Tuesday, November 14, 2006

Disjunctions, Conjunctions, and Their Truthmakers

(Cross-posted at bleb.)

A truthmaker for a given truth is something in virtue of which the truth is true. One plausible thesis about truthmaking is that it is closed under entailment, in the sense of obeying the so-called entailment principle:

If something makes a certain truth true, then it also makes true all of this truth’s consequences.

Though plausible, the principle seems to have some undesirable consequences: the explosion of truthmakers for necessities—every thing is a truthmaker for every necessary truth—, and indeed the truthmaker triviality—every thing is a truthmaker for every truth whatsoever—.

Gonzalo Rodriguez-Pereyra in his ‘Truthmaking, Entailment, and the Conjunction Thesis’ has recently argued against attempts to preserve (perhaps, a restriction of) the entailment principle while avoiding these results. In so doing, Gonzalo crucially both defends the disjunction thesis—if something makes true a disjunctive truth, then it makes true one of its disjuncts—, and rejects the conjunction thesis—if something makes true a conjunctive truth, then it makes true each of its conjuncts—.

I have written a short reply to his paper. I first provide plausible counterexamples to the disjunction thesis, and contend that Gonzalo’s general defense of it fails. Then I defend the conjunction thesis from Gonzalo’s case against it. I finally conclude that the envisaged attempts have not been proved, by Gonzalo’s considerations, to be at fault.

(My note originated from the discussion I had with Gonzalo here.)

All comments welcome!!

6 comments:

Dan López de Sa said...

Hi Joan!

Thank you very much for the very useful feedback, I really appreciate it. Looks like this other purpose of The bLOGOS might also work, which is certainly for the good :-)!!

Re (i): I really have to think more about this, hope to have something to say later. For the time being, which would be your reaction if we change the disjuction into a non-contingent one, like 'the coin will land head or not'?

Re (ii): But it is a bit better to claim that T is a truthmaker for the truth that p&q provided that it is a truthmaker for p, than having the full explosion of truthmakers for necessities, no? (BTW, don’t you like this Amstrongian locution better than GSN?)

Re (iii): I fully agree. (Officially, Gonzalo does not exclude non-minimal truthmakers, but as you say, it looks as if the kind of reasons provided would exclude them in general.) My point has only been that, at the crucial juncture, Gonzalo just appeal to alleged intuitions (a) which contradict those of many others as encapsulated in the relevant principles and (b) whose appearance seems to be explainable away “pragmatically.”

This leaves open that there might be a further consideration issuing from truthmaking purportedly being explanatory that goes against the conjunction thesis, after all. (Benjamin Schnieder made a similar remark to me.) For what it is worth, I don’t quite see how this would tell against non-minimal truthmakers, but this is maybe due to the fact that I tend to find the relevant notion of explanation here quite elusive ;-). You have some work made on this, right?

Dan López de Sa said...

Hi Joan, many thanks again!

ReReRe(i): I take it that we agree then, right? The logical case problematizes the unrestricted disjunction principle, which is the one used for making the trouble. I am still thinking about the original, contingent disjunction case, though.

ReReRe(ii): Yeah, something along these lines is what I had in mind. So we agree here as well?

ReReRe(iii): Probably here is where we still disagree. I take it that, with respect to the ordinary notion of explanation, we normally have different explanations of one and the same phenomenon (say, the raising of my arm). Of course, they are not wholly independent, and there are some more basic than others and, in some appropriate sense, more complete and/or satisfactory. Now perhaps the (elusive ;-)) notion operative with respect to truthmakers and truths is different in this respect, so that the more basic explanations preclude there being other, not wholly independent, less basic explanations. But this is hard to assess, unless something else—even if perhaps nonreductively—is said about the relevant notion, or so it seems to me.

Dan López de Sa said...

Once again, thanks!! This is being terribly useful for me! I still resist, though ;-).

Re5(i): But the application of the disjunction principle making the trouble actually concerns excluded middle!

Anyway, what about the following non-logical necessary cases?
‘The number of my children will be odd or it’ll be even.’
‘The first thing I’ll drink tomorrow will be water or it won’t be H2O.’

As to vagueness, I fully acknowledge (and also tried to do in the note) that my point requires certain plausible but controversial views about the nature of vagueness—which, in particular, make the relevant disjunction true, although lacking a true disjunct. But this is all fine, dialectically, don’t you think?

Re5(ii): I this pre-(iii) stage, I took it, we are dealing with someone who does find the full explosion unsatisfactory (FWIIW, I myself have some sympathies for things one might say for the explosion, see footnote 10), but need not necessarily buy the explanatory stuff. S/he might think there should be some kind of connection between truthmakers and truths, which is lacking between a given entity and any necessary truth whatsoever. But such a connection might still be present between a truthmaker and the conjunction of something it makes true with something that holds anyway, no?

If the explanatory stuff gets into, I still have the predictable worries: why should one believe that the fact that T has nothing to do with the truth that q precludes its explaining the truth that p&q, provided that admittedly it does explain, in the appropriate sense, the truth that p?

Re5(iii): Yeah, I feel the analogy does work after all: I am inclined to say that the longer explanation explains, if the sorter one does. Of course, were one to have the shorter available, there would be no point in giving the longer: that’s the “pragmatic” move I suggested. Ohterwise, it seems to me, explanations containing "redundant" or "unnecessary" bits would go missing, and I take a lot of ours are such.

Dan López de Sa said...

Hi there again!

Re7(ii): I intended my second case so that if I die the second will turn out true, and hence the disjunction. Re the first, yes, I was assuming “finitariety” (at least, concerning the number of my sons and daughters) to be a necessary feature of worlds.

In any case, I insist that the application of the disjunction principle making the trouble is to an instance of excluded middle, so that even the more innocuous restriction excluding logic cases would serve in the defense of the entailment principle.

Re vagueness, I took it that it would be bad news for Gonzalo’s argument it it requires the falsity of controversial but plausible views like the suggested ones, regardless of whether one thinks or not that these are the right ones after all. Maybe there is something here I am missing, sorry if this is the case, Ezequiel is voicing a worry similar to yours here.

Re7(ii): You say “If, on the contrary, q is grounded in reality then Tp is at best a partial ground for p&q, and hence at best part of the truthmaker for p&q.” Interesting thought, but it’s not transparent to me how it follows. So suppose T is a turthmaker of the truth that p, and T’ is a truthmaker for the necessary truth that q. Why is it then the case that T is at best merely a (proper) part of whichever is the truthmaker for the truth that p&q?

Re7(iii): I was thinking about this the other day, and seems to me that the right analogy is rather this: whether whatever it is that explains that I raised my hand and that Democrats won the elections is such that (a fortiori) it explains that I raised my arm, right? That there are something wrong, even deeply wrong, with the more complex explanations in the simpler ones are available is common ground among all us: the issue is to whether this precludes the more complex one from being, literally, an explanation after all.

Esa suggested that there might be room for further argument here, provided that there be some appropriate necessary condition on explanation involving counterfactuals, and given the general failure from A>C to A&B>C. Maybe, I don’t know. Maybe she would elaborate on this here somewhen… ;-).

Dan López de Sa said...

Sorry about the mess. Says 'Re7(ii)' (first occurrence), should say 'Re7(i)'; says 'it it requires', should say 'if it requires'; says 'I rasied my hand', should say 'I raised my arm', maybe others ;-).

Dan López de Sa said...

Thanks again, Joan, for all your very useful feedback here! (I meant to have done this long ago, apologies ;-)!)