{"id":38280,"date":"2017-01-07T09:49:28","date_gmt":"2017-01-07T14:49:28","guid":{"rendered":"http:\/\/trinities.org\/blog\/?p=38280"},"modified":"2017-03-09T21:01:11","modified_gmt":"2017-03-10T02:01:11","slug":"identity-and-necessity","status":"publish","type":"post","link":"https:\/\/trinities.org\/blog\/identity-and-necessity\/","title":{"rendered":"Identity and necessity"},"content":{"rendered":"

This week I have been pondering the question of whether the God of the Philosophers (a being who is omniscient, omnibenevolent, omnipotent etc.) is the same being as the God of the scriptures (Eleanor Stump thinks he is<\/a>, for example),\u00a0and in particular\u00a0the question of whether, if he is identical, he is necessarily<\/i> identical. The philosopher Saul Kripke is famous for upholding the so-called \u2018necessity of identity\u2019 thesis, and for many years – I first studied his magisterial and influential Naming and Necessity<\/i> in 1979 – I thought I understood what his argument was. Now I am less sure.<\/p>\n

My puzzle is that there are various ways we can get to the thesis of the Necessity of Identity, yet Kripke\u00a0apparently accepts none of these. The thesis was first proposed (as far as we know) by modal logic pioneer Ruth Barcan Marcus in 1947 (\u2018Identity of Individuals in a Strict Functional Calculus of Second Order\u2019, JSL 1947 12-15), although her paper was nearly\u00a0rejected after Quine, the reviewer, found her methods \u2018laborious and often rather obvious, while she seems to avoid the more difficult and interesting questions\u2019. Quine later published a less laborious demonstration of the thesis in 1953 (\u2018Three Grades of Modal Involvement\u2019 JSL 1953, 168-169), which involves just two assumptions, namely the Principle of Identity, that necessarily a=a, and Substitutivity, that a=b and Fa implies Fb. From these two it clearly follows that if a = b, then necessarily a = b. (Hint: let \u2018F\u2019 be \u2018necessarily a = —\u2019, start with Fa, and substitute \u2018b\u2019 for \u2018a\u2019).<\/p>\n

That is all clear and good. The problem is that Kripke doesn\u2019t want<\/em> to assume Substitutivity. He questions the universal substitutivity of proper names (N&N p.20), and as is well known he agrees with Frege that the identity of Hesperus the evening star and Phosphorus the morning star had to await discovery by a scientist (Pythagoras) and is thus not knowable from first principles. So \u2018It is true from first principles that Hesperus is Phosphorus\u2019 is false,\u00a0yet \u2018It is true from first principles that Hesperus is Hesperus\u2019 is true! If we can change the truth value of the statement simply by substituting a name for the same planet, how can Substitutivity be true?<\/p>\n

Nor does he want to assume that \u2018Hesperus is Phosphorus\u2019 is true in virtue of its meaning. He says (N&N p.20) that some critics of his doctrines, (\u2018and some sympathizers\u2019) have taken him to be implying<\/p>\n

that a sentence with \u2018Cicero\u2019 in it expresses the same \u2018proposition\u2019 as the corresponding one with \u2018Tully\u2019, that to believe the proposition expressed by the one is to believe the proposition expressed by the other, or that they are equivalent for all semantic purposes. Russell does seem to have held such a view for \u2018logically proper names\u2019, and it seems congenial to a purely \u2018Millian\u2019 picture of naming, where only the referent of the name contributes to what is expressed. But I (and for all I know, even Mill) never intended to go so far. My view that the English sentence \u2018Hesperus is Phosphorus\u2019 could sometimes be used to raise an empirical issue while \u2018Hesperus is Hesperus\u2019 could not shows that I do not treat the sentences as completely interchangeable.<\/p><\/blockquote>\n

This blocks a second route to the necessity of identity. Clearly if \u2018a=a\u2019 means<\/i> the same thing as \u2018a=b\u2019, and if \u2018a=a\u2019 is necessarily true in virtue of its meaning, then \u2018a=b\u2019 is also necessary, since it expresses exactly the same proposition. But Kripke does not endorse\u00a0such equivalence of meaning. Why then does he believe that the necessity of identity is a universal principle?<\/p>\n

It is surprisingly difficult to find any positive argument in his work. Most of his well-known arguments are negative ones, demonstrating that apparent exceptions to the necessity principle are not exceptions at all. For example, we can suppose a situation in which some planet other<\/i> than Hesperus was called \u2018Hesperus\u2019. But that would not be a situation in which Hesperus itself was not Phosphorus<\/i> (N&N p.108). The only positive argument I could find is this:<\/p>\n

If names are rigid designators, then there can be no question about identities being necessary, because \u2018a\u2019 and \u2018b\u2019 will be rigid designators of a certain man or thing x. Then even in every possible world, \u2018a\u2019 and \u2018b\u2019 will both refer to this same object x, and to no other, and so there will be no situation in which a might not have been b. That would have to be a situation in which the object which we are also now calling \u2018x\u2019 would not have been identical with itself. Then one could not possibly have a situation in which Cicero would not have been Tully or Hesperus would not have been Phosphorus. (\u2018Identity and Necessity\u2019 p. 154, there is a similar argument in N&N p.104).<\/p><\/blockquote>\n

Let\u2019s unpack this.\u00a0Kripke\u2019s notion of a rigid designator is clear enough, and is an important contribution to the philosophy of language. A rigid designator is one which designates the same object in every possible world. Or if you don\u2019t like \u2018possible world\u2019 talk, a term which designates the same in a proposition prefixed by a modal operator like \u2018it is necessary that\u2019 or \u2018it is possible that\u2019 as when not so prefixed. Then his argument looks like this:<\/p>\n

1. Let \u2018a\u2019 rigidly designate a and \u2018b\u2019 rigidly designate b
\n2. Suppose a=b
\n3. Then there is a single thing x, such that x=a and x = b
\n4. \u2018a\u2019 designates x and \u2018b\u2019 designates x<\/b>
\n5. If \u2018a\u2019 designates x rigidly, \u2018a\u2019 designates x in every possible world, likewise \u2018b\u2019
\n6. If \u2018a\u2019 and \u2018b\u2019 designate x in some possible world w, and not a=b, then not x=x
\n7. Therefore a=b in w
\n8. But w was any<\/i> possible world. Therefore, necessarily a=b.<\/p>\n

Steps 1 and 2 are suppositions, step 3 follows from 2 by the nature of identity. Step 4 I will discuss shortly. Step 5 follows from the definition of rigid designator, step 6 probably requires further assumptions, but looks OK. Step 7 follows by contradiction, and step 8, the conclusion, by the principle that if we can prove p for any<\/i> arbitrary w, then p holds for every<\/i> w.<\/p>\n

Let\u2019s return to step 4, as I promised. We agree that \u2018a\u2019 designates a. And that a=x, by assumption. Why on earth would it follow that \u2018a\u2019 designates x? Well, let F be \u2018\u2018a\u2019 designates —\u2019, so \u2018Fa\u2019\u00a0says that \u2018a\u2019 designates a. And let x=a. How do we get from Fa and x=a to Fx? By our old friend Substitution, no less. Yet Kripke claims to reject the universal applicability of Substitution. He could argue that it simply fails to hold in this case, but the thing about being a logical principle is that if it fails in even one<\/em> case, it has to fail in every<\/em> case, unless we can find a sufficient reason why it fails in that case, but then of course the principle has to include that reason. Heavy stuff.<\/p>\n","protected":false},"excerpt":{"rendered":"

Is the God of the philosophers the God of the scriptures?<\/p>\n","protected":false},"author":6,"featured_media":38279,"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":[10,9,3],"tags":[83],"class_list":["post-38280","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-logic","category-philosophy","category-theories","tag-identity"],"_links":{"self":[{"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/posts\/38280","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\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/comments?post=38280"}],"version-history":[{"count":5,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/posts\/38280\/revisions"}],"predecessor-version":[{"id":38635,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/posts\/38280\/revisions\/38635"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/media\/38279"}],"wp:attachment":[{"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/media?parent=38280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/categories?post=38280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/trinities.org\/blog\/wp-json\/wp\/v2\/tags?post=38280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}