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In what text does Aristotle state "A is A"?

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Where do people draw the connection between Aristotle's writings and The Law of Identity? From what I've heard it was written in a 13th century textbook, attributed to Aristotle, and has grown into a great myth. How did that person way back when, extrapolate the Law of Identity from Aristotle's works? What did Aristotle say that would lead you to it?

-Regis

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I've read somewhere that Aristotle didn't officially say "A is A," but I seriously doubt that he didn't make a similar statement. You really can't have any form of logic otherwise :worry:

I've never read any of Aristotle's works (though I've tried :lol: ), but even if he didn't say something similar, it seems pretty obvious, I suppose.

Something can't be A and not-A: something can't be two diametrical things.

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Where do people draw the connection between Aristotle's writings and The Law of Identity?
I don't know. Rand never speaks of a "Law of Identity" as having derived from Aristotle. The first place I would look, if I were you, is in Aristotle's Metaphysics to see exactly what he said. I don't think you will get very far if you just look for words, since AFAIK there is no word that actually translates "identity" in the relevant sense in Ancient Greek (admittedly I am not an Ancient Greek scholar, but I did research the topic on the online Lidell/Scott dictionary and concluded with respect to this particular question that AG did not have a suitable equivalent). You would need to look at the concepts that "identity" subsumes.
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I found this on a site that claims to refute Aristotle on the Basis of Quantum Physics...Not sure what the heck is going on with that. http://www.quantonics.com/Aristotle_Connection.html

Aristotle gave us his three laws of propositional logic (used for syllogistic thinking):

1. a law of identity - (A is A);

(See Aristotle's Organon, 'On Interpretation' - [17a-35]: "The identity of subject and object must not be equivocal.")

Critical aside - 20May2003 - Doug.

Aristotle says here, literally, "subject is object." If a subject is not objective, then it does not 'exist,' and therefore may not be "identical" to its predicable objective representation. Aristotelian 'identity' demands classical objective localability, isolability, separability, and reducibility. Aristotelian 'identity' demands classical temporal immutability (objects do not emerge/evolve with time). Our uses of 'not' here are classically Aristotelian. See n¤t. See negati¤n. See Bergson's "negation is subjective."

End aside.

a law of contradiction - (A must be either A or not A);

(See Aristotle's Organon, 'On Interpretation' - [17a-34]: "We will call such a pair of propositions a pair of contradictories. Those positive and negative propositions are said to be contradictory which have the same subject and predicate.")

(See Aristotle's Metaphysics, 'Further Refutation of Protagoras' - . [1011b-13]: "(1) ...that the most indisputable of all beliefs is that contradictory statements are not at the same time true...")

and a law of an excluded middle - (A cannot be both A and not A).

(See Aristotle's Metaphysics, 'Chapter 7 - 'The Connexion of Such Denial with Protagoras' Doctrine of Relativity; the Doctrine Refuted' - [1010b-29]: "...for the necessary cannot be in this way and also in that, so that if anything is of necessity, it will not be 'both so and not so.'")

(See Aristotle's Metaphysics, 'Chapter 7 - 'The Law of the Excluded-Middle Defended' - [1011b-23]: "But on the other hand there cannot be an intermediate between contradictories...")

Edited by Regis
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A taste of the genius of this "Doug" guy (sigh):

So, what did Aristotle assume about 'A' in his laws above? He assumed 'A' represents something real. He assumed 'A' exists. Therefore 'A' must stand for something which exists. 'A' must stand for a real object.

<snip>

What do we know for sure today about real objects in a classical macro world? No two classical objects of similar categories are identical (e.g., snowflakes, hemoglobin molecules, diamond crystals, zebra, corn, pennies, water molecules, etc. See The Sciences, Sep/Oct 1997 issue, 'Tiny Doubles,' by Hans Christian von Baeyer, pp. 11-13) No two classical real objects, in general, can possibly be identical to one another.

So, we surmise, Aristotle tells us that an object is identical to itself. We would ask, "When?" When is an object identical to itself? Now, we know every classically real object in a real multiverse may changæ, however subtly, at least as fast as Planck's frequency, or about 1043 times per unit spatial reference. So every classical real object is different from itself, in general, more frequently than Planck's multiversal quantum rate. (Change time base reference to space based reference. 16Mar2002 - Doug.)

There is no A separate from itself that is identical to itself in a classical real world! Practically speaking, there is no A identical to itself in a classical real world! Quantum reality denies both interpretations of Aristotle's first law of syllogistic logic.

This is a rat's nest of equivocations, stolen concepts and gross misunderstanding.

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Where do people draw the connection between Aristotle's writings and The Law of Identity? From what I've heard it was written in a 13th century textbook, attributed to Aristotle, and has grown into a great myth. How did that person way back when, extrapolate the Law of Identity from Aristotle's works? What did Aristotle say that would lead you to it?

-Regis

Maybe this will help you:

http://forums.4aynrandfans.com/index.php?showtopic=881

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as far as I know, the first instance of A = A actually appears with Plato and The Symposium. In Socrates' speech, he rebukes one of his compatriots, saying: a Father is a father of something, and a mother is a mother of something. Though it never says the actual words A = A, it clearly demonstrates that everything which exists possesses an identity.

I'll try to find my copy of the symposium and get details.

Edited by the tortured one
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...What did Aristotle say that would lead you to it?

THERE is a science which investigates being as being {underline by slave} and the attributes which belong to this in virtue of its own nature. Now this is not the same as any of the so-called special sciences; for none of these others treats universally of being as being. They cut off a part of being and investigate the attribute of this part; this is what the mathematical sciences for instance do. Now since we are seeking the first principles and the highest causes, clearly there must be some thing to which these belong in virtue of its own nature. If then those who sought the elements of existing things were seeking these same principles, it is necessary that the elements must be elements of being not by accident but just because it is being. Therefore it is of being as being that we also must grasp the first causes.

If I am wrong, I would appreciate being corrected.

Edited by slave
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  • 10 months later...
Where do people draw the connection between Aristotle's writings and The Law of Identity? From what I've heard it was written in a 13th century textbook, attributed to Aristotle, and has grown into a great myth. How did that person way back when, extrapolate the Law of Identity from Aristotle's works? What did Aristotle say that would lead you to it?

-Regis

I believe the actual comment by him is as follows.

"If a man says that A is true, and also not-A is true, then he is really nothing but a cabbage-head."

I have always remembered that quote because it's so damn funny but I don't recall now where he wrote it. I think it may have been Analytica prioria.

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Aristotle only stated the law of non-contradiction and the law of excluded middle. The law of identity was a reformulation of these statements made by medieval scholars who were students of Aristotle (I have the name of the guy they think was the first to name it in the form A=A somewhere, but it's not really important, because the law of identity is fairly clearly implied in the law of non-contradiction and the law of the excluded middle, although it is stated in a more essential form as the law of identity. (If anyone is still interested in this, I can look up references, but I don't have any handy right now...)

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