{"id":7973,"date":"2014-05-07T15:20:38","date_gmt":"2014-05-07T15:20:38","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2014\/05\/07\/logical-form-and-the-symmetry-thesis\/"},"modified":"2014-05-07T15:20:38","modified_gmt":"2014-05-07T15:20:38","slug":"logical-form-and-the-symmetry-thesis","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2014\/05\/07\/logical-form-and-the-symmetry-thesis\/","title":{"rendered":"Logical Form and the Symmetry Thesis"},"content":{"rendered":"
\n

"The most conspicuous purpose of logic, in its applications to science and everyday discourse, is the justification and criticism of inference<\/em>." (Emphasis added, Willard Van Orman Quine, Methods of Logic<\/em>, 2nd revised ed., Holt, Rinehart & Winston, 1959, p. 33.<\/span><\/p>\n<\/blockquote>\n

Perhaps the dispute in the earlier thread<\/a> could be resolved if we all could agree on the following.<\/span><\/p>\n

1. The most specific logical form of a deductive argument A is the form relevant for assessing whether the reasoning embodied in A is valid or invalid.<\/span><\/p>\n

2. Every deductive argument has exactly one most specific form.<\/span><\/p>\n

3. Symmetry Thesis<\/em>:  if the most specific form of A is valid, then A is valid; if the most specific form of A is invalid, then A is invalid.<\/span><\/p>\n

In case 'most specific logical form' needs explanation, consider the difference between the following valid  form from the predicate calculus and the following invalid form from the propositional calculus:<\/span><\/p>\n

Fa<\/span>
Ga<\/span>
——-<\/span>
(Ex)(Fx & Gx)<\/span><\/p>\n

p<\/span>
q<\/span>
——-<\/span>
r.<\/span><\/p>\n

The former is the most specific logical form of 'Al is fat, Al is gay, ergo, something is both fat and gay.'  The latter, if a form of the argument at all, is less specific: it abstracts from the internal subpropositional logical structure of the constituent propositions.<\/span><\/p>\n

Now three examples in illustration of (1)-(3).<\/span><\/p>\n

Example One<\/strong>.  Call the following argument 'Charley':<\/span><\/p>\n

Tom is tall<\/span>
——-<\/span>
Tom is tall.<\/span><\/p>\n

Although the above display, which is a written expression of the argument and not the argument itself, shows two tokens of the sentence type 'Tom is tall,' the argument consists of exactly one proposition.  Anyone who executes the reasoning displayed infers the  proposition *Tom is tall* from itself.  (I am using asterisks to mention propositions.  So '*Tom is tall*' is an abbreviation of 'the proposition expressed by a tokening of the sentence type "Tom is tall".') <\/span><\/p>\n

It is perfectly clear that the reasoning embodied by Charley is valid and that its form is 'P ergo P.'  The reasoning is not from P to some proposition that may or may not be identical to P.  Therefore the concrete episode of reasoning<\/em> does not have the form 'P ergo Q.' <\/span><\/p>\n

But let us irenically  concede that if one wished, for whatever reason, to abstract not only from the content of the argument but also from the plain fact that the argument involves exactly one proposition, one could view the form 'P ergo P' as a special case of 'P ergo Q.'   And I will also concede, to keep peace between Phoenix and London, that the argument instantiates the second invalid form, even though I don't believe that this is the case.<\/span><\/p>\n

Either way, the Symmetry Thesis stands and the Asymmetry Thesis falls.  For as G. Rodrigues in the earlier thread pointed out, 'P ergo P' is the most specific form of Charley. <\/span><\/p>\n

Example Two<\/strong>.  Call the following argument 'Kitty Kat.'<\/span><\/p>\n

If cats like cream, then cats like cream<\/span>
Cats like cream<\/span>
——-<\/span>
Cats like cream.<\/span><\/p>\n

Please note that there is no equivocation in this example: 'Cats like cream' has the same sense in all four of its occurrences.<\/span><\/p>\n

Kitty Kat's most specific form is 'P –> P, P, ergo P.'  This form is valid.  So Kitty Kat is valid, notwithstanding the fact, if it is a fact, that Kitty Kat also instantiates the formal fallacy, Affirming the Consequent: P –> Q, Q, ergo P.  By (1) above, the fact, if it is a fact, that Kitty Kat instantiates Affirming the Consequent is irrelevant to the assessment of the validity\/invalidty of the reasoning embodied in Kitty Kat.<\/span><\/p>\n

Example Three<\/strong>.  Call the following example 'Massey':<\/span><\/p>\n

If God created something , then God created everything.<\/span>
God created everything.<\/span>
——-<\/span>
God created something.<\/span><\/p>\n

 <\/p>\n

This argument fits the pattern of the formal fallacy, Affirming the Consequent:<\/span><\/p>\n

 <\/p>\n

If p then q<\/span>
q<\/span>
——-<\/span>
p.<\/span><\/p>\n

 <\/p>\n

But the argument also has a valid form:<\/span><\/p>\n

 <\/p>\n

Every x is such that Cgx<\/span>
——-<\/span>
Some x is such that Cgx. <\/span><\/p>\n

Please note that if an argument is valid, adding  a premise can't make it invalid; this principle is what allows us to disregard the first line.<\/span><\/p>\n

 <\/p>\n

(Example adapted from Gerald J. Massey, "The Fallacy behind Fallacies," Midwest Studies in Philosophy<\/em> VI (1981), pp. 489-500)<\/span><\/p>\n

The most specific form of Massey is the predicate logic form above displayed.  Since it is valid, Massey is valid. <\/span><\/p>\n

Symmetry Thesis vindicatus est<\/em>.<\/span><\/p>\n

Is everybody happy now?      
<\/span><\/p>\n

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\"\"<\/a>Eric Voegelin's 1948 Definition of Scientism<\/a><\/div>\n<\/div>\n<\/fieldset>\n","protected":false},"excerpt":{"rendered":"

"The most conspicuous purpose of logic, in its applications to science and everyday discourse, is the justification and criticism of inference." (Emphasis added, Willard Van Orman Quine, Methods of Logic, 2nd revised ed., Holt, Rinehart & Winston, 1959, p. 33. Perhaps the dispute in the earlier thread could be resolved if we all could agree … Continue reading “Logical Form and the Symmetry Thesis”<\/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":[108],"tags":[],"class_list":["post-7973","post","type-post","status-publish","format-standard","hentry","category-logica-docens"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/7973","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=7973"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/7973\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=7973"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=7973"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=7973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}