Monday, May 18, 2009

Disjunctions, Conjunctions, and their Truthmakers, II

My discussion of Rodriguez-Pereyra 2006 is finally out in Mind, yay!!

Following it, Gonzalo’s response:

López de Sa has objected both to my defence of the Disjunction Thesis and my case against the Conjunction Thesis. I shall show that his objections are unfounded and based on serious misunderstandings of my position, what the relevant debate is, and some fundamental notions of Truthmaker Theory.


Rhetoric aside, however, I did not really find in the piece replies to my objections.

A. My main objection against the the contention that if something is a truthmaker for a disjunctive truth, then it is a truthmaker for one of its disjuncts is simply that assuming some plausible but controversial views (on, say, vagueness, or open futures), there can be disjunctions that are (made) true, without true disjuncts. Gonzalo seems to concede the case against the principle, but then contends that the principle he was interested in was the restriction to "truth-conditional disjunctions". As I discussed in my paper (p. 420), it is not clear how to understand talk about a given disjunction being truth-functional in the present context. In any case, I considered one candidate such restriction (fn. 8):
(∨–) If T is a truthmaker for the truth that p or q, then—provided it is true that p or it is true that q—either T is a truthmaker for the truth that p or T is a truthmaker for the truth that q.
This seems capable of sustaining the relevant step in the trivializing argument (see my fn. 3) but, I contended, inherits the concerns one may have with respect to the unrestricted principle: in a nutshell, if something can be a truthmaker for a disjunctive truth and still fail to make true any of its disjuncts, then this can be so even if something else makes some of its disjuncts true.

The restriction I did not consider, of course, is something along the lines of:
(∨– –) If T is a truthmaker for the truth that p or qand its truth is "entirely due" to the truth that p or to the truth that q—, then either T is a truthmaker for the truth that p or T is a truthmaker for the truth that q.
Arguably, some ways of understanding the clause would guarantee the truth of this restriction, but it seems to me it ceases to be capable of sustaining the trivializing argument: that the instance of excluded middle for an arbitrary truth is of this sort would then require motivation.

B. In connection with Gonzalo's objection against the contention that if something is a truthmaker for a conjunctive truth then it is a truthmaker for each conjunct, I claimed that in the paper he does not provide reasons to believe that the more embracing thing is a truthmaker when another more discerning truthmaker is available (p. 423), and that the suggestion that the excess does not "contribute" to the truthmaking of the more discerning one by itself merely amounts to a re-description of the fact that the more embracing candidates are precisely more embracing than other available truthmakers (fn. 17).

Fruitful discussion with David Liggins, Joan Pagès, and Benjamin Schnieder has convinced me that perhaps some considerations against the conjunction principle, exploring connections of truthmaking with explanation, might be forthcoming. I am still a bit skeptical, but I am open to be persuaded. To my mind, however, the point remains that these have not been provided by Gonzalo's paper I was discussing. Nor, for that matter, by his response now:

But it is not always the case that the more embracing or inclusive entity involves entities that are irrelevant to the truth of the proposition in question. For instance Calliope, Melpomene, and Thalia contribute and are relevant to the truth of [There are more than two muses], but the more inclusive group of Calliope, Melpomene, Thalia, and Clio also contribute and are relevant to its truth. Indeed both the group of three muses and the group of four are truthmakers for the proposition [There are more than two muses]. (p. 434)

Why not so in the present case at hand? This is in my view the kind of question answering which might provide the required considerations.

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