{"id":10489,"date":"2011-08-01T11:22:02","date_gmt":"2011-08-01T11:22:02","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2011\/08\/01\/the-aporetics-of-singular-propositions\/"},"modified":"2011-08-01T11:22:02","modified_gmt":"2011-08-01T11:22:02","slug":"the-aporetics-of-singular-propositions","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2011\/08\/01\/the-aporetics-of-singular-propositions\/","title":{"rendered":"The Aporetics of Singular Sentences"},"content":{"rendered":"

I should issue a partial retraction.  I wrote earlier<\/a>,"The TFL representation of singular sentences as quantified sentences does not capture their logical form, and this is an inadequacy of TFL, and a point in favor of MPL."  ('TFL' is short for 'traditional formal logic'; 'MPL' for 'modern predicate logic with identity.' )<\/span><\/p>\n

The animadversions of Edward the Nominalist have made me see that my assertion is by no means obvious, and may in the end be just a dogma of analytic philosophy which has prevailed because endlessly repeated and rarely questioned.  Consider again this obviously valid argument:<\/span><\/p>\n

1. Pittacus<\/a> is a good man<\/span>
2. Pittacus is a wise man<\/span>
—–<\/span>
3. Some wise man is a good man.<\/span><\/p>\n

The traditional syllogistic renders the argument as follows: <\/span><\/p>\n

Every Pittacus is a wise man<\/span>
Some Pittacus is a good man<\/span>
—–<\/span>
Some wise man is a good man.<\/span><\/p>\n

This has the form:<\/span><\/p>\n

Every P is a W<\/span>
Some P is a G<\/span>
—–<\/span>
Some W is a G.<\/span><\/p>\n

This form is easily shown to be valid by the application of the syllogistic rules. <\/span><\/p>\n

In my earlier post<\/a> I then repeated a stock objection which I got from Peter Geach:<\/span><\/p>\n

\n

But is it logically acceptable to attach a quantifier to a singular term? How could a proper name have a sign of logical quantity prefixed to it? 'Pittacus' denotes or names exactly one individual. 'Every Pittacus' denotes the very same individual. So we should expect 'Every Pittacus is wise' and 'Pittacus is wise' to exhibit the same logical behavior. But they behave differently under negation.<\/span><\/p>\n

The negation of 'Pittacus is wise' is 'Pittacus is not wise.' So, given that 'Pittacus' and 'every Pittacus' denote the same individual, we should expect that the negation of 'Every Pittacus is wise' will be 'Every Pittacus is not wise.' But that is not the negation (contradictory<\/em>) of 'Every Pittacus is wise'; it is its contrary<\/em>. So 'Pittacus is wise' and 'Every Pittacus is wise' behave differently under negation, which shows that their logical form is different.<\/span><\/p>\n<\/blockquote>\n

My objection, in nuce<\/em>, was that 'Pittacus is wise' and 'Pittacus is not wise' are contradictories, not contraries, while 'Every Pittacus is wise' and 'Every Pittacus is not wise' ('No Pittacus is wise') are contraries.  Therefore, TFL does not capture or render perspicuous the logical form of 'Pittacus is wise.'<\/span><\/p>\n

To this, Edward plausibly objected:<\/span><\/p>\n

\n

As I have argued here before, \u2018Pittacus is wise\u2019 and \u2018Pittacus is not wise\u2019 are in fact contraries. For the first implies that someone (Pittacus) is wise. The second implies that someone (Pittacus again) is not wise. Both imply the existence of Pittacus (or at least \u2013 to silence impudent quibblers – that someone<\/em> is Pittacus). Thus they are contraries. Both are false when no one is Pittacus.<\/span><\/p>\n<\/blockquote>\n

I now concede that this is a very good point.  A little later Edward writes,<\/span><\/p>\n

\n

The thing is, you really have a problem otherwise. If 'Socrates is wise' and 'Socrates is not wise' are contradictories, and if 'Socrates is not wise' implies 'someone (Socrates) is not wise', as standard MPC holds, you are committed to the thesis that the sentence is not meaningful when Socrates ceases to exist (or if he never existed because Plato made him up). Which (on my definition) is Direct Reference.<\/span><\/p>\n

So you have this horrible choice:  Direct reference or Traditional Logic.<\/span><\/p>\n<\/blockquote>\n

But must we choose?  Consider 'Vulcan is uninhabited.'  Why can't I, without jettisoning any of the characteristic tenets of MPL, just say that this sentence, though it appears singular is really general because 'Vulcan' is not a logically proper name but a definite description in disguise?  Accordingly, what the sentence says is that a certain concept — the concept planet between Mercury and the Sun <\/em>— has as a Fregean mark (Merkmal<\/em>) the concept uninhabited<\/em>.<\/span><\/p>\n

Now consider the pair 'Socrates is dead' – 'Socrates is not dead.'  Are these contraries or contradictories?  If contraries, then they can both be false.  Arguably, they are both false since Socrates does not exist, given that presentism is true. Since both are false, both are meaningful.  But then 'Socrates ' has meaning despite its not referring to anything.  So 'Socrates' has something like a Fregean sense.  But what on earth could this be, given that 'Socrates' unlike 'Vulcan'  names an individual that existed, and so has a nonqualitative thisnsess incommunicable to any other individual?<\/span><\/p>\n

If, on the other hand, the meaning of 'Socrates' is its referent, then, given that presentism is  true and Socrates does not exist, there is no referent in which case both sentences are meaningless.<\/span><\/p>\n

So once again we are in deep aporetic trouble.  The proper name of a past individual cannot have a reference-determining sense.  This is because any such sense would have to be a Plantingian haecceity-property, and I have already shown that these cannot exist.  But if we say that 'Socrates' does not have a reference-determining sense but refers directly in such a way as to require Socrates to exist if 'Socrates' is to have meaning, then, given presentism,  'Socrates' and the sentence of which it is a part is meaningless. <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

I should issue a partial retraction.  I wrote earlier,"The TFL representation of singular sentences as quantified sentences does not capture their logical form, and this is an inadequacy of TFL, and a point in favor of MPL."  ('TFL' is short for 'traditional formal logic'; 'MPL' for 'modern predicate logic with identity.' ) The animadversions of Edward the … Continue reading “The Aporetics of Singular Sentences”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,408,108],"tags":[],"class_list":["post-10489","post","type-post","status-publish","format-standard","hentry","category-aporetics","category-language-philosophy-of","category-logica-docens"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/10489","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=10489"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/10489\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=10489"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=10489"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=10489"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}