tag:blogger.com,1999:blog-3891434218564545511.post9010168441739070334..comments2024-03-28T19:56:42.305-05:00Comments on Alexander Pruss's Blog: Material conditionals and quantifiersAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-3891434218564545511.post-12375395175887878652016-12-02T20:13:25.538-06:002016-12-02T20:13:25.538-06:00I'm an undergrad and a fan. Thanks so much for...I'm an undergrad and a fan. Thanks so much for your blog. I learn from it daily. <br />I'm wondering if the paradoxes of the material conditional can be resolved the following way:<br /><br />P = It's snowing in Fairbanks today<br />Q= It's snowing in Mexico City today<br /><br />Fact (F): If ~P, then it's true to say 'If P, then Q'. <br /><br />Claim (C): F is paradoxical.<br /><br />But using the material conditional, F can be symbolized as:<br /><br /> 1. ~P → (P → Q)<br /><br />(1) is equivalent to (2) by Exportation<br /><br /> 2. (~P • P) → Q<br /><br />There's nothing paradoxical about falsehoods being implied by contradictions.<br /><br />Consider:<br /><br />3. If P, then Q<br /><br />Hypothesis: <br />When material conditionals with false antecedents are judged to be paradoxically true, the antecedent of the conditional is being construed as true and not also false. To construe a false antecedent as 'true and not also false' is to entertain a counterfactual, not a material conditional. <br /><br /><br />So, to think (3) is paradoxically true is to confuse indicative conditionals with subjunctive conditionals. <br /><br />Argument:<br /><br />Either the operator in (3) is a material conditional or it's not. If it is, then (3) is not paradoxically true [it's just conforming to the principle of explosion]. If it's not, then (3) is a false subjunctive and so not paradoxically true. So, (3) is not paradoxically true. So, C is false. NaiveUndergradhttps://www.blogger.com/profile/00568462741774780045noreply@blogger.com