{"id":9407,"date":"2012-08-30T12:53:19","date_gmt":"2012-08-30T12:53:19","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2012\/08\/30\/beating-the-dead-horse-of-the-thin-theory-some-more\/"},"modified":"2012-08-30T12:53:19","modified_gmt":"2012-08-30T12:53:19","slug":"beating-the-dead-horse-of-the-thin-theory-some-more","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2012\/08\/30\/beating-the-dead-horse-of-the-thin-theory-some-more\/","title":{"rendered":"Beating the Dead Horse of the Thin Theory Some More"},"content":{"rendered":"

It is obviously true that something exists.  This is not only true, but known with certainty to be true:  I think, therefore I exist, therefore something exists.  That is my Grand Datum, my datanic starting point.  Things exist!  <\/span><\/p>\n

Now it seems perfectly clear to me that 'Something exists' cannot be translated adequately as 'Something is self-identical' employing just the resources of modern predicate logic (MPL), i.e., first-order predicate logic  with identity.    But it seems perfectly clear to van Inwagen that it can.  See my preceding post on this topic<\/a>. So one of us is wrong, and if it is me, I'd like to know exactly why.  Let me add that 'Something is self-identical' is the prime candidate for such a thin translation.  If there is a thin translation, this is it.  Van Inwagen comes into the discussion only as a representative of the thin theory, albeit as the 'dean' of the thin theorists.<\/span><\/p>\n

Consider the following formula in first-order predicate logic with identity that van Inwagen thinks adequately translates 'There are objects' and 'Something exists':<\/span><\/p>\n

1. (\u2203x) (x = x).<\/span><\/p>\n

It seems to me that there is nothing in this formula but syntax: there are no nonlogical expressions, no content expressions, no expressions like 'Socrates' or 'cat' or placeholders for such expressions such as  'a' and 'C.'  The parentheses can be dropped, and van Inwagen writes the formula without them. This leaves us with '\u2203,' three bound occurrences of the variable 'x,' and the identity sign '=.'  <\/span><\/p>\n

Now here is my main question:  How can the extralogical and extrasyntactical fact that something exists be a matter of pure logical syntax?  How can this fact be expressed by a string of merely syntactical symbols: '\u2203,' 'x,' '='?<\/strong><\/span><\/p>\n

It is not a logical truth that something exists; it is a matter of extralogical fact.  There's this bloody world out there and it certainly wasn't sired by the laws of logic.  Logically<\/em>, there might not have been anything at all.  It is true, but logically contingent<\/em>, that something exists.  Compare (1) with the universal quantification<\/span><\/p>\n

2. (x)(x =x).<\/span><\/p>\n

If (1) translates 'Something exists,' then (2) translates 'Everything exists.'  But (2) is a logical truth, and its negation a contradiction.  Since (1) follows from (2), (1) is a logical truth as well.  But (1) is not a logical truth as we have just seen.  We face an aporetic triad:<\/span><\/p>\n

a. '(x)(x =x)' is logically true.<\/span>
b. '(\u2203x) (x = x)' follows from '(x)(x = x).'<\/span>
c. '(\u2203x) (x = x)' adequately translates 'Something exists.'<\/span><\/p>\n

Each limb is plausible, but they cannot all be true.   The truth of any two linbs entails the falsehood of the remaining one. For example, the first two entail that '(\u2203x) (x = x)' is logically true. But then (c) is false:  One sentence cannot be an adequate translation of a second if the first fails to preserve the modal status of the second.  To repeat myself: 'Something exists' is logically contingent whereas the canonical  translation is logically necessary.<\/span><\/p>\n

Now which of the limbs shall we reject?  It is obvious to me that the third limb must be rejected, pace<\/em> van Inwagen.<\/span><\/p>\n

Now consider 'Everything exists.'  Can it be translated adequately as '(x)(x = x)'?  Obviously not.  The latter is a formal-logical truth. and its negation is a formal-logical contradiction.  But the negation of 'Everything exists' — 'Something does not exist' — is not a formal logical contradiction.  Therefore, 'Everything exists' is not a formal-logical truth.  And because it is not, it cannot be given the canonical translation.<\/span><\/p>\n

Finally, consider 'Nothing exists.'  This is false, but logically contingent: there is no formal-logical necessity that something exist.  One cannot infer the existence of anything (or at least anything concrete) from the principles of formal logic alone.  The canonical translation of 'Nothing exists,' however — (x)~(x = x)' -  is not contingently false, but logically false.  Therefore, 'Nothing exists' cannot be translated adequately as 'Everything is not self-identical.'<\/span><\/p>\n

Van Inwagen and his master Quine are simply mistaken when they maintain that existence is what 'existential' quantification expresses. <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

It is obviously true that something exists.  This is not only true, but known with certainty to be true:  I think, therefore I exist, therefore something exists.  That is my Grand Datum, my datanic starting point.  Things exist!  Now it seems perfectly clear to me that 'Something exists' cannot be translated adequately as 'Something is … Continue reading “Beating the Dead Horse of the Thin Theory Some More”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[142,408],"tags":[],"class_list":["post-9407","post","type-post","status-publish","format-standard","hentry","category-existence","category-language-philosophy-of"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/9407","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=9407"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/9407\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=9407"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=9407"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=9407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}