Talk:Identity of indiscernibles

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1 Mention of duck
2 Controversial applications
3 Leibniz?
4 From Subjective to Objective
5 Critique
6 Epistemological Version
7 Ontological principle

[edit] Mention of duck

I'm going to delete this text:

So "if it looks like a duck, walks like a duck, and quacks like a duck, then it is a duck".

Why? Because the text is about classification, not about identity. This may be the case: If someone walks like a duck and quacks like a duck then that person is to be classified as a duck.

[edit] Controversial applications

what kind of fucking logic is this? the first 3 statements are about bill's world the conclusion is not!

we would be correct in concluding "bill believes 49/7 and the square root of 49 are two different things. And that is really how the world is!!!

Leibnitz was a genius. We have gone from an age of enlightenment to an age of darkness. We now live in a world of wikipedia half-wits RWS

I agree with you there, however you are raising a philosophical reply, some people do believe what is in the ariticle disputes Leibniz's law. Make a new section and call it replies if you want. --Aceizace 20:54, 19 February 2006 (UTC)

I think you are mistaken and the argument does not raise a valid philosophical reply. Note what you think problem with the argument is : “"bill believes 49/7 and the square root of 49 are two different things” à and therefore “And that is really how the world is!!!” This is EXACTLY the point the criticism is trying to make. The critique says that if we accept “identity of indiscernible” (Leibniz’s law) we will be led into absurd proposition that what Bill thinks makes the world that way. And since this is absurd(“what kind of fucking logic is this?” being your quote) the Leibnitz’s law is wrong.

The correct response to this attack on leibnitz’s law is to claim that what a person thinks about the object is not the property of an object.--Hq3473 04:12, 20 February 2006 (UTC)

I just stumbled across this page and I also found the argument found in this section to be, uh, weak. I'll try to express it a little more mathematically.

The claim in step 6 is that " $49 \over 7$ is not identical to $\sqrt{49}$ is absurd".

This is not absurd. They *aren't* identical. One has a 7 and a horizontal line, the other has a line with a bunch of corners. Just looking at them you can see that they are different.

To be more precise, $49 \over 7$ " and $\sqrt{49}$ mathematical expressions, and they are *different* expressions.

In some contexts, these expressions reduce to the same integer, but in others they don't. For example, if the default base is hexidecimal instead of decimal, these expressions yeild different numbers, neither of which is an integer. In other contexts, not all operators are defined, which is what is going on with poor Bill. Once you introduce some more complicated operations, Gödel's incompleteness theorems shows that even if you know how to preform all operations and have a well defined context, there exists two expressions that are equal, but that you can not prove that they are equal. (Also see the halting problem.)

It is important to distinguish between "identical" and "equivalent (under some context)".

So, on a very simplistic visual level, you can see that $49 \over 7$ is not identical to $\sqrt{49}$ , and on a much higher mathematical level you can understand that, indeed, determining if two expressions are the same can be a very hard problem. It is only fairly basic formulas that people automatically do the reductions and mentally classify them as "the same" and then make the incorrect leap to thinking they are "identical". Wrs1864 05:21, 18 November 2006 (UTC)

I changed this to a different example that does not involve evaluating math expressions, but presreves the basic problem of imperfect knowledge.--Hq3473 20:22, 18 November 2006 (UTC)

Thanks, I like your example *much* better. I think it is proably a good idea to leave the dispute tag for a little while to make sure that others agree, but as far as I'm concerned, my objections have been satisfied. Wrs1864 03:56, 19 November 2006 (UTC)

I there is no further objections i will remove the tag in a couple of days.--Hq3473 20:51, 19 November 2006 (UTC)

I am removing the tag--Hq3473 21:23, 22 November 2006 (UTC)

[edit] Leibniz?

I find it strange that Descartes lived and wrote Meditations before Leibniz was around, yet even the article itself says that Descartes used this reasoning. Might someone who knows more be able to include an explanation on why it is attributed to Leibniz? --Aceizace 20:54, 19 February 2006 (UTC)

The principle existed LONG before Descartes, probably can be attributed to Plato. His theory of Forms had a similar concept. The law got called Leibniz law, for his formulation not for content. Therefore it is not weird that Descartes uses the principle before Leibniz formulation.--Hq3473 15:34, 23 February 2006 (UTC)

[edit] From Subjective to Objective

This principle of the identity of indiscernibles makes the claim that a subjective judgment is to be taken as correctly describing the objective world. It claims that what appears to one person has true being for everyone. Perception is reality. However, that is precisely the problem that is to be solved by almost all philosophy. Kant's whole philosphy was written in order to determinine the correctness of assuming that subjective opinions are objective. Einstein's Relativity is also about the subjective observer and his experience of objects. Berkeley, Schopenhauer, Descartes, and many others have dealt with subjectivity and its relation to objectivity. For Leibniz to proclaim the identity of indiscernibles was, itself, an attempt to assert that his own subjective observations should be considered as being truly descriptive of the objective world of experience.Lestrade 01:43, 3 June 2006 (UTC)Lestrade

Feel free to edit the article acordingly. And do not forget to site your sources!--Hq3473 18:15, 7 June 2006 (UTC)

[edit] Critique

Max Black has argued against the identity of indiscernibles by counterexample. Notice that to show that 2. is false, it is sufficient that one provide a model in which there are two distinct (non-identical) things that have all the same properties. He claimed that in the symmetric universe where only two symmetrical spheres exist, the two spheres are two distinct objects, even though they have all the properties in common.

I know that Max Black is correct because I am in possession of a wonderful counterexample from pure mathematics--in other words, I have an elegant simple model--which proves, conclusively and persuasively, that there is at least one pair of numerically distinct objects which--nevertheless--have all their properties in common. And as soon as I have my proof published, or submitted, to a scholarly peer-reviewed philosophical journal, I look forward of the opportunity of publishing it here in this excellent Wikipedia article. Ludvikus ~~03:50, 2 September 2006 (UTC)~~

    I've transcribed here the above from the Article page - before reversion. I have written the
    comment before having become an experienced Wikipedian, understanding and following WP policy.
    Nevertheless, my observation remains true. But like Fermat? - No space to ellaborate?
    Yours truly,--Ludvikus 03:22, 14 December 2006 (UTC)

[edit] Epistemological Version

The articles gives the above rather than an ontological principle:

  The identity of indiscernibles is an ontological principle that states that if there is no way of
  telling two entities apart then they are one and the same entity. That is, entities x and y are
  identical if and only if any predicate possessed by x is also possessed by y and vice versa.

Yours truly,--Ludvikus 03:53, 14 December 2006 (UTC)

[edit] Ontological principle

I've modified/corrected the opening sentence from the above, to the following:

    The identity of indiscernibles is an ontological principle; i.e., that if (two
    or more) object(s), or entity/ies have all thier/its property/ies in
    common then they (it) are identical (are one and the same entity). That is, entities x and
    y are identical if and only if any predicate possessed by x is also possessed by y and
    vice versa.

Yours truly,--Ludvikus 04:05, 14 December 2006 (UTC)

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Talk:Identity of indiscernibles

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