{"id":9866,"date":"2012-03-12T05:44:21","date_gmt":"2012-03-12T05:44:21","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2012\/03\/12\/another-stromboli-logic-problem\/"},"modified":"2012-03-12T05:44:21","modified_gmt":"2012-03-12T05:44:21","slug":"another-stromboli-logic-problem","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2012\/03\/12\/another-stromboli-logic-problem\/","title":{"rendered":"On the Expressibility of ‘Something Exists’"},"content":{"rendered":"

Surely this is a valid and sound argument:<\/span><\/p>\n

1. Stromboli exists.<\/span>
Ergo<\/span>
2. Something exists.<\/span><\/p>\n

Both sentences are true; both are meaningful; and the second follows from the first.  How do we translate the argument into the notation of standard first-order predicate logic with identity? Taking a cue from Quine we may formulate (1) as<\/span><\/p>\n

1*.  For some x, x = Stromboli. In English:<\/span><\/p>\n

1**. Stromboli is identical with something.<\/span><\/p>\n

But how do we render (2)?  Surely not as 'For some x, x exists' since there is no first-level predicate of existence in standard logic.  And surely no ordinary predicate will do.  Not horse, mammal, animal, living thing, material thing, or any other predicate reachable by climbing the tree of Porphyry.  Existence is not a summum genus<\/em>.  (Aristotle, Met. 998b22, AnPr. 92b14) What is left but self-identity?  Cf. Frege's dialog with Puenjer<\/a>.<\/span><\/p>\n

So we try,<\/span><\/p>\n

2*. For some x, x = x.  In plain English:<\/span><\/p>\n

2**. Something is self-identical.<\/span><\/p>\n

So our original argument becomes:<\/span><\/p>\n

1**. Stromboli is identical with something.<\/span>
Ergo<\/span>
2**. Something is self-identical.<\/span><\/p>\n

But what (2**) says is not what (2) says.   The result is a murky travesty of the original luminous argument.<\/span><\/p>\n

What I am getting at is that standard logic cannot state its own presuppositions.  It presupposes that everything exists (that there are no nonexistent objects) and that something exists.  But it lacks the expressive resources to state these presuppositions.  The attempt to state them results either in  nonsense — e.g. 'for some x, x' — or a proposition other than the one that needs expressing.  <\/span><\/p>\n

It is true that something exists, and I am certain that it is true: it follows immediately from the fact that I exist.  But it cannot be said in standard predicate logic.<\/span><\/p>\n

What should we conclude?  That standard logic is defective in its treatment of existence or that there are things that can be SHOWN but not SAID?  In April 1914. G.E. Moore travelled to Norway and paid a visit to Wittgenstein where the  latter dictated some notes to him.  Here is one:<\/span><\/p>\n

\n

In order that you should have a language which can express or say<\/em> everything that can be said, this language must have certain properties; and when this is the case, that<\/em> it has them can no longer be said in that language or any<\/em> language. (Notebooks 1914-1916<\/em>, p. 107)<\/span><\/p>\n<\/blockquote>\n

Applied to the present example:  A language that can SAY that e.g. island volcanos exist by saying that some islands are volcanos or that Stromboli exists by saying that Stromboli is identical to something must have certain properties.  One of these is that the domain of quantification contains only existents and no Meinongian nonexistents.  But THAT the language has this property cannot be said in it or in any language.  Hence it cannot be said in the language of standard logic that the domain of quantification is a domain of existents or that something exists or that everything exists or that it is not the case that something does not exist.<\/span><\/p>\n

Well then, so much the worse for the language of standard logic!<\/span>  That's one response.  But can some other logic do better?  Or should we say, with the early Wittgenstein, that there is indeed the Inexpressible, the Unsayable, the Unspeakable, the Mystical?  And that it shows itself? <\/span><\/p>\n

\n

Es gibt allerdings Unaussprechliches.  Dies zeigt sich, es ist das Mystische. <\/em>(Tractatus Logico-Philosphicus<\/strong> 6.522)<\/span><\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"

Surely this is a valid and sound argument: 1. Stromboli exists.Ergo2. Something exists. Both sentences are true; both are meaningful; and the second follows from the first.  How do we translate the argument into the notation of standard first-order predicate logic with identity? Taking a cue from Quine we may formulate (1) as 1*.  For … Continue reading “On the Expressibility of ‘Something Exists’”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[142,408,108,275],"tags":[],"class_list":["post-9866","post","type-post","status-publish","format-standard","hentry","category-existence","category-language-philosophy-of","category-logica-docens","category-wittgenstein"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/9866","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/comments?post=9866"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/9866\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=9866"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=9866"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=9866"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}