The Truth In-Truth At Distinction and the Modal Arguments

In what follows it will be shown that one of the arguments for Propositional Necessitism previously presented, the Possibility Argument, is unscathed by the common way of understanding the modal operators in terms of the common account of truth relative to a world. This will be shown by considering, without loss of generality, particular instances of each one of the assumptions of the Possibility Argument, namely, assumptions from which (NecPropObama) follows.

the notion of truth at a world. More specifically, only weak readings of modal expressions will be considered, ones giving rise to the following semantic account of ‘necessity’ and ‘possibility’, to which I will be calling the ‘Truth At Account’:

Truth At Account

1. Possibility

• Jx3ϕyKis the proposition thatJϕKis true at some worldw.

• _Jx3ϕyKis true at a worldwif and only ifJϕKis true at some worldw’ accessible fromw. 2. Necessity

• Jx2ϕyKis the proposition thatJϕKis true at every worldw.

• _Jx2ϕyKis true at a worldwif and only ifJϕKis true at every worldw’ accessible fromw. The initial modal occurring in the readings of the instances of the premises of the argument for (NecPropObama), ‘it is necessary that’, will be left unanalysed, since analysing it would add extra complexity to the statements without any gains. Let ‘T..._’ be a binary predicate standing for the relationbeing true at, and thus which obtains between worlds and propositions. Also, let ‘∃w(ϕ)’ be used as shorthand for ‘∃x(W x∧ϕ)’.24

(P1-PAi) It is necessary that it is possible that Obama is a president or it is possible that Obama is not a president.

(P1-PAi-TrAt) Truth At Reading:

1. It is necessary that some possible worldw is such that it is true atw that Obama is a president or some possible worldwis such that it is true atwthat Obama is not a president. 2. ₂(∃w(T wp)∨ ∃w(T w¬p)).

(P2-PAi) It is necessary that if it is possible that Obama is a president then the proposition that Obama is a president is something.

(P2-PAi-TrAt) Truth At Reading:

1. It is necessary that if some possible worldwis such that it is true atwthat Obama is a president, then the proposition that Obama is a president is something.

2. ₂(∃w(T wp)→ ∃q(p=q)).

(P3-PAi) It is necessary that if it is possible that Obama is not a president then the proposition that Obama is not a president is something.

(P3-PAi-TrAt) Truth At Reading:

1. It is necessary that if some possible worldwis such that it is true atwthat Obama is not a president, then the proposition that Obama is not a president is something.

2. ₂(∃w(T w¬p)→ ∃q(¬p=q)).

24_{I remain neutral here on the question what is the type of possible worlds, even though I am sympathetic to the view} that possible worlds themselves are propositions.

(P4-PAi) It is necessary that the proposition that Obama is a president is something if and only if the proposition that Obama is not a president is something.

Briefly, (P1-PAi) is an instance of Seriality, (P2-PAi) and (P3-PAi) are instances of Thorough Serious Actualism, and (P3-PAi) is an immediate consequence of Contradictoriness.

Starting with (P1-PAi), this is a theorem of propositional modal logic, and so it seems reasonable to think that (P1-PAi-TrAt) is true, since this reading of (P1-PAi) is given in terms of the weaker understanding of the modals available, i.e., in terms of truth at a world.

As previously mentioned, all that the truth at a worldwof a propositionprequires is thatwand

pbe related, not thatpwould have had the property of being true hadwbeen realised. Now, ifpand

ware related, then it follows thatpis something (and thatwis something as well) by an application of Thorough Serious Actualism, regardless of whetherpwould have been something hadwbeen realised. But this means that necessarily, ifpis true at some worldw, thenpis something, since the truth ofp

at some worldwrequires thatpand some worldwbe related. Similarly, if¬pis true at some world

w, this requires that¬pbe related to some worldw, and so, that¬pis something. What this shows is thus that (P2-PAi-TrAt) and (P3-PAi-TrAt) are both true.

There is also no risk of an ambiguous reading of the modalities as they occur in (P4-PAi). The only modality present in each one of the premises, the expression ‘it is necessary that’, may itself be given a univocal weak reading, in terms of truthatevery world.

Thus, the distinction between truth in a world and truth at a world gives no reason to reject the truth of any of the premises of the argument. Moreover, the argument from (P1-PAi-TrAt) - (P4-PAi-TrAt) to (NecPropObama) may be seen to be valid straightforwardly. Thus, the Possibility Argument is itself valid, and the truth of its premises is not called into question by the availability of the distinction between truth in a world and truth at a world. So, the distinction does not afford propositional contingentists with the resources to reject the Possibility Argument.

The current state of the dialectic is the following. The distinction between truth in a world and truth at a world gives propositional contingentists the resources enabling them to resist the cogency of Plantinga’s Argument and of the Truth-Values Argument. It was shown that the distinction does not, in and of itself, offer the resources to resist the cogency of the Possibility Argument for Propositional Necessitism. On the contrary, the cogency of the Possibility Argument is left unscathed by an understanding of the modalities in terms of truth at a world.

This seems to pose a dilemma to propositional contingentists. If the Truth In-Truth At Objection is pursued, then it seems that the Possibility Argument turns out to be congent. And if the Truth In-Truth At Objection is abandoned, then a promising line of objection to Plantinga’s argument and to the Truth-Values Argument is lost. Let me call this dilemma for propositional contingentists theTruth At Dilemma.

In what follows I will explore the prospects of a possible way out of the Truth At Dilemma. The Truth In-Truth At Objection presupposed the Truth At Account of ‘necessity’ and ‘possibility’. One option available to propositional contingentists is to reject the Truth At Account while still maintaining

the view that modal expressions can be accounted for in terms of truth at a world. Pursuing this line requires offering a different account of ‘necessity’ and ‘possibility’. A different account is presented in what follows, and its prospects are investigated.