{"id":8154,"date":"2014-02-04T13:28:04","date_gmt":"2014-02-04T13:28:04","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2014\/02\/04\/every-proposition-is-affirmative\/"},"modified":"2014-02-04T13:28:04","modified_gmt":"2014-02-04T13:28:04","slug":"every-proposition-is-affirmative","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2014\/02\/04\/every-proposition-is-affirmative\/","title":{"rendered":"*Every Proposition is Affirmative*"},"content":{"rendered":"

\"Buridan's<\/a>Nicholas Rescher cites this example from Buridan.  The proposition is false, but not self-refuting.  If every proposition is affirmative, then of course *Every proposition is affirmative* is affirmative.  The self-reference seems innocuous, a case of self-instantiation. But *Every proposition is affirmative* has as a logical consequence *No proposition is negative.*  This follows by Obversion<\/a>, assuming that a proposition is negative if and only if it is not affirmative.<\/span><\/p>\n

Paradoxically, however, the negative proposition, unlike its obverse, is<\/em> self-refuting.  For if no proposition is negative then *No proposition is negative* is not negative.  So if it is, it isn't.  Plainly it is. Ergo, it isn't.<\/span><\/p>\n

Rescher leaves the matter here, and I'm not sure I have anything useful to add. <\/span><\/p>\n

It is strange, though, that here we have two logically equivalent propositions one of which is self-refuting and the other of which is not.  The second is necessarily false.  If true, then false; if false, then false; ergo, necessarily false.  But then the first must also be necessarily false.  After all, they are logically<\/em> equivalent: each entails the other across all logically possible worlds.<\/span><\/p>\n

What is curious, though, is that the ground of the logical necessity seems different in the two cases.  In the second case, the necessity is grounded in logical self-contradiction.  In the first case, there does not appear to be any self-contradiction.<\/span><\/p>\n

It is impossible that every proposition be affirmative.  And it is impossible that no proposition be negative.  But whereas the impossibility of the second is the impossibility of self-referential inconsistency, the impossibility of the first is not.  (That is  the 'of' of apposition.)<\/span><\/p>\n

Can I make an aporetic polyad out of this?  Why not?<\/span><\/p>\n

\n

1. Logically equivalent logically impossible propositions have the same ground of their logical impossibility.<\/span><\/p>\n

2. The ground of the logical impossibility of *Every proposition is affirmative* is not in self-reference.<\/span><\/p>\n

3. The ground of the logical impossibility of *No proposition is negative* is in self-reference.<\/span><\/p>\n<\/blockquote>\n

The limbs of this antilogism are individually plausible but collectively inconsistent.<\/span><\/p>\n

REFERENCES<\/span><\/p>\n

Nicholas Rescher, Paradoxes: Their Roots, Range, and Resolution<\/em>, Open Court, 2001, pp. 21-22.<\/span><\/p>\n

G. E. Hughes, John Buridan on Self-Reference,<\/em> Cambidge UP, 1982, p. 34. Cited by Rescher.<\/span><\/p>\n

\nRelated articles<\/legend>\n
\n
\"\"<\/a>Some Notes on Rescher's "Nonexistents Then and Now"<\/a><\/div>\n
\"\"<\/a>When Is Retorsion Probative?<\/a><\/div>\n<\/div>\n<\/fieldset>\n","protected":false},"excerpt":{"rendered":"

Nicholas Rescher cites this example from Buridan.  The proposition is false, but not self-refuting.  If every proposition is affirmative, then of course *Every proposition is affirmative* is affirmative.  The self-reference seems innocuous, a case of self-instantiation. But *Every proposition is affirmative* has as a logical consequence *No proposition is negative.*  This follows by Obversion, assuming … Continue reading “*Every Proposition is Affirmative*”<\/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":[21,108,541,328],"tags":[],"class_list":["post-8154","post","type-post","status-publish","format-standard","hentry","category-aporetics","category-logica-docens","category-propositions","category-self-self-awareness-self-reference"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/8154","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=8154"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/8154\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=8154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=8154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=8154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}