{"id":9701,"date":"2012-05-15T16:40:58","date_gmt":"2012-05-15T16:40:58","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2012\/05\/15\/abbreviations-place-holders-and-logical-form\/"},"modified":"2012-05-15T16:40:58","modified_gmt":"2012-05-15T16:40:58","slug":"abbreviations-place-holders-and-logical-form","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2012\/05\/15\/abbreviations-place-holders-and-logical-form\/","title":{"rendered":"Abbreviations, Place-Holders, and Logical Form"},"content":{"rendered":"

It is one thing to abbreviate an argument, another to depict its logical form. Let us consider the following argument composed in what might be called 'canonical English':<\/span><\/p>\n

1. If God created some contingent beings, then he created all contingent beings.
2. God created all contingent beings.
—–
3. God created some contingent beings. <\/span><\/p>\n

The above  is an argument, not an argument-form. The following abbreviation of the argument is also an argument, not an argument-form:<\/span> <\/span><\/p>\n

\n

1. P –> Q
2. Q
—
3. P
<\/span><\/p>\n

Both are arguments; it is just that the second is an abbreviation of the first in which sentences are replaced with upper-case letters and the logical words with symbols from the propositional calculus. But it is easy to confuse the second argument with the following argument-form<\/em>:<\/span><\/p>\n

1. p –> q
2. q
—
3. p
<\/span><\/p>\n

An argument-form is a one-over-many: many arguments can have the same form. And the same goes for its constituent propositional forms: each is a one-over-many. 'p –> q' is the form of indefinitely many conditional statements. But an argument, whether spelled out or abbreviated, is a particular, and as such uninstantiable. One cannot substitute different statements for the upper-case 'P' and 'Q' above.<\/span><\/p>\n

Some of you will call this hair-splitting. But I prefer to think of it as a distinction essential to clear thinking in logic. For suppose you confuse the second two schemata. Then you might think that the original argument, the one in 'canonical English,' is an instance of the formal fallacy of Affirming the Consequent. But the second schema, though it is an instance of the third, is also an instance of a valid argument-form:<\/span><\/p>\n

(x)(Cgx)
—
(Ex)(Cgx).
<\/span><\/p>\n

In sum, the confusion of abbreviations with place-holders aids and abets the mistake of thinking that an argument that instantiates an invalid form is invalid. Validity and invalidity are asymmetrical: if an argument instantiates a valid form, then it is valid; but if it instantiates an invalid form, then it may or may not be invalid. <\/span><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

It is one thing to abbreviate an argument, another to depict its logical form. Let us consider the following argument composed in what might be called 'canonical English': 1. If God created some contingent beings, then he created all contingent beings.2. God created all contingent beings.—–3. God created some contingent beings. The above  is an … Continue reading “Abbreviations, Place-Holders, and Logical Form”<\/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-9701","post","type-post","status-publish","format-standard","hentry","category-logica-docens"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/9701","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=9701"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/9701\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=9701"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=9701"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=9701"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}