Re: How much intelligence?

Lester Zick said:
On Wed, 22 Mar 2006 12:09:39 -0500, Tony Orlow <aeo6@xxxxxxxxxxx> in
comp.ai.philosophy wrote:

Lester Zick said:

[. . .]

"Blue contradicts red" is certainly a statement and a true statement.
Saying "blue not red" is just another way of saying it.

I don't see that, Lester. Your use of the word "not" is a bit vague here.

Tony, in mechanically exhaustive terms all that can be said about the
word "not" is that alternatives "not not" are self contradictory and
whatever else we can infer about "not" or even "contradiction" are
ultimately rooted in that single property. I grant you my usage seems
vague and imprecisely qualified. But I have no choice to preserve any
exhaustive mechanical reduction for "not" or "contradiction". There
are lots of things we might say in generic terms but we're talking
here about universal mechanical reductions and not conventions.


And you say the philosophers are vague! Sorry, I have to rib you a bit on this.

I completely understand, Tony, and sympathize with you here. In fact I
have even asked myself what I mean by "differences" "contradiction" or
"not"? And it's scarcely comfort to note that only really exact thing
I can say is that alternatives are self contradictory. It's a strange
thing but I'm not sure a lot more about the properties of "not" etc.
in formal terms.The only thing we can say further are grammatical
considerations like usage, conventions, symbols, and so on.

Well, that's what symbolic logic is all about, establishing the grammar and
operations needed for the processing of logical statements with truth values.


For all your talk of precise mechanics of truth, you are woefully resistant to
putting your statement in any kind of formal language, like JP was saying about
the drawbacks of natural language for discussing the nature of truth.

The inadequacies of generic language are the result of imprecise
usage, Tony, not any general lack of predicative ability. If you
refine usage generic predication can be just as rigorous and a lot
less obscure than technical academic predication.

I don't know about that. If one is not familiar with formal logic or truth
tables, then the language or construction might be obscur, but the leanring
curve is rather small, and the foundations are quickly laid.


If you
want to talk about true vs. false, try using truth tables or logical operators,
otherwise you're not exhaustively examining anything.

Well you know, Tony, truth tables, logical operators, etc. all have
established rules and conventions which is pretty much where you and I
have had difficulty in the past. Generic language doesn't have that
problem.

Why is it a problem to have estalished rules and conventions? If you discover
that the established rules and conventions lead to unsatisfactory results, then
you might want to consider changing them, but having explicit rules about what
you're doing is part of science.

I'm free to say what I mean in plain language and then go on
to specify what I mean in plain language that is a lot more accessible
than truth tables and logical operators. I don't see truth tables and
logical operators adding anything whatsoever to the explication of
tautological mechanics and I see a lot of confusion using established
academic conventions because just as we're doing here we'd spend an
enormous amount of time arguing the conventions instead of the logic
and mechanics.

And yet, those arguments would be moot if we could quickly agree on a
convention for processing and communicating these ideas. It also takes less
space. Of course, the drawback is that it's a lot harder to wax poetic with
only 1's and 0's, but hey, we can intersperse, can't we?


"not not" is not a
contradiction in any common world. It's the negation of the negation, it's 1-
(1-x)=x, and doesn't do anything to any proposition you apply it to, much less
cause any contradiction that didn't already exist in x.

Tony, that is only because you insist on talking about these things in
formal academic terms which may or may not apply to what I discuss
in terms of generic predication.

Well, that's the question. I am having a hard time relating what you are saying
about logic to what is normall considered the science thereof. It would be
helpful to me and others if the differences between what you propose and what
we already have we better explained, mechanically.


So, if it means
something different to you, make up some mechanics. Invent a language and a set
of operators on that language so people can actually see the mechanics you seem
to desire so much, while rejecting the mechanics that exist and seem to work.
If they didn't, we wouldn't be communicating like this.

The formal academic logical mechanics that we have doesn't work or
people would use to describe generic language instead of generic
language. Remember that argument I had with Bob Kolker over whether
"red car" meant "red AND car" or not? I had that rather intense and
ultimately disappointing discussion because what I was trying to say
but didn't realize until later was that "red car" doesn't mean "red
AND car" just because the boolean AND function is commutative and
predicate sequencing in generic language is not commutative and non
commutative generic predication and its underlying mechanics is what
I'm talking about and not about academic formalisms.

Well, now you're getting back into grammar, which is related to the
communication of truth, but not so much to truth itself. If we agree to use a
paranthetical prefix notation, such that A dn B is and(A,B), then any order
amibiguities disappear, and we know without a doubt what each other is saying.
maybe "red car" doesn;t mean and(red,car). Since neither red nor car is a
predicate or a truth value, the and'ing of them doesn't produce a predicate
either. If "red car" is to be a predicate, I would duggest it means red(car),
or, some particular car has the value of true for its property of redness: "the
car is red". That becomes a predicate, as a statment of implication: "if X is
that car, then red(x) is true". Does it make any sense to you that any actual
predicate must have the notion of logical implication in it somewhere?


If I
say, "blue is not red" that is true, but not because they contradict each
other, since they are not statements. They are different colors, and in that
sense blue is not red, because they are different, not contradictory. Now, if
you use them in propositions, and say "A is entirely red AND A is entirely
blue", then given the definition of "entirely", which makes whatever color you
name mumutally exclusive with all other colors, then you have a contradiction
within that compound statement, because A cannot be both blue (and therefore
not red) and red (and therefore not blue) at the same time.

Sure. And if I do that I wind up with a host of mechanically unreduced
explanations for a whole bunch of qualifications having nothing to do
with whether "not" or "contradiction" are true or false because their
alternatives "not not" or the "contradiction of contradiction" are
self contradictory. So if you want to discuss basic logic in terms of
mechanically exhaustive tautological reductions you more or less have
to do it in these or very similar terms. Going off into boolspace with
"AND's" "NAND's" or whatever just has no bearing on basic logic in
tautologically mechanical terms.

The contradiction or negation of contradiction is consistency. It's the lack of
contradiction. Everything that is is not not. If the formal mathematical system
of logic is not mechanical enough for you, I have no idea what you want.

Well we've been arguing about this since day one, Tony, and I just
don't see any way to further advance my arguments constructively.
You insist generic language predication can only be described and
must be used the way ti is in academic logic formalisms and I don't
agree. The closest comparable academic formalsim I know of is ordinal
numeration and arithmetic but even here the ideas are so far apart
from generic concepts as to be mechanically useless.

So, what approach do you see as having promise for elucidating the nature of
truth and the search for universal truths? I don't see a formal method of any
sort here, or really an idea for one. I guess that's what I'm missing.


Now my take on "difference" versus "contradiction" is that each denies
the other. In other words "red" is "not" "blue" and a "car" is "not" a
"truck".So in this sense there is a contradiction in the form of "not"
between "red" and "blue" as well as between a "car" and a "truck"
because each denies the other.

Yes, if they are different values for the same aspect of something, applied to
the same thing, and that thing can only have one value for that aspect of
itself, then they can form a contradiction through statements of two different
values for the same one-valued aspect.

Don't understand what you're saying here, Tony.

Hopefully my paragraph abve eplains it better. I thought that paragraph sounded
shitty. Sorry. What I am saying is, if one property is mutually exclusive with
another property, and both are applied to the same object, then you create a
contradiction, but not until then.

Well I disagree for reasons and with examples stated previously.

Well, your disagreement seems to rest on a private and secret definition of a
predicate, as far as I can tell. You certainly haven't defined in any precise
terms what you think a predicate is. Perhaps you could do that? What is a
predicate?

Haha! Yeah really gonna happen. I can't even define "not" to anyones
satisfaction so now I have to start defining predicates?

Well, yes. Not to be a hardass or anything (who, me?) but if you are going to
put forth "not" as a central idea, and claim it is a "predicate", and that "not
not" is self-contradictory, and those ideas don't fit anyone else's notions of
those words, then it behooves you to define what you're talking about, or
resolution of the question is hopeless. For my part, I define "not x" as being
1-x in arithmetic terms. Implication, x->y, may be thought of most commonly as
1-y+xy, or more esoterically as y^x, arithmetically. And, to me, any logical
construction which contains a logical implication of any sort constitutes a
predicate. Maybe that's not fully fleshed out, but it's the beginnings of about
as mechanical description of general logic as I can muster at this time.


Seriously though, Tony, let me give you an idea of what I had in mind.
I can't tell exactly what a predicate is except that it gives meaning
to other predicates of which it's predicated. Furthermore predicates
are what make a thing real.

Sure, they are statements regarding the logical relationships between
properties of an object. Perhaps, when you say "predicated", that could also be
read as "implied"?


And if we consider predicates in relation to one another, such as
"red car" we find that "red" is "car" but "car is not necessarily
"red". In any event I can tell this won't satisfy you but it's all
I've got to work with at the moment.

"red" is "car"? But red apple blue car. Red is a property which may apply to a
car or might not. So, why is "red" "car"?


Now I also understand the sense in which you use "contradiction" as a
logical contradiction within a concept.And there is no "contradiction"
within "red" or "blue" or a "car" or a "truck" in this sense. However
there is a contradiction between "red" and "blue" on the one hand as
well as between a "car" and a "truck" because each denies the other.

Yes, they are mutually exclusive properties, unless of course something is red
AND blue or reddish blue, or is a giant SUV, in which cases the difference
becomes less clear. This applies to the partial truth values I was mentioning
before.

Don't understand this either.

Where you are drawing distinctions between blue and red or car and truck,
sometimes there is no doubt.

Where the predicates are actually present there is no doubt possible.
Whether the predicates are actually present in a given instance there
can be doubt but none if they are.

The fire engine is red, not blue, and is a truck,
not a car. There is no ambiguity about the fire engine, but there is about the
maroon SUV, in which case the truth value of "A is a red truck" is not 100%
true or false.

Sure it is.

So, it's 100% a red car, or 100% not? Which is it?

I thought you were talking about a truck? What I was talking about was
a "red car". No percentage involved.

I dunno. It's an SUV. It's shaped like a car, but it takes up the entire lane
and guzzles gas like a truck. Is a wolf a dog? Is a human an animal? Is an
Mbuti tribesman a human? It depends who you ask. To some, those little guys are
just "bush meat".


On the other hand there is no contradiction between "red" and "truck"
since neither denies the other and we can have a "red truck" or "blue
car". So the only problem we really have here is figuring out how all
these pieces fit together. And the only way we have to fit them all
together is by means of the differences or forms of contradiction
between them vis-a-vis each and every other piece of reality.

Well, yeah. "Blue" and "red" both describe the same measure of something, its
color. If something is one color, and red is distinctly different from blue,
then both cannot be applied with veracity to the same object. It's all about
application in propositions, and comparison of properties along the dimensions
they measure. So, identification of the dimensions of reality is key, I think,
to all sciences, and the palce to start when trying to classify which
properties might be mutually exclusive alternatives to each other.

Well, Tony, I don't see any serious prospect for mutual comprehension
if we can't even agree on the meaning of basic terminology and simple
examples.

Well, that's true, and why people have been urging you to use proper logical
statements in your examples. "blue, not blue" is not a statement. The comma is
ambiguous. Does it mean "and", "or", "equals", "implies" or one of the other 12
possible logical operators?

Well that's a problem with doing elementary science in informal
conversations on the usenet. However there is no way to use formal
logic of the kind you suggest is "proper" because "proper" logic is
not necessarily mechanically exhaustive or reducible. Nothing I can
do about that short of reforming "proper" logic. That's exactly what
got me into all that trouble with respect to Planck's constant and
mathematical usage on transcendentals and irrationals etc. etc. That
wasn't "proper" usage either in conventional terms. It was just
necessary.

But I already showed you how the 16 possible logical operators are derived from
the very most basic concepts, mechanically, and how this enumeration was
exhaustive.

It was exhaustive? And where and how did you demonstrate that, Tony? I
didn't see any evidence the operations were "very most basic concepts
mechanically" and certainly not why they're exhaustive.

I started with two values, and mapped out all the ways that one can be mapped
to one, or two can be mapped to one. There are no other mappings to a single
returned Boolean truth value, given one or two input values. One can go on to
list operators on three logical variables, but those can be built from the
unary and binary operators, and just haven't been discussed here yet. There may
be something interesting there to discover, but I can't imagine what it is
right now. In any case, all logical operators on fewer than three variables
have been mapped out, exhaustively.


When moving into probabilistic models, it seems we may encounter
more complex questions, given the continuous nature of the approach, but that
this form of logic can be exhasutively analyzed as well. If you have an idea
for a different logistical model, I'd be interested, but if it doesn't include
the language (symbols) amd the allowed operations, then it's not a system.

The logical model is tautological regression, Tony. I've made no
private, secret language secret of that.

And what, exactly, are the mechanical operations involved in tautological
regression, as you see it? What are the steps in the discrete process of
regressing to more fundamental truths?


When it comes to simpl examples, we can draw simple inferences, but if we want
to delve deeply into the subject, we have to prepare ourselves to deal with
more complicated questions, and sometimes this requires an extension of the
system we are using to answer those questions. That's why I brought up the
probability issue and the tenuous nature of ascertained truth.

Mechanically reduced exhaustive truth is however less problematic
whether simple or complicated.

Well, we need mechanics to do that, eh?

Sure we do, Tony.You know I'd rather have these kinds of conversations
than trying to explain epistemological concepts when we're talking at
cross purposes terminologically and every other way.

I am not sure I have a purpose here, except to discuss something other than the
Cantorian foolishness I have been battling for months to no avail. If I can't
help them get a reasonable system started instead of that mess, then maybe I
can help you focus in on the questions you are trying to answer. Or, maybe none
of us can help anyone but ourselves, and this is just an interesting
conversation. I guess that's good enough for right now. :)


~v~~



--
Smiles,

Tony
.

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