{"id":1088,"date":"2023-02-17T15:38:48","date_gmt":"2023-02-17T20:38:48","guid":{"rendered":"http:\/\/alanrhoda.net\/wordpress\/?p=1088"},"modified":"2023-02-17T16:29:16","modified_gmt":"2023-02-17T21:29:16","slug":"a-misguided-argument-for-conditional-excluded-middle","status":"publish","type":"post","link":"http:\/\/alanrhoda.net\/wordpress\/2023\/02\/a-misguided-argument-for-conditional-excluded-middle\/","title":{"rendered":"A Misguided Argument for Conditional Excluded Middle"},"content":{"rendered":"

I have finished reading Kirk MacGregor’s new book<\/a> defending Molinism. In my previous post<\/a> I commented on his first 3 chapters and shared why I don’t think his reply to the grounding objection to Molinism is any good. I plan to do another blog post on chapters 4\u20136 of MacGregor’s book. But right now I want to comment on a paper by J. Robert G. Williams<\/a> that MacGregor footnotes in his concluding chapter. MacGregor commends the paper as an “outstanding defense of conditional excluded middle” (p. 136).<\/p>\n

Williams’ paper is titled “Defending Conditional Excluded Middle”. I’m going to comment on the first section of the paper where he presents a positive argument for<\/em> conditional excluded middle (CEM). The rest of the paper contains rebuttals to arguments against<\/em> CEM by David Lewis and Jonathan Bennett. I’m not going to comment on those. But first, I’m going to provide some general background on CEM and conditionals in general.<\/p>\n

1. Defining CEM<\/strong><\/p>\n

First of all, let’s define CEM. It’s the thesis that for any given antecedent (A) and any given consequent (C) to a subjunctive<\/em> conditional, either C\u00a0would\u00a0<\/em>be true given A, or C\u00a0would not<\/em> be true given A. If we use \u2610\u2192 to represent a\u00a0would-<\/em>conditional and \u25c7\u2192\u00a0 to represent a\u00a0might<\/em>-conditional, then CEM takes the following form:<\/p>\n

CEM: (A \u2610\u2192 C) \u2228 (A \u2610\u2192 ~C)<\/strong><\/p>\n

What CEM says, in a nutshell, is that the implications of any hypothetical scenario (A) are always fully\u00a0<\/em>determinate<\/em>, such that for any consequent C it is either determinately the case that C (given A) or determinately the case that ~C (given A).<\/p>\n

2. Conditionals in general and what it would take to show that CEM is true<\/strong><\/p>\n

To see what it would take for CEM to be true, let’s take a step back and consider conditionals in general. Every<\/em> conditional says that the antecedent A is sufficient<\/em> in some way for the consequent C. I say “in some way” because there are different kinds of sufficiency. For example, there is material or extensional<\/em> sufficiency. If we suppose that all swans are in fact white\u2014this is not actually the case, but who cares\u2014then being a swan (A) is extensionally sufficient for being white (C) since the extension of A is wholly included in the extension of C. Likewise, A could be logically<\/em> sufficient for C (e.g., “If x is a red ball then x is red”), conceptually <\/em>sufficient for C (e.g., “If x is a prime number then x is not a prime minister”), causally\/nomologically<\/em> sufficient for C (e.g., “If you set off that dynamite, then you’ll blow us all to kingdom come”), and so forth. The important point is that the truth<\/em> of the conditional, whatever type of conditional it is, depends on the truth of a sufficiency claim. Is A actually<\/em> sufficient for C (in the relevant way)?<\/p>\n

The difference between indicative and subjunctive conditionals is simply that, in the latter case, the speaker conveys that he does not <\/em>accept\u00a0the antecedent and thus regards it as merely hypothetical<\/em>, whereas in the former case, the speaker does not signal such doubt and so remains\u00a0neutral<\/em> on whether the antecedent is true or not. Consider, for example, the difference between “If you mix those chemicals, you will regret it” (indicative) and “If you were<\/em> to mix those chemicals, you would<\/em> regret it” (subjunctive). In many circumstances either conditional could be used to nearly the same effect (warning someone against mixing the chemicals), but the subjunctive doesn’t convey any sense that the addressee’s mixing the chemicals is a likely <\/em>occurrence\u2014it’s left in the realm of the merely hypothetical\u2014whereas the indicative conveys the idea that the addressee’s mixing the chemicals is at least somewhat likely. CEM is supposed to apply to subjunctive conditionals, or ones where A is regarded as merely hypothetical and thus presumptively contrary-to-fact. That’s why these conditionals are often called “counterfactuals”.<\/p>\n

Now, to show<\/em> that CEM is true one would have to show that, no matter what ideas A and C convey, A is always<\/em> either sufficient for C (in some way) or sufficient for ~C (in the same way). If A is sufficient for C, then it follows that A \u2610\u2192 C, where the “would” connective (\u2610\u2192) carries the force of whatever kind of sufficiency is in view. And if A is sufficient for ~C, then it follows that A \u2610\u2192 ~C, where the “would” connective (\u2610\u2192) again carries the force of whatever kind of sufficiency is in view. This is a tall order because, again, there seem to be cases where A is clearly not<\/em> sufficient either for C or for ~C. The Molinist’s CCFs are a case in point. In CCFs the antecedent (A) contains a full causal specification of an indeterministic scenario and the consequent (C) is but one of several causally possible outcomes of that scenario. Because the scenario is explicitly indeterministic, this is a clear-cut situation where A is neither sufficient for C nor sufficient for ~C. Accordingly, both “If I were to toss this fair coin under perfectly indeterministic conditions, it would<\/em> land heads (C)” and “If I were to toss this fair coin under perfectly indeterministic conditions, it would not<\/em> land heads (~C)” are intuitively false<\/em>. What’s true, rather, is that “If I were to toss this fair coin under perfectly indeterministic conditions, it\u00a0might<\/em> land heads (C)” and “If I were to toss this fair coin under perfectly indeterministic conditions, it\u00a0might not<\/em> land heads (~C)”. We thus arrive at the principle of would\/might duality<\/em>:<\/p>\n

Would\/Might Duality (WMD)<\/strong>:
\nwould<\/em>\u00a0(A \u2610\u2192 C) =\u00a0not-might-not<\/em>\u00a0~(A \u25c7\u2192 ~C)
\nmight<\/em>\u00a0(A \u25c7\u2192 C) =\u00a0not-would-not<\/em>\u00a0~(A \u2610\u2192 ~C)<\/p>\n

If WMD is true, then CEM is false because (A \u2610\u2192 C) \u2228 (A \u2610\u2192 ~C) is not<\/em> a proper instance of LEM since there are three<\/em> possible ways in which A can be related to C:<\/p>\n