Sunday, August 25, 2013

Thoughts on the Grounding Objection to Molinism

So, I want to get a bit more clear on what the grounding objection to Molinism is saying. As far as I can tell at this moment, the grounding objection seems to go something like this.

The anti-Molinist says that some general statement about the relation between grounding and truth such as the following holds:

(A) If some proposition is true then there is an entity which grounds its truth.

It seems in this context 'grounds the truth of p' just means 'is the truthmaker of p'. The objector to Molinism then proposes:

(B) There could be no entity to ground the truth of CCF's.

Of course from A and B it follows that all CCF's, if they are meaningful, are necessarily false. Hopefully this is all a correct representation of the objection.



Now, one problem is that we seem to be starting with abstract principles and moving to judgments about cases, whereas we should probably go the other way around; for instance, supposing it is true CCF's can't be 'grounded', then in this case we should recognize the truth of some CCF's and conclude there is something wrong with (A), rather than vice versa. For it is more clear to me that I would have gotten chicken had I gone to Panda Express earlier than it is that all truths need to be grounded in the sense we're talking about.

Another problem is that there is no immediate reason to accept either (A) or (B). What are the arguments for them?

Also, there seem to be problems with both premises. Let's start off with (B): Why can't the fact that I would do such and such action in such and such circumstances be the 'ground' of the counterfactual? Note, facts are not propositions. Maybe take facts to be necessarily existing entities.

If for some reason this is not allowed according to (A), then there are still problems for (A) itself. Since it seems to entail the immediate falsity of presentism given that statements about the future are true, (A) would have to be more plausible than presentism, and why think that? And why is (A) true in the face of, say, negative propositions (e.g. the proposition that there does not exist a chair)? Also, is (A) necessarily true? If so, what is the truthmaker of (A)?

Regarding that last question, there seems to be a lurking circularity or something in (A). This is a real problem. Consider the following argument (which I'll admit I came up with rather quickly and thus it may be problematic). Note beforehand: I'm going to define S below as a set; that's inaccurate since it's really supposed to be a sum of entities, but that makes it easier to deal with and there is a sort of function from the relevant statements about the set to the corresponding statements about the sum. Also, I will just assume for ease that S is finite, which is probably not a plausible assumption, but the argument could be made to work in the infinite case if one really wanted it to. Anyway, let us consider the argument:

1. Suppose all true propositions have a truthmaker. [assumption, called (A)]
2. (A) is a true proposition. [premise] Then,
3. (A) has a truthmaker. [by 1 and 2] But,
4. If (A) has a truthmaker, then the truthmaker of (A) would have to be the sum S = {t : For some truth P, t is a truthmaker of P} = {t1, ..., tn, tn+1} [premise]
5. The truthmaker of (A) is the sum S = {t1, ... , tn, tn+1} = {t : For some truth P, t is a truthmaker of P} [by 3 and 4]
6. Suppose S is in S and let S = tn+1. [assumption]
7. For all sums A, if A = {x} U {x1, ..., xn} and A =/= {x1, ... , xn}, then x is a proper part of A. [definition]
8. Then S would be a proper part of S, since S would be {S} U {t1, t2, ... , tn} and S =/= {t1, t2, ... , tn}. [by def. of proper part]
9. But no sum can be a proper part of itself; that is impossible. [premise]
10. So S is not in S. [by 8 and 9]
11. But S must be in S, for S is a truthmaker of some truth (viz. (A)). [by 5 and definition of S]
12. That's a contradiction right there^.
13. So one of 1 - 3 is false, which implies (A) is false. [1-11]

So it's false that all true propositions have a truthmaker.

Also, if (A) entails there are no true CCF's, then we can argue against (A) by giving a very strong argument for the truth of CCF's. Let us consider the following argument, which I will call the 'direct argument' for the truth of CCF's. It seems to have first been endorsed by the great Jesuit theologian Francisco Suarez. Take a CCF like the following:

(*) If Alfredo were to defend Molinism, Reginald would have accepted it.

This is of the form A => B. We can verify either A => B or its counterpart A => ~B as follows: Have Alfredo defend Molinism, and see if Reginald accepts it or not. If he accepts it, then someone would have been correct in asserting (*) at some time e beforehand. If Reginald does not accept it, then someone asserting the counterpart CCF of the form A => ~B at time e would have been correct instead. Either way, at least one CCF was true at e, so at least some CCF's are true at some time. But whether the antecedent A is true in the actual world or not shouldn't make a difference metaphysically speaking; for why does the truth about this counterfactual depend on the actual world's in fact being actual? Also, there is nothing special about this particular CCF nor its being said at e. So all CCF's or their counterparts are true. And that entails (A) is false.

So, while it's not even clear to me CCF's can't be grounded as per (B), we have a lot of reasons to think (A) is incorrect anyway and not much reason to think it is true (it seems to me whatever intuitive force (A) has can probably be captured just as well by weaker principles). Hence, we should reject the proposition that all propositions must have a truthmaker, and thus the grounding objection to Molinism fails.

5 comments:

grodrigues said...

How would you square a rejection of (A) with the dictum that truth follows being, e.g. St. Thomas in De Veritate "To every true act of understanding there must correspond some being".

awatkins69 said...

So, one thing is, in 'De Ente et Essentia' Aquinas defines two senses of being. I'll just paste the quote, since I think it is perfectly clear:

"We should notice, therefore, that the word “being,” taken without qualifiers, has two uses, as the Philosopher says in the fifth book of the Metaphysics. (1) In one way, it is used apropos of what is divided into the ten genera; (2) in another way, it is used to signify the truth of propositions. The difference between the two is that in the second way everything about which we can form an affirmative proposition can be called a being, even though it posits nothing in reality. It is in this way that privations and negations are called beings; for we say that affirmation is opposed to negation, and that blindness is in the eye. In the first way, however, only what posits something in reality can be called a being. In the first way, therefore, blindness and the like are not beings."

So in the second sense of being, we would call certain things 'beings' which we normally wouldn't in the full, primary sense. So, if Aquinas's De Veritate statement is using being in this second sense, then I admit it is true and don't see how it's inconsistent with what I've said (in fact, if anything, it seems to be analytically true; in this sense of 'being', being is whatever our sentence is true of, and thus there will always be a being for every true sentence).

But if what Aquinas is saying is using the first sense of being, i.e. what falls under the ten categories, then that would seem to make him to be saying something equivalent to (A). And ultimately if Aquinas is saying something equivalent to (A) then I would reject Aquinas's statement as well for the reasons I've stated in this post.

awatkins69 said...

I think it's also worth noting that Aquinas uses the word 'corresponds', whereas (A) uses the word 'grounds'. Those are very different words and have importantly different meanings. Though on the face of it I think my argument could be run against even Aquinas's statement (again, if he is using being in the substantive, first sense from the De Ente quote).

grodrigues said...

@awatkins69:

Thanks for the explanation; intuitively, it looks correct. I am far from knowledgeable, but further evidence, unearthed by some casual reading, is in St. Thomas' treatment of what grounds the truth of past-tense contingent propositions in ST I.16.8.4.

note: on rereading it, my question may have sounded like a gotcha question or that I was disputing your rejection of (A). I was just thinking out loud on how we would go about reconciling it with the fact that truth follows being.

Anonymous said...

Check this out, http://www.academia.edu/1021568/Presentism_and_the_Grounding_of_Truth

The grounding problem for Presentism is only a problem if one accepts truthmaking maximalism, which seems false in virtue of the negative existentials problem and necessary truths problem.

To reformulate the problem for Presentism, one argues that the truth-supervenes-on-being thesis is true, which seems plausible. But, arguing from this thesis also fails as well as Baia demonstrates. This is because the b-theorist usually saddles the presentist with an eternalist version of the supervenience thesis. But, it seems that the Presentist only has reason to accept the presentist supervenience thesis about truth and existence. So, I don't think you can use Presentism to help out Molinism here, as WLC does. Further, it just seems like a bad practice in general to rely upon another doctrine like Presentism to support Molinism when a main objection to Presentism is the same one being launched against Molinism.