself is a thing of beauty:

"Unicorns don't have wings!"

Contemplate the truth value of *that* for a while, when you can't afford drugs.

(Giraffe/31681) Not every collection of words expresses an idea clearly. So we s...

Giraffe@rss.iscabbs.com — Sun, 01 Jan 2012 15:25:00 -0600

Not every collection of words expresses an idea clearly. So we shouldn't be
surprised that a truth value cannot be ascribed to every proposition. We should
just be grateful that pretty frequently we do find propositions which are
clearly true or false.

(Vanity/31680) I was just trying to evaluate the truth value of the proposition...

Vanity@rss.iscabbs.com — Sun, 01 Jan 2012 14:57:00 -0600

   I was just trying to evaluate the truth value of the proposition "George
Washington is 279 years old".  In one sense, it's obviously true: age is
determined by subtracting the time of birth from the present time, and
Washington was born in 1732, so he must be 279 years old.  In another, and
quite possibly more salient sense, it's complete nonsense: age is something we
only attribute to living things when they are alive.  One might say that
Washington's corpse is 212 years old (though that would be a very weird thing
to say) but you can't really attribute an age to George Washington, the man,
since he no longer exists.  This isn't even a matter of context -- it's more
that the phrase "is X years old" has at least two different senses which,
however, are obviously closely related and which we rarely bother to
distinguish.  It's not immediately obvious that "Mikhail Gorbachev is 80 years
old" and "the Empire State Building is 80 years old" are different kinds of
proposition; nor how "James Dean is 80 years old" relates to either one.

(Peccavimus/31679) If you admit contradiction, the whole system of logic IS flawe...

Peccavimus@rss.iscabbs.com — Sun, 01 Jan 2012 13:31:00 -0600

If you admit contradiction, the whole system of logic *IS* flawed.  Taht's the
point.

Vanity>  Actually, quite a lot has been done with that, all of which I dimly
remember from grad school.  The whole idea of implictures arises as a way to
explain the role of context in such utterances.

And, of course, such exmples as "the president of France is bald" are trotteed
out to show how formal, symbolic logic doesn't offer an adequate account of
semantic meaning.

(John Public/31678) Gwynn> Your examples are misleading; it's a trick. Your "P" prop...

John Public@rss.iscabbs.com — Sun, 01 Jan 2012 13:01:00 -0600

Gwynn> Your examples are misleading; it's a trick. Your "P" proposition always
seems quite reasonable in everyday common sense. Socrates is a man. Water is
wet, etc. Your "Q" proposition is always absurd. You own horses, are stabbed
in the face, etc. So when you replace P with ~P, and logically conclude that Q
must be true, you are relying on our sensibilities to deem Q to be ludicrous,
and you expect that we will conclude that the whole system of logic if flawed.
After all, you don't own a horse.

But the absurdity or sensibility of each proposition is irrelevant. It relies
on outside information -- outside the universe of discourse. The English
descriptions exist for our entertainment, to relieve the boredom of the purely
abstract logical system that it is.

(Vanity/31677) What's the conventional way of dealing with statements which cou...

Vanity@rss.iscabbs.com — Sun, 01 Jan 2012 13:19:00 -0600

   What's the conventional way of dealing with statements which could be true
or false dependent on context, but for which the essential context is not
provided?  E.g., if I say "the President is fifty years old", the statement
might be true or false depending on (a) which President I'm talking about, (b)
what year I'm talking about, (c) whether I'm talking about Earth years or
Martian years (etc.), and possibly several other contextual factors.

(Peccavimus/31676) But that's the point! I am not being stabbed in the face, so th...

Peccavimus@rss.iscabbs.com — Sun, 01 Jan 2012 12:56:00 -0600

But that's the point!  I am not being stabbed in the face, so there's something
seriously wrong with the liar's paradox and the contradiction it appears to
contain.

To "prove" something is to show that it's logically true.  But you have
"proven" something as logically true that *ISN'T* true, so there's something
wrong with your logic.  What's wrong with it is that you've admitted a
contradiction, which allows you to "prove" false things.

another way of putting it: once you introduce contradiction, you make logic
useless.

(Gwynn/31675) Pecc:

Gwynn@rss.iscabbs.com — Sun, 01 Jan 2012 12:46:00 -0600

Pecc:

I think if you'd said that before, we wouldn't have had this long go around.
So:

Epimenides the Cretan said, "All Cretans are always liars."
Either Epimenides was telling the truth, or these words are stabbing you in the
face as you read them.

Are you suggesting that Q is true, within the logic world, the rules of the
game as it were, but not true in the world? Because I'd surely hope you're not
being stabbed in the face by anything. But it should be true, because of the
liar paradox, e.g. if P is true, then P is also false, which makes Q true.

I guess I can accept that, but then my only real issue is, this whole thing
started when we said you couldn't have an actual paradox/contradiction in the
real world, because it would be all kinds of bad, because you could "prove"
anything. Clearly you can't, you aren't being stabbed in the face by words,
that's not actually occurring in the real world.

Which goes right back to what I said, and Vanity just reiterrated, saying
there's no contradiction is just some definitional thing we have, and if
there's some actual paradox in the world, so much the worse for classical
logic, we need something new. That's why we have things like relevance logics,
paraconsistent logics, dialetheism, multivalent logics, Etc., I'm pretty sure.
But I mean, the above example is exactly why I'm saying you can't "prove" any Q
via contradiction, you can say that all you want, but words aren't stabbing
anybody, no matter how much classical logic insists that I've just proven it.
It's just not happening, and it's something that's pretty damn unlikely to ever
be the case, though I guess you could have it be possible, if you worked at it.

(Peccavimus/31674) I think the rest of my post kind of did that, saying there seeme...

Peccavimus@rss.iscabbs.com — Sun, 01 Jan 2012 12:26:00 -0600

I think the rest of my post kind of did that, saying there seemed to be two
different kinds of true, a conventional kind applicable to the sensible world,
and another, more certain kind applicable to the intelligible world.

(JL/31673) Pecc> "what is it to know that something is true?"

JL@rss.iscabbs.com — Sun, 01 Jan 2012 12:15:00 -0600

Pecc> "what is it to know that something is true?"

Are you talking about objective truth? How are you defining "true"?

(Peccavimus/31672) Vanity> Well, that gets into one of my favorite philosophical p...

Peccavimus@rss.iscabbs.com — Sun, 01 Jan 2012 11:20:00 -0600

Vanity>  Well, that gets into one of my favorite philosophical problems, one I
haven't worked out to my satisfaction at all yet (hence, it's one of myf
avorites!).  Namely: what is it to know that something is true?  Essentially,
it's a question of epistemology, it seems to me the most fundamental question
of epistemology.

One class of experiences, mediated through the senses, have no certain truth at
all.  One never knows that one's senses are true; one only rounds off the
fractions and calls it good.  I *assume* I'm drinking coffee and not something
else, but how the hell do I know that I even exist in teh form I think I exist
in?  For all I know, I'm a giant space amoeba who is suffering severe
delusions.  It's not *likely*, but I can't *know* with one hundred percent
certainty that it isn't the case.

Another class of experiences, those not mediated through the senses, are
subject to what you call "arbitrary" truth.  I know, with one hundred percent
certainty, that the diagonal of a euclidean square is irrational and for any
Euclidean square you might give me, no matter its size, I know that the ratio
of a side to its diagonal is 1:sqrt2.  I don't know that in the same sense that
I know my neighbor has a snowblower; I know it in another way, a way that's
more certain than any sensory knowledge I might have.

Now, the question is, is it more certain because I have laid down the rules to
the game to make it that way, quite arbitrarily?  Or is it more certain because
it partakes of a more *real* reality than the sensory world?  Is the
intelligible world, in other words, more certain because it is more real?  Or
is it more certain because we've defined "certain" in such a way that it
applies best to the intelligible world?

I know what I *think* to be the case, but the rebuttal of what I think to be
the case calls into question the very logic that I used to get there.  What
disatisfies, even annoys, me about the nonrealist position is that I can't
attack it.  I don't mean it's obvious; I mean it denies the validity of any
method that might attack it.  I can make any number of such systems, and how
can I judge between them?

(Vanity/31671) Given the way that the function NOT (! or ~) is defined -- that ...

Vanity@rss.iscabbs.com — Sun, 01 Jan 2012 10:59:00 -0600

   Given the way that the function NOT (! or ~) is defined -- that ~A is true
if and only if A is false, or conversely, that the falsity of A implies the
truth of ~A, then the law of non-contradiction is trivially valid on the
assumption that a statement that is true cannot be simultaneously false.  It
doesn't really follow from anything -- it's essentially defined into the
system that what is true is not false and what is false is not true.
   But the logical terms TRUE and FALSE, though they operate excellently in
terms of mathematical abstraction, are a lot harder to deal with in real life
(as, for that matter, is the operator ->).  In ordinary language, we use the
words "true" and "false" in very subtle, contextually dependent ways, which
have little or no relationship to the logical TRUE and FALSE, which in a sense
have no *meaning* in logic -- they're just interchangeable labels.  They might
as well be labelled SKWOG and FLINK, of which all we have to know is that they
apply to statements, and that what is SKWOG is not FLINK, and what is FLINK is
not SKWOG, and that there is no possibility of something being both SKWOG and
FLINK, or neither SKWOG nor FLINK.  These aren't facts about the way that the
universe, or even human discourse, works -- they're just the rules of an
arbitrary game.

(Vanity/31670) Popular representations of eastern religions, such as Zukav and ...

Vanity@rss.iscabbs.com — Sun, 01 Jan 2012 10:35:00 -0600

   Popular representations of eastern religions, such as Zukav and Hofstadter,
are almost invariably both highly selective and highly misleading.  Zen
anecdotes (when genuine) are highly allusive and assume an existing knowledge
of very sophisticated and detailed Buddhist philosophical systems -- sometimes
affirming, sometimes critiquing them.  But to attempt to understand Zen without
this background, by taking a handful of decontextualized Zen anecdotes, and
then to work backwards and try to construct a philosophical framework for them,
based on apparently parallel ideas in Western philosophy -- well, it can tell
you something about the author's philosophical preoccupations, but almost
nothing about Zen.

(JL/31669) What Pecc said. If you state that "P or Q" is true, then you can...

JL@rss.iscabbs.com — Sun, 01 Jan 2012 09:03:00 -0600

What Pecc said. If you state that "P or Q" is true, then you can't give
evidence as to why it's not. That's absurd. Your premise is that it's true. If
you show that it's false, then you lied!

Interestingly, I've been catching up with my reading of GEB and it's talking
about exactly this stuff.

In "The Propositional Calculus", section "Proofs vs Derivations", it starts
with the premise of "P or !P". The author then shows that "From a
contradiction, anything follows! Thus, in systems based on the Propositional
Calculus, contradictions cannot be contained; they infect the whole system like
an instantaneous global cancer."


On a related note, about GEB:

1) I'm so pleased to see that it is getting into recursive and self-referential
systems, and recognizing systems at different levels, like molcules and gasses.
This is exactly what my mind ponders these days. Interesting.

2) Is its discussion of Zen a fair representation of the Buddhist Zen? If so,
that's kind of fucked up, IMO. I kind of get it, but it seems almost worthless
and devoid of meaning. Like if you abstract too far, you just get mush. I have
to read more about Zen. I'm curious...

(Peccavimus/31668) Here is the error in your understanding:

Peccavimus@rss.iscabbs.com — Sun, 01 Jan 2012 05:50:00 -0600

Here is the error in your understanding:

"So this is what happens with a perfectly normal disjunction in
these universes. In water, negating either disjunct affects the other, in
Socrates, nothing really happens, because these are two totally unrelated
disjuncts, one or both or neither could be true.
"

If I say P or Q, then one or both can be true.  But both cannot be false,
because if so, "P or Q" is false.

Once you establish that P or Q is true, it is true.

Disjunction does not lead logically to Q always being true: I don't know where
you get that.

Contradiction leads to everything always being both true and false, meaning
that anything can be true.

P and Q do not have to have anything to do with each other at all.  They're
place holders for any statement whatsoever that one might make that has truth
value.  I don't understand why you think they must have something to do with
each other.

(Steppenwolf/31667) That's very close to my argument, Gwynn. I'm going to rephrase i...

Steppenwolf@rss.iscabbs.com — Sun, 01 Jan 2012 05:19:00 -0600

That's very close to my argument, Gwynn. I'm going to rephrase it, just
because:

Our argument is that you can ONLY introduce a disjunction if there is a reason
to believe that ~P --> Q. That is, that if not P, then Q.

One way to deal with that is the relevance-based standard that Gwynn and to
some extent Vanity have suggested: that you look at the content of the
propositions. It's realistic, but sort of shaky in the context of classical
logic.

Another way is to say that DI doesn't work if you accept both P and not-P as
true. The only reason you are allowed to introduce a disjunction in the first
place is because you know that not-P is false, so you never have to worry about
the truth of Q. If that's not the case, then DI becomes an invalid argument,
period. I like this better because you're not worrying about the content of the
propositions at all, but simply making a statement about how logic works.

Either way, I like that Gwynn reduced his to the importance of believing that
not-P implies Q. Suddenly, I realized that our arguments were almost perfectly
analogical, hitting the same point in different directions. That's cool. :)

(Gwynn/31666) OK, since I can't sleep, here we go. Everybody kind of jumped wa...

Gwynn@rss.iscabbs.com — Sun, 01 Jan 2012 01:54:00 -0600

OK, since I can't sleep, here we go. Everybody kind of jumped way ahead of
where I was going, but let me set up a couple of universes and get started
explaining myself. We'll call one Water and the other Socrates.

Water:
Premises: temperate climate's temperature range, freezing and boiling points of
water, water left undisturbed outdoors for a day, we're in a temperate climate.
P: the water is ice
Q: The temperature is greater than freezing
Either P xor Q

OK, I've compressed those premises, but hopefully they're obvious. Here we have
a classic !P implies Q, because of the xor, and we have the xor because we know
things about the temperatures. So both can't be true, only one can, if the
water's frozen it's below freezing, if not, then Q.

Socrates:
P: Socrates is a god
Q: I am being chased by a knife-wielding maniac at this instant
Either P or Q

OK, now if P is true, the DI is true, but Q's truth value is unknown, hereafter
Q(u). If !P, the DI could still be true, but since Q is still unknown, we have
to test Q, Q(t). We've all agreed to this, because we know we can have a false
disjunction. So this is what happens with a perfectly normal disjunction in
these universes. In water, negating either disjunct affects the other, in
Socrates, nothing really happens, because these are two totally unrelated
disjuncts, one or both or neither could be true.

OK, now let's throw some contradiction into our universes. So now we have P and
!P. It is my understanding that if we have P and !P at the same time, we also
have whatever Q is for P and !P at the same time. You should be able to see
where this is going, but I'll spell it out to be clear. For Water, the DI is
yet another contradiction, because the water is both frozen and not frozen, the
temperature must be both below and above freezing. That's a problem, though I
should add that it doesn't really "prove Q", it's just yet another
contradiction.

Things get more interesting when we get to Socrates. P, so Q(u), but !P, so
also Q(t). But recall, Q(t) is just a special case of Q(u), where now we have
to care about Q's truth in order to know whether the DI is true or not. That's
why I don't think a contradiction can prove any Q true. Without a
contradiction, in either case I know nothing about Q, unlike Water, because
there is no connection between P and Q whatsoever. And we agree that the DI of
Socrates can be entirely false. Introducing a contradiction doesn't seem to
affect that at all, again, since there's no connection between the disjuncts,
ala Water, I'm still left with no knowledge of Q whatsoever, unless I go get
it.

So I accept that !P can imply Q, that's basically xor. However, with or, where
either, both, or neither can be the case, I don't see where !P implies Q at
all, I assume "implies" here in logic means something like, "makes it
necessarily true". So I'm with Vanity, assuming he's actually adopted his post
as a position. The content matters, because it's how we can determine
relationships, the xor exists because of temperature relationships surrounding
water, while NO relationship exists between Socrates' godhood and my being
chased by a knife-wielding maniac.

If there's no necessary relationships between your disjunctions, ala Socrates,
then you can't, ordinarily, use one to prove or disprove the other, the way you
can with Water, that's why we can have a false DI. Introducing a contradiction
doesn't change that, there's still no relationship between them whatsoever, P
has nothing to do with Q, with or without contradiction. If you say that's not
the case, then that seems, as far as I can tell, to mean that !P always makes Q
true, contradiction or no, so you don't even need contradiction to create
logical absurdities at that point, disjunction introduction will do that for
you all by itself.

(Peccavimus/31665) All? Golly. I don't recall saying "all." If you got that out ...

Peccavimus@rss.iscabbs.com — Sat, 31 Dec 2011 11:15:00 -0600

All?  Golly.  I don't recall saying "all."  If you got that out of what I said,
I must have misspoke.

(Steppenwolf/31664) I completely agree, Vanity: I don't see what's so interesting ab...

Steppenwolf@rss.iscabbs.com — Sat, 31 Dec 2011 11:09:00 -0600

I completely agree, Vanity: I don't see what's so interesting about these
artifical disjunctions, and what useful conclusions they lead to. Sorry if I
wasn't clear.

I also am fairly skeptical that introducing a disjunction based on the truth of
only one of the propositions is all that useful in computer programming,
either.

(Vanity/31663) As long as we're on logic, maybe somebody can explain the differ...

Vanity@rss.iscabbs.com — Sat, 31 Dec 2011 11:03:00 -0600

   As long as we're on logic, maybe somebody can explain the difference between
Bramantip and Bokardo to me. :)
   (Despite the smiley, not a joke...)

(Peccavimus/31662) Well, it leads to the conclusion that contradiction is logically...

Peccavimus@rss.iscabbs.com — Sat, 31 Dec 2011 10:59:00 -0600

Well, it leads to the conclusion that contradiction is logically impossible,
which is what started this whole tohubohu in the first place.

(Vanity/31661) Isn't there a difference, though, between human and computer use...

Vanity@rss.iscabbs.com — Sat, 31 Dec 2011 10:55:00 -0600

   Isn't there a difference, though, between human and computer uses of logic?
Computers are slaves, tasked with doing things: so logic is used to force a
computer down a certain pathway of actions.  But human beings are (supposedly)
free, and are usually expected to use logic to reason out a conclusion, and
I'm having a hard time seeing what conclusion an artificial disjunction could
lead to.

(Peccavimus/31660) Ahh, but now you're talking about content rather than structur...

Peccavimus@rss.iscabbs.com — Sat, 31 Dec 2011 10:55:00 -0600

Ahh, but now you're talking about *content* rather than structure.

Whoah, is that where the problem lies?

(Vanity/31659) Um... your ideas of 'rewarding' may be different from other peop...

Vanity@rss.iscabbs.com — Sat, 31 Dec 2011 10:51:00 -0600

   Um... your ideas of 'rewarding' may be different from other people's. 
"Either birds have feathers, or George Washington ate pizza" may be a *true*
statement, but it's not a terribly *interesting* one, except as a demonstration
that language could use an international convention protecting it from torture.

(Peccavimus/31658) Not a particularly rewarding move, unless you're a computer prog...

Peccavimus@rss.iscabbs.com — Sat, 31 Dec 2011 10:52:00 -0600

Not a particularly rewarding move, unless you're a computer programmer . . .

(Steppenwolf/31657) Why would the two terms have something to do with each other? I ...

Steppenwolf@rss.iscabbs.com — Sat, 31 Dec 2011 10:48:00 -0600

Why would the two terms have something to do with each other? I mean, it seems
like it would make sense. But it certainly follows from "The sky is blue" that
it's true "either the sky is blue, or I am the eggman".

I don't think it's a particularly rewarding move, though.

(John Public/31656) Vanity> They don't have to, no. But it certainly makes the logic...

John Public@rss.iscabbs.com — Sat, 31 Dec 2011 10:23:00 -0600

Vanity> They don't have to, no. But it certainly makes the logic more obvious!

(Vanity/31655) Shouldn't the two terms in the disjunction have something to do ...

Vanity@rss.iscabbs.com — Sat, 31 Dec 2011 10:15:00 -0600

   Shouldn't the two terms in the disjunction have something to do with each
other?  Like "Either the sky is black, or the sky is blue"?  "Either Sally is
pregnant, or Sally is not pregnant?"

(John Public/31654) I think I see two problems here. The first problem is the confus...

John Public@rss.iscabbs.com — Sat, 31 Dec 2011 09:45:00 -0600

I think I see two problems here. The first problem is the confusion between a
proposition and the truth value of that proposition.  "P or Q" is a
proposition about two other propositions, P and Q.  It is not a proposition
about itself! In other words, "P or Q" does not claim that "P or Q" is always
true, irrespective of whatever P or Q happen to be. "P or Q" is a proposition
just like P and just like Q ... it may be true, it may not be, depending upon
whatever premise you'd like to establish. So yes, of course you must
"reevaluate" the proposition if you change the universe.

The second problem is between a premise and a conclusion. "Socrates is a man"
is a premise. You can't change a premise. You just have to create a new
universe and declare new premises.  If you want to consider a new universe
where Socrates is not a man, that's fine. But it has no bearing on the other
universe where Socrates was declared a man.

(Peccavimus/31653) Yes, we can have a disjunction that is of false truth value.

Peccavimus@rss.iscabbs.com — Sat, 31 Dec 2011 09:49:00 -0600

Yes, we can have a disjunction that is of false truth value.

1)  Either Socrates is a God, or Herman Cain is President = 0

Because neitehr 1a) Socrates is a God or 1b) Herman Cain is President is true.

However:

2)  Either Socrates is a God, or Barack Obama is President = 1

Because even though 2a is false, 2b is true, ergo 2 is true.

The problem comes in when you create a true disjunction, then simultaneously
affirm the truth and falsity of one of its two parts.

3)  Either Socrates is a God, or Barack Obama is President = 1
4)  Barack Obama is president = 1
5)  Barack Obama is not president -- if this is made to also =1, to be true,
then
6)  Socrates is not a god = 1
AND
AT THE SAME TIME
7)  Socrates is a god = 1

Which is incoherent, therefore logical contradiction cannot exist at the same
time as logic.

(Steppenwolf/31652) Terminology point that may be important: we can have a false dis...

Steppenwolf@rss.iscabbs.com — Sat, 31 Dec 2011 09:14:00 -0600

Terminology point that may be important: we can have a false disjunction.
However, as long as one of the premises is true, in classical logic we can
always introduce a disjunction and know it's true as long as one of its
components is that premise.

This is close to the point where _I_ object, but mine is quite different from
Gwynn's. :)

(Gwynn/31651) OK, so Pecc agrees that we can have a false DI, i.e. if both dis...

Gwynn@rss.iscabbs.com — Sat, 31 Dec 2011 09:09:00 -0600

OK, so Pecc agrees that we can have a false DI, i.e. if both disjuncts are
false, the DI is false, which means we have to evaluate both disjuncts. So JL,
you're saying that if I find out Socrates is a man, I'd better go feed my
horse? That seems pretty damn counterintuitive.

(Peccavimus/31650) JL's quibble aside, yes, that's correct. We can judge the truth...

Peccavimus@rss.iscabbs.com — Sat, 31 Dec 2011 05:12:00 -0600

JL's quibble aside, yes, that's correct.  We can judge the truth value of
Either P or Q as true because P is true.

You're also correct in that whether or not Q is true, we can judge Either P or
Q to be true.

(Assuming, of coure, that it's an inclusive or and not the exclusive xor, in
which case P's being true would automatically make Q false)

A huge swath of the functionality of computers is based on this logical
structure.

(JL/31649) I'll stop you there.

JL@rss.iscabbs.com — Sat, 31 Dec 2011 01:24:00 -0600

I'll stop you there.

"Either P or Q" is not true because of P, it's true because you say it's true.
If you're judging the truth of "Either P or Q" based on P and Q themselves,
then "Either P or Q" is a conclusion, not a premise.

(Gwynn/31648) Pecc:

Gwynn@rss.iscabbs.com — Fri, 30 Dec 2011 21:55:00 -0600

Pecc:

Let's see if I can take this step by step, because I don't think it's so much
that I don't understand something, though I don't know the mechanism of your
argument, i.e. what in logic makes it work, an axiom, whatever. I think it's
rather that I'm objecting to something, hence my suggesting that I've stumbled
on the reason(s) for a couple different logics. That having been said, here we
go. I'll take each thing in turn, one post at a time, waiting for a response,
and we'll see where it all breaks down. Take as a given that I know "either P
or Q" means "either P is true or Q is true or both are true".

P: Socrates is a man
Q: I own a horse
Either P or Q (true because P)

Now we know the DI is true, but we know nothing of Q's truth value.

(JL/31647) I admit, I don't really understand either where the confusion is...

JL@rss.iscabbs.com — Fri, 30 Dec 2011 15:47:00 -0600

I admit, I don't really understand either where the confusion is.

If you accept that "If P then Q" is true, and you accept that P is true, but
you don't believe that Q is true, then that's a contradiction. No matter what P
and Q are. It doesn't even matter.

Similarly, if you accept "Either P or Q" as true, and accept "Not P" as true,
then you must accept "Q" as true.

(Peccavimus/31646) I didn't mean that to be snotty, you know. I just meant, I don'...

Peccavimus@rss.iscabbs.com — Fri, 30 Dec 2011 15:31:00 -0600

I didn't mean that to be snotty, you know.  I just meant, I don't understand
what part of it you don't understand.  If you just reject the possibility of
logical disjunction, I guess that's not a lack of understanding, although I
find the arguments against logical disjunction unconvincing myself.

(Peccavimus/31645) ~P or Q only always means Q is true if you simultaneously affirm...

Peccavimus@rss.iscabbs.com — Fri, 30 Dec 2011 15:22:00 -0600

~P or Q only always means Q is true if you simultaneously affirm both P and ~P
to be true.  If *both* are true, the disjunct can prove anything you choose to
put in Q.

I don't know why you don't understand this.

(Gwynn/31644) Jl:

Gwynn@rss.iscabbs.com — Fri, 30 Dec 2011 15:07:00 -0600

Jl:

But again, we can have a false disjunction. I've posted the example in here
fifty five million times, so I won't do it again. Saying that a disjunction is
true, i.e. yields true output, only if at least one of its disjuncts is true,
pretty much means we're concerned with the content of its disjuncts. If not,
there's no problem with a contradiction, because "either P or Q" is just a true
statement, a true relationship, everywhere and always, then "either ~P or Q"
always means Q is true, which is exactly the supposed issue with a
contradiction, we can prove any Q true.

(JL/31643) > So doesn't that depend on the content?

JL@rss.iscabbs.com — Fri, 30 Dec 2011 12:34:00 -0600

> So doesn't that depend on the content?

No. Logic is independent of the truth of the statements.

Logic isn't meant to determine the truthiness of the statements, but whether
the conclusions are valid based on previous truths.

If you state that "Either P or Q", then you are stating that it's true, no
matter what P or Q are. If you _DON'T_ actually accept it as true, and try to
base conclusions on it, then what's the point?

(Peccavimus/31642) The contradiction is a contradiction because both P and !P are t...

Peccavimus@rss.iscabbs.com — Wed, 28 Dec 2011 10:58:00 -0600

The contradiction is a contradiction because both P and !P are true at the same
time.  P, then later !P isn't a contradiction.

I don't have a car today, but tomorrow I get a car isn't a contradiction.

The DI is established as true because it *MUST BE* true because P is still true
*WHILE* !P is true.  So at the same time, P and !P, whichi s logically
incoherent and leads to the principle of explosion.

(DesCartes/31641) The two have exactly the same truth values. They are false exact...

DesCartes@rss.iscabbs.com — Wed, 28 Dec 2011 10:56:00 -0600

The two have exactly the same truth values. They are false exactly when P is
true and Q is false.

(Steppenwolf/31600) Doesn't disjunction introduction rely on the idea that a contrad...

Steppenwolf@rss.iscabbs.com — Tue, 20 Dec 2011 16:52:00 -0600

Doesn't disjunction introduction rely on the idea that a contradiction can't
exist? Why not put it the other way: since P and not-P can both be true,
disjunction introduction must not be a valid argument.

(Gwynn/31576) Pecc:

Gwynn@rss.iscabbs.com — Mon, 19 Dec 2011 16:23:00 -0600

Pecc:

I don't see it. Consider:

P1: I own a car
S1: It is true that either I own a car or I am President of the US.

OK, good, I do own a car, so that's true.

P2: I do not own a car
S2: It is true that either I own a car or I am President of the US.

I do not own a car, but nothing from my lack of car ownership necessitates that
I actually be the President of the US, which I am in fact not. Have your P and
!P all you like, I don't think it follows that "it is true that either P or X"
necessitates if !P then X.

(Steppenwolf/31575) From a pragmatic point of view, where we're not really trying to...

Steppenwolf@rss.iscabbs.com — Mon, 19 Dec 2011 15:35:00 -0600

From a pragmatic point of view, where we're not really trying to come up with
the perfect set of axioms, it's not as big a problem. That is, as long as we
don't actually use the contradictory theorem in our derivations, all our other
syllogisms may be valid.

My problem is more that they signify a dead end, knowledge-wise. Once you've
hit a contradiction, you're stuck--there's no more knowledge to be derived. You
can't learn anything from a contradiction.

(Peccavimus/31574) It doesn't matter what the contradiction is, Gwynn. If I admit ...

Peccavimus@rss.iscabbs.com — Mon, 19 Dec 2011 14:36:00 -0600

It doesn't matter what the contradiction is, Gwynn.  If I admit a contradiction
into logic, I can construct a perfectly good syllogism showing that any
proposition I like is true, using that contradiction.  The color of lemons
doens't have to have anything to do with santa clause.

A better example is mathematical.  If I decide 2 = 2 and 2 != 2, then I can
prove anything I like.

(Gwynn/31573) OK, Wikipedia helps, a bit. From the article on principle of exp...

Gwynn@rss.iscabbs.com — Mon, 19 Dec 2011 14:12:00 -0600

OK, Wikipedia helps, a bit. From the article on principle of explosion:

An informal statement of the argument for explosion is this: Consider two
inconsistent statements, "All lemons are yellow" and "All lemons are not
yellow",
and suppose for the sake of argument that both are true. We can then prove
anything, for instance that Santa Claus exists: Since the statement that "All
lemons are yellow and all lemons are not yellow" is true, we can infer that all
lemons are yellow. And from this we can infer that the statement "Either
all lemons are yellow or Santa Claus exists" is true (one or the other has to
be true for this statement to be true, and we just showed that it is true
that all lemons are yellow, so this expanded statement is true). And since
either all lemons are yellow or Santa Claus exists, and since all lemons are
not yellow, (this was our first premise), it must be true that Santa Claus
exists.

I question the "either all lemons are yellow or Santa Claus exists" statement.
I don't see why I have to infer anything whatsoever about that statement.
"Either plastic is a human being or I own a dead antelope". Neither of those
things are actually true, and I also fail to see what one has to do with the
other. I invoke Step.'s idea of an effective field, the yellowness of lemons,
or lack thereof, has nothing whatsoever to do with the existence of Santa
Claus. After a bunch of examples using logic symbols I don't understand, and
which might not even be read properly by my screen reader, Wikipedia says:

Proof-theoretic
 paraconsistent logics usually deny the validity of one of the steps necessary
for deriving an explosion, typically including
disjunctive syllogism,
disjunction introduction,
and
reductio ad absurdum.

I don't know what that means, and I don't even know if my objection corresponds
with one of those denials, but there you go anyway.,

(Peccavimus/31572) That is pretty much the point I'm making. Although I'm somewhat...

Peccavimus@rss.iscabbs.com — Mon, 19 Dec 2011 12:51:00 -0600

That is pretty much the point I'm making.  Although I'm somewhat less
pesimistic about perceiving the underlying reality.

(JL/31571) Hell, I'm an amateur thinker! Every time I open a new door of ...

JL@rss.iscabbs.com — Mon, 19 Dec 2011 12:39:00 -0600

Hell, I'm an amateur *thinker*! Every time I open a new door of learning, I'm
again amazed at how much there is that I don't know. And didn't even know I
didn't know!

Pecc> I'm not sure I totally understand the point you are making, but I do
think there is some underlying structure that we cannot perceive, and "matter"
is just an expression of it. But it is out of our reach, so matter is the best
we can get.

IMO, our communication is yet another expression of the underlying structure.
We are just the vessels for the transfer of something that we don't
understand. We recognize communication because we see it at a granular level.

I'm certain that crickets - which seem to communicate themselves - cannot even
recognize our communication as existing, even though it is all around them.

Similarly, I think there is communication happening all around *us* that we
cannot perceive, because it is outside of our perception. Perhaps too big, or
too stretched out in time.

(Side note: We exist for such small pockets of time, I wonder what reality
would look like if we could observe it spend up 1 billion times. What new
patterns would we see? What objects and motion would emerge? Surely our
existence wouldn't even be noticed at this macro level. Surely forms exist that
change too slowly for us to even notice, but nevertheless they are moving and
changing and exchanging information as well. In our world, photons move fast
and carry information. Maybe in this sped-up view of reality, *we* are the
super fast particles, transferring information. Or something).

On a somewhat related note, I saw this today:

   http://www.bouletcorp.com/blog/hidden/quantum-pixel/

It seems relevant to our discussions here, somehow.

(Peccavimus/31570) (::raises hand:: Amateur philosopher here too. I imagine most p...

Peccavimus@rss.iscabbs.com — Mon, 19 Dec 2011 12:35:00 -0600

(::raises hand:: Amateur philosopher here too.  I imagine most philosophers
would roll their eyes at *all* of us, but screw those guys, except for Mark,
he's cool))

(Steppenwolf/31569) I don't think there's any necessary contradiction in saying that...

Steppenwolf@rss.iscabbs.com — Mon, 19 Dec 2011 12:31:00 -0600

I don't think there's any necessary contradiction in saying that we can refer
to someone simultaneously as a whole and as parts. That doesn't mean that we
are a man and not a man, but that "man" is so defined as to include those
component parts.

I'm a total philosophy dilettante too, so who knows what experienced
philosophers think the score is here. :)

To explain the cachet thing a little, though, it just seems to me that you
want, for some reason, to find contradictions. Not that they happen to be
there, but that you find a positive value in these existing. And I don't really
get why (if that's even true).

(Peccavimus/31568) I'm not talking about labels. I'm talking about, do you believe...

Peccavimus@rss.iscabbs.com — Mon, 19 Dec 2011 12:22:00 -0600

I'm not talking about labels.  I'm talking about, do you believe that matter is
the substance (the thing underlying) the universe, or are some sort of
non-material things the substance.  It can't be both: to believe both is to
engage in a contradiction, which I know you won't want to do.

Communication>  Early, you said that definitions break down because we can't
encode our experiences into information perfectly (I'm paraphrasing to produce
a statement of what you said that I agree with -- if you didn't mean that, let
me know).  I agree with that:  We can't encode our experiences perfectly. 
Moreover, every system of transfer of information introduces noise, randomness
that inteferes with the message.  Finally, we can never know that we have
accurately and correctly decoded something without recourse to another act of
communication, subject to all the same uncertaintities.

Logically speaking, therefore, communication should at the very least be
highly, highly unlikely.  And yet it's not: it happens constantly, as you point
out, even among inanimate objects (again, that's a definition of communication
I heartily agree with).  So how can that be?

One explanation, and the one I prefer, is that we are not simply taking
experiences, encoding them imperfectly, and transmitting them willy-nilly. 
Instead, there are a set of concepts underlying communication that constrain it
such a way to make it possible; there are, in other words, givens of existence.

As you point out, communication occurs even in inanimate objects, and would
occur whether we observe it or not.  These givens must therefore be outside of
the human mind.

Yet they cannot be the feature of any given arrangment of matter, because they
seem to happen across and cut through all possible arrangments of the material
elements of communication.  Whether my nervous system causes my fingers to
twitch to make marks that your nervous system can read, or whether a ficus
releases a chemical that attracts bees -- some given seems to govern these acts
of communication so that, mostly, we communicate despite the very clunky
methods we have devised.  (Oh, and of course, if we were face to face we could
vibrate air molecules by flapping our meat at each other, and if you were deaf
perhaps we could communicate with ASL . . . in any configuration of physical
mechanisms, we communicate ideas)

This is one argument of about two dozen that convince me of the truth of
rational realism, or as it used to be called, Platonism.

(JL/31567) Gwynn> I don't really know how to label my thoughts, and of cour...

JL@rss.iscabbs.com — Mon, 19 Dec 2011 11:26:00 -0600

Gwynn> I don't really know how to label my thoughts, and of course they are
always evolving.

I think that science and rational, deductive reasoning is our best tool to
understand the world around us, because based on everything we see, our
universe is a logical place. It follows rules. The rules seem really, really
consistent. And the more we understand the rules, the "simpler" they seem to
get. Not that math, per se, but the reduction in the number of rules and
functions running the thing. We find that complexity emerges from simple
underlying rules, and that's elegant.

I believe that science will continue to evolve to a more "macro" understanding
of reality, and find that it's much more liquid than the cold and static
system we often think of it as.

When I think of trees communicating with the earth, I'm trying to recognize a
pattern of information exchange that really is no different than humans
communicating, or birds flying together in a flock. It's just at a different
scale, almost out of our perceptual reach.

I like to dissect things we take for granted, like information. Why do we
believe that information flow between humans is any different than the
information flow that happens in a forest that a human has never seen? Or any
different than what is happening in our brains?

Why do we think of ourselves as individuals? If we could view our universe from
the outside, would we be just another organic process that has emerged at a
certain resolution of the fractal reality, which mirrors the same structure
seen at higher and lower levels? Aren't we just another variation of the same
underlying hum of reality?

I don't have the answers, but the questions intrigue me. I'm always trying to
see the universe and reality from as outside a perspective as possible. To step
back and try to see the god in the machine, and better appreciate this ride
we're on.

btw, I use a lot of descriptive words. I don't know if they mean anything to
anyone but me, but I try to convey the kind of waves of thought that go on in
my head that strict science doesn't really lend itself to.

There is a magestic beauty to reality. It's elegant, simple, self-referential,
recursive, and one big feedback loop. Science is our best way to try to
understand it. But science is not "it".


Oh, and on that thought... I really need to finish Godel, Escher, & Bach, which
I never quite made it through :)

(Gwynn/31566) You know Jl, it's funny. You seem really against religion. But y...

Gwynn@rss.iscabbs.com — Mon, 19 Dec 2011 10:56:00 -0600

You know Jl, it's funny. You seem really against religion. But you take really
animist-looking positions. I'm fine with, let's see, fractal reality, more ore
less, rivers having memory, rocks having memory, e.g. erosion paths, trees
communicating with the earth ... If you're ever willing to write something up
about that, I'd sure as hell be interested to read it. When you talk about
rationality, it's like it's all science, all the way, bust out the test tubes
and the measuring equipment, and if you can't do that, then it doesn't count.
But then you start talking about trees communicating with the earth right along
with that, and I'm kind of going, yeah, exactly, so what in the hell are we
disagreeing about, precisely?

On the one hand you articulate an almost positivist position, assuming I
remember my positivism correctly. It's all science and repeatability and
measurement and logic Etc., and some day, we'll figure out everything about the
world, i.e. we're really capable of doing that, whether we actually manage it
or not. But then you start talking about fractal reality, sounds very Daoist,
rivers and trees, very animist, and then my head hurts.

The way you talk about rationality very much fits in with the way a lot of
people seem to conceptualize science, as a reductive illiminative materialism,
i.e. it's all material and no room for anything else. I suspect that's why
Pecc. levelled the charge at you that he did. That wasn't always the
understanding of science by any means, I believe I've mentioned Newton and
Kepler already.

Step:

just one quick thing, I'm not trying to lend anything a "certain cachet", I'm
not even sure what that really means. Sure, my approach is definitional, but as
I think I've mentioned already, I'm pretty sympathetic to pragmatism's claim
that this is all we've got anyway. But it does seem to me that I am both a man,
I can type on a keyboard, we can have this discussion, and not a man, I'm a
bunch of forces, at the same time.

As I've said though, if it's not a paradox, it's pretty damn weird. So I mean,
I'm admitting here that it might not be a paradox, i.e. I am man and !man
simultaneously, but simply my flawed understanding that makes it seem that way.
I'll also admit, this argument had to have been discussed even back in the
ancient world, though I don't know where. But really, you could make it in lots
of ways, how can I be a man and combinations of the four elements, how can I be
a man and composed of inanimate indivisible bits (atoms), Etc. So I mean, it
surely occurred to Aristotle or somebody to address it.

All I can say is that these are my own thoughts, and my own struggle for
understanding, and should anybody have any good reading on any of it, I'll
happily go track it down. I make no pretensions to devistating arguments, or
even sensible ones. I'll freely admit that one good book on the history of
philosophy could make me go, "oh, so somebody proposed that same thing 700
years ago and got shot down", though I doubt it because I'm fairly sure some of
my concerns echo debates that are still with us today. But I mean, I think I'm
making meaningful points, but maybe somebody who really studies philosophy
would be rolling their eyes with the equivalent of, "yeah, when you wanna quit
getting high at three in the morning and thinking you're all profound and come
study some real philosophy, let me know, OK?" I'd hope I'm not that inept, of
course, but one never really knows.

(JL/31565) Pecc> I don't like labels. I am neither a materialist nor a plat...

JL@rss.iscabbs.com — Mon, 19 Dec 2011 10:21:00 -0600

Pecc> I don't like labels. I am neither a materialist nor a platonist. I find
such labeling to be restrictive to free thought. Nobody puts JL in a corner.

>do you believe that communication is possible?

Umm, yes? You haven't really defined communication. To me it means transfer of
information, which may be a bit broader than you prefer. As such, I believe
that trees communicate with the earth. For example.

(Peccavimus/31564) I was under the impresion that you were a materialist, JL. But ...

Peccavimus@rss.iscabbs.com — Mon, 19 Dec 2011 05:18:00 -0600

I was under the impresion that you were a materialist, JL.  But now you're
apparently a Platonist.

by the way, I wans't being a jerk: I was really wondering, do you believe that
communication is possible?

(Giraffe/31563) I've demonstrated to my students that if you allow one error to ...

Giraffe@rss.iscabbs.com — Mon, 19 Dec 2011 03:09:00 -0600

I've demonstrated to my students that if you allow one error to creep into a
proof, anything can be proven. Once you allow a single dvision-by-zero for
example (which can happen inadvertantly pretty easily) to take place, you can
end up proving that any number or variable or expression is equal to anything
you want. Is that a demonstration of "explosion"?

(Steppenwolf/31562) Gwynn:

Steppenwolf@rss.iscabbs.com — Mon, 19 Dec 2011 01:53:00 -0600

Gwynn:

You said:
"If it's OUR language, and OUR definitions, then can't
we just always just rearrange them to remove the problem? That kind of makes it
a lot less "OMG contradictions will break things!", and a lot more of a
language game, if I understand Wittgenstein correctly, I probably don't. That
makes lack of contradiction less an axiom and more of a triviality then."

Well, to a point. Most axioms look trivial until you assume their opposite and
see what you get. :) But I'd suggest that deductive logic's power is that it
can lead you to unexpected conclusions based on your initial axioms, and
allowing a contradiction in prevents all that... within the scope of your
initial axioms, which is why any attempt to prove JL's statuehood based on the
swan and color axioms is less than convincing.

The best example of this is E= mc^2, which wasn't really conceived of until it
dropped naturally out of the formulas for special relativity. If there were a
true contradiction in there, then Einstein could have derived anything at all,
and it all would have been meaningless.


You said:

"If that's not a contradiction, it's pretty damn weird, anyway.
From my perspective, saying it is or isn't a contradiction is potayto,
potahto." [referring to, essentially, effective field theory--that at one level
we're energy,and another we're grouped into people]

You see, you completely lose me here, because there's no principle of explosion
for "pretty damn weird." It's as if calling such things a contradiction,
instead of an unusual juxtaposition, provides it a certain sort of cachet. But
you can't find anything there that you can believably, knowing everything we
know about physics, reduce to a P and~P contradiction.

Where I've gotten the most from your posts on this thread is the idea that in
liminal cases (like JL cutting the foot off a swan), our ability to define
starts to break down, and our ability to successfully separate concepts doesn't
work anymore. That strikes me as a very human failing--it's based on our own
ability to perceive. In that sense, especially if "truth" is to some extent a
human creation, there may be more than one truth, and they might be
contradictory, since our language can only contain part of the truth with each
model. But to me, that's not the sort of contradiction that really tears apart
deductive logic, because it represents a problem with our axioms, and we're
probably not getting any information out of it anyway.

To go back to science, you can assert general relativity, and learn a ton about
the universe. You can assert QM, and learn a ton about the universe. But when
you try to do both at the same time, you get such a contradiction that you
can't learn much. So scientists have to figure out a way to unify the two.

THinking as I type again, I suppose this would be a way to find a true
contradiction in the world! Imagine, somehow, that some feature of the universe
meant that there was no universal law: GR was right in its own way, QM was
right in its own way, and NO WHERE does it break down. It's almost an
inconceivable thought; the universe being founded on two contradictory laws.
But it's so counter to the way we discover objective fact that of course
physicists are trying to find a unifying theory instead.

More likely, it seems to me, there is such a law, but it's still possible that
this law is beyond human determination. In that case, there would be a
contradiction in our ability to define truth, but not in reality itself. I
suspect this is the actual situation of the world; truth is beyond our
definition to ever consistently and without contradiction define. But when it
comes to objective fact, assuming no contradictions is still the best way to go
about learning something new.

(Gwynn/31561) I'm still trying to track down something on explosion, which see...

Gwynn@rss.iscabbs.com — Sun, 18 Dec 2011 20:10:00 -0600

I'm still trying to track down something on explosion, which seems to be the
big issue here. the SEP's article on the liar paradox mentions it, but doesn't
explain it, I'm not even sure the article on contradiction even mentions it.
Right now I chuck myself in with the dialetheists, but I admit that's partially
because I just don't understand explosion. It doesn't seem obvious to me at all
that if I accept P and !P I can thus prove Q, R, S, !Q, !R, !S, Etc. Thus, I'm
with the dialetheists, I reject explosion. I'll probably shut up about it all
though, until I find out more about it. I also think I've found a meaningful
paradox, but I need to look into it more to see that it's nontrivial.

(JL/31560) I'm lacking time to read all posts in detail, but I'll throw out...

JL@rss.iscabbs.com — Sun, 18 Dec 2011 18:49:00 -0600

I'm lacking time to read all posts in detail, but I'll throw out two comments:

1. The book "Is God A Mathemetician?" explores the familiar question of whether
math was discovered or invented. It was a great read. I come down on the side
of 'discovered', but I don't think our math is universal. It's only universal
from our perspective in the fractal universe.

2. I'm not sure what to make of the idea, nor have I read much about it (and
I'm sure it's been written about plenty), but I think a lot of questions being
raised boil down to recognition of higher-level forms.

By that, I mean the idea that we can recognize a collection of atoms as a
specific formation, and give it the label of "swan". To a truly outside
observer, would they even be able to distinguish a swan from the other atoms
around it? What makes it special? Why does it get a name?

We find forms in things because of our perspective. We give labels to different
forms, even though they are never quite perfect, which is why I sometimes have
an issue with definitions, because they are ALWAYS fuzzy.

Even a "swan" - if I cut off a foot, is it still a swan? So, is the foot not an
essential part of swan-ness? How much of the swan can I cut away before it's
not a swan anymore? Where is the "swan-ness" held, exactly?

It's not! There is no magic swan place. We find this form and label it, because
our granular view of reality makes it seem to be a 'thing' to us.

Other forms are not quite so clear. And surely there are even higher-level
forms that we don't even recognize, because our perspective prohibits it.

But, much of our confusion and debate over definitions and contradictions and
comparisons seems to boil down to defining forms, for which there is no
perfect answer. Because when you keep breaking it down, I'm not sure we can
really define much of anything unless we can ignore some of the fuzziness and
just accept the higher-level forms without worrying about the specifics.

(Gwark/31559) Steppenwolf> I'm curious about why you would think he probably ...

Gwark@rss.iscabbs.com — Sun, 18 Dec 2011 10:16:00 -0600

Steppenwolf>  I'm curious about why you would think he probably evaluated his
experience correctly and why you (presumably) consider the truth of his belief
to be implausible.

To what extent does our culture and expectations impact our experience?  Do our
cultural/philosophical filters do the equivalent of seeing under a sodium vapor
light where we are unable to differentiate yellow and white?  Perhaps with our
rational/skeptic western science approach, we are unable to distinguish between
coincidence and synchronicity, even if there is a difference that exists in
reality.

I also wonder if there is something even more fundamental that can
happen, perhaps taking on a certain view will prevent some things from
being observed at all.  I guess this would be the idea that faith/belief can
actually make a difference in what happens.  This is something that has been
observed for individuals in certain circumstances - I have read about a study
where people told they were not keeping up with their best time (even though
they were) ended up beating their best prior times.  Of course he jump from
individual psychology to one's beliefs making a difference in a broader way
is a significant one.  Still it's an idea that seems possible to me, though
I'm not sure how could be tested.

Anyway, one of the stories that this guy told me was about being at a tree
planting ceremony with a man from an indigenous tradition.  The indigenous man
was doing the ceremnoy, saying the prayers and such, and as he was finishing
up a hawk, (or maybe an eagle, I don't remember specifically - but it was
something that wasn't especially common for the location) flewe over, circled
and then flew off.  Given the timing and context, the guy I know was kind of
excited about it and later asked the indigenous man about it, since it seemed
pretty amazing that it would happen that way.  The indigenous man told him
that in his culture/tradition those sort of happenings were the norm.  When
synchronicities (like that one with the hawk/eagle) were not happening, you
knew something was wrong - so he had noticed the bird, but was not surprised
by it.

(Gwynn/31558) Let me try to put this problem in the opposite way. I agree ther...

Gwynn@rss.iscabbs.com — Sun, 18 Dec 2011 09:07:00 -0600

Let me try to put this problem in the opposite way. I agree there are no
"natural contradictions". That is, I think nature is however it turns out to
be. If it turns out that it happens to be contradictory in our
understanding/language, well there you go. That's why it doesn't really concern
me if WPD turns out to be a real contradiction, and not simply a
misunderstanding/misspecification of definition. If WPD, or something like it,
truly drives us to a contradiction, so much the worse for us.

But it also seems trivial from both sides then. The real issue isn't something
in the world, it's how we're talking about it. I say, a thing can be both a man
and not a man at the same time, because I'm somebody you can interact with and
such, the typical understanding of "a man", but I'm also a bunch of forces,
which you can't talk to at all. You want to say, ah, but that's different
contexts. I say, yes, but they hold at the exact same time. We're just arguing
over who's definitions are right. You want to say, in order to understand
forces, you're dealign with the subatomic, a different thing from interacting
with you as a person.

I say, remember they're active at the same time, and ala Zeno's paradoxes, I'm
nothing but forces and such, if we understand science. So how in the hell can
you talk to energy? Can you go out for a beer with magnetism and the strong
nuclear force? If that's not a contradiction, it's pretty damn weird, anyway.
From my perspective, saying it is or isn't a contradiction is potayto, potahto.
If you admit that the LNC is in essence unprovable, and thus a form of faith,
and the rearranging of definitions really makes it look that way to me, then
fine, I have faith that there are contradictions/paradoxes.

(Gwynn/31557) Is that even possible? I think you asked this question of Vanity...

Gwynn@rss.iscabbs.com — Sun, 18 Dec 2011 07:58:00 -0600

Is that even possible? I think you asked this question of Vanity, or maybe
Vanity proposed it. Note, I'm not asking quite what you think. I think it's
impossible by definition. If it's OUR language, and OUR definitions, then can't
we just always just rearrange them to remove the problem? That kind of makes it
a lot less "OMG contradictions will break things!", and a lot more of a
language game, if I understand Wittgenstein correctly, I probably don't. That
makes lack of contradiction less an axiom and more of a triviality then.

(Steppenwolf/31556) Gwynn:

Steppenwolf@rss.iscabbs.com — Sun, 18 Dec 2011 07:31:00 -0600

Gwynn:

Sorry if I'm being confusing; I'm actually saying that I'm not at all sure
wave-particle duality is a contradiction. I've shifted a little on that in the
course of this discussion after thinking it through. Giraffe's position sums up
mine pretty well.

So, thinking about real belief and swans, I agree with this completely:
"That's why I said I don't think anybody would hold that belief about swans,
the
most likely counters would be, it's not a swan, or it's black by some other
process, e.g. the way flamingos are pink, but that's not inherrently a property
of the swan."

You see, that's why I say that no natural contradictions should be an axiom:
because we don't actually think that way! If we have a belief that leads us to
logical contradictions, and we can be convinced of that, we don't say, "Oh
well," we figure out where it's wrong, usually somewhere in our definitions.
Deductive logic is valuable because it's an incredibly useful tool for sorting
the ways we categorize the world.

In order for you to convince me that contradictions are anything more than us
having bad definitions, you would have to give me an example of a natural
phenomenon that literally can not be defined without leading to a
contradiction.

(Giraffe/31555) >You sort of agreed

Giraffe@rss.iscabbs.com — Sun, 18 Dec 2011 07:02:00 -0600

>You sort of agreed
>that wave particle duality was some sort of contradiction, and it seems that
>at least a lot of popular books on the subject, ones written by scientists to
>explain it to the rest of us, take that as some sort of paradox.

I don't know about popular science literature, but as a scientist who has spent
a great deal of time studying the mathematics and theory behind QM, I don't see
any logical contradictions. I see nature behaving at the micro-scale in ways
that we didn't expect from looking at nature at the macro-scale. But that's not
a contradiction, just a new (and hence strange) way of understanding nature.
Well, not even that new any longer. QM has been around for the better part of a
century now. If there were genuine contradictions, our theories would not be
able to provide sensible predictions, but they do, often to tremendously high
precision. The only contradictions are when people (either scientists or
non-scientists) make overly-broad statements, such as "light is a wave" or
"light is a particle."  Nature is more complex than that and so our statements
about nature need to be more nuanced. So I see those contradictions as being
purely a consequence of our language either being inadequate or used without
due care.

(Gwynn/31554) LOL! But Step., i still says you's wrong. Why? Because one thing...

Gwynn@rss.iscabbs.com — Sun, 18 Dec 2011 06:36:00 -0600

LOL! But Step., i still says you's wrong. Why? Because one thing that's been
happening in this discussion, and it's on both sides so I'm not accusing
anybody here, is that we haven't been dealing with thought in the real world.
Because people don't really think informal logic. Which is another reason I
find this whole conflicting beliefs thing to be an issue. It's like we've set
up an ideal form of thought, and then we're going, hey 99% of people don't
think like this, they're wrong, maybe even I'm wrong because I might hold some
conflicting beliefs too, but I'm trying to get rid of them.

That's why I said I don't think anybody would hold that belief about swans, the
most likely counters would be, it's not a swan, or it's black by some other
process, e.g. the way flamingos are pink, but that's not inherrently a property
of the swan. But, you want to say, we're dealing with philosophy, that doesn't
count! OK, but again let's tie this to the real world. I don't care how much
somebody tells you everything is white, I don't even care if you yourself
believe it because of your reasoning about swans. It's pretty demonstrable just
by staring at the world that not everything is white.

I'm also not sure it even matters. Let's take color. Every color is light waves
hitting your eyes. There IS NO color, as such. By which I mean to say, yeah,
everything's white, i.e. everything's just light. It's all the same basic thing
when you get right down to it. I'm not saying entirely of course, there are the
wavelengths and that's how we're perceiving it. But if the big problem is, hey
this is sort of all boiling down to one thing, we've already got that, in a
way.

Finally, I'm honestly not trying to assume contradiction. You sort of agreed
that wave particle duality was some sort of contradiction, and it seems that at
least a lot of popular books on the subject, ones written by scientists to
explain it to the rest of us, take that as some sort of paradox. So I guess I
was taking that as a given we could all agree on. And what I'm still trying to
figure out is, if matter really works that way, at that level, well, how am I
proving anything? How am I getting your mom's phone number, or proving that I'm
a woman, or that cheese can't exist, or that all swans are white, or ... I'll
try to find some stuff on explosion, since I think that's what I'm missing at
this point. But if we agree that WPD is in fact a genuine paradox, under the
Copenhagen interpretation I mean, then I'm still not seeing the issue, since
clearly they got work done back in the day, while holding to said
interpretation.

(Steppenwolf/31553) Gwynn:

Steppenwolf@rss.iscabbs.com — Sun, 18 Dec 2011 03:59:00 -0600

Gwynn:

Let's say that I overstated a bit and take a weaker version of my thesis: You
can't learn anything from a fact based on a contradiction. As long as you
accept a fact that is contradictory, you can get no more knowledge out of it,
because you can prove the converse as easily as the fact sought. That's what
the Liar's Paradox means: those sentences have no intrinsic meaning, because
you can't get any information out of them. That's fine for a linguistic field,
but really problematic for, well, science.

That is, if you have somehow defined waves and particles so that they're
contradictory (and you haven't clearly explained how that would be the case),
then you're not going to be able to say anything useful about their behavior.
So that's why contradictions are bad for knowledge.

BUt more interesting is the question of why I don't believe they exist, and
it's because I don't think you've articulated how a natural contradiction
_could_ exist. You've said to assume it, but that's not sufficient; in order
for there to be a contradiction, you need two terms that are so defined as to
be mutually exclusive. In the swan example, we've defined swans one way,
and then added a test case that breaks it. And as you can see from it, that
shows that our definitions are completely screwed--no useful information comes
from it, because you can't tell the useful stuff from the crap (i.e. the whole
world is white). Anything new you learn, you can't tell if it's true or not.

All that said, I feel obligated to post this comic on the same subject:

http://xkcd.com/704/

(Transcript follows):
Person 1: If you assume contradictory axioms, you can derive anything. It's
called the Principle of Explosion.

Person 2: _Anything?_ Lemme try.
*scribble scribble* Hey, you're right! I started with P and ~P, and derived
your mom's phone number!

Person 1: That's not how that works.

Person 2 (on phone): Mrs. Lenhart?

Person 1 (holding paper): Wait, this _is_ her number! How-

Person 2: Hi, I'm a friend of--why yes, I AM free tonight!

Person 1: MOM!

Person 2: No, box wine sounds lovely!

(Steppenwolf/31552) Gwark:

Steppenwolf@rss.iscabbs.com — Sun, 18 Dec 2011 03:39:00 -0600

Gwark:

That post is why I talk about rational processes, rather than rational beliefs.
If this person you're talking about was honestly trying to evaluate the
evidence and calling all the possibilities into question, I'd be hesitant to
say he was irrational, because weighing evidence is in the end a partly
intuitive affair anyway. So in my view he probably did it wrongly, but not
necessarily irrationally.

(Gwynn/31551) But see, I don't know that A is A tells us anything. I mean, it ...

Gwynn@rss.iscabbs.com — Sat, 17 Dec 2011 20:49:00 -0600

But see, I don't know that A is A tells us anything. I mean, it does, but I'm
not suggesting that things aren't themselves. What I mean is, take wave
particle duality. Step. prefers many worlds, because it gets rid of wave
particle duality, how I'm not quite sure, I think everything's waves in many
worlds. But suppose that's not right, and we do have real wave particle
duality.

Step. seems to feel that's a contradiction, but I'm saying, OK, so what? The
whatever it is doesn't act like a wave or a particle, but like both. A is A,
and A is some crazy thing we've never encountered before that acts like both a
wave and a particle. We already have things like dialetheism, which says that
by and large, the LNC holds, just not at the limits, i.e. there are places
where it can break down, e.g. the liar paradox within language. So wave
particle duality is a limit case in reality. I don't really see the issue.

Let me put it this way. I'm not REALLY trying to destroy deductive logic,
although I honestly think that would be really fun to try. I'm just trying to
figure out why saying, hey there could be actual contradictions, is sort of the
equivalent of a philosophical nuclear weapon. Because first if they existed, we
could prove anything. Then we figured out, nope, no we really couldn't, WP
duality is no threat to my testicles, I still get to keep 'em, woo! But then we
hit a snag, because well, they'd still totally devistate whatever they referred
to. So while WP duality was nice enough to leave me my man bits, it's being
really mean to our ability to understand whatever in the hell ultimately makes
up the man I still am.

So being the nice guy I am, I attempted to rescue our understanding of the
universe by saying, wait, hang on a sec, the liar paradox! That's in logic and
philosophy and language, three fields, and we can still totally understand
those and say meaningful stuff about them and all, right? There we somehow hit
a snag. Because everybody agrees, they're contradictions, they're paradoxes,
they're the real mind-bending deal. Except, apparently we can say meaningful
stuff about language and logic and philosophy, because they're special
contradictions that don't count.

And this is what makes me still think I'm dealing with faith, not axioms. Look
at Euclid's axioms, they define things, here's a line, here's a point, here's a
plane, Etc. Then you build on them. When we found out, oops, here's a case
where parallel lines don't meet, poof!, we got curved geometry. We learned
something new when Euclidian understanding got broken.

Well, the liar paradox breaks things. Nobody's contended that it's not a
contradiction. It's just some sort of special meaningless contradiction. OK, so
now not only do we have the destructive effects of contradictions limited to a
particular field, now the contradictions have to have special, though unknown
at least to me, characteristics in order to do their terrible terrible damage
to our minds, understanding, and deductive logic in general.

Come on, I thought these things were dangerous? We've gone from "OMG run, it'll
kill us all, run!", to "yeah you'll wanna put your clothes in a cedar chest or
something, or they'll totally get eaten by moths". I'm being hyperbolic of
course, hopefully to humorous effect. But my point should be obvious, the
danger of contradictions has had quite a defanging. So I'm still wondering if
we can't take that further, myself.

(Peccavimus/31550) I think something quite a bit like it is. Deductive logic as we...

Peccavimus@rss.iscabbs.com — Sat, 17 Dec 2011 20:42:00 -0600

I think something quite a bit like it is.  Deductive logic as we know it is a
function fo a human mind, but I think it is a reflection of a logic that exists
prior to any human mind (prior both in sense of time,a nd in sense of
substantialness, if I may coin a word).

(Gwynn/31549) Pecc:

Gwynn@rss.iscabbs.com — Sat, 17 Dec 2011 13:55:00 -0600

Pecc:

Are you saying deductive logic is a fundamental feature of the universe? I'm a
little clear. And yes, I know Rand bastardized the fuck out of Aristotle, heh.

(Gwark/31548) I'm curious about a belief which is often described by rationali...

Gwark@rss.iscabbs.com — Sat, 17 Dec 2011 08:40:00 -0600

I'm curious about a belief which is often described by rationalists as being
irrational, though as far as I can tell, the people who hold those beliefs
often do so because of direct experience suggesting they are true.

Consider the notion of synchornicity.  That is, events that would seem to be
unrelated and/or unlikely to occur just by chance that do occur together in a
meaningful manner.  I'm conversant with the argument (and the mathematics
behind it) that such things can be explained by random chance - in fact, what
would be most surprising is if they didn't happen at all.  I accept that
perspective and find it reasonably compelling.  On the other hand, I frequently
interact with people who have a different take on it.

In brief, with them, the approach/experience is the more you develop awareness
of, sensitivity to, and strong connections with the natural world (including
people) around you, the more synchronicity will come into your life.  It's not
entirely clear to me whether synchronicities are there all along and people
don't necessarily notice them, or whether the place that people get to when
they cultivate the awareness/sensitivity/connection makes synchronicities more
likely to occur.

In any case, one of the people I've talked to extensively has described his
coming to terms with synchronicity (something he was resistant to for a long
time).  He says his mentor (who had been working with him for years to
cultivate his awareness/sensitivity/connection to nature) had him journal all
the coincidences/synchronicities that were happening in/around his life and
asked him, "when the 99th coincidence becomes 100, will you still say it's
all just a coincicdence?"  At some point the evidence in his own life just
became too compelling to dismiss the hypothesis that synchronicities can
and do occur.  That said, he is careful to acknowledge that skeptics will
not find his experience compelling (nor should they, necessarily).  He puts it
out there as an example of a practical approach for people to try - and notes
that other who have tried it have had similar experiences.  I can't say I've
given it a full try to the point where I'm utterly convinced, but I've seen
glimpses, and have no good reason to doubt the experiences described to me, so
I also find this understanding reasonably compelling.

In the end, I am curious if people here would consider this belief irrational,
and if so, on what basis?  Is there a contradiction that needs to be worked
out (to put it in JL's terms)?  Wouldn't it be irrational to dismiss the
evidence of your own experience?

(Peccavimus/31547) 1. I'm not convinced that our systems of thought -- or at least...

Peccavimus@rss.iscabbs.com — Sat, 17 Dec 2011 08:14:00 -0600

1.  I'm not convinced that our systems of thought -- or at least, the existence
of our minds, which isn't the same thing -- is something we've invented.  I
think it's a function of the type of universe we live in, as much a part of
reality as the four fundamental laws of physics.  Perhaps more so, as I think
it's substantial to our physical reality.
2.  Deductive logic is built upon certain axioms, one of them being that A=A. 
I'm not quoting Rand there; I'm quoting Aristotle.  If we get rid of any of the
axioms, we end up with a system that isn't deductive logic anymore.  It might
be something else, something useful even, but it's not deductive logic.

(Gwynn/31546) Step:

Gwynn@rss.iscabbs.com — Sat, 17 Dec 2011 07:53:00 -0600

Step:

A couple things, first of all, OK, that's pure deductive logic. So you've used
it to prove something about color, but you've just said in an earlier post that
if we have say, a contradiction about the makeup of matter, that doesn't
necessarily mean it proves I'm a woman and not a man. So I still say, even
though "all swans are white, but a black swan exists", has implications beyond
swans, I am still in no way convinced you can use that one contradiction to
prove anything you choose.

This is also why I'll come back to the real world again, I'm weird like that.
We can't use a contradiction in matter, i.e. emptiness Vs. solidity, wave
particle duality, whatever, to demonstrate that I'm a woman, for a couple of
reasons. In the first place, as you've said, it's really not in the same domain
at all. In the second place, we can actually examine me and determine that I'm
not a woman. Maybe that's only by our current definitions, as I've said, but it
should be clear by now that this is fine with me. So I hold that your thesis
that if we have a contradiction, somewhere, we can use it to prove anything we
want and thus the whole ediphace of logic and reason is meaningless, is wrong.

Secondly, if rationality is contextual, not universal, then fine, we can use
deductive logic to prove that color doesn't exist, if we hold contradictory
beliefs about the color of birds. Groovy. Why the hell does it matter? It sure
is a problem in the context of purely deductive logic, but I can kind of look
out of my window and go, "hey, those birds sure do look like they're different
colors, and not all white!" Well, I can't, but you get the idea here.

Finally, you know, I think I'd like to see somebody seriously deal with
throwing out deductive logic, just to see what it looks like. I don't have a
problem with deductive logic, as such. I do have a problem that people seem
to want to universalize it, and think it's the tool for all occasions. I do
think it's interesting that people seem to react with horror if you suggest
abandonning it. But I don't as such, because I think it would be at least
interesting to consider philosophically, and because we don't really seem to
think in terms of formal deductive logic, it's something we kind of do after
the fact.

Also, there are other types of logic, not even modern ones. People like to try
to explain it away to save Aristotelian logic. For instance, look up
"contradiction" on plato.stanford.edu. There's a whole section where the author
tries to explain that any contradictions derived from the Buddhist tetralemma
aren't really contradictions. I'm not saying they're wrong, I just think it's
interesting that the reaction is, oh there's no WAY that can be right, I'd
better try to fix that, as opposed to going, wait, does this thing really lead
to contradictions? And if so, what does that mean? Oh, and I'm also still not
sure that a contradiction, anywhere, invalidates all deductive logic, see
matter and whether I'm a woman, for instance.

I guess so far I can sum up my thesis thusly:

1. It's entirely possible that there are meaningful contradictions in the
world, because the world is the world. It is how it is. We're the ones who find
contradiction to be a problem, because of one system of thought we've
developed.
2. Deductive logic might not be universal, but that doesn't mean it's still not
a very useful tool. I.e. contradiction doesn't invalidate the whole of
deductive logic, in all places and times.

(Gwark/31545) Steppenwolf> It seems to me that if there is something inherent...

Gwark@rss.iscabbs.com — Sat, 17 Dec 2011 08:00:00 -0600

Steppenwolf>  It seems to me that if there is something inherently
contradictory in reality, deductive logic would not be the appropriate tool to
investigate it.  I'm not sure what would be, but I'm unconvinced that formal
logic is the only/best means of interpreting/understanding reality in all cases
In fact, it seems plausible to me that, by prioritizing deductive/inductive
logic as our means of discovering the world around us, we will tend to enforce
a non-contradictory experience/understanding.  To a certain extent this could
be regardless of the underlying reality.  In a sense, perhaps it's like the
double-slit experiment wherein we find light is a wave - our results (wave, not
particle) are constrained by our approach.

(Steppenwolf/31544) I agree, it's not falsifiable. I'm suggesting it as an axiom, be...

Steppenwolf@rss.iscabbs.com — Sat, 17 Dec 2011 04:59:00 -0600

I agree, it's not falsifiable. I'm suggesting it as an axiom, because I have
yet to see a case put forth of a natural contradiction that I would consider
even meaningful.

In order for a natural contradiction to exist, it would have to be
pre-linguistic, wouldn't it? That is, no matter how we talked about it, what
words we used, it would inevitably lead us to contradictory language.

So I'm trying to conceive of a case where that would even make sense.

(Vanity/31543) If any apparent natural contradictions can be explained away as ...

Vanity@rss.iscabbs.com — Sat, 17 Dec 2011 04:36:00 -0600

   If any apparent natural contradictions can be explained away as a fault of
human perception or analysis or description, then isn't the thesis "there are
no natural contradictions" unfalsifiable?  Can you come up with a robust
version of the thesis which can actually be tested?

(Steppenwolf/31542) Giraffe:

Steppenwolf@rss.iscabbs.com — Sat, 17 Dec 2011 03:50:00 -0600

Giraffe:

We're trying to figure out if there are contradictions in nature that don't
just boil down to the ambiguity and vagueness in language. Gwynn, to me, seems
to be saying that there could be; JL and I are saying that there aren't, and
that any apparent contradictions are either a result of our premises being
wrong or our terms being wrong.

Gwynn:

The argument I gave you holds true for any proposition; it's pure deductive
logic. To get around it by saying I'm equating the two just means that you're
weakening another of the terms, either "all" or "there exists." Once you have a
contradiction, it can be boiled down into the form P = not-P. In deductive
logic, that's basically what a contradiction is. So you better have a really,
really good reason for trying to dumpt deductive logic entirely. :)

(Giraffe/31540) I understand how the ambiguity and vagueness inherent in languag...

Giraffe@rss.iscabbs.com — Sat, 17 Dec 2011 03:41:00 -0600

I understand how the ambiguity and vagueness inherent in language allows these
paradoxes to arise. I just don't understand how it is very interesting,
philosophically. It's certainly something we need to be aware of because
politicians and other dishonorable people will use misuse language to gain
power. But that doesn't seem to be the concern here.

(Gwynn/31539) I question step 1. If you say a black swan is white, then you're...

Gwynn@rss.iscabbs.com — Fri, 16 Dec 2011 17:15:00 -0600

I question step 1. If you say a black swan is white, then you're equating them,
and there's no contradiction. The whole contradiction turns on the fact that I
hold both that all swans are white, and there is a black swan, i.e. a swan that
is not white. If you're just equating them, then you're actually ignoring the
difference. You're essentially saying, there are no black swans because I'm
saying the swan you call black is also white, because it's a swan, and swans
are white, by definition.

(Steppenwolf/31538) I'll write a more substantive post later, but it's pretty easy t...

Steppenwolf@rss.iscabbs.com — Fri, 16 Dec 2011 14:45:00 -0600

I'll write a more substantive post later, but it's pretty easy to prove that,
say, the whole world is white.

Premises:
1) All swans are white.
2) There exists a black swan.
3) Black means absorbing all light; white means reflecting all light.
4) Any given color is made by reflecting some light and absorbing others.

Steps:
1) A black swan is white.
2) Black = white.
3) Therefore, absorbing all light = reflecting all light.
4) So if green = reflecting green light, and reflection = absorbtion, then
green both reflects green light, and not-green light, i.e. all light.
5) Therefore, anything that is green reflects all light, i.e. is white.
6) Repeat for all colors.

I strongly suspect that I could prove from the swan example that swans fly like
helicopters, too, by taking the logical converse of premise 1 ("Nothing that is
not white is a swan") and showing that a swan = not a swan. Not sure I could
get to JL's being a metallic statute, but don't tempt me to try, dude.

(Peccavimus/31537) I am really quite glad I kept at this discussion, because I've j...

Peccavimus@rss.iscabbs.com — Fri, 16 Dec 2011 14:28:00 -0600

I am really quite glad I kept at this discussion, because I've just had a bit
of an insight.

JL>  Do you think that we are communicating?

(Gwynn/31536) Step:

Gwynn@rss.iscabbs.com — Fri, 16 Dec 2011 11:17:00 -0600

Step:

I'm asking you to assume it is, for the sake of argument. Or invent whatever
contradiction for matter you feel more comfortable with.

Jl:

But Step. said that if we have contradiction in a field, we then can't say
anything about that field. Well the liar's paradox is in, let's see, language,
deductive logic, just to name two off the top of my head. So now we can have
contradictions, as long as they're a certain sort of contradiction. I guess
what I'm coming out of this with so far is, you want to insist that
contradictions are super bad, but nobody's really provided me with a real world
example of how.

Step. admits that in my example, we can actually have a contradiction in one
realm, as it were, that has nothing to do with lots of others. Then he says, if
we restrict ourselves to a particular field, contradictions are bad because if
we have one, we can't say anything meaningful about said field. Except we have
quite a number of standard philosophical paradoxes, which impinge on several
fields of study. But now they're some sort of special contradiction, you've
decided they don't "interact with anything", so they don't count.

I'm not trying to be offensive, but this is seriously starting to look like all
the things people typically gripe about religion for. You seem to be imposing
quite a lot of special conditions on this theory that contradictions are a
problem. It begins to look like faith, in other words.

Which is fine with me, if lack of contradiction is an aesthetic and utilitarian
preference, i.e. it seems to give us the best results, that's great, that's
sort of what I've been arguing. Not that it gives us the best results in all
domains, but that doesn't mean I'm saying it's useless. Like you and Step., I'd
say it's by and large preferrable, well I think you'd both say it's ALWAYS
preferrable, but you get the idea. But what I'm unclear on is if you both think
it's just incredibly useful, or some sort of actual feature of reality.

If you think it's just incredibly useful, then it seems the whole thing is just
that, a human preference, and it may very well be that there are actual
contradictions in the world. It also seems that you should have little to
complain about, figuratively speaking I mean, if somebody says that imagining
the world with contradictions can be useful too, and this is what they choose
to do.

So that's kind of what I'm trying to find out, really, what does it mean to say
we should get rid of all conflicting beliefs, or as Step. says, that there
can't be any contradictions in a field, because then we won't be able to say
anything meaningful about it whatsoever? For instance, I still don't see how
Step's claim follows, if we accept contradictions, anything is true. Suppose I
say, there are no white swans, but there's a black swan. However I manage it, I
firmly hold both of these things to be absolutely true, beyond doubt.

I then say, Jl is composed entirely of metal and is thus a rigid immobile
statue. How does it follow, because I hold a conflicting belief concerning the
color of birds, thatJl's existence as an immobile metallic statue is true?
Suppose I still hold my conflicting beliefs about the color of birds. Then I
say, "you claim sharks are fish, but they're really mammals". Again, how does
my belief concerning the color of birds make this any more or less true? Still
holding obstinately to my beliefs about birds, I then say "you think swans fly
by flapping their wings, but really, they fly like a helicopter".

OK, now we're not only dealing with birds, but with swans directly. How narrow
do I have to get until we start having issues with a contradiction making
things invalid or unintelligible or causing everything to be true or whatever?
"Swans are actually colorless". Now we've got swans and colors again. Remember,
I still believe there are both black swans and no such things as black swans.
How does it follow from those conflicting beliefs that "swans are colorless" is
in any way true, or capable of being demonstrated or accepted as such,
whatsoever?

Let me assure you, I'm not trying to be obtuse, I'm clearly not getting
something in this argument here. I mean, really, I don't see how anybody could
actually honestly hold the beliefs I've outlined above. That's sort of why I
asked for a contradiction in the world, something somebody actually holds. It
seems to me if you can successfully argue the details of any contradiction,
this was Jl's concern, we'd get hung up on arguing facts/individual cases, then
it's really open to question whether that's actually a conflict or not anyway.
So we'll stick to some philosophical abstractions with swans and liars and
such. But then, I'm still kind of at a loss.