{"id":7996,"date":"2014-04-25T15:06:33","date_gmt":"2014-04-25T15:06:33","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2014\/04\/25\/logical-form-instantiation-and-pattern-matching\/"},"modified":"2014-04-25T15:06:33","modified_gmt":"2014-04-25T15:06:33","slug":"logical-form-instantiation-and-pattern-matching","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2014\/04\/25\/logical-form-instantiation-and-pattern-matching\/","title":{"rendered":"Logical Form, Instantiation, and Pattern-Matching"},"content":{"rendered":"

David Brightly comments:<\/span><\/p>\n

\n

We can't say that an argument is invalid because it instantiates an invalid form. The argument Socrates is a man; all men are mortal; ergo Socrates is mortal<\/em> instantiates the invalid form a is F; all Hs are G; ergo a is G<\/em>, but modulo equivocation, it is truth-preserving. Instantiation of form is just pattern-matching, and the argument does match the pattern of the invalid form.<\/span><\/p>\n<\/blockquote>\n

I reject this of course.The sample argument is an example of correct reasoning.  But anyone who argues in accordance with the schema argues incorrectly.  Why?  Because the schema is not truth-preserving. Therefore the sample argument does not<\/em> instantiate the invalid form. <\/span><\/p>\n

I don't think Brightly understands 'truth-preserving.'  This is a predicate of argument forms, primarily, and the same goes for 'valid' and 'invalid.'  Here are some  definitions:<\/span><\/p>\n

D1. An argument form is truth-preserving =df no argument of that form has true premises and a false conclusion.<\/span><\/p>\n

D2. An argument form F is valid =df F is truth-preserving.<\/span><\/p>\n

D3. A particular argument A is valid =df A instantiates a valid form.  (This allows for the few cases in which an argument has two forms, one valid and one invalid.)<\/span><\/p>\n

D4. A particular argument A is invalid =df there is no valid form that it instantiates. 
<\/span><\/p>\n

Now what is it for an argument to instantiate an argument form?  To answer this question we need to know what an argument is.  Since deductive arguments alone are under consideration,  I define:<\/span><\/p>\n

D5. A deductive argument is a sequence of propositions together with the claim that one of them, the conclusion, follows from the others, the premises, taken together.<\/span><\/p>\n

If the claim holds, the argument is valid; if not, invalid.<\/span><\/p>\n

Now the main point for present purposes is that an argument is composed of propositions<\/em>.  A proposition is not a complex physical object such as a string of marks on paper. Thus what you literally SEE when you see this: <\/span><\/p>\n

\n

7 + 5 = 12<\/span><\/p>\n<\/blockquote>\n

is not a proposition, but a spatiotemporal particular, a physical item subject to change: it can be deleted.  But the proposition it expresses cannot be deleted by deleting what you just literally SAW.  That suffices to show that the proposition expressed by what you saw is not identical to what you saw. Whatever propositions are (and there are different theories), they are not physical items.<\/span><\/p>\n

What's more,  you did not SEE (with your eyes) the proposition, or that it is true, but you UNDERSTOOD the proposition and that it is true. (A proposition and its being true are not the same even if the proposition is true.)  So this is a second reason why a proposition is not identical to its physical expression.<\/span><\/p>\n

Now what holds for propositions also holds for arguments: you cannot delete an argument by deleting physical marks, and you cannot understand an argument merely by seeing a sequence of strings of physical marks. <\/span><\/p>\n

An argument is not a pattern of physical marks.  So there is no question of matching this physical pattern with some other physical pattern.   Instantiation of logical form is not<\/em> just pattern-matching.<\/span><\/p>\n

If a sentence contains a sign like 'bank' susceptible of two or more readings, then no one definite proposition is expressed by the sentence.  Until that ambiguity is resolved one does not have a definite proposition, and without definite propositions no definite argument.  But once one has a definite argument then one can assess its validity.  If it instantiates a valid form, then it is valid; if it instantiates an invalid form, then it is invalid.<\/span><\/p>\n

It is as simple as that.  But one has to avoid the nominalist mistake of thinking that arguments are just collections of physical items.
<\/span><\/p>\n

\nRelated articles<\/legend>\n
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\"\"<\/a>Abbreviations, Place-Holders, and Logical Form<\/a><\/div>\n
\"\"<\/a>The Stromboli Puzzle Revisited<\/a><\/div>\n
\"\"<\/a>Types, Tokens, and Logical Form<\/a><\/div>\n
\"\"<\/a>Validity and Semantics: Will the Real Frodo Baggins Please Stand Up?<\/a><\/div>\n
\"\"<\/a>On the Enforcing and Permitting of Coreferentiality by Argument-Forms<\/a><\/div>\n<\/div>\n<\/fieldset>\n","protected":false},"excerpt":{"rendered":"

David Brightly comments: We can't say that an argument is invalid because it instantiates an invalid form. The argument Socrates is a man; all men are mortal; ergo Socrates is mortal instantiates the invalid form a is F; all Hs are G; ergo a is G, but modulo equivocation, it is truth-preserving. Instantiation of form … Continue reading “Logical Form, Instantiation, and Pattern-Matching”<\/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-7996","post","type-post","status-publish","format-standard","hentry","category-logica-docens"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/7996","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=7996"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/7996\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=7996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=7996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=7996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}