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!!

12 comments:

joan said...

Just three brief comments on Dan’s reply to Rodriguez-Pereyra:

(i) Although I agree that vagueness cause trouble to the disjunction thesis, the case of open futures is not so clear to me, at least if we stick to truthmaker necessitarianism. Indeed, I fail to see why present conditions at t determine in a non causal way that the coin will land tails or heads at t’ after t. After all the coin could disappear or be destroyed between t and t’. Well, it cannot given the actual laws and present conditions. But then we should say that the fact that the coin will land tails or heads at t’ is causally or nomically determined by conditions at t. And it seems that if you take any other contingent disjunction, the same problem arises.

(ii) I have also a doubt on Dan’s suggestion of restricting the entailment principle merely to contingent truths and resticting also the conjunction principle in the same way in order to avoid Global Supervenience of Necessity. In so doing, he has to allow that, given both that e is a truthmaker for p, and also that q is any necessary truth, then e is a truthmaker for p&q. I can’t see that this is any better than saying that e is a truthmaker for q.

(iii) I agree that Rodriguez-Pereyra’s argument against the conjunction thesis seems unconvincing and Dan is right in saying that he does not provide reasons good enough for believing that non-minimal truhmakers are not truthmakers after all. However, I think that there may be a ground for R-P’s tenet, but we are misled by his dull “true in virtue of” basic concept. On my view, he employs this concept to define the truthmaking relation because it is intended to convey an important ingredient of the truthmaking relation: it is an explanatory relation. Truthmakers are theoretical entities posited to (help to) ontologically explain truths. This essential explanatory element can help to sustain that only minimal truthmakers (for p) are genuine truthmakers (for p). Non-minimal truthmakers (for p) are not explanatory relevant as to the truth of p since they are explanatorily redundant. They are not genuine truthmakers (for p) since they are not needed to fulfill any explanatorily role as to the truth of p.

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?

joan said...

ReRe (i): Then the Disjunction Principle restricted to contingent disjunctions will be secured, and that’s good enough if are not keen of truthmakers for necessary truths (as far as the open future objection goes). The unrestricted principle will assumedly fail for logical truths at least. For instance, if we read 'the coin will land heads or not' as a logical truth I wouldn’t have any inclination to say that it is made true by present conditions at t concerning the piece of metal and physical surroundings. Being a logical truth, its truth supervenes on its logical properties, so its truthmaker (assuming there is any) will be constituted by these logical properties. But they are of course not enough to grant the truth of any of the disjuncts ‘the coin will land heads’ or ‘the coin will not land heads’.

ReRe (ii): Well, for each necessary q wrt Tp has (undesireably) to be a truthmaker you will have a conjunction p&q wrt Tp has (undesireably) to be a truthmaker (where Tp is a truthmaker for p). But you still can say that Tp is totally unrelated to the truth of q but partially related to the truth of p&q, in the sense of presumably being part of the truthmaker for p&q. Put in terms of the “elusive” notion of explanation, Tp is (presumaby) part of the explanans of p&q, whereas it has nothing to do with whatever explains q’s truth.

ReRe (iii): Yes, Ben has an account of truthmaking in terms of the connective ‘because’ instead of ‘in virtue of’ which make more apparent the explanatory commitments of the notion. I don’t know how to fully explicate the notion of explanation I think it is involved in the notion of truthmaking, but I gave you the main reason to reject non-minimal truthmakers relying on the explanatory involvements of the notion. Take as a necessary condition for making true p being required to explain the truth of p. Then if a part of T fully explains the truth of p, the whole of T is not required to explain the truth of p, so it cannot be a truthmaker for p. There is sense of 'explains' in which we want to say that Socrates being bald is a truthmaker for the truth of 'Socrates is bald' because it fully explains the truth of the sentence. Then Socrates being bald and Plato being bearded is not required to explain the truth of 'Socrates is bald' and hence should no count as a truthmaker of it. I agree, it would be nicier to say something about the notion of explanation involved and not take it as a primitive.

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.

joan said...

Hi Dan,

Re4(i): Yes I agree in that the unrestricted disjunction principle fails for logical truths, but this seems to obey to the peculiarities of logical truths. In a way, it doesn't make much sense to allow that truthmaker principles apply to them. Necessary but logically contingent disjunctions seems to obey the principle.
On the other hand, maybe the case by vagueness is not so clear either. What about this answer? Vague disjuntions as such a path is red or orange has indeterminate truth value. Only non-vague interpretations of it has truth value. Any of them is, we assume, true. But in any such interpretation one of the disjuntions is also true. Disjuntion pinciple can be formulated along these lines for vague disjuntions.

Re4(ii): Well, not sure... you have to say that Tp is a truthmaker for p&q, so there is nothing extra to be added to Tp to make p&q true, nor nothing extra to explain p&q's truth. But Tp does not make true p&q nor explain its truth ince it has nothing to do with q.

Re4(iii): I'm not sure the analogy works. We can have different, but in some way dependent, explanations of one explanandum (as your raising your arm) but you wouldn't count as an explanantion of it a story consisting in a detailed report of your neural relevant states plus a detailed report of Bush cooking an omelete last night. Should I say that my story explains your raising your arm?

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.

joan said...

Hi Dan! This is helping me a lot to clarify several issues, so thanks to you as well and to your resistance!

Re6 (ii): The second example is not necessarily true: you could die today (hope not!) so the sentence would be false. The second sentence will work assuming that there is no metaphysically possible worlds where you can have an infinite number of children. If there are clear cases of metaphysically necessary true disjunctions, then I think they are much more of a problem for R-P’s position. Having to restrict the disjunction principle to non-logically true disjunctions it’s not such a bad move for a reasonable truthmaker maximalist: logically true sentences or propositions seem not be grounded in things as the rest of truths are. But metaphysically necessary truths are another matter: they seem to be grounded on the nature of things.

Concerning vagueness, I would say that you move is fine dialectically since you have added those provisos, but what I meant is that (i) the strenght of your point depends on not being certain other “plausible though controversial views about the nature of vagueness” that respects the disjunction principle and (ii) the one I suggested may be such a kind of view.

Re6 (ii): Forget about explanation by now, and let’s take the grounding relation as implementing the connection that according to you should (you said ‘might’, but you meant should, didn’t you?) still be present between Tp and p&q. Now, if q is not grounded in reality (if, for instance, q is a logically true proposition) then I agree that Tp grounds p&q. 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. But being part of a truthmaker for a proposition is not being a truthmaker for it.

And mutatis mutandis for explanation.

Re6 (iii): It seems there is something deeply wrong with me if I give you that story as an explantion of our raising your arm. It is true that what I say contains information that may be given in a way that constitutes a good explanation of your raising your arm. But it also contains information that is not merely redundant but at all lights absolutely irrellevant since it mentions facts that are totally independent of the explanandum. It’s not just that I’m giving unnecessary information: it’s that I am giving misleading information as to why the explanandum happened.

I hope I'm not being unnecessarily stubborn.

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 ;-).

joan said...

Hi Dan, it's me again!


Re8(i): Yes, you're right about your point against R-P's use of the disjunction principle against the entailment principle. I was just trying to see how deep the problem was for the disjunction principle by itself -that is, whether strong enough restricted versions remained untouched by your considerations.
Vagueness: yes, it's better if the view you take on truthmakers is neutral as to what we should say in treating vague sentences, since the issues seem to be quite independent. But I'm not sure that's SO bad; maybe the issues are not so independent after all.

Re8 (ii): You ask: '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?' I’m assuming that T’ is different from T, i.e., that T is not also the ground for q. Then the truthmaker for p&q should be some complex composed by T and T’.
From this and the discussion around (iii) it is apparent that you are employing a more liberal notion of truthmaker, which is related to the notion I intend in this way: your truthmakers are (or at least may be) whatever contains or is contained in my truthmakers. I guess that in the end these differences have to do with my explanatory commitments of the notion of truthmaker or with our different understanding of explanations.

And this leads me again to the last point (iii): I cannot see any relevant difference between this new way of expressing the analogy and the old one. What I would say in this case is that the explanans for the complex fact contains the explanans for the more simple fact, but it does not constitute a correct explanation for it, since I fails to satisfy the standard contextual conditions of relevance.
Well, you can say that, although incorrect, they are still explanations.At the end, I won’t push hard for the word here, I just merely say that truthmakers are tied to correct explanations of the truth of truthbearers.

Dan López de Sa said...

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

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