Plantinga’s Argument and the Truth-Values Argument

The Truth-Values Argument is quite similar to an argument for the falsity of Existentialism put forward by Plantinga (1983). If Plantinga’s argument is cogent, then it happens to have important consequences for the status of the Classical Conception of propositions. As shown in §3.2, Existentialism is a straightforward consequence of Essential Aboutness and Thorough Serious Actualism. This means that, together, Plantinga’s argument and the defence of Thorough Serious Actualism offered in this chapter constitute an argument for the falsity of the Classical Conception of Propositions.

The similarity between the Truth-Values Argument and Plantinga’s argument reveals a weakness in the Truth-Values Argument. Plantinga’s argument for the falsity of Existentialism has been objected to on the grounds that it ambiguates between two senses of the modalities, weak and strong senses, otherwise relying on an assumption that is not common ground between him and many existentialists.20

The same objection turns out to apply to the Truth-Values Argument. For this reason it will be helpful to consider Plantinga’s argument for the falsity of Existentialism, and the ambiguity objection to that argument.21

The premises of Plantinga’s argument against Existentialism are the following:

Premises of Plantinga’s Argument

(P1-PlA) Obama could have been nothing.

(P2-PlA) The proposition that Obama is nothing is about Obama.

(P3-PlA) Necessarily, if Obama is nothing, then it is true that Obama is nothing.

(P4-PlA) Necessarily, if it is true that Obama is nothing, then the proposition that Obama is nothing is something.

Premise (P1-PlA) is supported by unreflective common sense. Premise (P2-PlA) is intended to witness the claim that some propositions are about contingent beings, a claim that Plantinga takes to be common ground between him and many supporters of Existentialism. Premise (P3-PlA) is an instance of Truth Introduction, and premise (P4-PlA) is an instance of Thorough Serious Actualism. 20_{Defences of Existentialism against Plantinga’s argument similar to the one to be presented are adopted by, among others,}

Adams(1981),Fine(1977) ,Fine(1977),Speaks(2012),Stalnaker(2012).

21_{Actually, the argument to be considered is a slight reconstruction of Plantinga’s. The main difference is that the} argument to be presented contains Truth Introduction as one of its premises, whereas Truth Introduction is not a premise of Plantinga’s Argument. Instead, a consequence of Truth Introduction plays the role of Truth Introduction in Plantinga’s Argument. This formulation of the argument has been chosen to make clearer the similarities between Plantinga’s Argument and the Truth-Values Argument.

Briefly, Plantinga’s Argument proceeds as follows. Premises (P1-PlA) and (P3-PlA) jointly imply (22):

(22) It could have been that both Obama was nothing and the proposition that Obama is nothing was true.

Moreover, (22) and (P4-PlA) imply (23):

(23) It could have been that both Obama was nothing and the proposition that Obama is nothing was something.

Also, (23) and (P2-PlA) imply (24):

(24) There could have been a propositionpabout somexsuch that it could have been thatpwas something andxwas nothing.

Thus, (P1-PlA) - (P4-PlA) jointly imply the falsity of Existentialism. According to the objection to Plantinga’s Argument to be considered there is no reading of ‘necessity’ and ‘possibility’ such that: i) premises (P1-PlA) and (P3-PlA) are both true, and ii) Plantinga’s Argument is valid.

The two senses of the modalities are distinguishable via two notions of truth relative to a world, namely, truthina world and truthat(orof) a world.22_{As will be seen, virtually the same objection can}

be applied to the cogency of the Truth-Values Argument. Let me call this objection to both Plantinga’s Argument and the Truth-Values Argument theTruth In-Truth At Objection. I will begin by introducing the distinction between truth in a world and truth at a world. Then, I will show how the distinction affords the resources to object to the cogency of Plantinga’s argument. I will also show that, for exactly the same reasons, the distinction affords the resources to object to the cogency of the Truth-Values Argument.

One instructive way to understand the difference between the two notions is as follows. It is true

ata possible worldwthat, say, Obama is a president only if a certain relationactuallyholds between the possible worldwand the proposition thatObama is a president. However, it is trueina possible worldwthat, say, Obama is a president only if the proposition that Obama is a president would have had a certain property had worldwbeen realised, namely, the property of being true.23

The important difference is thus that for a propositionpto be trueina worldw,pis required to have a propertyatw, namely, the property of being true, whereas for a proposition to be trueata worldw, it is not required thatphas any propertyatw. Put it another way, ifpis trueinw, then not only is it the case that propositionpis trueatw. It is also the case that the proposition thatpis trueis 22_{The truth in-truth at distinction first appears in the first and second sophisms in (Buridan,2001, ch. 8), the basis for}

Prior(1969)’s distinction between possibility and possible truth.

23_{Some will prefer to use ‘actual’ instead of ‘realised’, since it does not beg any questions with respect to the nature of} possible worlds. On the other hand, this use of ‘actual’ seems to require a reading of ‘actual’ which is neither indexical nor rigid, whereas ‘actual’ is used in the dissertation mostly with its rigid sense. Since, as I see it, the relevant reading of ‘actual’ is, in this context, the one captured by ‘is realised’, I will be using ‘realised’ instead of ‘actual’ to capture this nonindexical and nonrigid reading of ‘actual’.

also true atw. The following is perhaps a helpful image. If an actual propositionpis trueata world

w, thenpcharacteriseswfrom the standpoint of the actual world. If a propositionpis trueinw, then

pcharacteriseswfrom the standpoint ofw.

Briefly, proponents of the truth in-truth at distinction have available an account of what it is for the proposition thatpis trueto be true at a worldw. If the proposition thatpis trueis true atw, then it is also the case that it is true atwthatp. And ifpis true atwand the proposition thatpis something

is true atw, then the proposition thatpis trueis true atw. That is, the proposition thatpis trueis true atwif and only if it is true atwthat i)pand ii)pis something. Thus,pis trueinwif and only if it is true atwthat i)pand ii)pis something.

Accompanying the distinction between truth in a world and truth at a world is a distinction between weak modalities and strong modalities. A propositionpis weakly necessary if and only if, for every worldw,pis trueatw. A proposition is strongly necessary if and only if, for every worldw,p

is trueinw. A proposition is weakly possible if and only if, there is some worldwsuch thatpis true

atw. A propositionpis strongly possible if and only if there is some worldwsuch thatpis trueinw. The Truth In-Truth At Objection relies on the thought that some propositions are trueatw

even though they are not trueinw. These propositions are not true inwbecause ifwwere realised, then they would have been nothing. This would have been so despite the fact these propositions appropriately characterisewfrom the standpoint of the actual world.

Suppose, for the purposes of the example, that there could have been no proposition whatsoever, even though there actually are some propositions — and in particular the proposition that there are no propositions is actually something. Assuming that there could have been no propositions, there is a possible worldwsuch that the proposition that there are no propositions is trueatw. Yet, the proposition that there are no propositions is not trueinw, since it is not the case that it is true atw

that the proposition that there are no proposition is something.

The distinction between weak and strong modalities enables proponents of the Truth In-Truth At Objection to account for the intuition that all of the assumptions of Plantinga’s Argument are true, while at the same contesting the argument’s cogency. There are two readings of premise (P1-PlA), namely:

(25) a. There is some possible worldwsuch that it is trueatwthat Obama is nothing. b. There is some possible worldwsuch that it is trueinwthat Obama is nothing. The intuition that (P1-PlA) is true arises from the fact that(25-a)is indeed true, since the actual proposition that Obama is nothing is trueat, orof, some possible worldw. It correctly characterises some worldw. Yet, it is false that there is some possible worldwsuch that it is trueinwthat Obama is nothing, since, according to them, there is no possible worldwsuch that both i) it is true atwthat Obama is nothing and ii) it is true atwthat the proposition that Obama is nothing is something.

Consider the following readings of (P3-PlA):

is nothing.

b. For every worldw, if it is trueinwthat Obama is nothing, then it is trueinwthat Obama is nothing.

c. For every worldw, if it is trueatwthat Obama is nothing, then it is trueatw(andinw) that the proposition that Obama is nothing is true.

The intuition that (P3-PlA) is true arises from the fact that(26-a)and(26-b)are indeed true. Yet, (26-c)is false. The fact that, as characterised from our world,wis a world at which Obama is nothing, does not imply thatwis a world in which the proposition that Obama is nothing is itself something at it.

Since the only true reading of (P1-PlA) is, according to the objection,(25-a), consider how the argument proceeds on this reading of (P1-PlA). Premises (P1-PlA) and (P3-PlA) together imply(22). The only reading of (P3-PlA) and(22)on which the argument from(25-a)and (P3-PlA) to(22)is valid is when (P3-PlA) is understood as(26-c)and(22)is understood as follows:

(27) There is some possible worldwsuch that it is trueatwthat Obama is nothing and it is true

atw(andinw) that the proposition that Obama is nothing is true.

But, according to the proponents of the Truth In-Truth At Objection,(26-c)is false. Thus, according to the objection, Plantinga’s Argument is valid only if one of the premises is false. A fortiori, Plantinga’s Argument is not cogent.

It is important to bear in mind that the Truth In-Truth At Objection is not aimed to establish the truth of Existentialism. Rather, it is aimed to show that the argument is successful only if claims that are not common ground between Plantinga and many Existentialists are assumed to be true, namely, at least one of(25-b)and(26-c). Let me now briefly show how the distinction between weak and strong modalities enables the formulation of a reply to the Truth-Values Argument accounting for the intuitions in favour of the truth of each premise, and yet on which the argument is not cogent.

The distinction between truth in a world and truth at a world shows that Excluded Middle, Truth Introduction and Falsity Introduction have four possible readings each. I will begin by focusing only on one particular instance of Excluded Middle and Truth Introduction, namely, claims (P1-TVAi) and (P2-TVAi). Claim (P1-TVAi) may be understood in one of the following ways:

(28) Every worldwis such that it is true relative towthat Obama is a president or it is true relative

wthat Obama is not a president.

a. Every worldwis such that it is true atwthat Obama is a president or it is true atwthat Obama is not a president.

b. Every worldwis such that it is true inwthat Obama is a president or it is true inwthat Obama is not a president.

c. Every worldwis such that it is true atwthat Obama is a president or it is true inwthat Obama is not a president.

d. Every worldwis such that it is true inwthat Obama is a president or it is true atwthat Obama is not a president.

Of these readings, the objector takes(28-b)to be immediately false. After all, it requires that every possible world be such that it is true at it that the proposition that Obama is a president has the property of being true, or it is true at it that the proposition that Obama is not a president has the property of being true. Hence, by Thorough Serious Actualism, it requires that every possible world

wbe such that it is true atwthat the proposition that Obama is a president is something, or it is true atwthat the proposition that Obama is not a president is something. But the objector rejects this. Since both propositions are about Obama, none of them is something if Obama is nothing.

Moreover, according to the objector there are possible worldswsuch that it is true atwthat Obama is nothing. It is true at no such possible world that Obama is a president, and it is true at no such possible world that the proposition that Obama is a president is true (if it were true atwthat the proposition that Obama is a president is true, then it would be true atwthat the proposition that Obama is a president is something, in which case Obama would have been something and yet the proposition that Obama is a president, a proposition about Obama, would have been nothing, thus contradicting Existentialism). So, there are possible worldswsuch that it is not true atwthat Obama is a president and it is not true inwthat Obama is not a president. So, according to the objection, (28-c)is also false. This means that the only options available are(28-a)and(28-d).

Claim (P2-TVAi) has the following readings:

(29) a. Every worldwis such that if it is true atwthat Obama is a president, then it is true atw

that the proposition that Obama is a president is true.

b. Every worldwis such that if it is true atwthat Obama is a president, then it is true in

wthat the proposition that Obama is a president is true.

c. Every worldwis such that if it is true inwthat Obama is a president, then it is true at

wthat the proposition that Obama is a president is true.

d. Every worldwis such that if it is true inwthat Obama is a president, then it is true in

wthat the proposition that Obama is a president is true.

The objector rejects the truth of reading(29-a)because a propositionpmay be true at a worldw

without it being true atwthatphas the property of being true, sincepmay be nothing atw. Since (29-b)implies(29-a), the objector also rejects(29-b).

The options available are thus(29-c)and(29-d). From(28-a)and either(29-c)or(29-d)it does not follow that every worldwis such that it is true atwthat the proposition that Obama is a president is true or it is true atwthat Obama is not a president. Thus, the reading of (P1-TVAi) as (28-a) renders the Truth-Values Argument invalid (on the assumption that (P2-TVAi) is given a true reading, i.e., either(29-c)or(29-d)). When (P1-TVAi) is understood as(28-a)and (P2-TVAi) is understood as either(29-c)or(29-d),(10)does not follow from (P1-TVAi),(P2-TVAi) and (P3-TVAi), contrary to what is required for the validity of the Truth-Values Argument.

So, the only option available is to adopt(28-d)as the true reading of Excluded Middle, and to take as true readings of Truth Introduction(29-c)or(29-d).

Finally, (P3-TVAi) has the following readings:

(30) a. Every worldwis such that if it is true atwthat Obama is not a president, then it is true atwthat the proposition that Obama is a president is false.

b. Every worldwis such that if it is true atwthat Obama is not a president, then it is true inwthat the proposition that Obama is a president is false.

c. Every worldwis such that if it is true inwthat Obama is not a president, then it is true atwthat the proposition that Obama is a president is false.

d. Every worldwis such that if it is true inwthat Obama is not a president, then it is true inwthat the proposition that Obama is a president is false.

By reasoning similar to the one applied with respect to the readings of (P2-TVAi) it is easy to see that, according to the objector, the only available readings of (P3-TVAi) are(30-c)and(30-d).

But from(28-d), either one of(30-c)and(30-d), and either one of(29-c)and(29-d)it does not follow that every worldwis such that it is true atwthat the proposition that Obama is a president is true or it is true atwthat the proposition that Obama is a president is false. The most one can get is that it is true atwthat the proposition that Obama is a president is true or it is true atwthat the Obama is not a president.

This claim is innocuous from the standpoint of propositional contingentists. What follows from it is just that every worldwis such that it is true atwthat the proposition that Obama is a president is something, or it is true atwthat Obama is not a president. This last claim does not imply the necessary being of the proposition that Obama is a president. Moreover, it does not conflict with the truth of Existentialism.

It should be clear that the truth in-truth at distinction affords the resources for a similar objection to the Truth Argument. The overall conclusion is that the truth in-truth at distinction offers a promising