A Tale of Two Defintions: The definition of "Logic"

[Dragonfly]

This is an excellent reason why I say "logic" is useless. Why would someone go around making statements that don't tell us anything about reality? That sounds like something people do in insane asylums.

And something mathematicians do. Is that useless? I don't think so. Trivial tautologies may be useless, but that doesn't imply that logic is useless. You are throwing the baby out with the bathwater. We may apply statements that in themselves don't tell us anything about reality (like mathematical theorems) in models describing reality, like countless physical theories and their applications in technology, which is hardly useless.

BTW, Korzybski studied under a well known psychiatrist at one of said asylums and used his experience in developing his theory of sanity. Even the most basic tautology of all, 'dragonfly is dragonfly' is not strictly true since dragonfly is constantly changing at sub-microscopic levels. All this 'analytically true' stuff is nonsense. Either you are speaking about something in the real world (synthetic) or you are not (mathematics) or you are suffering from some sort of nervous system disorder.

I think that is a bit too black-and-white. Tautologies about the real world may be trivial and uninteresting, but that doesn't make the person who uses them immediately a psychiatric case. Not everything we say is some Very Deep Truth, banalities are also part of life. On the other hand I have to admit that people who continuously utter "A is A" may have a problem. Oh, and that dragonfly is continuously changing at sub-microscopic levels doesn't meant that "dragonfly is dragonfly" is false, as both sides of the equation are changing simultaneously, it doesn't imply that dragonfly doesn't change with time. Dragonfly (t1) ≠dragonfly(t2) if t1 ≠ t2, but dragonfly(t) = dragonfly(t) for all t.

[Selene]

the Tyranny of Definition.

Oh, come now. On the other active thread you defined modern Judaism. I accepted it, because you know more about it than I do. Where's the tyranny?

W.

Hmmm. Don't you hate the pointed horns on that dilemna?

[BaalChatzaf]

This is an excellent reason why I say "logic" is useless. Why would someone go around making statements that don't tell us anything about reality? That sounds like something people do in insane asylums. BTW, Korzybski studied under a well known psychiatrist at one of said asylums and used his experience in developing his theory of sanity. Even the most basic tautology of all, 'dragonfly is dragonfly' is not strictly true since dragonfly is constantly changing at sub-microscopic levels. All this 'analytically true' stuff is nonsense. Either you are speaking about something in the real world (synthetic) or you are not (mathematics) or you are suffering from some sort of nervous system disorder.

Abstract, non-applied mathematics tells us nothing about reality either. Not a blessed thing.

Logic, in its modern guise as Boolean Algebra and first order logic got its uses in logic circuits for computers, and relational databases. Relational database theory is an exercise in the logic of n-ary relations.

Ba'al Chatzaf

[Michael Stuart Kelly]

Abstract, non-applied mathematics tells us nothing about reality either. Not a blessed thing.

Bob,

Of course it does. I can think of a whole lot of things:

1. We exist and are conscious (otherwise we could not even think the math).

2. Law of identity ("1 is 1" to coin a phrase).

3. Units exist.

4. Systems can be organized through rules.

There's lots more reality that underpin "abstract, non-applied" math, and the math tells us about it very clearly if we look.

Michael

[tjohnson]

Abstract, non-applied mathematics tells us nothing about reality either. Not a blessed thing.

Yes, and your point?

Logic, in its modern guise as Boolean Algebra and first order logic got its uses in logic circuits for computers, and relational databases. Relational database theory is an exercise in the logic of n-ary relations.

Yes, this is applied mathematics, synthetic stuff.

[tjohnson]

And something mathematicians do. Is that useless? I don't think so. Trivial tautologies may be useless, but that doesn't imply that logic is useless. You are throwing the baby out with the bathwater. We may apply statements that in themselves don't tell us anything about reality (like mathematical theorems) in models describing reality, like countless physical theories and their applications in technology, which is hardly useless.

what I am trying to say is what Russell said that logic is the childhood of mathematics, meaning that logic has evolved into mathematics and we no longer need a formal field called Logic. We can learn everything we need to know about logic by learning mathematics.

I think that is a bit too black-and-white. Tautologies about the real world may be trivial and uninteresting, but that doesn't make the person who uses them immediately a psychiatric case. Not everything we say is some Very Deep Truth, banalities are also part of life. On the other hand I have to admit that people who continuously utter "A is A" may have a problem. Oh, and that dragonfly is continuously changing at sub-microscopic levels doesn't meant that "dragonfly is dragonfly" is false, as both sides of the equation are changing simultaneously, it doesn't imply that dragonfly doesn't change with time. Dragonfly (t1) ≠dragonfly(t2) if t1 ≠ t2, but dragonfly(t) = dragonfly(t) for all t.

Hey, it is NOT an equation, it's a sentence . So 'dragonfly' represents a process and "the process called dragonfly is the process called dragonfly", ok but dragonfly_t1 is not dragonfly_t2.

[Roger Bissell]

And something mathematicians do. Is that useless? I don't think so. Trivial tautologies may be useless, but that doesn't imply that logic is useless. You are throwing the baby out with the bathwater. We may apply statements that in themselves don't tell us anything about reality (like mathematical theorems) in models describing reality, like countless physical theories and their applications in technology, which is hardly useless.

what I am trying to say is what Russell said that logic is the childhood of mathematics, meaning that logic has evolved into mathematics and we no longer need a formal field called Logic. We can learn everything we need to know about logic by learning mathematics.

A number of Aristotelian logicians would beg to differ.

Henry Veatch in Intentional Logic (1952) and Two Logics (1968) lays out in clear detail the difference between the "what-logic" of traditional or classical logic and the "relating-logic" of modern, mathematical logic. He argues that not only hasn't the latter completely displaced the former, it cannot do so.

My own perspective is that there are some interesting areas of overlap between the two, despite their being somewhat like apples and oranges, and that the issue of Existential Support, which supposedly rang the death knell for Aristotelian logic (and in particular, the Square of Opposition), is largely overblown.

To anyone interested in following up on these claims, I suggest trying to locate a copy of Two Logics, either as a second-hand book on the Internet or in a university library.

REB

[BaalChatzaf]

My own perspective is that there are some interesting areas of overlap between the two, despite their being somewhat like apples and oranges, and that the issue of Existential Support, which supposedly rang the death knell for Aristotelian logic (and in particular, the Square of Opposition), is largely overblown.

Do you mean Existential Import? In classical logic (pre-Boole, pre-Frege) the categorical assertion all A are B also implied that some A exists. In modern logic this supposition is not made.

See http://en.wikipedia.org/wiki/Square_of_opp...stential_import

for a brief description of this matter.

Ba'al Chatzaf

[tjohnson]

Abstract, non-applied mathematics tells us nothing about reality either. Not a blessed thing.

Bob,

Of course it does. I can think of a whole lot of things:

1. We exist and are conscious (otherwise we could not even think the math).

2. Law of identity ("1 is 1" to coin a phrase).

3. Units exist.

4. Systems can be organized through rules.

There's lots more reality that underpin "abstract, non-applied" math, and the math tells us about it very clearly if we look.

Michael

I think what Baal should have said is that abstract, non-applied mathematics tells us nothing about what is going on around us but, as Micheal has pointed out, it does tell us something about what is going on inside our heads. 'reality' includes us after all.

[BaalChatzaf]

Abstract, non-applied mathematics tells us nothing about reality either. Not a blessed thing.

Bob,

Of course it does. I can think of a whole lot of things:

1. We exist and are conscious (otherwise we could not even think the math).

2. Law of identity ("1 is 1" to coin a phrase).

3. Units exist.

4. Systems can be organized through rules.

There's lots more reality that underpin "abstract, non-applied" math, and the math tells us about it very clearly if we look.

Michael

I think what Baal should have said is that abstract, non-applied mathematics tells us nothing about what is going on around us but, as Micheal has pointed out, it does tell us something about what is going on inside our heads. 'reality' includes us after all.

The real Reality is what is independent of sentient consciousness. It is what would be there if all the sentience in the cosmos disappeared. A person doing math knows if -he- is doing math. For all he knows the others are just making marks on paper or blackboard or computer screen although we often -assume- otherwise.

Ba'al Chatzaf

[Michael Stuart Kelly]

Bob,

That's a good basis for knowledge. Long live the Matrix.

(Reality ain't out there. They eat us...)

Michael

[John Dailey]

~ It is really fascinating how so many arguments castigating this-or-that method of 'logical' argumentation themselves imply a ntl presumed validity of them as a supporting logical base for them. Lottsa 'stolen concepts'...floating (!) around...in these threads.

~ Has no one yet picked up on my chronic points about applying the criticisms one gives re logic/defs/etc to one's OWN 'arguments'? I get so tired of being Socrates here spelling out such...only for it to be evaded via subject-change.

LLAP

J:D

[Roger Bissell]

My own perspective is that there are some interesting areas of overlap between the two, despite their being somewhat like apples and oranges, and that the issue of Existential Support, which supposedly rang the death knell for Aristotelian logic (and in particular, the Square of Opposition), is largely overblown.

Do you mean Existential Import? In classical logic (pre-Boole, pre-Frege) the categorical assertion all A are B also implied that some A exists. In modern logic this supposition is not made.

See http://en.wikipedia.org/wiki/Square_of_opp...stential_import

for a brief description of this matter.

Ba'al Chatzaf

Arrrrgh, yes, Existential Import. Sorry. What a hideous typo. :-/

I'm aware of the supposition by modern logic, and the examples they trot out to try to support it.

I'm off for 5 days of traveling and performing, including three days at a jazz festival in Sun Valley, Idaho, and an appearance at my nephew's wedding reception in Cedar Rapids, Iowa. So, I won't be keeping up with the discussion here.

REB

[John Dailey]

~ I don't care what any 'logician' has asserted about the term 'ALL' as NOT having 'existential import.' They certainly never really 'argued' it, in any sort of 'deduced' fashion (what other 'logical' way of arguing could there be, hmmm? Certainly not 'Induction.') --- It is not purely synonomous with merely a 'hypothetical' IF (which is then considered as unequivocally re-translatable into a categorical negative-conjunctive, myopicizing the meaning of 'hypothetical' on top of things.) Indeed, it is inapplicable to non-existence fantasy ideas to begin with. The mix of 'ALL' with centaurs is doing the fallacy of presumption as in "When did you stop beating your wife?" with the supposed implications of the true response (by some) of "Never."

~ To say (or should I say: innuend) that "All universal-categoricals have no existential import" seems a bit...existentially importing about 'all' categorical statements, when you think about it.

LLAP

J:D

[BaalChatzaf]

Arrrrgh, yes, Existential Import. Sorry. What a hideous typo. :-/

I'm aware of the supposition by modern logic, and the examples they trot out to try to support it.

Making set intersection and set union well defined is not "trotting". It is a mathematical necessity.

Boole and Frege were not fools, nor did they trifle with logic.

Without empty sets there are no meaningful algebraic logics.

Ba'al Chatzaf

[tjohnson]

A number of Aristotelian logicians would beg to differ.

I'm sure they would, no one likes to be told that their work is useless.

[tjohnson]

The real Reality is what is independent of sentient consciousness. It is what would be there if all the sentience in the cosmos disappeared.

We can sense "reality" and we can speak about "reality", both of which require an observer. For all practical purposes, there would be nothing without any observer.

[merjet]

Yes, it is an example of an analytic statement. Another example is the statement "a thing acts according to its nature", because its "nature" is defined as the way the thing acts, so you can't draw any conclusions about "things" from such a statement. Such tautologies are trivial and therefore uninteresting. There are also less trivial tautologies, like mathematical theorems, where the result may be far from obvious.

1. Hmm. That's exactly what I've long thought about the analytic-synthetic distinction (dichotomy). It's trivial and uninteresting.

2. One can't draw any conclusions about "things" from such a statement? Well, strictly speaking, no, it's not specific enough, just as x - y = 9 is not specific enough to conclude what specific numbers x and y represent. (Of course, it's obvious x is greater than y.) However, "a thing acts according to its nature" is a summary of a vast number of more specific statements, e.g. fish by nature bite on worms on fishhooks. Clearly one can draw a conclusion from it. If you want to catch some fish, use worms as bait and you will likely catch some fish.

Edited October 17, 2007 by Merlin Jetton

[Brant Gaede]

The real Reality is what is independent of sentient consciousness. It is what would be there if all the sentience in the cosmos disappeared.

We can sense "reality" and we can speak about "reality", both of which require an observer. For all practical purposes, there would be nothing without any observer.

Nothing is nothing so how can you refer to it? There is no nothing. Metaphysically there is always something. It is "nothing" that requires a brain for it only exists epistemologically. It is not reality that requires an observer, it is "nothing." The observation is that there is no nothing to observe.

--Brant

[Dragonfly]

Abstract, non-applied mathematics tells us nothing about reality either. Not a blessed thing.

Bob,

Of course it does. I can think of a whole lot of things:

1. We exist and are conscious (otherwise we could not even think the math).

2. Law of identity ("1 is 1" to coin a phrase).

3. Units exist.

4. Systems can be organized through rules.

There's lots more reality that underpin "abstract, non-applied" math, and the math tells us about it very clearly if we look.

That we have to exist and to be conscious to think about abstract mathematics doesn't tell us anything about its content, and it is obviously that what Bob is referring to. It is of course a trivial truth that we have to exist and to be conscious to have any thought, no matter how "floating" or illogical and full of contradictions, but it would be a stretch to conclude that any nonsensical idea therefore tells us something about reality. That thinking is a physical activity doesn't alter the fact that some theories don't tell us anything about reality and other theories do. Further no one denies that a substantial part of mathematics can be applied in physical theories, but Bob wrote specifically about non-applied mathematics.

[Dragonfly]

2. One can't draw any conclusions about "things" from such a statement? Well, strictly speaking, no, it's not specific enough, just as x - y = 9 is not specific enough to conclude what specific numbers x and y represent. (Of course, it's obvious x is greater than y.)

Well, x and y might be complex numbers...

However, "a thing acts according to its nature" is a summary of a vast number of more specific statements, e.g. fish by nature bite on worms on fishhooks. Clearly one can draw a conclusion from it. If you want to catch some fish, use worms as bait and you will likely catch some fish.

Of course it is often very useful to find out what the nature of a thing is, in other words, what it does in all kinds of circumstances (for example that fish bite on worms on fishhooks), but that doesn't alter the fact that the statement that a thing acts according to its nature is a trivial tautology that doesn't tell us what its nature is.

[tjohnson]

Nothing is nothing so how can you refer to it? There is no nothing. Metaphysically there is always something. It is "nothing" that requires a brain for it only exists epistemologically. It is not reality that requires an observer, it is "nothing." The observation is that there is no nothing to observe.

I don't understand what you wrote, sorry. I orient myself by what Korzybski said which makes sense to me, there is no such thing as an object in perfect isolation, there needs to be an observer at the very least. To deny this one would have to produce an object in perfect isolation, which is impossible. So speaking about "reality independent of sentient consciousness" makes no sense to me. But I don't suppose I can convince you of that so we will have to agree to disagree.

[Michael Stuart Kelly]

That we have to exist and to be conscious to think about abstract mathematics doesn't tell us anything about its content, and it is obviously that what Bob is referring to. It is of course a trivial truth that we have to exist and to be conscious to have any thought...

Dragonfly,

I mentioned 4 items. You only dealt with the first? We disagree about existence and consciousness being a "trivial truth" derived from mathematics, even if you want to call it a tautology. From what I observe, the conclusion is based on experience, not merely a word game.

Here is another item pure math tells us about reality. It tells us that reality is constructed so as to contain correspondence to its formulations (if they are correct). This is tougher to understand since it is arrived at essentially through induction. The idea is that we are part of reality, thus we are constructed according to the same laws of nature that are observed in everything else. Our so-called analytic systems are organized in the same manner reality is organized. We see a phenomenon repeated over and over in science: an observation or result ends up corroborating correspondence-wise what, up to that point, had been a purely mathematical formulation.

I do not expect you to agree since you hold that analytic systems are divorced from reality. Rand calls these "concepts of method" and such methods are derived from reality according to the identification mechanism (discrimination/integration) in the human mind. I am of this second view.

Michael

[BaalChatzaf]

I do not expect you to agree since you hold that analytic systems are divorced from reality. Rand calls these "concepts of method" and such methods are derived from reality according to the identification mechanism (discrimination/integration) in the human mind. I am of this second view.

I suppose all ideas and memes are derived from reality in the sense that one has to have some kind of experience to even conceive or express such notions. But some mathematical abstractions are so far-fetched that the connection to concrete experience is distant or obscure. Where in the cosmos will you find a Klein Bottle? Many of the mathematical ideas are the result of analogy and metaphor, not similarity and difference. Cantor derived some of his set theoretical ideas from the operation of matching. How do you tell when two heaps of whatever discrete objects have the same number of items? Cantor extended the idea to infinite sets. Some mathematicians reacted in a very hostile manner to the notion of a completed infinite set of anything, however abstract. Very few mathematical ideas of any consequence are readily derived from ordinary experience. Even the objects of Euclidean Geometry, points, lines, circles, etc. etc. as Euclid conceived them are nowhere to be found in the real world. Are there any physical objects that have no parts, for example? That is Euclid's definition of a point.

While abstract mathematical systems, qua abstract systems, have a very distant relation (if any) to physical reality some can be made useful by associating a mathematical object with either a physical object or operation performed on a physical objects. That is how mathematics becomes a tool for physicists. This is somewhat analogous to making the characters of a novel or other fantasy "come alive", by dramatizing them with real live people. Fictional characters do not exist in the real world. Neither do dragons or unicorns, but we can have very real stories about them. Or we can liken out fictions to real live people. That is how satires bite. Fiction, qua fiction, is divorced from reality. There is no John Galt. There never was a John Galt who invented an atmospheric electric generated that violated several thermodynamical laws. I am sorry to bring you such disappointing news.

Ba'al Chatzaf

[Michael Stuart Kelly]

Where in the cosmos will you find a Klein Bottle?

Bob,

Huh?

In a Klein Bottle. They are built all the time.

Michael