Re: How much intelligence?

Lester Zick said:
On Wed, 22 Mar 2006 11:48:17 -0500, Tony Orlow <aeo6@xxxxxxxxxxx> in
comp.ai.philosophy wrote:

Lester Zick said:
On Tue, 21 Mar 2006 14:24:59 -0500, Tony Orlow <aeo6@xxxxxxxxxxx> in
comp.ai.philosophy wrote:

Lester Zick said:
On Mon, 20 Mar 2006 15:38:52 -0500, Tony Orlow <aeo6@xxxxxxxxxxx> in
comp.ai.philosophy wrote:

Lester Zick said:
On Thu, 16 Mar 2006 14:50:33 -0500, Tony Orlow <aeo6@xxxxxxxxxxx> in
comp.ai.philosophy wrote:

Lester Zick said:
On Wed, 15 Mar 2006 20:02:16 -0500, "Allan C Cybulskie"
<allan.c.cybulskie@xxxxxxxx> in comp.ai.philosophy wrote:

[. . .]

Let me put it to you this way: is the exhaustive alternative to what
is false perforce true and are tautologies in the form of "A, not A"
exhaustive of truth and is self contradiction exhaustively false?

You know, Lester, I am beginning to explore this very question. The answer is
not so clear as you might think. If we generalize logic quantitatively, and
consider truth values to be probabilities between 0 and 1 inclusive, then "p
and not p" can have a non-zero value. In other words, if the certainty of
proposition p is not absolute, then the mutually exclusive relationship between
a proposition and its negation is mitigated.

Consider that "and" has a geometric interpretation as the intersection of two
regions, as in a Venn diagram, and that this geometric interpretation
corresponds to an arithmetic operation, namely x and y is interpreted as x*y.
Also consider the arithmetic interpretation of "not x" as 1-x. Then, x and not
x is equal to x*(1-x), or x-x^2. This value is always 0, as long as x is either
0 or 1. But, for fractional values of x, the excluded middle is no longer null.
This appears to be the intuitionistic logic approach, and not entirely invalid.
What do you think?

The most interesting thing, which I discovered last weekend, is as follows.
Logical implication is generally thought of such that a->b means "b or not a".
It's false if a is true and b false, so it's equivalent to 1-(a and not b),
which in normal quantitative terms, as above, becomes 1-(a*(1-b)), or 1-a+ab.
For a and b being either 0 or 1, this formula produces a 0 when a is 1 and b 0,
and a 1 otherwise, as one would expect. But, there is another interpretation of
logical implication, which I intend to explore further. For x and y in [0,1],
1-x is in [0,1] and corresponds to "not", x*y is in [0,1] and corresponds to
"and", and x^y is also in [0,1]. If x^y is interpreted as "y->x", then for x
and y in {0,1}, it produces the same binary Boolean truth values as standard
implication, but gives a slightly different spread of probabilities when using
continuous truth values for x and y in [0,1]. I'll be examining the differences
and their implications in the near future. It's not trivial. It may be key.

Tony, I think you'd agree the proposition "red not blue" is 100% true
and I also think you'd agree that "car not car" is 100% false.Thus the
proposition ["red car" "not" "blue car"] becomes 100% false as well
because "car" factors out of the contradiction between "red car" and
"blue car" in basic mechanical terms.

I would agree that "red<>blue" is true and "red=blue" is false, and "a car is
not a car" is false. 100%? Hmmm, is a Ford Sequoia a car or a truck? That car
is not really a car.

Did you mean ["red car" "not" "blue car"] becomes 100% true?

It doesn't become anything. The statement is just true.

Oh. Well, you said it "becomes" 100% false.

Aha! The "becomes" I was talking about just referred to the reductive
process and not whether the truth content of the statement changes.
You used the word "true" so I just copied it. ["Red car" not "blue
car"] is just true and the truth of it becomes evident by factoring
out "car" through tautological negation. Where I said "false" above
I should have said "true" in the sense that "red not blue" is true.

Right, that's what I meant. I kind of understand what you are saying, but I
think you need to define the mechanics you're using a little better. Like, what
is the *general* rule for factoring out the object to which properties belong
to remove contradiction, if that's what you're doing? How does what you're
suggesting realte to classical logic?

Not sure.That would require someone with formal training to
determine. All I can see at present is predicates of the same name
factor if predicated of one another by "not". Effectively the result
is self contradiction as in "A not A". It's curious the absence of
difference and self contradiction have the same form as in "A not A".

Hmmm.....

A AND not A is self-contradictory by the law of the excluded middle, in
whatever form. A is not different from A, but is different from not A, and
difference is indicated also by a "not". That's why I was saying there are two
different kinds of nots. Let's call "not A" "B". Then "A is not B" is a
statement of difference. Notice that if we replace B again by "not A", we have
"A is not not A", and the nots cancel out to leave "A is A", a tautological
statement. So, I think you need to distincguich between these two nots a bit
better, because they have different properties, as I was saying to JP.


It's really hard
to tell exactly what these statements mean without actual predicates.

"Red" "blue" and "car" are actual predicates.

No, that sentence no verb. A predicate a verb. Without a verb no predicate. So
verb in predicate, or not predicate. You must verb in predicate.

"Not" is the predicate. You may not like that usage, Tony.
Conventional linguistics may or may not agree. But "not" is
the only predicate I provide just to avoid linguistic arguments.

"Not" is the only Boolean unary operator, and the basis of "or" in conjunction
with "and", but "not" is not a predicate in itself. It's a modifier of a single
predicate. That's why it takes one argument, a predicate, and inverts the truth
value x to 1-x.

We're talking apples and oranges again here, Tony. "Not" is not only a
boolean operator. It's a predicate in generic language.

yes, there are two kinds of not, which need to be distinguished.


"car" is not a predicate either.

Oh? So in "it is a car" "car" is not a predicate? I don't think so
since "car" is predicated of "it".

"it is a car" IS a predicate. Do you see the verb, "is"? That makes all the
difference. Basically, when we say "X is a car", what this means is that, for
every property P, if for all c in the set of cars P(c) is true then p(X) is
true, and if for all c in the set of cars P(c) is false, then P(X) is false.
That's what makes X a car. It shares all the necessary properties that any car
shares, and this set of properties places it as a member of the set of cars.
So, P(c)->P(X) and P(X)->P(c) for all P. The implication implied is what makes
that statement a predicate. That's down to mechanical brass tacks and glue.
How's the carpet look? ;)


Ultimately, I think a predicate may be
universally thought of as a logical construction containing the operator
"implies". "X is a car" means "x->car", which means that everything true of
every car is true of X. But, what is the truth value of the concept "car"
without application to any particular instance?

More generic apples and boolean organges.

It's all about the nature of truth itself.


How did those statements read?

Just like an English teachers.

That not sentence. No recess. ;)


If that
means not(and(red(car),blue(car)), or, the car is not red AND blue, then I
guess.

My examples just mean what they say. They may or may not mean whatever
and however people reinterpret them semantically according to academic
notions of logic which are not demonstrable in exhaustive terms.

That's the point of using more specific logical language to communicate, to
avoid ambiguity. Do you have an objection to standard logical language?

When it's not mechanically exhaustive, yes. I use the language I
use in examples precisely to avoid arguments over mechanically
inexhaustive terminology.

But, didn't you think the binary logic breakdown of all operators was
exhausive? Could there be any more operators? I think all ground was covered
there.

Well every boolean operator I'm familiar with can be built of "not" so
I don't think there are others which can't be.Nor do I consider binary
logic breakdown to be applicable. That's your schtik not mine, Tony.

How do you construct "AND" or "OR" simply from "NOT"? You can build all of
logic from NOT and AND, but not just from NOT. You need combinations as well as
eliminations, which perhaps relates to JP's point about similarities ebing as
important as differences. Maybe he has a point.


I really think you need to think about propositions as grammatical
constructions in order to make this stuff clear. Like, an object is a core
entity. An intransitive verb is an action tht takes an object as a parameter,
and a transitive one takes two object parameters. An adjective takes an object
parameter, and an adverb takes a verb parameter. Then, logical arguments take
propositions, or predicates, as arguments, and one can keep track of exactly
what the meaning of something is.

Language depends on tautological mechanics and not vice versa using
ambiguous and undemonstrable linguistic principles.

But these are not ambiguous principles, and are demonstrated every time someone
complies a program or runs an interpreted program. Grammar parsing is well
established in comouter science. It needs to be extended fully to propsitional
calculus to avoid problems there. I believe a good deal of work has been done
in that area.

Well the problem here is that we're right back to whether language
is a computable number or not and I maintain it is not and it is not
exactly because the subjective aspects of universal negation are not
taken into account. This is the reason there can be no necessarily
correct Searle dictionaries of unsubsumed languages.

I missed the Searle discussion. Looked a couple times but it seemed all over
the place and I didn;t know what was going on, so you lost me there. By the
way, these 118 letters comprise a 944-bit binary number. :)

If you'll remind me I'll try to dig something out.

Oh, that's okay. I already have too many conversations going. With my luck,
that'll be interesting or something, and I'll become even less productive here.
;)



However even in abstract terms there is a difficulty with the idea of
quantitative analogies for true and false because various predicates
do not have the same weight. "Red" and "car" don't necessarily have
the same weight for "red cars". So saying ["red car" not "blue car"]
is 50% true and 50% false would not necessarily be correct if that is
what you are suggesting.

If you use proper logical operators, I can translate a proprosition from
Boolean logic to probabilistic logic. Say I have an SUV that 30% think is a
truck and 70% as a car. Say I have some shade of maroon that 60% think of as
red, and 40% as purple. Is that a red car? Well, it's 70% car and 60% red, so
it's 42% a red car.

We can say all kinds of things about all kinds of things as long as we
can assume whatever we want about whatever we say and don't have to
demonstrate the truth of what we say.

Are you saying that, given those percentages of perception, and assuming the
redness and carness are independent of each other, that we should not expect
42% of the people to call it a red car? If so, why?

I don't care what people call it or in what percentages only whether
it is or is not a "red car" and whether "red" contradicts or is "not"
"blue".

Well, if it's a maroon SUV, then YOU decide if it's a red car or not, but don't
expect there to be any absolute truth on that issue. If you asked God, he'd
shrug and say, "Who can tell these days??"

If you mix red and blue paint, will it cause a rift in the logical fabric of
the universe?

Who cares whether it's maroon if we're talking about whether "red"
is truly or falsely predicated of a car, Tony? The whole point is the
truth or falsity of what is predicated of something and not whether
that predicate shares predicates with other potential predicates not
predicated of the same thing.

But is maroon a kind of red? What if we take pure red paint and pure orange
paint and make a 50-50 mix. Is that red or orange now? Does it have an absolute
truth value for either property?


On an even higher level of abstraction though I think you might be
able to see that trying to mechanize true and false in conceptual
terms quantitatively is futile if tautological daisy chaining of "not"
type differences and contradiction lies at the foundation of mechanics
in general. In other words we can't very well describe the basis for
tautological mechanics in quantitative terms where that mechanics
forms the mechanical basis for quantitative analysis.

But, what if other means besides symbolic logic are used as a basis for
quantitative foundations, like geometry? If we define quantity in terms of
geometry, and logic in terms of quantity, then we don't really end up with
circular definitions. We just start at the most concrete and work towards the
abstract.

Except that logic is what governs geometry and the mechanics of
definition for all things great and small including number.

Listen, our innate logical capability is what enables us to do all sorts of
things, including formal geometry, but that doesn't mean that, as a discipline,
logic underlies geometry.

Sure it does.

Then why does out logic depend on our geometry?

It doesn't. Our geometry depends on our logic.

You mean we logically decided to have left and right hemispheres, a reptilian
brin and a midbrain, and to put out language processing capabilities in our
left temporal lobe? Did we come to a logical decicion to have a six-layered
neocortex? I don't think so. But then again, maybe the Churh of the Funky
Nazarene are right.


If that's your argument, then consider that our
innate geometry is what provides our innate logical capability, so in that
sense, geometry also comes first. We can use simple logical arguments regarding
objects, and regarding counts and measures of those objects, before defining
the formal system of symbolic logic.

All that is after the fact.

Symbolic logic is after the fact of logical comprehension and thought. Did we
leanr to think logically from symbols, or from space?

We learned to think logically from tautologies. Tony. Space next and
symbols long afterward.

Tautologies are logical constructs. That's kind of like saying we learned to
walk by chasing animals. We had to walk first, and then apply it to chasing
animals. We learned to think logically due to a geometric and or chemical
change which perhaps allowed the associative machinery to form quick and
absolute associations as logical implications.


Our innate logical capability is daisy
chained tautological regression. And geometry, arithmetic, and
formalized and informal logic and arguments involving them come
long afterward. That innate logical capability is what I describe as
tautological mechanics.

Yes, and it's performed by tiny little quantitative computers in a network we
call our brain. Logic is a subset of calculation, just like contradiction is a
very specific kind of difference.

Quantitative computers, Tony? I hope you're kidding.

Of course not. Neurons fire at one rate or another, sending out pulses, not
unlike Curt's network model. I don't think that's necessarily the best way to
implement intelligence on a standard computer, but it appears to be what
neurons do, in repsonse to the pulses they receive and in acordance with the
neurochemical state of the cell, calculating when a pulse is due. That wouldn't
have been a very funny joke, anyway, would it Lester?

Now, there's this joke called The Aristocrats........never mind.


~v~~



--
Smiles,

Tony
.

Relevant Pages

  • Re: How much intelligence?
    ... think you need to define the mechanics you're using a little better. ... That's why it takes one argument, a predicate, and inverts the truth ... We're talking apples and oranges again here, Tony. ... "it is a car" IS a predicate. ...
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  • Re: How much intelligence?
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  • Re: How much intelligence?
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  • Re: How much intelligence?
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