Abstract
In Prior’s tense-logical analysis, we can avoid mentioning instants in our language by construing them as propositions of a special kind. Instead of qualifying instants by predicates, we may qualify propositions by modalities. Prior shows that by changing the informal interpretation of our modal-like language, we can similarly attempt to avoid ontological commitments to worlds (modal logic) and even to selves and other bona fide individuals (egocentric logic). As he notes, the paraphrasing strategy works too generally to be of direct metaphysical use. I wish to speak of several types of entities within one and the same language. This leads to the issue of cross-context identity: how to make sense of speaking of the same entity of one type relative to distinct entities of another type. My analysis employs the notion of world line. I discern a structure of mutually interrelated categories with three informal interpretations: tense, modal and egocentric. They correspond to different metaphysical views on the interrelations of time, logical alternatives and individuals. Prior’s dilemma regarding the possibility of modalizing, not only our talk concerning times and worlds, but even our discourse pertaining to the ‘real world of individuals’ does not vanish but reappears also in my setting.
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Notes
It would be better to speak of ‘values of variables involved in predications’: surely a formula with explicit higher-order quantifiers such as \(\exists X \exists x X(x)\) is ontologically committed to values of the variable X.
This idea is problematic. Are we entitled to postulate a class of all propositions independently of a fixed language and a fixed set of possible worlds? Can we exclude the possibility that two instants make true the same set of propositions? If we can, we must have logical reasons for ruling out that time is linear but has qualitative periodicity, say, of the form \( \ldots pqpq \ldots \). Plainly no such reasons are available.
Prior does not systematically take up quantified modal languages when discussing egocentric logic; see, however, Prior (1968, pp. 143–144).
For some values of X and Y, cross-contextual questions corresponding to entity types X and Y might seem pointless or even meaningless. However, in many philosophically interesting cases such questions invite us to reflect on the precise ways in which entities of the two types may be interrelated.
For a discussion, see Tulenheimo (2015).
I use persons as examples of bona fide individuals. I am not dealing with any specific problems of personal identity as opposed to problems of identity of material objects.
If X is a set and \(\kappa \) is any cardinal number, a collection \(\mathscr {C} = \{C_i : i < \kappa \}\) of pairwise disjoint non-empty sets is a partition of X, if \(X = \bigcup _{i < \kappa } C_i.\)
Overlapping world lines could be considered in epistemic settings, cf. Hintikka (1969).
We write \(g[x / \mathbf {c}]\) for the assignment that differs from g at most in that it assigns \(\mathbf {c}\) to x.
Note that \(\exists x\) is not a first-order quantifier, if the criterion for the first-order status of a quantifier is that for the purposes of the semantics we need not consider its values as having an internal structure. Values of quantifiers \(\exists x\) are elements of \(\mathbf {C}\), but the semantics of atomic formulas needs elements of elements of \(\mathbf {C}\).
The semantics of \(\exists x\) is ‘actualist’: its values in \(\mathbf {b}\) must in effect be realized in \(\mathbf {b}\). In a generalized setting we could let the range of \(\exists x\) in \(\mathbf {b}\) be any partition \(\mathbf {C}_\mathbf {b}\) of \(\mathbf {A}\), without requiring that all \(\mathbf {c}\in \mathbf {C}_\mathbf {b}\) be realized in \(\mathbf {b}\). The resulting semantics would not be ‘possibilist’: we could have \(\mathbf {C}_\mathbf {b}\ne \mathbf {C}_{\mathbf {b}'}\) when \(\mathbf {b}\ne \mathbf {b}'\).
The exterior language of comparison would not be first-order logic, but a generalization of third-order logic, with predicates applicable not only to first- but also to second- and third-order variables.
As for modal properties, \(\exists x(\lnot P(x) \wedge \square _s[\exists yQ(y) \rightarrow P(x)])\) expresses in \(\mathsf {TI}\) that a person who is not P has the disposition of being P: she is P in any environment with at least one Q. In \(\mathsf {EI}\),
or its equivalent 
expresses that I share an object of perception with another person.
or its equivalent 
expresses that I share an object of perception with another person.References
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Acknowledgments
I am indebted to the anonymous referees for their useful remarks. An earlier version of this paper was presented in the Arthur Prior Centenary Conference at Balliol College, Oxford; I am grateful for the comments received from participants.
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Tulenheimo, T. Worlds, times and selves revisited. Synthese 193, 3713–3725 (2016). https://doi.org/10.1007/s11229-015-0895-x
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DOI: https://doi.org/10.1007/s11229-015-0895-x