'Existential Import'...does such a 'concept' have such?

[Michael Stuart Kelly]

GS,

Have you seen David Kelley's book on logic? I suspect not.

Bob was really snarky about it for a while. Then he got a copy and saw what it was. Then he got respectful.

The fact that he was really respectful makes me wonder why the strategic omission. Maybe it didn't fit his itch to proclaim himself to the world at large that he was the expert on logic above all Objectivists.

(Therefore, we should take his every opinion on faith... Oops... Am I being illogical by refusing to do that? )

Michael

[BaalChatzaf]

The fact that he was really respectful makes me wonder why the strategic omission. Maybe it didn't fit his itch to proclaim himself to the world at large that he was the expert on logic above all Objectivists.

(Therefore, we should take his every opinion on faith... Oops... Am I being illogical by refusing to do that? )

Michael

David Kelley's book -The Art of Reasoning- is a good straightforward college text book on various topics in logic and induction. Let me tell you what is not in his book

1. Rand's definition of logic

2. References to Rand

3. References to Objectivism.

The most unusual feature of the book is a chapter on Term Logic a system invented by Fred Sommers to capture, in symbolic form, the kind of categorical logic which Aristotle wrote of in Prior Analytics. It is a symbolic system for dealing with the logic of categorical propositions with existential import and is, in some ways, more natural (i.e. closer to ordinary language) than first order predicate logic. If you did not know that David Kelley was an O'ist you would not have found out in -The Art of Reasoning-.

On page 3 of 1994 he states "The core of logic is inference ....". There it is. The standard definition of logic used by people who do it for a living. Logic is about correct inference and valid arguments. It is not about determining what is or is not a fact.

Kelley does not wander off into metaphysics in the course of his book. He deals with logic deductive and inductive. And in deductive logic he treats classical (along the lines established by Aristotle) and modern (along the lines established by Boole, Frege, Russell and others). The book is not written for people who will go on to do research in formal or mathematical logic. It is a practical book and rather well writen.

Ba'al Chatzaf

Edited May 5, 2009 by BaalChatzaf

[Roger Bissell]

[...]

Thom, some comments:

1. Your defense of the modern interpretation of universal and particular propositions makes no sense to me. Universal propositions "assert absence" while particular ones "assert presence"?? Tilt. Ain't buyin' that, my friend. In my understanding, I am asserting the same thing in each case: either all or some of the instances of a particular thing, ~if~ any exist, have a certain nature. I think that unless you specify otherwise, you are implicitly asserting that such things exist, whether you are referring to some or all of them. They may in fact ~not~ exist. So? The King of France is bald. The King of France is not bald. Since they are (?) contradictories, one must be true, the other false, right? Wrong. They are both meaningless, unless you further specify: the King of France is a real human being who is bald vs. the King of France is a real human being who is NOT bald--which is presumably what the speaker is meaning to say. Aha, now we're getting somewhere. BOTH statements are false, because the King of France is not a real human being, bald or otherwise. Suppose I had said: the King of France is NOT a real human being who is bald vs. the King of France is NOT a real human being who is not bald. Aha, again. BOTH are TRUE.

The moral of this pedantic flogging of a dead logician's hobby horse is this: to judge truth and falsity validly, you must say what you mean and mean what you say. You can't get away with ambiguity (e.g., the King of France is bald...or not bald). The same reasoning applies to propositions about imaginary beings (e.g., from fairy tales, mythology, fiction).

2. You may be right in your comments about the traditionalist logicians, but I cannot make head nor tails out of your comments.

3. Ditto for your assertion that I am trying to "fuse" concretes and concepts.

REB

Roger,

On Point 1, I am taking John Venn's interpretation literally. Check out DK's Venn diagrams for the four classical propositional forms.

Thom, I'm aware of that. But why embrace John Venn's dogmatic, unsupportable interpretation of his very useful diagrams?

As for "The King of France is/isn't bald," we are dealing here not with a class but with a concrete. In this case the subject is a description of a nonexistent concrete.

The central issue in Points 2 and 3 concerns the separation of singular propositions and general propositions (universal and particular). Traditionalists lump singulars together with universal propositions. This package deal is what generates the issue of existential import.

Not true. Singular and universal propositions are treated the same because of how they refer to reality, which is what the issue of "existential import" completely misses (evades?). Consider "Dinosaurs are/aren't scaly." Now we are dealing not with a concrete but with a class. What is crucial is not concrete vs. class, but presently existing vs. NOT presently existing. Neither "King of France" nor "Dinosaurs" refer to anything presently existing, so nothing predicated of either of them IN PRESENT TENSE can be true. (Also, ANYTHING DENIED of them in present tense MUST be true.)

Also, I really don't know what you mean by "the subject is a description of a nonexistent concrete." "The King of France" is not a description of ANYTHING, but instead is DESCRIBED BY "is/isn't bald."

I would suggest that, given the Objectivist epistemology as the base, logical statements should be taught as having six propositional forms (instead of just the classical four). The extra two take concretes for subjects. U: x is P -- Y: x isn't P. U-statements and Y-statements require the existence of x as part of their truth conditions. If x does not exist, then both "x is P" and "x isn't P" are meaningless and are neither true nor false.

This is completely unnecessary and misleading to boot. Please concretize to see this. For instance, you would say "The King of France is bald" is meaningless and thus neither true nor false, because there is no King of France. I would instead say "The King of France" is ambiguous, and that once you specify what you are assuming about the King of France in your statement, it becomes clearly meaningful and thus either true or false. In the case that you are assuming that the King of France is a REAL PERSON, the proposition is unambiguously expressed "The King of France is a real person who is bald," which is clearly meaningful and clearly false! (So is "The King of France is a real person who is NOT bald.")

This kind of analysis works for EVERY--repeat: EVERY--alleged denial of truth and falsity due to lack of "existential import."

REB

[Michael Stuart Kelly]

David Kelley's book -The Art of Reasoning- is a good straightforward college text book on various topics in logic and induction. Let me tell you what is not in his book

1. Rand's definition of logic

2. References to Rand

3. References to Objectivism.

The most unusual feature of the book is a chapter on Term Logic a system invented by Fred Sommers to capture, in symbolic form, the kind of categorical logic which Aristotle wrote of in Prior Analytics. It is a symbolic system for dealing with the logic of categorical propositions with existential import and is, in some ways, more natural (i.e. closer to ordinary language) than first order predicate logic. If you did not know that David Kelley was an O'ist you would not have found out in -The Art of Reasoning-.

Bob,

Just so we are clear, this is not due to Kelley not agreeing with Rand. If read in a certain manner, your post insinuates this (although I am not sure this was your intention). It is due to the bias against her in academia. Kelley's book would not have been authorized for class use if she were quoted.

I am not 100% certain of this since I did not ask David, but from the stories all over the net about the difficulties people interested in Rand have encountered in academia (especially around the time David wrote the book), I am pretty sure it is true.

Also, it should be made clear that nothing in his book contradicts Rand's views. And if there is any doubt, one should ask him about the specific idea where the doubt occurs.

Michael

[BaalChatzaf]

Also, it should be made clear that nothing in his book contradicts Rand's views. And if there is any doubt, one should ask him about the specific idea where the doubt occurs.

Michael

Nothing I read in the book contradicts Rand's ideas except Kelley's characterization of logic, given on page 3. David Kelley writes: "The core of logic as always been the study of inference and most of this book is devoted to that subject. We will be talking about different kinds of inferences and about which ones to use in which sorts of situations. We will study rules for evaluating inferences and learn to distinguish the good ones from the bad ones....". In short logic is about the quality of inferences and arguments (which are chains of inferences).

His statement is not at odds with anything that Rand wrote, but it is NOT Rand's definition of reason of logic either. As I have pointed out, logic is about valid inferences. It is not about identifying facts. That is done by other means. Logic will not tell you the freezing temperature of water under various conditions. That is a matter of measurement and observation, not deduction.

David Kelley's book -The Evidence of the Senses- was published by a university press and it does reference Rand. So referencing Rand is not ipso facto a matter of academic disqualification.

Ba'al Chatzaf

[thomtg]

Roger,

Why embrace Venn's interpretation of his very useful diagrams? Because the contrary doctrine is untenable. It is possible Venn's interpretation may be wrong, but I think not.

[...]

Not true. Singular and universal propositions are treated the same because of how they refer to reality, which is what the issue of "existential import" completely misses (evades?). Consider "Dinosaurs are/aren't scaly." Now we are dealing not with a concrete but with a class. What is crucial is not concrete vs. class, but presently existing vs. NOT presently existing. Neither "King of France" nor "Dinosaurs" refer to anything presently existing, so nothing predicated of either of them IN PRESENT TENSE can be true. (Also, ANYTHING DENIED of them in present tense MUST be true.)

Also, I really don't know what you mean by "the subject is a description of a nonexistent concrete." "The King of France" is not a description of ANYTHING, but instead is DESCRIBED BY "is/isn't bald."

[...]

I mean that "the King of France" is a descriptive phrase purported to name a single concrete, which in this case doesn't exist; and this phrase takes the subject position in the statement ascribing baldness to it.

Ah, so let us suppose that dinosaurs, which are now extinct, were scaly,

- "all dinosaurs are scaly" would be false, because none now presently exists.

- "no dinosaur is scaly" would be true, because anything denied of nonpresence is fine.

- "all unicorns are horned horses" would be false, because none now presently exists.

- "no unicorn is a horned animal" would be true, because a denial of nonpresence is fine.

- "The present King of France is bald" would be false, because none now presently exists.

- "The present King of France isn't bald" would be true, ...

BUT

- "all dinosaurs were scaly" would be true;

- "no dinosaur were scaly" would be false;

- "all unicorns were horned horses" would be true;

- "no unicorn was a horned animal" would be false;

- "The present King of France was bald" would be true;

- "The present King of France wasn't bald" would be false.

All dinosaurs were scaly, but now they aren't? All unicorns were horned horses, but now they aren't? The present King of France was bald, but now he isn't? I think there is something wrong here with making verb tense a critical condition of predication. Of course a person's state of knowledge of reality must consider the state of existence of referents of the classes in the present and/or in the past, but the predication itself should express one's identification of reality as one finds it, right?

If, on the other hand, what you meant to say is that existential import is a condition of having reference in the statement for any assertion, then I am all for it. But then this condition is not called existential import, as interpreted by anyone else that I know.

A squared-circle is traditionally called a repugnant concept; as such, it has no place in any assertion. But in your conception of existential import, you would still judge statements about it as true or false.

- "all squared-circles are triangular" would be false;

- "no squared-circle is triangular" would be true;

Even traditionalists would shy from judging these statementsk, and this has nothing to do with existential import.

I am beginning to suspect that there may be some unclarity about the principle of bivalence. In my view, the statements about squared-circles are neither true nor false, because "squared-circle" doesn't mean anything. The same goes with "present King of France."

So, in a sense, we have veered away from the issue of existential import to make judgments about our statements of repugnant concepts and nonexisting concretes. The issue of existential import, about which modernists attack against traditionalists, remains unexamined.

[...]

This is completely unnecessary and misleading to boot. Please concretize to see this. For instance, you would say "The King of France is bald" is meaningless and thus neither true nor false, because there is no King of France. I would instead say "The King of France" is ambiguous, and that once you specify what you are assuming about the King of France in your statement, it becomes clearly meaningful and thus either true or false. In the case that you are assuming that the King of France is a REAL PERSON, the proposition is unambiguously expressed "The King of France is a real person who is bald," which is clearly meaningful and clearly false! (So is "The King of France is a real person who is NOT bald.")

[...]

I would go one step further, Roger, to say that there is such a thing as an elliptical statement, but what you are suggesting is not elliptical.

The statement "John Smith is a lottery winner" is ambiguous, because there are many men with such a name. When a newspaper reports him as a winner, the statement is really elliptical to mean "John Aaron Smith of 123 Main Street, Sometown, Somestate, etc., is a lottery winner." It is still one simple assertion, asserting one individual having won the lottery.

What you are suggesting is to make three or more separate assertions. That is not what ambiguity means. You want to assert two "is" and one compound "and" altogether; you want to assert that TpKOF is a real person, and that he is bald. The compound statement is not the same as the original statement. You are simply translating Russell's faulty theory of description to suit your proposal.

On the other hand, I could be persuaded to go along with you if you had said that the original statement "The present King of France is bald" is enthymematic. But then I am unpersuaded, because in this case the argument with its implicit premises can't even get off the ground on account of earlier-cited problems.

As I stated in my previous post, the core issue about existential import is the conflation of singular propositions with universal propositions.

[Roger Bissell]

Roger,

Why embrace Venn's interpretation of his very useful diagrams? Because the contrary doctrine is untenable. It is possible Venn's interpretation may be wrong, but I think not.

[...]

Not true. Singular and universal propositions are treated the same because of how they refer to reality, which is what the issue of "existential import" completely misses (evades?). Consider "Dinosaurs are/aren't scaly." Now we are dealing not with a concrete but with a class. What is crucial is not concrete vs. class, but presently existing vs. NOT presently existing. Neither "King of France" nor "Dinosaurs" refer to anything presently existing, so nothing predicated of either of them IN PRESENT TENSE can be true. (Also, ANYTHING DENIED of them in present tense MUST be true.)

Also, I really don't know what you mean by "the subject is a description of a nonexistent concrete." "The King of France" is not a description of ANYTHING, but instead is DESCRIBED BY "is/isn't bald."

[...]

I mean that "the King of France" is a descriptive phrase purported to name a single concrete, which in this case doesn't exist; and this phrase takes the subject position in the statement ascribing baldness to it.

Ah, so let us suppose that dinosaurs, which are now extinct, were scaly,

- "all dinosaurs are scaly" would be false, because none now presently exists.

- "no dinosaur is scaly" would be true, because anything denied of nonpresence is fine.

- "all unicorns are horned horses" would be false, because none now presently exists.

- "no unicorn is a horned animal" would be true, because a denial of nonpresence is fine.

- "The present King of France is bald" would be false, because none now presently exists.

- "The present King of France isn't bald" would be true, ...

BUT

- "all dinosaurs were scaly" would be true;

- "no dinosaur were scaly" would be false;

- "all unicorns were horned horses" would be true;

- "no unicorn was a horned animal" would be false;

- "The present King of France was bald" would be true;

- "The present King of France wasn't bald" would be false.

All dinosaurs were scaly, but now they aren't? All unicorns were horned horses, but now they aren't? The present King of France was bald, but now he isn't? I think there is something wrong here with making verb tense a critical condition of predication. Of course a person's state of knowledge of reality must consider the state of existence of referents of the classes in the present and/or in the past, but the predication itself should express one's identification of reality as one finds it, right?

The above examples ~terribly~ jumble up my view, if that is what they purport to illustrate (for purposes of reductio ad absurdum?). Let me run through them and give ~my~ interpretations and evaluations of them:

- "all dinosaurs are scaly" would be false, because none now presently exists [i.e., because there are no such presently existing creatures: "all dinosaurs are presently existing scaly creatures." This is clearly false.]

- "no dinosaur is scaly" would be true, because anything denied of nonpresence is fine. [i would say it is true, because no dinosaur is a presently existing creature: "no dinosaur is a presently existing scaly creature." This is clearly true.]

- "all unicorns are horned horses" would be false, because none now presently exists. [Here you open up the realm of imaginary creatures. By convention, unicorns are imaginary horned horses, so "unicorns are imaginary horned horses" is true. However, if the speaker really ~believed~ (wrongly) in the real existence of such creatures, then ~his~ statement would actually instead mean "unicorns are REAL horned horses," which of course is FALSE, because since all unicorns are imaginary horses, and no imaginary horses are real horned horses, no unicorn is a ~real~ horned horse.]

- "no unicorn is a horned animal" would be true, because a denial of nonpresence is fine. [Here you have changed the predicate. You are in good company. At least one of the major logic text writers does this little trick, perhaps not intentionally, but he totally messes up and invalidates his discussion of existential import in so doing. Anyway, again, by convention, unicorns are imaginary horned animals, so "no unicorn is an imaginary horned animal" is FALSE! However, let's trot out the guy who (rightly) disbelieves in the real existence of unicorns and let him spell out ~his~ meaning: "no unicorn is a REAL horned animal." This of course is TRUE, because since no unicorn is a ~real~ horned animal.]

- "The present King of France is bald" would be false, because none now presently exists. [i would say it is false, because the statement is really saying: "The present King of France is a ~presently existing~ person who is bald." This is clearly false.]

- "The present King of France isn't bald" would be true, ... [No!!! Again, this proposition is FALSE, because the statement is really saying: "The present King of France is a ~presently existing~ person who is NOT bald." Again, this is clearly false.]

BUT [Thom, these examples are god-awful distortions of what I advocate, but I'll address them anyway]

- "all dinosaurs were scaly" would be true; [Yes. This means that all dinosaurs were past-existing creatures that were scaly. True.]

- "no dinosaurs were scaly" would be false; [Again, you are correct. This means that no dinosaurs were past-existing creatures that were scaly, which is false.]

- "all unicorns were horned horses" would be true; [Arrrrgh. All unicorns were REAL past-existing horned horses? False. All unicorns were IMAGINARY past-existing horned horses? True. At least, once the idea of unicorns was created.]

- "no unicorn was a horned animal" would be false; [Double-arrrrrgh, for the reason cited above. No unicorn was a REAL past-existing horned animal? True. No unicorn was an IMAGINARY past-existing horned animal? FALSE!!]

- "The present King of France was bald" would be true; [Arrrrgh. The present King of France was a past-existing person who was bald? FALSE!!]

- "The present King of France wasn't bald" would be false. [You are right, but probably for the wrong reason. The present King of France was a past-existing person who was NOT bald? False.]

*****************[before reading on, please scroll down and read the P.S.]*******************************

A squared-circle is traditionally called a repugnant concept; as such, it has no place in any assertion. But in your conception of existential import, you would still judge statements about it as true or false.

- "all squared-circles are triangular" would be false;

- "no squared-circle is triangular" would be true;

Even traditionalists would shy from judging these statements, and this has nothing to do with existential import.

I am beginning to suspect that there may be some unclarity about the principle of bivalence. In my view, the statements about squared-circles are neither true nor false, because "squared-circle" doesn't mean anything. The same goes with "present King of France."

So, in a sense, we have veered away from the issue of existential import to make judgments about our statements of repugnant concepts and nonexisting concretes. The issue of existential import, about which modernists attack against traditionalists, remains unexamined.

Unexamined? Not by me! I have voluminously examined supposed examples that purport to show how the Aristotelian Square of Opposition does not hold for propositions about non-existent subjects, due to the supposed lack of Existential Import of the universal forms of those propositions.

As for Traditionalists, it's their shortcoming (not mine) that they would shy from judging statements about squared circles! Oh ye of little rational grasp of propositional intent!

The concept of "squared-circle" has "no place in any assertion"??? It "doesn't mean anything"??? Come on! A squared-circle is just a specific kind of contradictory idea, a "real circle that has an impossible attribute"--and we Randians are comfortable asserting (with Rand) that "contradictions don't exist," aren't we? So why can't we say "contradictions are real things with contradictory attributes"? Surely that is meaningful and false!

Obviously I disagree with you and the Moderns about the meaninglessness of statements referring to "squared-circles" and "present King of France." I would indeed judge statements about them as true or false, but ONLY after carefully specifying WHAT MODE OF BEING IS BEING IMPLICITLY ASSUMED FOR THEM BY THE SPEAKER!! (And do I have to belabor how specifying the mode of being of a subject completely vitiates the claim by Moderns that universal propositions lack Existential Import because of the phony examples of unicorns and squared-circles and present Kings of France?)

In regard to squared-circles, you have needlessly complicated the example. You are saying that circles that are square are (or are not) also triangular. But fine, let's work with that.

If I assert: "all squared-circles are real circles that are square and triangular," that is not intelligible and meaningful? Seems to me it jolly well ~is~ intelligible and meaningful! And false, to boot! For that is what "all squared-circles are triangular" ~really means~. That is what it really ~intends~ to assert. Which is clearly an incorrect assertion of an identification of reality.

"No squared-circle is triangular" similarly really means "no squared-circle is a real circle that is square and triangular." Here we have an intelligible, meaningful, TRUE proposition. It is a FACT that there are no real circles that are square and triangular! This is a correct assertion of an identification of reality!

Thom, I have steeped in this stuff for DECADES. It makes perfect sense to me, and I think that all the major logicians and their texts are out to lunch on this issue! You have done nothing to shake my grasp of this or my confidence that I am correct, not one iota. I only regret that I don't have a philosophy Ph.D., so that I could wangle a contract to write a university logic text and blast all this modern logic crap sky-high, where it belongs.

REB

P.S. to those whose eyes may have glazed over and accidentally come back to alertness on this P.S.--the reason I go to such pedantic lengths to untangle all of Thom's examples (as I have done many, many others for nearly 20 years now in private correspondence to others) is that Modern Logicians want to eviscerate or emasculate (whichever is worse) Aristotle's Square of Opposition. David Kelley seems to have bought into the Modernists' theory that most of the logical relations between A, E, I, and O propositions do not hold when a proposition is made about non-existent objects. I think that this is one of the most pernicious and deadly false things that has been injected into philosophy in the past 150 years, and I am shocked and dismayed that Objectivists have not jumped on it with both feet.

[BaalChatzaf]

P.S. to those whose eyes may have glazed over and accidentally come back to alertness on this P.S.--the reason I go to such pedantic lengths to untangle all of Thom's examples (as I have done many, many others for nearly 20 years now in private correspondence to others) is that Modern Logicians want to eviscerate or emasculate (whichever is worse) Aristotle's Square of Opposition. David Kelley seems to have bought into the Modernists' theory that most of the logical relations between A, E, I, and O propositions do not hold when a proposition is made about non-existent objects. I think that this is one of the most pernicious and deadly false things that has been injected into philosophy in the past 150 years, and I am shocked and dismayed that Objectivists have not jumped on it with both feet.

They have, darling, and they have landed in deep shit.

The categorical statement (A form using the AEIO scheme) All A are B is rendered in first order predicate calculus as (x)[A(x) -> B(x)] (translated: For all x if A is true of x then B is true of x). Now suppose A is empty. The it must be the case that A(x) -> B(x) since A(x) is false. For suppose it were not the case. Then there would exist s such that A(s)&~B(s). If that were so then it would follow that A(s) since when a conjunction of the form W&V is asserted it implies each of W and V. But A(s) implies there is an x such that A(x) and we assumed that for all x ~A(x) (A is the empty set). So the problem is not corruption, it is the way inclusion is rendered in predicate logic. There is a perfect fine mathematical reason why the empty set is a subset of every set. This insures that set intersection is defined for any pair of sets and that the class of sets form a complete lattice partially ordered by inclusion. It also insures that set complementation (which is the counterpart in set theory to negation of a number in algebra) is defined for all sets. In short, the empty set has a similar function for the Boolean algebra of sets that the zero (0) has for addition in the standard algebra of numbers.

This crapdoodle about philosophical corruption is symptomatic of the ignorance of mathematics that is positively endemic among Objectivists. The square of opposition has been trimmed for purely mathematical reasons which have existed since Boole and Frege mathematized logic back in the middle of the 19th century. Boole and Frege did the service of liberating formal logic from metaphysics and turning it into a powerful mathematical tool which has been used since to formulate the structure and operation of logical circuits in computers. Boolean algebra, to put it briefly, is the algebra of computer circuits (one of its most important applications). If only categorical logic existed (the kind of logic Aristotle formulated in -Prior Analytics-) we would have no computers or their design would be so difficult as to be nearly impossible. Boole and Frege jumped logic to a new level for the first time in over 2000 years. Leibniz almost did the same thing 200 years prior, but he missed by a little bit. If you call this improvement evisceration or emasculation you have a very strange idea of evisceration and emasculation.

Note to our Moderator: MSK, now do you see why I get testy? Do you? When it comes to formal logic, mathematics and physics I have the same general opinion of O'ists as Karl Friedrich Gauss (one of the five greatest mathematicians of all time) had of the metaphysicians. Gauss said when the metaphysicians are right they are dealing in trivialities and when they make substantial statements they are almost always wrong. Ditto for O'ists with regard to formal logic, mathematics and physics (by and large --- there are some rare and notable exceptions). With regard to formal logic, mathematics and physics, the O'ists are mostly Phillistines (nyekultornye as they say in Russian).

Ba'al Chatzaf

Edited May 6, 2009 by BaalChatzaf

[Michael Stuart Kelly]

Folks,

I'm going to need some time to digest all this.

Bob,

Rand did not state that logic is the art of "identification." She stated that it is the art of "noncontradictory identification." What is "noncontradictory" if not an inference? And what is a conclusion if not an identification?

I see her definition more like a synonym of the classical definition than a whole new ballgame. And I believe the English language is rich enough to have synonyms, even for technical matters.

This is why I have always gotten the feeling from these discussions that people are essentially saying, "No. Rand said is is big. It is not big. It is large. Rand is wrong."

I don't mind Rand being wrong. I do mind that kind of pretext for claiming she was wrong. It comes off as bashing qua bashing.

Michael

[BaalChatzaf]

Folks,

I'm going to need some time to digest all this.

Bob,

Rand did not state that logic is the art of "identification." She stated that it is the art of "noncontradictory identification." What is "noncontradictory" if not an inference? And what is a conclusion if not an identification?

Non contradictory identification of what? An inference is a proposition that is derived from other propositions by means of inference rules. If you want to stretch meanings you must just as well include playing chess in Rand's definition. Chess is the non-contradictory identification of good moves. Or movie reviewing; movie reviewing is the non-contradictory identification of movie characters, plots etc.. Or cooking; cooking is the non-contradictory identification of tasty ingredients and ways of preparing them. And so on.

If Rand meant to say logic is the non-contradictory identification of valid arguments, she should have said so. Are we to assume that Rand was at a loss for words? I doubt that.

Rand's definition of logic is not in line with what logicians do for a living. It does not match what David Kelley said on page 3 of his book -The Art of Reasoning- (quote given in another positing). Rand just plain did not comprehend what logicians have been doing since 1850 when Boole published -The Laws of Thought-. Not only have logicians been extending the scope of logic but they have identified the limitations of logic (e.g. Goedel Incompleteness Theorem). Logicians have been determining the valid basis of mathematics (an ongoing process, not yet completed). Mathematicians have been returning the favor by incorporating the principles of formal logic into mathematical systems. That is how the rigorous theory of infinitesimals was established by A. Robinson in 1960.

Ba'al Chatzaf

[Michael Stuart Kelly]

Sorry, Bob.

It doesn't wash.

Your examples are too forced for much comment. Chess is a game, for instance, not logic. It does use logic, though, including conclusions from inferences or noncontradictory identifications.

I believe your commitment to your judgment that Rand was a dummy about math and logic is too strong for accepting the facts or even contemplating that your judgment might have been not well-thought-out.

To me, when facts are discarded the way you are doing and any old thing that doesn't even fit is used as an example, this is an issue of faith, not reason, and especially not logic.

Your faith is that you are superior to Rand and this is crucially important to you. Who am I to argue with that? I don't argue with Christians, either.

Michael

[Dragonfly]

Bob, what Rand said must be true, just as everything in the bible must be true (and those pesky mathematicians with their corrupt philosophy of course don't get it). And if it isn't true, we'll make it true. If there seems to be a slight discrepancy between the notion of a creation in six days and the scientific evidence, you just declare that the "days" in the bible are not our days, but periods of billions of years, so you see, the bible was right after all! That it still doesn't make any sense, doesn't matter. The parallel with reinterpreting Rand's definition of logic is striking.

[Michael Stuart Kelly]

"Bob, what Rand said must be wrong, just as everything in ITOE must be wrong (and those pesky Objectivists with their corrupt philosophy of course don't get it). And if it isn't wrong, we'll make it wrong..."

Need I go on?

But OK, Dragonfly. You stated that "The parallel with reinterpreting Rand's definition of logic is striking."

What got reinterpreted?

Is "noncontradictory" an inference or not?

Is a conclusion (or even a proposition) an identification or not?

If not, what are they?

I'm listening.

Michael

[BaalChatzaf]

"Bob, what Rand said must be wrong, just as everything in ITOE must be wrong (and those pesky Objectivists with their corrupt philosophy of course don't get it). And if it isn't wrong, we'll make it wrong..."

Need I go on?

But OK, Dragonfly. You stated that "The parallel with reinterpreting Rand's definition of logic is striking."

What got reinterpreted?

Is "noncontradictory" an inference or not?

Is a conclusion (or even a proposition) an identification or not?

If not, what are they?

I'm listening.

Michael

Many other things are identification or identifications as I pointed out. Her description (non-contradictory identification) is not specific to logic. Hence it is a thoroughly bad definition, if it is a definition at all. In any case it does no square well with what logicians say logic is. Now who is more likely to know what logic is? A novelist or a logician? The central core of logic, as David Kelley points out is inference, not identification. Logic is about getting from premise to conclusions in one piece and intact

Ba'a Chatzaf

[BaalChatzaf]

I believe your commitment to your judgment that Rand was a dummy about math and logic is too strong for accepting the facts or even contemplating that your judgment might have been not well-thought-out.

Not a dummy. An ignoramus. There is a difference. The first is can't know (due to mental deficiency) the second is doesn't know (due to lack of instruction or experience). I am a musical ignoramus but I am not a dummy. Before I became 3/4 deaf I was perfectly capable of learning music. I didn't because I was more interested in other matters.

Ba'al Chatzaf

[Michael Stuart Kelly]

Bob,

What you show signs of not seeing is that Rand made a connection between concept formation and the rules of logic. She essentially claims that concept formation is a simpler form of the way logic works, or that logic is the natural (or biological) extension of how we integrate abstractions. This goes for math, also.

She did not believe in the mind-body dichotomy, i.e., that there are rules for the mind that are totally cut off—and obey a separate reality—from the way the body works.

Your arguments from authority are falling on deaf ears because I see all this clearly—that this was her point. With a little good will, you will see it, too.

Or not...

(btw - I have some problems with Rand's definition of logic, but it has nothing to do with bowing down before the eminence of the enshrined ones or any other form of snobbishness. I might discuss them later, but not in this context.)

Michael

[BaalChatzaf]

To me, when facts are discarded the way you are doing and any old thing that doesn't even fit is used as an example, this is an issue of faith, not reason, and especially not logic.

Your faith is that you are superior to Rand and this is crucially important to you. Who am I to argue with that? I don't argue with Christians, either.

Michael

It is important to me. She and Imam Peikoff denigrated my trade. She, L.P. and some other Objectivists have libeled, slandered, insulted and mischaracterized logic, mathematics and physics, the most important intellectual undertakings of Western Civilization. We are told how corrupt physics is. The same physics based on quantum theory that has produced computer networks which enable them to promulgate their untruths and half-truths world wide. And you wonder that I am a bit testy?

If Madam Rand had restrained herself to exposing the flawed moral and ethical premises that are currently destroying the West, I would not have said boo!. In fact I would have and even have agreed with her on such matters. But in a fit of apparent hubris she overextended herself and denigrated the one healthy, progressive and productive aspect of Western thinking. As Winston Churchill once said, this is something up with which I will not put. Western science based primarily on Platonic idealization happens to be in good shape, because it is checked, vetted, validated and constrained by empirical testing, something that Rand's hero Aristotle hardly ever bothered with. The old saw about babies and bathwater comes to mind.

Ba'al Chatzaf

[Dragonfly]

I believe your commitment to your judgment that Rand was a dummy about math and logic is too strong for accepting the facts or even contemplating that your judgment might have been not well-thought-out.

Not a dummy. An ignoramus. There is a difference. The first is can't know (due to mental deficiency) the second is doesn't know (due to lack of instruction or experience).

Exactly. That Rand's knowledge about mathematics and logic was very elementary (she apparently didn't even know what an imaginary number is) is in itself not so important, just as it isn't important that Darwin's ideas about genetics were completely wrong. Nobody can know everything, and we leave the incorrect statements and theories behind. Trying afterwards to make them valid by some very athletic verbal gymnastics and stretching of the meaning of words beyond all breaking points is not doing a service to Rand (neither would it be to Darwin if we insisted that his ideas about genetics were correct after all by sophistic reasoning). Nobody (except an Objectivist) could care less that Rand had some incorrect ideas about science and mathematics, until her defenders start trying to vindicate her incorrect ideas. That kind of behavior is typical for crackpots and cultists, and the predictable result is that the people who are knowledgeable about these things will tend to dismiss them as such.

[Michael Stuart Kelly]

She and Imam Peikoff denigrated my trade. She, L.P. and some other Objectivists have libeled, slandered, insulted and mischaracterized logic, mathematics and physics, the most important intellectual undertakings of Western Civilization.

Bob,

That they have done and it is inexcusable.

I fully agree with you on this point.

I might even understand where they are coming from, but there is really is no excuse for such irrational pronouncements by Rand or her emulators. I consider their treatment of academics a black mark on Objectivism. Thank goodness there are people like Chris Sciabarra who help show that both worlds can be compatible.

On the other end, I do notice that when scientists and other academics get yelling at each other, it gets quite annoying if you are on the outside trying to ask a question. For an easy example, look at the global warming discussion (almost anywhere) for case after case. Even on Michael Crichton's blog for State of Fear (when he was still alive), they simply closed the discussion down for all the nastiness and nothing but "the same old same old" (to quote the moderator).

Also, there is academic snobbishness, which is quite abundant in this little world of ours. Thick as flies on shit, to be frank. I think it is simply assholishness to the nth degree by insecure little souls who are intelligent enough to know better.

I don't believe there is any reason to emulate any of this, neither join Rand's charge against the Evil Windmills of the Mind nor become one of the Experts in Superficial Profundity.

There are great ideas in both worlds, and great people, too. Getting things right is a task large enough for a lifetime. It's really a shame that there is all this mess.

Who started it? Well, academic assholishness was around long before Rand was even born. But I think Rand would have been a belligerent Rand whether it existed or not. (And monkey-see-monkey-do suck-ups are monkey-see-monkey-do suck-ups, whether academic or Objectivist.) So I think it doesn't matter and both approaches of piss-poor behavior in discussing the other are wrong and childish.

They turn The Virtue of Selfishness into The Virtue of Shallow Vanity. And both are far better than that. Shame on them all.

Michael

[tjohnson]

On the other end, I do notice that when scientists and other academics get yelling at each other,

Yes, scientists are humans with emotions too. Sometimes the objectivity practiced by the scientist in their specific field disappears when they deal with personal issues. I think you need to look at science as a process that occurs over many generations and sometimes there are blind alleys and false starts but in the end it works out because the scientific method prevails. It is an ongoing process that requires the adjusting of our theories as new information becomes available.

[Roger Bissell]

P.S. to those whose eyes may have glazed over and accidentally come back to alertness on this P.S.--the reason I go to such pedantic lengths to untangle all of Thom's examples (as I have done many, many others for nearly 20 years now in private correspondence to others) is that Modern Logicians want to eviscerate or emasculate (whichever is worse) Aristotle's Square of Opposition. David Kelley seems to have bought into the Modernists' theory that most of the logical relations between A, E, I, and O propositions do not hold when a proposition is made about non-existent objects. I think that this is one of the most pernicious and deadly false things that has been injected into philosophy in the past 150 years, and I am shocked and dismayed that Objectivists have not jumped on it with both feet.

They have, darling, and they have landed in deep shit.

The categorical statement (A form using the AEIO scheme) All A are B is rendered in first order predicate calculus as (x)[A(x) -> B(x)] (translated: For all x if A is true of x then B is true of x). Now suppose A is empty. The it must be the case that A(x) -> B(x) since A(x) is false. For suppose it were not the case. Then there would exist s such that A(s)&~B(s). If that were so then it would follow that A(s) since when a conjunction of the form W&V is asserted it implies each of W and V. But A(s) implies there is an x such that A(x) and we assumed that for all x ~A(x) (A is the empty set). So the problem is not corruption, it is the way inclusion is rendered in predicate logic. There is a perfect fine mathematical reason why the empty set is a subset of every set. This insures that set intersection is defined for any pair of sets and that the class of sets form a complete lattice partially ordered by inclusion. It also insures that set complementation (which is the counterpart in set theory to negation of a number in algebra) is defined for all sets. In short, the empty set has a similar function for the Boolean algebra of sets that the zero (0) has for addition in the standard algebra of numbers.

This crapdoodle about philosophical corruption is symptomatic of the ignorance of mathematics that is positively endemic among Objectivists. The square of opposition has been trimmed for purely mathematical reasons which have existed since Boole and Frege mathematized logic back in the middle of the 19th century. Boole and Frege did the service of liberating formal logic from metaphysics and turning it into a powerful mathematical tool which has been used since to formulate the structure and operation of logical circuits in computers. Boolean algebra, to put it briefly, is the algebra of computer circuits (one of its most important applications). If only categorical logic existed (the kind of logic Aristotle formulated in -Prior Analytics-) we would have no computers or their design would be so difficult as to be nearly impossible. Boole and Frege jumped logic to a new level for the first time in over 2000 years. Leibniz almost did the same thing 200 years prior, but he missed by a little bit. If you call this improvement evisceration or emasculation you have a very strange idea of evisceration and emasculation.

Note to our Moderator: MSK, now do you see why I get testy? Do you? When it comes to formal logic, mathematics and physics I have the same general opinion of O'ists as Karl Friedrich Gauss (one of the five greatest mathematicians of all time) had of the metaphysicians. Gauss said when the metaphysicians are right they are dealing in trivialities and when they make substantial statements they are almost always wrong. Ditto for O'ists with regard to formal logic, mathematics and physics (by and large --- there are some rare and notable exceptions). With regard to formal logic, mathematics and physics, the O'ists are mostly Phillistines (nyekultornye as they say in Russian).

Ba'al Chatzaf

Sometimes, dear Ba'al, people get "testy" when other people refuse to acknowledge their imaginary clothing and other luxurious fantasies. I suppose such other people might be thought of as "Philistines."

Let me concretize. You wrote:

There is a perfect fine mathematical reason why the empty set is a subset of every set. This insures that set intersection is defined for any pair of sets and that the class of sets form a complete lattice partially ordered by inclusion. It also insures that set complementation (which is the counterpart in set theory to negation of a number in algebra) is defined for all sets. In short, the empty set has a similar function for the Boolean algebra of sets that the zero (0) has for addition in the standard algebra of numbers.

Do you not see what an absurdity this is -- to define "the empty set [as] a subset of every set"?? Call me old-fashioned, but I would argue precisely the opposite: that the empty set is not a subset of ANY set!

There are two ways to show the absurdity of your position, without getting too technical. I borrow the first from Hugh MacColl's essay "The Existential Import of Propositions" (MIND, Vol. 14, No. 55, July 1905, p. 401) and the second from his essay "Existential Import" (MIND, Vol. 14, No. 54, April 1905, pp. 295-296).

1. Round squares constitute an empty set, correct? By your argument, they must be included in every set, including, for example, the set of all triangles. Thus, you are arguing, are you not, that "Every round square is a triangle"?....I, on the other hand, hold that the empty set of round squares must be EXCLUDED from every set, and thus that "NO round square is a triangle."

2. According to Boolean logic conventions, the statement (XA = X) asserts that "Every X is A," whatever X and A may represent. By their conventions also the symbol 0 represents NON-EXISTENCE. Let A represent EXISTENT. It follows that the statement (0A = 0) asserts that "Every NON-EXISTENCE is EXISTENT." This assertion is self-contradictory. Thus, the Boolean statement (0A = 0) is NOT always true for all values (i.e., meanings) of A. (Of course the formula holds good in mathematics for every number A, such as 0 x 2 = 0; but then in mathematics 0 x 2 = 0 does NOT assert that "Every 0 is 2." (!!)

Which one of us is living in the real world, Ba'al? Which one of us is using logic as a tool for non-contradictorily identifying reality??

Finally: you claim to justify Boolean algebra on the grounds that it gave us many of the technological wonders that we now enjoy -- and that (supposedly) without it, we wouldn't have them. Well, I could reply colloquially that there is "more than one way to skin a cat." Or I could just cite your godfather, Bertrand Russell, who said that a false statement implies ~every~ statement. One can indeed stumble on truth from false premises, as I'm sure you know. (Nice try, though.)

What REALLY bothers me is that the fact that you cannot stumble on falsity from true premises is used, sophistically, by the Moderns, along with their attempts to "demonstrate" that Aristotle's Square of Opposition does not hold for all categorical propositions (viz., those about non-existent objects), to claim that the SOO leads to error and thus must be (as I said previously) eviscerated and emasculated. (For further details, read David Kelley's section on this topic, which does nothing to solve the problem.)

REB

P.S. -- I am not a computer genius, nor well versed in programming logic, but I did minor in both philosophy and mathematics in college, and I know intellectual fraud and/or incompetence when I see it. And the whole Modern Logic denigration and dismissal of Aristotle's Square of Opposition and the Existential Import of universal propositions is a prime example of it/them.

[BaalChatzaf]

Reply to REB.

The empty set 0' is a subset of any set A.

Proof:

A set B is not a subset of set C if there is an element in B such is not in C.

(This is equivalent to the definition of subset to wit, B is a subset of C if and only if any element of B is an element of C).

Now suppose 0' is not a subset of A. Then there is an element in 0 which is not in A. So there is an element in 0' and that element is not in A. Which implies there is an element in 0' (the conjunction X&Y implies each of X and Y). But this says there is an element in 0' which is a contradiction. The empty set has no elements.

Q.E.D.

The lattice of sets has a minimal element, to wit, 0 the empty set. This is cognate or similar to the assertion there is an integer less than or equal to every integer (integer = the set {0,1,2...}). It is the integer 0 This is also cognate to the assertion that any set of real numbers bounded below has a greatest lower bound, some times call the inf (abbreviation of latin for smallest) of the set.

Get a refund from the school that taught you your math and logic. They have failed you.

Ba'al Chatzaf

Edited May 8, 2009 by BaalChatzaf

[Michael Stuart Kelly]

I'm still trying to figure out how more than one is not a quantity.

Maybe it is hiding between the Q and E or the E and D...

For some reason I think this question will never be addressed by those who preach it.

Michael

[BaalChatzaf]

I'm still trying to figure out how more than one is not a quantity.

Maybe it is hiding between the Q and E or the E and D...

For some reason I think this question will never be addressed by those who preach it.

Michael

It can be defined independent of any system of measurements or numbers. I showed you how. All it depends on is the denial of equality i.e. x != y which is to say x and y are not the same object.

If you admit denials of equality as positive assertions of quantity than any system in which equality is meaningful is about quantities. So essays about daffodils and roses (daffodil != rose) is an essay about quantity. Such nonsense would render the concept of quantity meaningless.

In short everything is about measurement and quantity, which is to say nothing in particular is about measurement or quantity.

Is that what you want?

Ba'al Chatzaf

[Roger Bissell]

Reply to REB.

The empty set 0' is a subset of any set A.

Proof:

A set B is not a subset of set C if there is an element in B such is not in C.

(This is equivalent to the definition of subset to wit, B is a subset of C if and only if any element of B is an element of C).

Now suppose 0' is not a subset of A. Then there is an element in 0 which is not in A. So there is an element in 0' and that element is not in A. Which implies there is an element in 0' (the conjunction X&Y implies each of X and Y). But this says there is an element in 0' which is a contradiction. The empty set has no elements.

Q.E.D.

The lattice of sets has a minimal element, to wit, 0 the empty set. This is cognate or similar to the assertion there is an integer less than or equal to every integer (integer = the set {0,1,2...}). It is the integer 0 This is also cognate to the assertion that any set of real numbers bounded below has a greatest lower bound, some times call the inf (abbreviation of latin for smallest) of the set.

Get a refund from the school that taught you your math and logic. They have failed you.

Ba'al Chatzaf

Ye gods, could we please stick to plain English? Enough with the jargon and arm-waving. Also, your logic is way screwy, because of sloppy "equivalences." Let's see where you went amiss.

First, the definition of empty set needs to be cleaned up. Try this:

B is a subset of C iff there is an element of B that is an element of C. This biconditional resolves into:

1. If B is a subset of C, then there is an element of B that is an element of C.

2. If there is an element of B that is an element of C, then B is a subset of C.

Now, since you gave a negative form you claimed was equivalent to the definition, it can only be the negation of one of the two conditionals:

1a. If there is not an element of B that is an element of C, then B is not a subset of C.

2a. If B is not a subset of C, then there is not an element of B that is an element of C.

Applying this to the empty set argument:

1b. If there is not an element of 0' that is an element of A, then 0' is not a subset of A.

2b. If 0' is not a subset of A, then there is not an element of 0' that is an element of A.

Now, what you stated ~looks~ a bit like 1a, but with a crucial twist that undoes your attempted proof. Your statement is:

1c. If there is an element of B that is not an element of C, then B is not a subset of C.

And by denying the consequent, you come up with:

2c. If B is not a subset of C, then there is an element of B that is not an element of C.

Notice how ~this~ applies to the empty set argument:

1d. If there is an element of 0' that is not an element of A, then 0' is not a subset of A.

2d. If 0' is not a subset of A, then there is an element of 0' that is not an element of A.

Now, compare my 2b with your 2d:

2b. If 0' is not a subset of A, then there is not an element of 0' that is an element of A.

2d. If 0' is not a subset of A, then there is an element of 0' that is not an element of A.

See the difference??

Because you have invalidly unpacked the biconditional (definition), you invalidly claim that denial that the empty set is a member of all sets entails that THERE EXISTS some element of the empty set that does not belong to A. And since the empty set contains no elements, THERE DOES NOT EXIST any such element, and therefore (you invalidly conclude) 0' MUST BE a subset of A.

Because I have ~validly~ unpacked the definition of empty set, I am able to validly claim that denial that the empty set is a member of all sets entails that THERE DOES NOT EXIST some element of the empty set that does not belong to A. And since the empty set contains no elements, whether also belonging or not belonging to A, there is no conflict, and I am able to ~validly~ conclude that 0' is NOT a subset of A.

The crucial difference is that my valid inference from the definition did not trap me into assuming the existence that the empty set contains any elements, whereas your invalid inference ~would~ trap me into such an assumption, were I to swallow your faulty inference from the definition. So, your reductio fails, and my claim stands: the empty set is not a subset of all sets (or any set).

I confess that I really thought that my specific example would be meat and potatoes enough to convince you that there is ~something~ fishy about the bogus claim that the empty set is a subset of all sets, but...oh, well...

You could perhaps see this better if you would first get clear on what you mean by "empty set." I was taught that an empty set is a set with no members, such as the set of prime numbers between 7 and 11 or the set of mammals with 8 wings. Now, you keep talking about "THE empty set," which also you say has no members. Is "THE empty set" different from "AN empty set"? If so, how? Is there one and only one set with no members that is called "THE empty set", which is somehow distinct from "AN empty set"? Is each of the specific empty sets a species of empty set? And is THE empty set also a species of empty set, or is it the genus empty set, of which all the specific empty sets are species? In the normal course of human cognition, we first grasp particulars -- in this case, specific empty sets -- before going on to form abstractions such as "THE empty set," if that's indeed what it is. If it is something OTHER than the general case of the specific empty sets we form from observation of and thinking about the world around us, then I don't have any earthly idea what it could be. Other than an arbitrary construct, used as a tool for bashing people who want to direct logic to the inferentially sound thinking about the facts of reality.

I'll let you puzzle all that out, if you can. To me, it's all double-talk. But it's obvious that AN empty set (such as the set of square circles) CANNOT be a subset of the set of triangles. That would mean that: "All square circles are triangles." Nonsense.

Now, maybe THE empty set -- whatever the hell that is, distinct from ANY SPECIFIC empty set -- can be a subset of all other sets, but I don't see how. If it's NO EMPTY SET IN PARTICULAR, then it has NO NATURE, and you cannot predicate set membership of it. A SPECIFIC empty set DOES have a nature, and you CAN predicate set membership of it, but only falsely. (Because no square circles are triangles.)

REB

P.S. -- I am sending a copy of our exchanges to the Philosophy and Mathematics and English departments at Iowa State University, and they can argue among themselves as to which of them "failed" me and "owe" me a refund.