{"id":12284,"date":"2009-10-27T18:05:59","date_gmt":"2009-10-27T18:05:59","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2009\/10\/27\/arguments-and-conditionals\/"},"modified":"2009-10-27T18:05:59","modified_gmt":"2009-10-27T18:05:59","slug":"arguments-and-conditionals","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2009\/10\/27\/arguments-and-conditionals\/","title":{"rendered":"Arguments and Conditionals"},"content":{"rendered":"

The early Stoic logicians were aware of a distinction that most of us make nowadays but that certain medieval logicians, according to David H. Sanford (<\/font>If P, then Q: Conditionals and the Foundations of Reasoning<\/font><\/a>, p. 31), either missed or did not make. I am referring to the difference between arguments and conditional statements. Note the difference between<\/font><\/p>\n

1. Since murder is wrong, suicide is wrong
<\/font><\/p>\n

and
<\/font><\/p>\n

2. If murder is wrong, then suicide is wrong.
<\/font><\/p>\n

<\/font><\/p>\n

\n<\/div>\n<\/p>\n


\n<\/font><\/p>\n

(1) contains an <\/font>enthymematic<\/a> argument which, made explicit by supply of the tacit premise, may be displayed as follows:
<\/font><\/div>\n

<\/font><\/p>\n

3. Murder is wrong
4. Suicide is murder
—–
5. Suicide is wrong.
<\/font><\/p>\n

Someone who gives (i.e., makes, mounts, forwards, advocates, etc.) this argument, as opposed to merely quoting it or mentioning it as I am doing here for purposes of logical theory, is asserting the premises and also asserting the conclusion as a logical consequence of the premises. But someone who asserts (2) or asserts
<\/font><\/p>\n

6. If murder is wrong, and suicide is murder, then suicide is wrong
<\/font><\/p>\n

is not asserting the antecedent or the consequent.
<\/font><\/p>\n

Therefore, arguments and conditionals should not be confused. Nevertheless, they are closely related in that arguments have corresponding conditionals and some conditionals have corresponding arguments. The early Stoics were onto this as well. Thus, (6) is the conditional corresponding to the (3)-(5) argument. We can go further and state that an argument is valid only if its corresponding conditional is a necessary truth. Furthermore, an argument is valid if and only if<\/em> its corresponding conditional is a narrowly-logical truth. If we are operating within the Propositional Calculus (PC), we can say that an argument encoded in PC whose validity\/invalidity rides on the logical structure captured by this encoding is valid if and only if its corresponding conditional is a tautology in the sense in which this term is used in the PC.<\/font><\/p>\n

Truth and validity are distinct, and one betrays logical ignorance if one speaks of an argument as either true or false. Still, for every valid argument there is a necessarily true corresponding conditional. <\/font><\/p>\n

I said that, for every argument, there is a corresponding conditional. It does not matter whether the argument is valid or invalid, explicit or enthymematic. But is it true that for every conditional there is a corresponding argument? In other words, can every conditional be unpacked as, be expressed in the form of, an argument? No, it is only some conditionals that can be expressed as arguments. These conditionals are ones in which antecedent and consequent are logically related, whether narrowly or broadly. Examples:
<\/font><\/p>\n

7. If Tom is tired, then someone is tired.
8. If Tom is tired, and all tired people are irritable, then Tom is irritable.
9. If Tom is a bachelor, then Tom is unmarried.
<\/font><\/p>\n

These propositions are arguments in conditional disguise. But the following are not:
<\/font><\/p>\n

10. If Tom is drunk, then he is apt to be belligerent.
11. If a fetus potentially possesses rights-conferring properties, then it is a person in the moral sense.
<\/font><\/p>\n

One who asserts (10) is not claiming that Tom's aptness for belligerence logically follows from his being drunk in the way that one who asserts (7) is claiming that someone's being tired logically follows from Tom's being tired. No doubt, there is the enthymematic argument:
<\/font><\/p>\n

Tom is drunk
—
Tom is apt to be belligerent
<\/font><\/p>\n

and the explicit argument
<\/font><\/p>\n

All who are drunk are apt to be belligerent
Tom is drunk
—
Tom is apt to be belligerent.
<\/font><\/p>\n

But these arguments are not implicit in (10). <\/font><\/p>\n","protected":false},"excerpt":{"rendered":"

The early Stoic logicians were aware of a distinction that most of us make nowadays but that certain medieval logicians, according to David H. Sanford (If P, then Q: Conditionals and the Foundations of Reasoning, p. 31), either missed or did not make. I am referring to the difference between arguments and conditional statements. Note … Continue reading “Arguments and Conditionals”<\/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-12284","post","type-post","status-publish","format-standard","hentry","category-logica-docens"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/12284","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=12284"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/12284\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=12284"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=12284"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=12284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}