Talk:Law of identity

Old unsectioned comments
feel free to delete this line, but i think someone should know that quote literally gave me a seizure... Longcheeseconey (talk) 05:53, 2 January 2008 (UTC)

Apparently Wundt credits Leibniz with the symbolic formulation, "A is A":

Wundt dit que "la loi d'identité a été exprimée pour la première fois sous une forme logique pure par Leibniz (Logik, t. II, p. 562)". De fait, celui-ci en a proposé un grand nombre de formules, parmi lesquelles : "Chaque chose est ce qu'elle est", "A est A, B est B" (Nouveaux Essais sur l'Entendement humain, IV, 2, éd. Gehrardt, p. 343, sq.). (http://perso.orange.fr/thomiste/eternelb.htm)

I am not sure why this is called a 'tautology' (it might just be one in ordinary language, but not in logic) since it cannot be expressed as such via the truth tables.

http://anti-dialectics.co.uk/index.htm

Rosa Lichtenstein 14:11, 24 December 2006 (UTC)

actually this is false. This is clearly a tautology if you use truth tables whether you use the conditional:

or whether you use the biconditional:

in both cases, it is a tautology. Xenfreak (talk) 18:36, 9 October 2011 (UTC) -

But, in "A=A", the "A" is a name or singular term variable, whereas in "A≡A" it is a propositional variable. You can't apply the truth tables to the use of a truth functional operator that would yield "Socrates if and only if Socrates" upon interpretation!

Rosa Lichtenstein (talk) 04:00, 1 June 2013 (UTC)

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I agree A is A (A=A) is not a TAUTOLOGY because A would be a TERM not a STATEMENT. Terms are neither true nor false, so we could not have a tuth table for A=A, or is(A,A). Perhaps the original author meant that A is A (A=A) is a LOGICAL TRUTH (is necessarily true) and of course not all logical truths are tautologies. Because A in A=A is term not a proposition it follows you cannot have a truth table for it.--Philogo 19:42, 29 July 2007 (UTC)

---

Once more, why is this called a 'tautology'. It isn't one in logic, even if it might be called one colloquially.

And what is the number one doing here:

In philosophy, the law is often attributed to Aristotle, although it is also claimed that Aristotle never gave this law1.

There is no footnote 1!

And the quotation takes this 'law' out of context, for not only does Aristotle not mention 'identity', he specifically talks about predication (and since identity is a relation, he cannot be talking about identity):

"Let us state what, i.e. what kind of thing, substance should be said to be, taking once more another starting-point; for perhaps from this we shall get a clear view also of that substance which exists apart from sensible substances. Since, then, substance is a principle and a cause, let us pursue it from this starting-point. The 'why' is always sought in this form--'why does one thing attach to some other?' For to inquire why the musical man is a musical man, is either to inquire -- as we have said why the man is musical, or it is something else. 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). But we can inquire why man is an animal of such and such a nature. This, then, is plain, that we are not inquiring why he who is a man is a man. We are inquiring, then, why something is predicable of something (that it is predicable must be clear; for if not, the inquiry is an inquiry into nothing). E.g. why does it thunder? This is the same as 'why is sound produced in the clouds?' Thus the inquiry is about the predication of one thing of another. And why are these things, i.e. bricks and stones, a house? Plainly we are seeking the cause. And this is the essence (to speak abstractly), which in some cases is the end, e.g. perhaps in the case of a house or a bed, and in some cases is the first mover; for this also is a cause. But while the efficient cause is sought in the case of genesis and destruction, the final cause is sought in the case of being also." [Bold emphasis added.]

http://www.rbjones.com/rbjpub/philos/classics/aristotl/m1717c.htm

So, I think the article needs amending.

Finally, since this 'law' is foreign to Aristotle, how can the author of this article say:

The law of identity has deep impact on Aristotle's ethics as well. In order for a person to be morally praiseworthy or blameworthy for an action, he or she must be the same person before the act as during the act and after the act. Without the law of identity, Aristotle notes, there can be no responsibility for vice

Personal identity is not the same as the 'law of identity'.

However, I could not find in the Nicomachean Ethics anything like this reference to personal identity; so perhaps the author of this article will provide an exact quotation?

Rosa Lichtenstein 22:39, 21 March 2007 (UTC)

--

The following 'quotation' cannot be found in the Book V11, Part 17 of Aristotle's Metaphysics, contrary to what the article asserts: "a fixed constant nature of sensible things".

It should be removed since it distorts what Aristotle is saying.

Rosa Lichtenstein (talk) 00:57, 23 September 2011 (UTC) --


 * I removed mention of Nichomachean Ethics. I think it was a hoax. &larr;Ben B4  19:32, 12 September 2007 (UTC)

Aristotelian Gobbledegook
This article is completely unacceptable. For one thing it misrepresents Aristotle entirely. I don't know what the quoted passage is supposed to prove but it sure is not Aristotle's formulation of the identity principle. All he said was you cannot consistently assert the same thing about the same object in the same way and there is no mention here of that at all. Moreover he did not claim to invent it and no one claims that he invented it. This is simply the first overt mention of it. I'm not working on this article right now so I am not going to give you the ref. All I can say is, if you can't cook, either stay out of the kitchen or learn to cook. So get yourself a nice book on the metaphysics with a nice index telling you where the "first principle" is and settle down to a nice winter of learning metaphysics, which is nice. PS. If this is all we are going to say about the identity principle it probably can be merged with no problem; in fact, if we don't merge there will be a content fork.Dave (talk) 12:31, 17 November 2007 (UTC)

Rather 'unchristian' comments, the above!

Rosa Lichtenstein (talk) 09:46, 2 February 2008 (UTC)

Locke's law of identity?
I can't find anyone before Locke who ever mentioned a canonical "law of identity". Locke attests it. Leibniz attests it at the same time as Locke. Joseph Butler attests it, a generation after Locke. Before Locke? Nothing. None of the Medieval Scholastics knew anything about it. Aquinas doesn't mention it. William of Ockham doesn't mention it. I've been told that Francisco Suárez attributes something similar to an obscure student of Duns Scotus (Antonius Andreas), but nobody made a big deal out of it at the time, and there was as yet no "law of identity". Interestingly, Descartes mentions no law of identity either, which implies that it was not known as such until 1650-1700. --70.131.116.104 (talk) 21:38, 6 May 2008 (UTC)

Kim Cameron's Laws of Identity
Should probably be moved to a separate page, since this page is about philosophy. --Nabeth (talk) 20:19, 16 March 2009 (UTC)


 * Someone removed this entry about Kim Cameron related to lack on notability. Well, well, ..., I would not want to be nasty here, but before doing this kind of thing, you should first check, or be an expert in the domain (in that case, the expert would know!). Please use the talk page before removing content like this and defend your perspective. --Nabeth (talk) 16:00, 4 May 2009 (UTC)


 * Additional note: Kim Cameron's Laws of Identity relates to digital identity, and therefore main need to be put somewhere else if this page is only about Physolophy. --Nabeth (talk) 16:05, 4 May 2009 (UTC)


 * Suggestion: Maybe a disambiguation page should be created to remove the confusion --Nabeth (talk) 16:11, 4 May 2009 (UTC)
 * Hi my question was about the notability of these 'laws'. Can you provide some references please. Peter Damian (talk) 16:43, 4 May 2009 (UTC)


 * Dear Peter, Yes, I will provide some references. Yesterday I started to search for references, but did not have the time to have something good enough. Kim Cameron's Laws of Identity is indicated in a Blog entry: Kim Cameron. The Laws of Identity. Microsoft Whitepaper, May 2005. http://www.identityblog.com/stories/2004/12/09/thelaws.html . Althought a blog entry may not be considered as "good enough" for Wikipedia, it is being cited by a numerous academic publication. See for instance in Google scholar : http://scholar.google.com/scholar?q=%22laws+of+identity --Nabeth (talk) 08:09, 5 May 2009 (UTC)

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What does this mean?

"A ≡ A."

"≡" is a propositional operator equivalent to the bi-conditional.

The article also needs updating with material from post-Leibnizean (philosophical) logic!

Rosa Lichtenstein (talk) 07:45, 3 November 2009 (UTC)

--

it should be noted that it litterally means "A if-and-only-if A." i.e. A is true if and only if A is true; and A is false if and only if A is false. Xenfreak (talk) 18:39, 9 October 2011 (UTC)

--

Thank you for that, Xenfreak, but in the law of identity, "A" is a name or singular term variable, whereas in "A ≡ A" it is a propositional variable. "Socrates if and only if Socrates" is unvarnished nonsense.

Rosa Lichtenstein (talk) 03:50, 1 June 2013 (UTC)

Exception that proves the rule
i'm pretty sure this phrase is used incorrectly in the end of the first section - the phrase refers to knowing that if something is an exception, a rule must exist for it to be an exception to, not an exception to a rule somehow making the rule more valid. however, i can't write anything to replace that paragraph. it seems unnecessary, since it's not an exception in the first place - to use the same example, the designator "a bear" and the designator "to bear" are different, and so each term is only ever used to refer to one concept. that this (and the implicit presence of the article and particle) is clear through context, not language, is information that needs to be included, i think, to make it clear that the initial statement is not a general rule precluding homonyms. however, like i said, i don't know what to do to that paragraph to sort it out. i'm not absolutely sure what i've written above is correct, let alone in terms that are commonly known. 94.193.221.42 (talk) 17:41, 21 September 2010 (UTC)

redundancy by using the biconditional operator?
Since the biconditional is, in one form, the conjunction of two material implication operators, in which the antecedent implies the consequent and vice versa, isn't it redundant to use the biconditional operator when the conditional would suffice? "A if and only if A" is essentially "if A then A" and "if A then A" and hence, redundant, and so, should just be simplified to "if A then A." I will change it to this in the article, if anyone has any objections, please bring them here.

Xenfreak (talk) 18:44, 9 October 2011 (UTC)

Axiom of extensionality
Maybe the article should include the fact that the law of identity is a special case of the axiom of extensionality in modern mathematics. — Preceding unsigned comment added by 188.104.185.150 (talk) 22:36, 19 June 2012 (UTC)

Is Objectivism relevant here?
Seeing as the law of identity is fairly self-evident and all but universally-accepted by virtually every philosophy, linking to specific philosophical and/or religious belief systems like Objectivism seems a bit out of place to me. If "law of identity" for some reason comes up frequently in Objectivist literature, it would make sense to link from there to here, but it doesn't make any sense to link from this page to Objectivism, nor does it make much sense to label this page as a part of WikiProject Objectivism. People who visit this page first (rather than coming from Objectivism) are not likely looking for Ayn Rand's philosophical musings.

At the very least, if Ayn Rand contributed something meaningful to the theory behind the law of identity which is well-recognized outside of her religion, there should be a subsection describing her contributions. Otherwise I don't see why the link to Objectivism belongs in this article, whether or not the concept is important to adherents. Am I off-base in finding this odd? TricksterWolf (talk) 17:24, 30 September 2012 (UTC)


 * The only links in the article are under "See also", which is normally used to link peripheral topics, so that seems OK (the law of identity is something Rand talked about frequently). But given the lack of article content about Objectivism, there does not seem any reason it should be tagged for WikiProject Objectivism. --RL0919 (talk) 03:25, 1 October 2012 (UTC)
 * In the absence of any comments to the contrary, I'm going to go ahead and remove the project tag. --RL0919 (talk) 15:45, 3 October 2012 (UTC)

In Need of Revision
This article is in need of a pretty decent overhaul:


 * Unlike what the note at the top claims, the article doesn't use any logical symbols at all.
 * The article doesn't mention the numerous ways to symbolize the law of identity (e.g. A=A, A→A, A↔A, etc.), nor does it mention that these various versions of the law turn out not to be exactly the same principle despite (ironically) having the same name.
 * The article seems to rely a bit too much on the history of other people talking about the Law of Identity, and not enough on describing the axiom, outside of the introduction. Further, in the history it focuses too much on elevating the identity axiom as unquestionable, rather than simply showing the evolution of views about the law over history (lack of Eastern views on it too).
 * It also lacks any mention of dissenting views, like those claiming there are some limitations to the axiom's applicability. For example, quasi-set theory and non-reflexive logic. Discussed by Schrodinger, Newton da Costa, Decio Krause, etc.

I think I'll try and make some alterations to the article soon, unless some of you feel there's good reason not to. MindForgedManacle (talk) 22:15, 28 January 2017 (UTC)

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As I have pointed out several times: in A=A, A is a name or singular term variable, whereas in A≡A, A→A, and A↔A it is a propositional variable. "Socrates if and only if Socrates" is unvarnished nonsense. So, there aren't, as you assert "numerous ways to symbolize the law of identity".

The article quotes the following as evidence that Aristotle used the Law of Identity [LOI] in a proof:

"When A belongs to the whole of B and C, and is predicated of nothing else, and B belongs to all C, A and B must convert; for since A is said only of B and C, and B is predicated both of itself and of C, it is clear that B will be said of everything of which A is said, excepting of A itself."

But, these variables are clearly not singular terms, so this can't be an example of the LOI!

Rosa Lichtenstein (talk) 01:45, 26 September 2017 (UTC)

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People section
What should it mean for the reader? --178.252.126.70 (talk) 15:41, 5 January 2019 (UTC)
 * It is a subsection of the "See also" section, so see WP:See also for explanation. --RL0919 (talk) 15:45, 5 January 2019 (UTC)
 * It's oversized and criteria for inclusion are undetermined. --178.252.126.70 (talk) 16:02, 5 January 2019 (UTC)
 * Also: "Editors should provide a brief annotation when a link's relevance is not immediately apparent". There's no person in the list whose inclusion is apparent (and "they discussed the topic" is not a good reason at all). --178.252.126.70 (talk) 16:06, 5 January 2019 (UTC)


 * Much of the "three laws of thought" are a meme. Cake  (talk) 11:26, 6 January 2019 (UTC)

Does anyone deny this?
The article gives no mention at all of any contrary opinions, which is really strange. There really ought to be some mention of dissenting views for any article on a philosophical doctrine, to avoid giving the impression that “everyone believes” that doctrine.

I think the most common argument against this law would be rooted in impermanence, as expressed in Eastern religions and by some Western thinkers such as Heraclitus and the process philosophers. Essentially the argument would say that “A=A” is wrong, because during the time it took you to say, read, or think the first “A” and the second “A”, whatever “A” is has unavoidably changed, to the point that it is no longer identical to its past self. Thus “A” can never refer to the same thing twice.

A more novel argument would be if “A” is something that changes by merely invoking it. For instance if “A” = “the number of times in my life I have thought of the letter A”, this would be a possible counterexample, though some might not consider such a concept allowable due to the inherent self-reference. 97.116.51.145 (talk) 23:52, 27 April 2020 (UTC)

Schrodinger logic section is a cut-and-paste
I'll leave it to those actively involved with this article to deal with, but the paragraph on Schrodinger logics is lifted verbatim (except for fixing a typo) from the abstract of this article: Michael Kinyon (talk) 17:46, 24 November 2020 (UTC)

Individuals and Propositions
I agree entirely with the comment fromm User:Rosa_Lichtenstein above concerning the importance of distinguishing between singular terms and propositions. As it stood the article confused the two. The law of identity states that every individual is identical with itself. It is about individuals. It has nothing to do with propositions or their meanings or with ambiguity. Logics that do not use the law of identity do not thereby commit equivocation.

In first-order logic we can treat identity (equality) as a logical constant or as an interpretable predicate. If it is interpreted, then we may choose to dispense with the law of identity and use a non-normal model. There is more information on this in the article on First-order_logic The law of identity is only a logical truth (tautology) in first order logic with identity.

I have removed the stuff about equivocation, and rewritten the section about Schrödinger logic to make this clearer. Dezaxa (talk) 18:05, 7 June 2021 (UTC)