"A is A" - Whose Formula?


jenright

Recommended Posts

In the "About the Author" afterword to Atlas Shrugged, Rand indicated that the titles of the book's three parts were a tribute to Aristotle. One of those section titles was: A is A, and that formulation figured prominently in the novel, and in Objectivist discussions ever since. Many have assumed that the formulation must be from Aristotle. But it's not - not directly.

"A is A" does occur in Leibniz, who, among his many endeavors, worked on fashioning a symbolic form of Aristotelian logic. I haven't found "A is A" in anyone earlier, so I have suspected Leibniz for a while. But neither had I found anything scholarly that asserted his authorship of the formula.

Some years ago, Thomas Stone had sent me a note saying that Leonard Peikoff, in his lecture series on the History of Philosophy, had credited Antonius Andreas, a 12th century philosopher, with the formulation of the law of identity - of which "A is A" is a symbolic statement.

Today I found a document in French which states that Wilhelm Wundt, the famous German psychologist, specifically credited Leibniz with "A is A". This same French document mentions Antonius Andreas, but ascribes to him only a verbal form of the law of identity.

I have only a smattering of French - so I relied on the Google Translation, and fixed a few small things that even I was able to correct:

“The identity principle: Wundt says that “the law of identity was expressed for the first time in a pure logical form by Leibniz (Logik, T. II, p. 562)”. In fact, this one in proposed a great number of formulas, among which: “Each thing is what it is”, “A is A, B is B” (New Essays on Human Understanding, IV, 2, ed. Gehrardt, p. 343, sq.)… However Suarez already allotted to Antonius Andreas the following formula: Omne ens est ens, that it rejects besides like useless (Metaph., Disp., sect. III, n° 4)."

If this is correct, Leibniz gets credit for "A is A" - since it shows up in his New Essays on Human Understanding. Antonius Andreas gets credit for "Omne ens est ens." (Which I've seen translated as "Every being is a being." ) Aristotle, it is true, had already touched on the issue that a thing is itself. (Metaphysics Book VII, Part 17)

The French source is here, which seems to be a site for Thomist philosophy:

http://perso.orange.fr/thomiste/eternelb.htm

The Suarez referred to is Francisco Suarez, and his book in which he discusses Antonius Andreas is his Metaphysical Disputations.

My next step is to track down the work of Wundt that was cited, his Logik. There's a copy of it in a library in Chicago, but it's in German, another language I don't know!

If anyone can further correct the French translation, I will thank you. I also have this snippet of Latin in which Suarez speaks of Antonius' contribution:

"Prima sententia est non esse primum illud quod ex Aristotele retulimus, sed hoc, omne ens est ens. Ita tenet Antonius Andreas, IV Metaph., q. 5. Et ad Aristotelem respondet vocasse illud aliud primum principium inter ea quae circumferuntur ut generalia, ut sunt illa: Omne totum est maius sua parte, etc. Sed hic auctor etiam in suis principiis non recte loquitur, quia illa propositio est identica et nugatoria; et ideo in nulla scientia sumitur ut principium demonstrationis, sed est extra omnem artem."

If anyone feels up to translating that, I will be ecstatic. Corrections or pointers of any kind are welcome.

I'm putting this in Epistemology because, outside of Objectivism, "A is A" usually comes up in logic discussions. Really this is more of a History of Philosophy question, but there doesn't seem to be a category for that.

Thanks,

John Enright

Edited by jenright
Link to comment
Share on other sites

Aristotle does, on the other hand, state the law of contradicion at length in Metaphysics Gamma, part of it quoted in the last chapter of Atlas Shrugged. Excluded middle appears at least once, in passing, in Beta as an example of a truth nobody disputes. The closest he comes to stating the law of identity is a passing remark in Zeta, which Gotthelf first pointed out in this connection, that asking if something is itself or not is nonsensical.

(And as long as I have the floor: "rational animal" was not his definition of man, nor does Rand attribute it to him.)

Link to comment
Share on other sites

(And as long as I have the floor: "rational animal" was not his definition of man, nor does Rand attribute it to him.)

Pete,

Wow.

I personally have been saying that after having read it in many places, but I never looked it up myself. (I remember reading Ron Merrill state that Rand used Aristotle's definition, for instance.) If that needs correcting, the best time to start is now.

I just did a quick Google search and from what I read, I gather that "man" is one kind of "rational animal" to Aristotle, meaning that man falls under "rational animal," he is not all of "rational animal."

Did I get that right?

Michael

Link to comment
Share on other sites

Aristotle does, on the other hand, state the law of contradicion at length in Metaphysics Gamma, part of it quoted in the last chapter of Atlas Shrugged. Excluded middle appears at least once, in passing, in Beta as an example of a truth nobody disputes. The closest he comes to stating the law of identity is a passing remark in Zeta, which Gotthelf first pointed out in this connection, that asking if something is itself or not is nonsensical.

Quite right. Aristotle is no stranger to the idea that a thing is itself. I suspect that within the context of Greek philosophy up to that time, it wasn't something that needed to be emphasized, partly because it wasn't much in dispute. After Hegel and Marx, I think it became really important to positively insist on it.

I suspect Leibniz's path may have involved his mathematical studies, where the positive form of an equation is usually regarded as more simplified than a double negative form.

"The great foundation of mathematics is the principle of contradiction or of identity, that is to say, that a statement cannot be true and false at the same time, and that thus A is A and cannot be not-A. And this single principle is enough to prove the whole of arithmetic and the whole of geometry, that is to say all mathematic principles." Leibniz, Second Paper.

"Primary truths are those which either state a term of itself, or deny an opposite of its opposite. For example, 'A is A', or 'A is not not-A'; 'If it is true that A is B, then it is false that A is not B, or that A is not-B; again, 'Each thing is what it is', 'Each thing is like itself or is equal to itself', 'Nothing is greater or less than itself' - and others of this sort which, thought they may have their own grades of priority, can all be included under the one name of 'identities'." - Leibniz, Primary Truths.

Link to comment
Share on other sites

Following up on #4:

Aristotle's definition is "two-footed footed." Some references are Parts of Animals A3, 644 a4 ff and Metaphysics Z11 1037b. As either Lennox or Gotthelf explained this in a talk, for Aristotle each successive differentia must be a way of belonging to its genus. Animals move. Having feet is a way of moving. Having two feet is a way of having feet. That way, the genus at each stage will imply the one above it. In this case, the genus "footed" implies "animal" as the next one up the hierarchy.

I once asked someone in the business about "rational animal", and he said that the definition originated in the Academy a few generations after Aristotle's death. His successors might have been taking off in turn from his classification of types of soul - nutritive, common to all living things, appetitive, common to all animals, and noetic or rational, special to man. This shows that he would have agreed with the statement that man is a rational animal but not that he would have considered it a correctly put-together definition.

Edited by Reidy
Link to comment
Share on other sites

Aristotle does, on the other hand, state the law of contradicion at length...

It's noteworthy that Plato has Socrates state the law pretty clearly:

"It is obvious that the same thing will never do or suffer opposites in the same respect in relation to the same thing and at the same time." -Republic (4:436b)

I hope Fred Seddon isn't reading this, or he'll remind me about his theory that Plato is a lot closer to Aristotle than most people think.

John

Edited by jenright
Link to comment
Share on other sites

Following up on #4:

Aristotle's definition is "two-footed footed." Some references are Parts of Animals A3, 644 a4 ff and Metaphysics Z11 1037b. As either Lennox or Gotthelf explained this in a talk, for Aristotle each successive differentia must be a way of belonging to its genus. Animals move. Having feet is a way of moving. Having two feet is a way of having feet. That way, the genus at each stage will imply the one above it. In this case, the genus "footed" implies "animal" as the next one up the hierarchy.

I once asked someone in the business about "rational animal", and he said that the definition originated in the Academy a few generations after Aristotle's death. His successors might have been taking off in turn from his classification of types of soul - nutritive, common to all living things, appetitive, common to all animals, and noetic or rational, special to man. This shows that he would have agreed with the statement that man is a rational animal but not that he would have considered it a correctly put-together definition.

I haven't read Aristotle's Parts of Animals closely or recently enough to be sure, but doesn't it seem that the statement man is "two-footed footed" is a bit lacking as a definition? Aren't birds two-footed footed, too? And apes? Or does he manage to distinguish them from humans somehow?

REB

Link to comment
Share on other sites

I remember a story I think told by Leonard Peikoff in one of his courses at NBI that there was a definition of man as a featherless biped that lasted until someone throw a plucked chicken into the discussion. I think this may have been at the Academy. Roger this sounds somewhat similar.

Link to comment
Share on other sites

Re #9: I didn't say it was a good definition, only that it was Aristotle's. Maybe the considerations you bring up are why "rational animal" replaced it as the standard. (Birds wouldn't be a counter-example for Aristotle because wings, not feet, are their primary means of getting around.)

Re 10: "Featherless biped" comes from Plato - Sophist, I think - as an example of a bad definition. I recall the plucked chicken from Barbara Branden's efficient thinking lectures, though Peikoff could have used it as well.

Link to comment
Share on other sites

The source I cited in #7 has this to say about the Suarez quote in #1:

I can't do a good job on this without the context. For example, "sententia" can mean various things. It means something like this ...

The first proposition is that the claim we took from Aristotle is not primary, but rather this (is primary): everything that is, is. (i.e., every entity is an entity; in Greek this would be "pan to on estin on") This is what A.A. maintains in his Quaestio 5 on Metaphysics Gamma (book 4). And he replies to Aristotle that he (Aristotle?) called that other thing (the Principle of non-contradiction, I suppose) the primary principle among those which are considered to be general (principles), such as "every whole is greater than its part" etc. But this author (i.e., A.A.) gets it wrong even in his principles, because that proposition (everything that is, is) is an identity and is superfluous, and this is why it is not assumed as a principle of demonstration in any science, but falls outside every branch of knowledge (ars).

I hope that this is helpful. Suarez is a name known to me, but A.A. seems to be pretty obscure. Apparently he had something to do with Duns Scotus.

Link to comment
Share on other sites

The source I cited in #7 has this to say about the Suarez quote in #1:

Peter, thank you - and your source - very much. That does help!

Yes, A.A. seems to have been an associate or follower of Duns Scotus. It turns out that Peikoff mentioned A.A. in his dissertation:

“Of the three ‘laws of thought’ which one commonly associates with the traditional logic, the Law of Identity, as far as I can tell, was not specifically formulated as such until the medieval era. Sir William Hamilton, who is ordinarily encyclopedic in such matters, was unable to find such a formulation of it until Antonius Andreas, at the end of the thirteenth century. (Cf. his Lectures on Metaphysics and Logic, ed. Henry Mansel & J. Veitch [2 vols., Boston, Gould & Lincoln, 1859], II, 65.)”

Bill Bucko quotes from P.'s dissertation here:

http://forums.4aynrandfans.com/lofiversion...x.php/t881.html

Link to comment
Share on other sites

John,

Thank you for introducing this topic.

Taken as the formula ‘Every A is A’, the principle of identity was being used by logicians at least by the time of Albert the Great (13th cent.). They used it, for example, to prove the convertibility of ‘No B is A’ to ‘No A is B’. They added ‘Every A is A’ to ‘No B is A’ to infer ‘No A is B’, relying on one of Aristotle’s forms of syllogism (first mood of the second figure):

No L is M

Every S is M

No S is L

No B is A

Every A is A

No A is B

[Kneale and Kneale The Development of Logic (235–36)]

Wundt is incorrect when he says that the logical formula of identity ‘A is A’ was expressed first by Leibniz. It is correct—as you have indicated—that Leibniz capitalized the law of identity in logic, in mathematics, and in metaphysics.

Leibniz knew that not all valid forms of deductive argument can be reduced to syllogistic form, but he maintained that the principle common to a properly enlarged theory of deduction is the substitution of equivalents, which is a logical license of identity.

Identity and contradiction are two opposites of the same fundamental law for Leibniz. “An identity corresponds to a proposition which implies a contradiction. For the primary impossibility in propositions is this: A is not A; just as the primary necessity in propositions is this: A is A (Ltr. to H. Conring, 19 March 1678).

Another logical use of the law of identity in addition to the substitution of equivalents is in the Aristotelian principle that the predicate of every affirmative proposition is included in the subject. Loemker writes that “the sources of this principle are in Aristotle’s Analytica post., A, iv; De inter., 17, a; Cat., 1, a; etc. It was current in Leibniz’s day, and Arnauld and Nicole used it as the test of axioms in the Port Royal Logic . . . . A criticism of Leibniz’s faulty extension of Aristotle’s principle to substance is to be found in H.W.B. Joseph, Lectures on the Philosophy of Leibniz, pp. 85–87” (Leibniz: Philosophical Papers and Letters, 60n25).

Here is a suggestion for anyone pursuing the differences between Rand and Leibniz on the law of identity in metaphysics: Check the Aristotle and Joseph references and see whether and how Rand’s system uses this principle of Aristotle—that the predicate of every affirmative proposition is included in the subject—and whether and how her system avoids faulty extension of the principle (not to substance, but) to existence and to entity. Compare also theory of definitions for Leibniz and Rand. The importance of definition for Leibniz is shown in the Letter to Conring: “All truths can be resolved into definitions, identical propositions, and observations.”

I want to turn now to Rand’s 1957 views on Aristotle and the law of identity. On page 1016 of Atlas Shrugged, Rand writes that Aristotle “stated the formula defining the concept of existence and the rule of knowledge: A is A. A thing is itself.” She takes herself to be completing the meaning of that statement by the following statements: “Existence is Identity, Consciousness is Identification.” What does Rand take herself to be stating that was not stated in Aristotle? What exactly is her completing element? Is she not only completing, but replacing some of Aristotle’s ideas on the relation of logic to metaphysics?

In amplification of her compact statement Existence is Identity, Rand goes on to say that the law of identity (and lack of contradiction) applies to objects, to attributes, to actions, and to their compositions into larger wholes (1016). Does this go beyond Aristotle? Beyond Leibniz? Beyond logic texts she studied? Against them?

In amplification of her compact statement Consciousness is Identification, Rand writes that “logic rests on the axiom existence exists” and that “logic is the art of non-contradictory identification” (1016). Beyond Aristotle? At odds with Aristotle?

Edited by Stephen Boydstun
Link to comment
Share on other sites

Stephen, thanks for all the excellent facts, questions, and suggestions.

I hadn't remembered that Rand had so directly, in Galt's speech, attributed "A is A" to Aristotle.

Your reference to the Kneale & Kneale book was enlightening. In my mind it has pushed the genesis of the "a is a" formula back several centuries! It's also interesting that such usage was a minority approach and that Albert the Great disdained using the identity principle. This foreshadows the predominant scholastic rejection of Antonius Andreas' claim that identity logically had priority over non-contradiction. Antonius came a bit after Albert, of course. Why was identity rejected as prior? Partly because Aristotle had said that nothing was more certain than the principle of contradiction. That meant nothing was prior - including identity. Also, "A is A" could be dismissed as trivial, or, as Locke put it centuries later, as a "trifling proposition". Aristotle only touches on the premise that "a thing is itself" as a way of answering a question he seems to regard as clueless.

You mention Leibniz's letter to Conring. That's the first place, so far, that I've seen "A is A" show up in Leibniz, who seems to the first great modern trumpeter of the formula.

The next year, in 1679, in the second of the Two Studies in Logical Calculus, he is presenting ideas on the logic of terms, which includes:

"Propositions true in themselves:

(1) a is a. Animal is animal.

(2) ab is a. Rational animal is animal.

(3) a is not non-a. Animal is not nonanimal.

(4) Non-a is not a. Nonanimal is not animal.

(5) What is not a is non-a is non-a. What is not an animal is nonanimal.

(6) What is not non-a is a. What is not a nonanimal is an animal.

From these many others may be derived."

You can see his notation doesn't make use of the some/all quantifier from the subject of the proposition. So instead of "All A is A" he uses "A is A".

Here is a suggestion for anyone pursuing the differences between Rand and Leibniz on the law of identity in metaphysics: Check the Aristotle and Joseph references and see whether and how Rand’s system uses this principle of Aristotle—that the predicate of every affirmative proposition is included in the subject—and whether and how her system avoids faulty extension of the principle (not to substance, but) to existence and to entity. Compare also theory of definitions for Leibniz and Rand. The importance of definition for Leibniz is shown in the Letter to Conring: “All truths can be resolved into definitions, identical propositions, and observations.”

This would be an interesting project.

I want to turn now to Rand’s 1957 views on Aristotle and the law of identity. On page 1016 of Atlas Shrugged, Rand writes that Aristotle “stated the formula defining the concept of existence and the rule of knowledge: A is A. A thing is itself.” She takes herself to be completing the meaning of that statement by the following statements: “Existence is Identity, Consciousness is Identification.” What does Rand take herself to be stating that was not stated in Aristotle? What exactly is her completing element? Is she not only completing, but replacing some of Aristotle’s ideas on the relation of logic to metaphysics?

Another good research project. I'll just venture a guess: I *think* she believes she is stepping away from the metaphysical essence vs. accident doctrine here. Thomists, to whom I think she is reacting, sometimes talk as if a thing's identity is just its essence, and that its accidents really don't count as part of its (ahem) essential nature. I think this strikes her as kind of a soul/body dichotomy within external things in the Thomist worldview. In ITOE she is a pains to paint essences as not metaphysical, even though based on the metaphysical. She may also be trying to step away from the primary/secondary quality distinction which appears in Locke.

In amplification of her compact statement Existence is Identity, Rand goes on to say that the law of identity (and lack of contradiction) applies to objects, to attributes, to actions, and to their compositions into larger wholes (1016). Does this go beyond Aristotle? Beyond Leibniz? Beyond logic texts she studied? Against them?

Another guess ventured: Above all, it goes against dialectical materialism, which maintains that contradictions were at work through-out reality.

In amplification of her compact statement Consciousness is Identification, Rand writes that “logic rests on the axiom existence exists” and that “logic is the art of non-contradictory identification” (1016). Beyond Aristotle? At odds with Aristotle?

More guessing: The emphasis on identification as the key process, I think, is largely congruent with Aristotle - but it is not his emphasis. I think it steps away from the "imprint" model he spoke of for ordinary awareness, and leans more into the active intellect querying as a general model for consciousness.

Link to comment
Share on other sites

  • 1 year later...
Yes, A.A. seems to have been an associate or follower of Duns Scotus. It turns out that Peikoff mentioned A.A. in his dissertation:

“Of the three ‘laws of thought’ which one commonly associates with the traditional logic, the Law of Identity, as far as I can tell, was not specifically formulated as such until the medieval era. Sir William Hamilton, who is ordinarily encyclopedic in such matters, was unable to find such a formulation of it until Antonius Andreas, at the end of the thirteenth century. (Cf. his Lectures on Metaphysics and Logic, ed. Henry Mansel & J. Veitch [2 vols., Boston, Gould & Lincoln, 1859], II, 65.)”

Antonius Andreas was a student of John Duns Scotus. The reason he is mentioned only once in known literature is because he is totally insignificant, and never produced anything noteworthy except this proposal which pissed off Suarez enough to write about it in Disputation III. Peikoff's attribution of the law of identity to this man is totally spurious.

Prima sententia est non esse primum illud quod ex Aristotele retulimus, sed hoc, omne ens est ens. Ita tenet Antonius Andreas, IV Metaph., q. 5. Et ad Aristotelem respondet vocasse illud aliud primum principium inter ea quae circumferuntur ut generalia, ut sunt illa: Omne totum est maius sua parte, etc. Sed hic auctor etiam in suis principiis non recte loquitur, quia illa propositio est identica et nugatoria; et ideo in nulla scientia sumitur ut principium demonstrationis, sed est extra omnem artem.

I'll give you as much of a translation as is pertinent, though it is written in very poor Latin.

The first judgment should not be Aristotle's first which we usually talk about, but another one: every being is a being. So maintains Antonius Andreas... Blah blah blah.

I stopped translating here because it's already apparent that this is not, in fact, a precursor to the law of identity, and means something totally different. In terms of objectivist metaphysics, this is the axiom of existence, not identity. The objectivist axiom of identity cannot be said to have a basis in Aristotle. It simply doesn't.

IV Metaphysics is of course the law of non-contradiction. Non-contradiction is "Aristotle's first" (primum illud quod ex Aristotele retulimus, lit. "the first which from Aristotle we refer"). Basically, Suarez is saying that Andreas is arguing that the first law of thought should not be non-contradiction (because it's non-affirmative: how things can't be) but rather omne ens est ens, an affirmative rule for what existence is. Both Andreas and Suarez understand that this contradicts Aristotle, and that's why Suarez doesn't like it.

Nor are Suarez or Andreas sources that Rand was likely to have ever heard of. You could probably count the Scholastics she was able to quote a single sentence from on zero hands. She was, after all, profoundly ignorant, not well-read, not classically educated, and generally faked everything she claimed, including an understanding of Aristotle and of laissez-faire capitalism itself.

Locke and Leibniz are pretty much the contemporaneous inventors of "A is A", and the understanding of it as a "law of identity". This idea can't be coherently placed before the Enlightenment.

Aristotle does not deserve ultimate credit for this, by any stretch of the imagination. Calling it "congruent with Aristotle" shifts the issue from whether Aristotle did say it -- by which criterion Rand was indisputably wrong -- to whether Aristotle would have agreed with it -- by which criterion Rand was still giving a false source, but it looks less ridiculous. Aristotle, in fact, never proposed a principle of identity, never said "A is A" or even a Koine Greek equivalent, and certainly cannot be supported as the originator of such a principle to any greater extent than that he is the originator of most Western philosophy.

Suarez here can even be read to imply that Aristotle only set down two "laws of thought", non-contradiction and excluded-middle. He chastises Andreas for proposing a third, which Andreas even has the audacity to place first.

It is patently obvious that Rand never once read Aristotle, and got her info on him from some other source. And incidentally, the parallels between the cult surrounding Ayn Rand and Scientology astound me. Leonard Peikoff is to Ayn Rand as David Miscavidge is to L. Ron Hubbard.

PS - Apparently this forum is being hosted on a walkie-talkie located on Mars, if the server lag is any indication. Either that or by someone who doesn't know how to run a webserver. This just proves my point: http://208.67.212.59/ My advice: get a colo.

Edited by cjkhs3qe6
Link to comment
Share on other sites

IV Metaphysics is of course the law of non-contradiction.

. . .

It is patently obvious that Rand never once read Aristotle, and got her info on him from some other source.

cjkhs3qe6,

Welcome to OL.

Despite your impressive domination of Latin and erudition, I suggest you get more familiar with the Objectivist theory of concepts and Rand's biography rather than making claims that show you are not familiar with them, or at least misunderstand them if you are (in which case I suggest rereading the material).

I recommend Introduction to Objectivist Epistemology. If you are interested in Rand's life and learning what books she referenced for Artistotle, I can suggest several. I am partial to The Passion of Ayn Rand by Barbara Branden.

Sorry if that sounds aggressive, but if you are going to make a first post in that tone of voice and try to teach us what Rand is or is not, you should get Rand's ideas and life right and then go on from there.

Michael

Link to comment
Share on other sites

Despite your impressive domination of Latin and erudition, I suggest you get more familiar with the Objectivist theory of concepts and Rand's biography rather than making claims that show you are not familiar with them...

Umm, Michael, in the first place, no one has a perfect command of everything Ayn Rand wrote. Second, she was not always non-contradictory herself, always being a Randian for sure, but not always an Objectivist. Third, he may not be right, but I cannot prove him wrong. Allow me to explain.

And allow me to apologize.

My classical Greek materials are in the attic in boxes. I did a lot of it about a decade ago and not much since 2002 when I wrote about Alexander the Great. (I retranslated passages or validated translations from Plutarch and other biographers.) Long ago, I went through the Metaphysics and never found "A is A." I did find Non-Contradiction. I translated it anew and created a nice printout on posterboard for my Objectivist friends, with the original and the translation.

As for my Latin, my last exposure was April 30 of this year when I graduated summa cum laude with a bachelor of science in criminology. The point is that my focus has been off the ancient world these last few years. So, I apologize for not having my Aristotle handy.

Basically, Suarez is saying that Andreas is arguing that the first law of thought should not be non-contradiction (because it's non-affirmative: how things can't be) but rather omne ens est ens, an affirmative rule for what existence is.

Can I call you "cj" or would you prefer "qe6" as Skywalker called his droids "R2" and "3PO".

Other than that, allow me to offer a hardier welcome than you got from our erstwhile host. This board is fairly tolerant.

Edited by Michael E. Marotta
Link to comment
Share on other sites

Locke and Leibniz are pretty much the contemporaneous inventors of "A is A", and the understanding of it as a "law of identity". This idea can't be coherently placed before the Enlightenment. Aristotle does not deserve ultimate credit for this, by any stretch of the imagination..

Maybe. I would check Aquinas' Commentaries.

Separately, welcome and howdy.

W.

Link to comment
Share on other sites

"Now 'why a thing is itself' is a meaningless inquiry (for—to give meaning to the question 'why'—the fact or the existence of the thing must already be evident—e.g., that the moon is eclipsed—but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical, unless one were to answer, 'because each thing is inseparable from itself, and its being one just meant this.' This, however, is common to all things and is a short and easy way with the question.)"

—Metaphysics, Book VII, Part 17

Link to comment
Share on other sites

I remember a story I think told by Leonard Peikoff in one of his courses at NBI that there was a definition of man as a featherless biped that lasted until someone throw a plucked chicken into the discussion. I think this may have been at the Academy. Roger this sounds somewhat similar.

(Belatedly) this was Diogenes the Cynic of Sinope - http://en.wikipedia.org/wiki/Diogenes_of_Sinope .

Link to comment
Share on other sites

  • 3 years later...

John,

Thank you for introducing this topic.

Taken as the formula ‘Every A is A’, the principle of identity was being used by logicians at least by the time of Albert the Great (13th cent.). They used it, for example, to prove the convertibility of ‘No B is A’ to ‘No A is B’. They added ‘Every A is A’ to ‘No B is A’ to infer ‘No A is B’, relying on one of Aristotle’s forms of syllogism (first mood of the second figure):

No L is M

Every S is M

No S is L

No B is A

Every A is A

No A is B

[Kneale and Kneale The Development of Logic (235–36)]

Wundt is incorrect when he says that the logical formula of identity ‘A is A’ was expressed first by Leibniz. . . .

Here is Robert Kilwardby in his commentary (c. 1240) on Aristotle's Prior Analytics using the formula 'Every A is A' to exhibit syllogisms back of conversions:

Page 77 of Logic and Ontology in the Syllogistic of Robert Kilwardby by Paul Thom (2007).

Link to comment
Share on other sites

I suspect that Rand got "A is A" and the three laws as a matched set from H. W. B. Joseph's Introduction to Logic, an early twentieth century tome which NBI Book Service used to sell and which, to judge from its Amazon entry, is still popular among Objectivists. Joseph was not primarily a historian, and he presents "Aristotelian" logic without emphasizing the difference between Aristotle himself and his tradition. A reader who doesn't spend more time on the footnotes than on the text might get the impression that Aristotle originated "A is A."

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now