{"id":11115,"date":"2010-11-18T15:42:01","date_gmt":"2010-11-18T15:42:01","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/11\/18\/my-lately-posted-logic-problem-pondered\/"},"modified":"2010-11-18T15:42:01","modified_gmt":"2010-11-18T15:42:01","slug":"my-lately-posted-logic-problem-pondered","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/11\/18\/my-lately-posted-logic-problem-pondered\/","title":{"rendered":"My Lately Posted Logic Problem Pondered . . ."},"content":{"rendered":"

. . . and pondered well by David Parker over at Pondering the Preponderance<\/a>.  I challenged the reader to spot what is wrong in the following argument, an argument I thought was interesting because it is fairly seductive, as compared to the stock examples in logic texts:<\/span><\/p>\n

The Argument<\/strong><\/span>
1. A necessary truth is true.<\/span>
2. Whatever is true is possibly true.<\/span>
3. Whatever is possibly true could be false.<\/span>
Therefore<\/span>
4. A necessary truth could be false.<\/span><\/p>\n

(I hope it is clear that 'possibly' and 'could' are not<\/em> being used epistemically in this argument.)  Since the conclusion is plainly false, the argument is unsound either in virtue of invalidity, or in virtue of one or more false premises, or both.  There is nothing wrong with the formal logic of the argument, so I pointed out, correctly, that while (1) and (2) are each true, (3) is false.  <\/span><\/p>\n

But there is an alternative analysis which Parker notes (and I didn't just to keep the post short), namely that one can see the argument as trading on an equivocal use of 'possibly true.'  And this alternative analysis helps explain why the argument is seductive.  After all (3) would be true if 'possibly true' meant 'contingently true.'  That is not what it means, but one could be forgiven for thinking so.  One could then say that the argument goes wrong because it commits the informal fallacy of equivovation: 'possibly true' is used with different senses in (2) and (3).  On this alternative analysis one could say that all the premises are true, but the argument commits the informal fallacy of equivocation.<\/span><\/p>\n

But there is another wrinkle, and one which Parker notes.   Equivocation is standardly classified as an informal fallacy, buy doesn't every case of equivocation in a deductive argeument induce a formal<\/em> fallacy?  Yes it does.  The form of the above argument could be depicted as follows:<\/span><\/p>\n

Every F is a G<\/span>
Every G is an H<\/span>
Every H is an I<\/span>
Ergo<\/span>
Every F is an I<\/span><\/p>\n

The form just depicted is clearly valid, whence it follow that every argument instantiating this form is valid.  It is of course assumed that the terms are being used univocally.  But if there is an equivocation on 'possibly true,' then the form of the original argument is not the above, but this:<\/span><\/p>\n

Every F is a G<\/span>
Every G is an H<\/span>
Every I is a J<\/span>
Ergo<\/span>
Every F is a J<\/span><\/p>\n

which is plainly invalid.<\/span><\/p>\n

One moral is that the distinction between formal and informal fallacies is not hard-and-fast. (Composition and Division would also be interesting to discuss in this connection).  One can analyze our original argument as involving an equivocation on  'possibly true' in which case the argument is invalid, or one can take the argument to be valid but reject it because of the falsity of premise (3).<\/span><\/p>\n

Ah, the pleasures of analysis!<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

. . . and pondered well by David Parker over at Pondering the Preponderance.  I challenged the reader to spot what is wrong in the following argument, an argument I thought was interesting because it is fairly seductive, as compared to the stock examples in logic texts: The Argument1. A necessary truth is true.2. Whatever is true … Continue reading “My Lately Posted Logic Problem Pondered . . .”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[108],"tags":[],"class_list":["post-11115","post","type-post","status-publish","format-standard","hentry","category-logica-docens"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11115","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=11115"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11115\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=11115"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=11115"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=11115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}