Abstract
This paper outlines a novel solution to the Ship of Theseus puzzle. The solution relies on situations, a philosophical tool used in natural language semantics among other places. The core idea is that what is true is always relative to the situation under consideration. I begin by outlining the problem before briefly introducing situations. I then present the solution: in smaller situations (containing only one of the candidate ships for identity with Theseus’s ship) the candidate is identical to Theseus’s ship. But in larger situations containing both candidates these identities are neither true nor false. Finally, I discuss some worries for the view that arise from the nature of identity, and suggest responses. It is concluded that the solution, and the theory that underpins it, are worth further investigation.
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Notes
In particular, analogue solutions can be given for cases of fission and fusion, arbitrary undetached parts (Tibbles or Theon/Deon cases), statues and lumps, paradoxes of increase and decrease, the problem of change and, with some extra analysis, the problem of the many. (In fact, the Ship of Theseus case can be seen as an example of asymmetric fission.) These solutions are explored in my book manuscript, Pickup (MS), which also gives much more detail on the theory underpinning the solutions.
I have particularly in mind two sorts of solution that seem similar: (1) those solutions that appeal to indeterminate or temporary identity: see Parsons (2000) and Gallois (1998) as paradigmatic examples; (2) those solutions that appeal to judgements between candidates, like Nozick’s (1981) ‘closest continuer’ theory of personal identity (Noonan 1985 discusses this in the Ship of Theseus case). I suggest in the next paragraph reasons to think that, in both cases, the resemblance is merely that.
This distinguishes the view both from the indeterminate/temporary identity views and the closest continuer approach. As a further point of contrast with Nozick, the underlying view of how objects persist through time is endurantist, rather than in terms of temporal parts. It might be possible to recast situationalism using temporal parts, or the closest continuer theory using endurantism, however.
Contrast this, for instance, with the proposal in Noonan (1985) according to which indeterminacy enters at the level of denotation. The fact that there is such indeterminacy distinguishes the view from Nozick’s, where identity statements are true or false (though their being so may depend on other candidates for identity): in the case of a tie both statements are false (see Nozick 1981, 33–34).
See especially Sect. 4.2 for the ‘determinately identical’ worry and reply.
Plutarch first mentions it in his Life of Theseus and Hobbes (1839) refined the example in De Corpore II:11.
This might be disputed. Some might think that in the third story Victory is clearly identical to one of the two later ships and clearly distinct from the other. This is sensitive to the precise story that is told: the time that has elapsed from the arrival of Victory, the number and size of the replacement parts and the precise process of replacement and storage all make a difference. I have aimed for a story according to which the motivations for taking Victory to be identical to Restoration and to Reconstruction are equally strong, though different. If you find the motivations significantly different in strength, we can adjust the story to bring these closer together to generate the same worries. At some point, the motivations will be equally strong: take this to be the example under consideration for the rest of the paper. Thanks to an anonymous reviewer for pushing me on this.
This, of course, would need further explanation before becoming a well-defined notion.
Exactly what this priority consists in has not been specified. I take it that what it is to be a possible world is less fundamental than what it is to be a situation, because the former is a conjunction of what it is to be a situation and some maximality constraint. But the conceptual and metaphysical dependence relations would need to be spelt out further (thanks to an anonymous reviewer for highlighting this).
Thanks to an anonymous reviewer for highlighting the slightly different formulation needed for merely possible situations. Of course, some views of which particulars exist would avoid the need for such a tweak (see, e.g., Williamson 2013 for the view that what I call here ‘merely possible’ particulars actually exist, and indeed are necessary).
Of course, this is an incomplete account, as we have not specified what particulars and relations are. But I don’t see any tension in what follows with any theory of these. It is also worth pointing out that we thus take situations to be compositional: composed of particulars and relations. For us they are not therefore ontologically primitive (though this is a coherent view).
This draws on the Austinian insight that the truth of our utterances depends both on what is said and of what the thing is said. See Austin (1950).
I will take propositional truth to be fundamental, so if any other entities are truth-apt (e.g. statements or utterances), the truth of these entities will be reducible to the truth of certain propositions in certain situations. These other entities might seem to be true simpliciter, but their truth depends on propositional truth in a situation.
There is an interesting question (raised by an anonymous reviewer) about the status of propositions that concern the truth of propositions in situations. For instance, imagine that the proposition ‘p is true in s’ is itself true. Given I want to deny that any proposition is true simpliciter, in which situation(s) is this proposition true? I think we have options here. One is to say that it’s true in the situation composed of all other situations, the situational top element (though this commits one to the existence of such a situation). Another is that it is true in all extensions of s (though this commits one to universal transference of such propositions, as discussed later). A third is that it is true in all situations whatsoever (though this commits one to such propositions having a very strong form of necessity argued against below). I prefer the first of these options, but any would do.
Austin’s way of dividing up the terrain was slightly different, as his propositions essentially refer to situations. For us, propositions are trans-situational; they are not generally restricted to particular situations. Statements or assertions of them may involve particular situations, however.
For example, whether one favours a correspondence or a coherence theory of truth will have an impact on one’s interpretation of truth in a situation.
Thus there are some situations in which [p ∧ ¬p] is neither true nor false. However on the definitions given in the “Appendix” p and ¬p are inconsistent and ¬[p ∧ ¬p] is valid. Similarly, ‘Tom is a married bachelor’ can be neither true nor false, for example in situations that don’t contain Tom. This connects to our later discussion of necessity in Sect. 4.1.
For the sake of simplicity, I assume that the mereological relations between situations will be classical.
This will have to be tweaked for us, given the situation theory we accept. Parthood will be defined negatively: s′ ≤ s iff s contains all the particulars in s′ and none of those particulars is not instantiating a property or relation which it does in s′. With ‘+’ indicating a more complicated combination function, we can still assert s′ ≤ s iff s + s′ = s.
There are more esoteric cases which also put pressure on universal transference, including time-travel, transworld identity and propositions which refer indexically to the situation they are in. There is not space to investigate these here.
There are significant connections between situationalism and other views in the philosophy of time. It is indebted to adverbialism and particularly the SOFism of Haslanger (2003), though it moves away from them in some key respects. One interesting candidate for the ontology and metaphysics that could underlie the denial of universal transference can be drawn from the realist view of tense called Fragmentalism, outlined in Fine (2005). According to this view reality as a whole is not fundamentally coherent, but smaller fragments of reality are. This primacy of smaller fragments of reality would correspond to the primacy of smaller situations in containing truths. Pickup (MS) gives a thorough treatment of these issues, which can only be mentioned here.
By this, I wish to claim not just that there is some representational indeterminacy (which would be akin to Noonan’s approach, for example), but that there is real metaphysical indeterminacy here, i.e. reality itself is not settled as to whether Victory is identical to Restoration (and likewise for Reconstruction) in S 3.
See note 7 for ways the case could be adjusted for those whose intuitions vary.
See Pickup (MS) for details. See also note 21 for some further references.
C.f. the definition of validity in the “Appendix”, which likewise states that a proposition is valid if it is not false in any situation. Vagueness would need to be discussed to give a full defence of this interpretation of necessity.
Kripke’s discussion raises but doesn’t answer the question of whether a = a in a world or situation in which a does not exist. See Kripke (1971), 137. He wants instead to use a weaker notion of identity (though not the one I use here). This question will matter below.
It is worth pointing out that if an identity p is neither true nor false in a situation then □p is also neither true nor false in that situation. Therefore the T-axiom, which states □p → p, holds within every situation. However, the truth of □p in some situation s will not entail p in some other situation s*.
Thanks to an anonymous reviewer for the prompt to consider this.
An unrestricted version of Leibniz’s Law would state that if a = b in any situation then they must share all properties in all situations. This goes against the partial ethos of situation theory; what is true in one situation needn’t be true in another. The necessity of identity, of course, is relevant here but has been discussed above.
I should also specify that the situationalist is able to identify particulars that are in different situations: e.g. she can capture the claim that a in s is identical to b in s′. She can do so by construing it as: a = b in the situation composed of s + s′. The identity of entities in different situations is their identity in the combined situation. Thus even cross-situational identities are identities within a situation, and Leibniz’s Law holds of such individuals within the combined situation.
Victory does have the property ‘is-identical-to-Reconstruction-in-S 2′, but Victory has this in situations other than S 1. By introducing the complex property, the situation we are considering changes.
See Stalnaker (1986) for a similar way of dealing with identity, though across possible worlds rather than situations.
Note that, as mentioned above, this principle holds within situations. The universal quantifiers are therefore restricted to the situation under consideration. Sometimes the principle is formulated with a biconditional [Fx ↔ Fy], but this doesn’t make a material difference here.
A formal contradiction can be derived if x being distinct from some y entails x = y not being indeterminate, which is plausible on standard interpretations of the determinacy operator.
Strictly speaking, Evans’s argument requires that the terms ‘Victory’ and ‘Restoration’ have precise designations in S 3, which might be dubious in the former case. This line of response will be passed over.
This might lead us to claim that Victory is indeterminate with respect to all properties in S 3. While this would guarantee a response to Evans’s argument, it is a stronger supposition than we need, so it seems more prudent to hold back from the claim.
One obscuring factor is that such an invariance of identity across situations would entail that identity is intrinsic. For if identity does not vary from situation to situation then the truth-value of a proposition expressing an identity will be fixed across all situations. This means that whether or not the identity holds is independent of the rest of the situation: it is independent of all external factors. However, although invariance of identity entails that identity is intrinsic, the converse is not the case. Identity being intrinsic doesn’t say anything about whether it can vary across situations.
The conditional is reducible, as with traditional propositional logic, to the other logical connectives. It is true and false in all the same cases as the negation of: [α and not β].
References
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Acknowledgments
I am grateful to a number of individuals for feedback on this paper: Gonzalo Rodriguez-Pereyra, Nick Jones, Josh Parsons, JD Lafrance, Al Wilson, Denis Robinson, Stephen Williams and two very helpful anonymous referees for this journal. The publication of this article has been supported by the Templeton World Charity Foundation, via my participation in The Metaphysics of Entanglement project based in the Faculty of Philosophy, Oxford University.
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Appendix
The following outline of a situation semantics is particularly indebted to Kratzer (1989) but there are significant theoretical differences.
Appendix
In this appendix I will provide some more technical material to flesh out the situation theory that undergirds the solutions given in the body of the paper. It takes the form of a semantics for a fragment of English, including the logical connectives and existential and universal quantifiers.
Ingredients
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S—a set, the set of possible situations
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A—a set, the set of possible individuals
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≤—a partial ordering on S ∪ A such that at least the following condition is satisfied:
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1.
For no s ∊ S is there an a ∊ A such that s ≤ a
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P—the set of propositions
≤ is intuitively understood to be the parthood relation.
We can now set down the logical properties and relations. Truth and falsity are not defined in terms of some other notions; they stand as a primitives in the theory.
Consistency
A set of propositions A ⊆ P is consistent iff there is an s ∊ S such that all members of A are true in s.
Compatibility
A proposition p ∊ P is compatible with a set of propositions A ⊆ P iff A ∪ {p} is consistent.
Logical Equivalence
Two propositions p and q ∊ P are logically equivalent iff the set of situations B ⊆ S in which p is true and the set of situations C ⊆ S in which q is true are such that B = C and the set of situations D ⊆ S in which p is false and the set of situations E ⊆ S in which q is false are such that D = E.
Logical Consequence
A proposition p ∊ P follows from a set of propositions A ⊆ P iff there is no s ∊ S such that all the members of A are true in s and p is false in s.
Validity
A proposition p ∊ P is valid iff p is not false in any s ∊ S.
These notions provide us with a theoretical handle on the formal relations between situations.
We can now provide the truth-conditions of the logical connectives and quantifiers (at the level of Logical Form). It will not be sufficient for us to give the truth conditions for sentences following a Tarski model; because we have two primitive notions (truth and falsity) we shall also have to give the conditions under which sentences are false. These are given below:
Negation True
For any variable assignment g: [not α]g is true in s ∊ S iff [α]g is false in s.
Negation False
For any variable assignment g: [not α]g is false in s ∊ S iff [α]g is true in s.
Conjunction True
For any variable assignment g: [α and β]g is true in a situation s ∊ S iff [α]g and [β]g are both true in s.
Conjunction False
For any variable assignment g: [α and β]g is false in a situation s ∊ S iff [α]g or [β]g is false in s.
Disjunction True
For any variable assignment g: [α or β]g is true in s ∊ S iff [α]g or [β]g is true in s.
Disjunction False
For any variable assignment g: [α or β]g is false in s ∊ S iff [α]g and [β]g are false in s.
The logical connectives, then, have strong Kleene truth-tables.Footnote 39
We shall now turn to universal and existential quantification. Let’s begin with existential quantification:
Existential Quantification True
For any variable assignment g: [(There is an x: α)β]g is true in a situation s ∊ S iff there is a variable assignment g′ which is just like g except possibly for the value it assigns to x (call such an assignment an “x-alternative of g”) such that [α]g′ is true in s and [β]g′ is true in s.
Existential Quantification False
For any variable assignment g: [(There is an x: α)β]g is false in a situation s ∊ S iff there is no x-alternative of g such that [α]g′ is true in s and [β]g′ is true in s.
Existential quantification always receives a truth-value; it is bivalent. By contrast, our conditions for universal quantification determine that it is not bivalent, as guaranteed by the first clause:
Universal Quantification True
For any variable assignment g: [(For all x: α)β]g is true in a situation s ∊ S iff both (1) there is an x-alternative g′ of g such that [α]g′ is true in s and (2) for all x-alternatives g′ of g the following holds: If [α]g′ is true in s then [β]g′ is true in s.
Universal Quantification False
For any variable assignment g: [(For all x: α)β]g is false in a situation s ∊ S iff there is an x-alternative g′ of g such that [α]g′ is true in s and [β]g′ is false in s.
This brings to a close our sketch of a semantics in terms of situations. It will be helpful to end by briefly commenting on the closure principles that hold for this theory of situations. According to the theory presented, the propositions which are in a situation are closed under negation, conjunction, disjunction, existential quantification and universal quantification. It is important, though, that they are not closed under logical consequence.
We have provided both truth conditions and falsity conditions for our logical connectives and quantifiers. In doing so, we hope that we have made it clearer how our theory of situations is to be understood and how it will work.
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Pickup, M. A Situationalist Solution to the Ship of Theseus Puzzle. Erkenn 81, 973–992 (2016). https://doi.org/10.1007/s10670-015-9777-3
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DOI: https://doi.org/10.1007/s10670-015-9777-3