{"id":4296,"date":"2013-02-12T17:09:08","date_gmt":"2013-02-12T22:09:08","guid":{"rendered":"http:\/\/trinities.org\/blog\/?p=4296"},"modified":"2017-05-08T13:04:45","modified_gmt":"2017-05-08T17:04:45","slug":"simplifying-the-indiscernibility-of-identicals","status":"publish","type":"post","link":"https:\/\/trinities.org\/blog\/simplifying-the-indiscernibility-of-identicals\/","title":{"rendered":"Simplifying the Indiscernibility of Identicals"},"content":{"rendered":"

\"equalsI’ve posted quite a few times here before about identity<\/a>, and about the principle often called “Leibniz’s Law” – the Indiscernibility of Identicals<\/strong>.<\/a> This is often put:<\/p>\n

Necessarily, for any x and any y, x is identical to y only if for any P, x has P if and only if y has P. (Compare, e.g. Colin McGinn, Logical Properties<\/i> (New York: Oxford University Press, 2000), 4-7.<\/p><\/blockquote>\n

I agree with other philosophers that this has apparent counterexamples, if “P” can stand either for any predicate or for any property.<\/p>\n

But in my view, the underlying metaphysical intuition<\/strong> – that a thing can’t at one time be and not be a certain way – is undeniable. (And of course, it has important theological implications<\/a>.)<\/p>\n

I would restrict the “P” above to intrinsic properties, if I believed in properties. But I don’t. So I’ve been putting the principle like this<\/strong>:<\/p>\n

The Indiscernibility of Identicals: Necessarily, any A and B are identical only if they (1) never have differed, (2) don\u2019t differ, (3) will not ever differ, and (4) could not differ.<\/p><\/blockquote>\n

This formula doesn’t import any assumptions about property-theory, either for or against. Rather, it uses only a primitive concept of differing, or being different – as to qualitative aspect or way of being, not as to number. I think this well captures the intuition and fundamental conviction noted above.<\/p>\n

But it now strikes me that the formula is needlessly complicated<\/strong>. Why not just this?<\/p>\n

Necessarily, any A and B are identical only if they could not simultaneously differ.<\/p><\/blockquote>\n

As with any version of Leibniz’s Law, this is supposed to give us a necessary condition for identity, and a sufficient condition for non-identity. If A and B really are numerically the same, they of course “they” (really: it) can’t at any time differ from how it is at that time. There’s the necessary condition. How about the sufficient condition? If A and B have, do, or will differ<\/em>, then of course they could<\/em> differ. Actuality implies possibility<\/strong>. So actually<\/em> differing at some time is sufficient for non-identity. But of course, merely possibly<\/em> differing at a time – being such that they could<\/em> simultaneously differ – is enough to prove non-identity too. This is just what the prior formulation said, then, in fewer words.<\/p>\n

To spell it all out<\/strong>, the claim is: Necessarily, for any x and any y, x and y are identical only if it is not possible that there is a z such that z is a time or a point in timeless eternity at which x and y differ.<\/p>\n

Philosopher-friends: what say you?<\/p>\n

\u00a0Update, in response to Anthony’s perceptive comment – I meant this:<\/em><\/p>\n

Necessarily, any A and B are identical only if they could not simultaneously or timelessly<\/em> differ.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"

I’ve posted quite a few times here before about identity, and about the principle often called “Leibniz’s Law” – the Indiscernibility of Identicals. This is often put: Necessarily, for any x and any y, x is identical to y only if for any P, x has P if and only if y has P. (Compare,… Read More »Simplifying the Indiscernibility of Identicals<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":4298,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","footnotes":""},"categories":[10,9],"tags":[],"class_list":["post-4296","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-logic","category-philosophy"],"_links":{"self":[{"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/posts\/4296","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/comments?post=4296"}],"version-history":[{"count":2,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/posts\/4296\/revisions"}],"predecessor-version":[{"id":38938,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/posts\/4296\/revisions\/38938"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/media\/4298"}],"wp:attachment":[{"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/media?parent=4296"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/categories?post=4296"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/tags?post=4296"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}