{"id":7584,"date":"2014-11-15T13:56:55","date_gmt":"2014-11-15T13:56:55","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2014\/11\/15\/is-it-a-contradction\/"},"modified":"2014-11-15T13:56:55","modified_gmt":"2014-11-15T13:56:55","slug":"is-it-a-contradction","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2014\/11\/15\/is-it-a-contradction\/","title":{"rendered":"Is it a Contradiction?"},"content":{"rendered":"

London Ed writes,<\/span><\/p>\n

I am interested in your logical or linguistic intuitions here. Consider<\/span><\/p>\n

\n

(*) There is someone called \u2018Peter\u2019, and Peter is a musician. There is another person called \u2018Peter\u2019, and Peter is not a musician.<\/span><\/p>\n<\/blockquote>\n

Is this a contradiction?  Bear in mind that the whole conjunction contains the sentences \u201cPeter is a musician\u201d and \u201cPeter is not a musician\u201d. I am corresponding with a fairly eminent philosopher who insists it is contradictory.<\/span><\/p>\n

Whether or not (*) is a contradiction depends on its logical form.  I say the logical form is as follows, where 'Fx' abbreviates 'x is called 'Peter'' and 'Mx' abbreviates 'x is a musician':<\/span><\/p>\n

\n

LF1. (\u2203x)(\u2203y)[Fx & Mx & Fy & ~My & ~(x =y)]<\/span><\/p>\n<\/blockquote>\n

In 'canonical English':<\/span><\/p>\n

\n

CE. There is something x and something y such that x  is called 'Peter' and x is a musician and y is called 'Peter' and y is not a musician and it is not the case that x is identical to y.<\/span><\/p>\n<\/blockquote>\n

There is no contradiction.  It is obviously logically possible — and not just logically<\/em> possible — that there be two men, both named 'Peter,' one of whom is a musician and the other of whom is not.<\/span><\/p>\n

I would guess that your correspondent takes the logical form to be<\/span><\/p>\n

\n

LF2. (\u2203x)(\u2203y)(Fx & Fy & ~(x = y)) & Mp & ~Mp<\/span><\/p>\n<\/blockquote>\n

where 'p' is an individual constant abbreviating 'Peter.'<\/span><\/p>\n

(LF2) is plainly a contradiction.  <\/span><\/p>\n

My analysis assumes that in the original sentence(s) the first USE (not mention) of 'Peter' is replaceable salva significatione<\/em> by 'he,' and that the antecedent of 'he' is the immediately preceding expression 'Peter.'  And the same for the second USE (not mention) of 'Peter.'<\/span><\/p>\n

If I thought burden-of-proof considerations were relevant in philosophy, I'd say the burden of proving otherwise rests on your eminent interlocutor.<\/span><\/p>\n

But I concede one could go outlandish and construe the original sentences — which I am also assuming can be conjoined into one sentence — as having (LF2).  <\/span><\/p>\n

So it all depends on what you take to be the logical form of the original sentence(s).  And that depends on what proposition you take the original sentence(s) to be expressing.  The original sentences(s) are patient of both readings.<\/span><\/p>\n

Now Ed, why are you vexing yourself over this bagatelle when the barbarians are at the gates of London?  And not just at<\/em> them?<\/span><\/p>\n

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London Ed writes, I am interested in your logical or linguistic intuitions here. Consider (*) There is someone called \u2018Peter\u2019, and Peter is a musician. There is another person called \u2018Peter\u2019, and Peter is not a musician. Is this a contradiction?  Bear in mind that the whole conjunction contains the sentences \u201cPeter is a musician\u201d … Continue reading “Is it a Contradiction?”<\/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":[6,408,108],"tags":[],"class_list":["post-7584","post","type-post","status-publish","format-standard","hentry","category-language-matters","category-language-philosophy-of","category-logica-docens"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/7584","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=7584"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/7584\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=7584"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=7584"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=7584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}