SORITES, ISSN 1135-1349
Issue #10. May 1999. Pp. 39-59.
Complementary properties and persisting objects: ontological constraints on the semantics of sentences of the type `O is φ at t'
Copyright © by SORITES and Montse Bordes
Complementary properties and persisting objects: ontological constraints on the semantics of sentences of the type `O is φ at t'
One of the problems which any ontologist must face today -- unless he is constrained to provide just models simply as devices for interpreting logical languages -- is called `the problem of change'. We could usually think that any arbitrary current object (a ball, a tree, a person...), say O, a persisting entity from t to t',Foot note 4_1 satisfies the two following requirements:
(1) It is possible that there is a property φ such that φ(O) at t, but no-φ(O) at t'.
(2) O-at-t = O-at-t'.
Nevertheless, Leibniz's Law or the so-called `principle of the indiscernibility of identicals', cannot allow (2), given the fact that φ(O) at t, but no-φ(O) at t': according to the principle, the object O cannot be the same at t and t', because O-at-t is not indiscernible of O-at-t'. If Leibniz's Law is valid, the existence of continuants is prima facie incompatible with the possibility of change. Indeed (3)
(3) If O-at-t = O-at-t', then, for every φ: φ(O-at-t) if and only if φ(O-at-t')
is incompatible with (1) and (2). If the continuant is wholly the same at t and t', then it must have the same properties at t and t'. This is the incompatibility that constitutes the problem of change for the continuants theorists, the philosophers holding that current objects are continuants or entities that endure or persist by being wholly present through time. Four-dimensionalists, who maintain that current objects are only partially present at each moment of their existence do not have to solve this problem:Foot note 4_2 they would deny the truth of (2), so that the object at t need not be indiscernible from the object at t'. O-at-t is a temporal part of O, different from the temporal part O-at-t'. On the other hand, the four-dimensional whole and each of its temporal parts, in so far as they are the same, fully satisfy the requirement of indiscernibility.
Supposing we espouse continuants, what solutions could a continuants theorist put forward to the problem of change? Basically, he has to impose temporal restrictions on certain notions linked to the notion of a property.Foot note 4_3 This can be done by means of three procedures: temporal relativization of the notion of property (relative property theory), relativization of the instantiation relation (relative instantiation theory) or constraint of the possession of a property to the present time (theory of present possession of properties).Foot note 4_4
According to the relative property theory, although Leibniz's Law is applied universally with no restriction, `φ' takes as values in (3) entities of the type t/white, t'/seated, t''/bald. Properties are relative to times. A sentence such as `the vase is white' is elliptical: it is not mentioned specifically but it is presuposed the time at which the object possesses the property. In fact, the logical structure of the sentence is provided not by `φ(O)' but by `(t/φ) (O)'.Foot note 4_5 In this way, Leibniz's Law is consistent with the existence of continuants and the possibility of change, since (3a) is true:
(3a). If O-at-t = O-at-t', then for every t/φ: (t/φ) (O-at-t) if and only if (t/φ) (O-at-t')
Indeed, any assigning of values which satisfies (t/φ)(O-at-t) also satisfies (t/φ)(O-at-t'). If yesterday at 3.30 the vase is green-yesterday-at 3.30, today at 10.15 the vase «is still» green-yesterday-at-3.30. If a property relative to a time applies to an object, it applies eternally, or to be more precise, timelessly. The only kind of impossible situation according to the law formulated in this way would be one in which an object had at the same time a property and its complementary.
Lewis says that any solution to the problem of change must respect our notion of intrinsic property. Objects possess what he terms `intrinsic temporary properties', that is, non-relational properties which objects possess at one time, but lose at another. The question is: how is it that the same thing can possess complementary intrinsic properties? If the vase is white and is then painted green, since the vase is one and the same before and after the change, how can it be white and green? What this amounts to in short is the old Parmenidean question: «How is it that the same object can possess contrary properties?» The quick answer, «because an object can possess contrary properties as long as it does so at different times»Foot note 4_6 only succeeds in admitting that it is possible «in some way», but the point at stake is precisely in what way, if there is one at all. As we can see, Lewis (1986, 202-204) shows the importance of respecting our notion of intrinsic property when tackling the problem of change. He terms it `the problem of temporary intrinsics'. It is clear that the relative property theory denies that there are temporary intrinsic properties: t/white is not an intrinsic property, not because it is not intrinsic, but because it is not a property, since it is a hidden relation.Foot note 4_7
Notice that relative property theorists cannot allow the current logical inference from (4) to (5)
because according to the theory's main claim (5) is badly constructed. The blocking of that inference, nonetheless, could not by itself constitute a powerful objection to that theory. But what follows is. Johnston (see Johnston, 1993, 267) points out that if the theory were correct, what we consider duplicates would not in fact be duplicates, unless they shared all their properties relativized to times. However, we consider duplicates to be objects that possess exactly the same properties, even if they possess them at different times. The causal effects of duplicates are the same regardless of the time at which they possess them. This is certainly a strong objection to the theory.
Some philosophers, Johnston among them, have maintained that, although the theory explained above is incorrect in letter, it is correct in spirit and some modifications can make it acceptable. It is not properties that are relative to times, but rather is the relation or the fact of instantiation of such properties. The relative instantiation theory may be built from the following line of reasoning. Recall that according to the relative property theory, every property is a relation to a time. Note that this relation may be contingent or necessary. If it were contingent, it would make sense to speak of properties regardless of the time at which the objects possess them, but this is precisely what the theory rejects. According to the relative property theory, as we saw, properties are necessarily relations to times. The property of being t/white, must be-at-t, it could not be-at-t', because, in that case, it would be a different property. All the same, it seems odd for someone to believe that properties as universals should have such essential features; it seems more reasonable if one considers them as particulars. The particular property of the whiteness of this object now would be different if the time were different. Relativization of properties is said of particulars, not of universals.
The first modification of the relative property theory relativizes the fact of instantiation. A second possible one relativizes the instantiations themselves, so that its associated ontology can do without universals, replacing them with similarity classes of particular properties (the `tropes' of D. C. Williams, 1953). The first modification, which I shall discuss in this section,Foot note 4_8 is the theory originally put forward by Johnston (1993) and Haslanger (1989).
According to Johnston, it is true that the property being white is the same at t as at t', and for this reason we cannot admit the relativity of properties with respect to the times to which they apply; but the instantiation relation is relative to time. Most temporal accounts are provided adverbially: time may be understood as the mode in which individuals possess properties.Foot note 4_9 For Johnston, (4) and (5) would be analyzed as follows:
(4a) (t/is) (O, φ) or else O instantiates-at-t φ
(5a) (is) (O, φ) or else O instantiates φ
However, parallel to the relative property theory, the relative instantiation theory (or, as it is usually called, `the adverbial theory') cannot accept the validity of the inference from (4a) to the ill-constructed (5a), as it does not admit a notion of non-relative or simpliciter instantiation. The relative property theory did not accept the notion of possession of simpliciter properties; the relative instantiation theory will not tolerate the notion of simpliciter possession of properties. If this is the case, the relative instantiation theory evades the objection of failing to recognize the intrinsic character of properties. Nevertheless, Lewis does not appear to think in this way, he considers this theory as a mere variation on the previous one: «the adverbial variant ... puts the relationality not in the shapes themselves but in the having of them: there is a three-place relation of instantiation, this relation holds between me and bentness and some times, and it holds between me and straightness and other times. I ask: what does standing in some relation to straightness have to do with just plain being straight? And the variant still claims that to be shaped is to stand in relations to other things, inter alia to times. I say it still amounts to a denial that things have temporary intrinsics.»Foot note 4_10 How can this last sentence be justified? In my opinion, Lewis would appear to believe that if the property is that of being white, the intrinsic character of the property is lost whether we relativize the subject (being-white-at-t) or we relativize the verb (being-at-t-white).Foot note 4_11 Even if this reading of the theory were not appropriate, I cannot see how the problem of duplicates can be made to disappear -- which Johnston regards as a definitive objection to the relative property theory that does not affect his own. A duplicate of an object is that which instantiates its own intrinsic properties. Now, since for the friend of relative instantiation it is not licit to refer to instantiation simpliciter, duplicates, in order to be duplicates, will have to instantiate-in-the-same-way the same intrinsic properties.
The friends of this theory consider that the semantic function of the temporal indicator is that of an adverbial which modifies the verb `to be'. `Being-at-t rich' functions like `being extremely rich', so we can express it as: `being tly rich'. Despite the lack of euphony, thinks Johnston, the analogy is correct. However, in my opinion, no basis has been given for the sense in which time can modify the possession of a property. We understand perfectly the sense in which the word `extremely' modifies in terms of precision `being rich', but we do not understand -- without a good explanation, at least -- how the supposed adverbial `tly' does. The friend of this theory, of course, will point out that no other adverbial can be strictly analogous to the adverbial `tly' as it is required specially for certain verbs which attribute properties to temporal objects. Johnston does not explain what this special modification of the time-adverbial mentioned might consist in, but he says that he considers it to be analogous to that which modal indicators perform.
The relative instantiation theory constitutes an effective response from the continuants theory to the problem of temporary intrinsics: it manages to maintain the compatibility between the changing of temporal objects and Leibniz's Law without sacrificing our notion of property simpliciter, an essential and fundamental element of our notion of a duplicate. Rejecting a notion of instantiation simpliciter, while it may be open to debate, does not involve, however, such a high cost as the rejection of the relative property theory did. Furthermore, with a sound metaphysical justification, it would not involve any cost at all.
There is another way, however, to solve the problem of change: to say that an object only possesses the properties it has at the actual or present time. This is the position of the theory of present possession of properties, which analyzes the verb `to be' as making an implicit reference to the time of utterance, in such a way that the verb `to be' is always elliptical with respect to (or has the same intension as) `being now'.
Let us suppose that Charles was blond in 1970, now he is grey-haired and in the future he will be bald. According to the usual interpretation of the sentences `Charles is blond', `Charles is grey-haired' and `Charles is bald', we attribute the truth-value false to the first and third sentences, and the value true to the second, since Charles is-now not blond and Charles is-now not bald, but is-now grey-haired. An object does not now possess its past properties nor does it yet possess its future properties, so `φ(O)' is true if and only if `now φ(O)' is true also.
According to this theory, neither properties nor their instantiations are time-relations: properties are genuine and intrinsic, and it makes sense to speak of their possession simpliciter. An object does not possess timelessly all its properties in any of the senses of the term `possess', but rather may possess complementary properties at different moments of time: properties are temporal. And none of this is in conflict with Leibniz's Law, since an object only possesses its present properties, not those of its past or future, so if O is φ but was or will be not-φ, there is no contradiction, whereas there would be if O were φ and not-φ now, in the present.Foot note 4_12
However, despite the ease with which this theory rids itself of the deficiencies of the two theories mentioned previously, it has at least three serious drawbacks.Foot note 4_13
The first, in fact, is something more than a drawback, since it denies the fact which it sets out to explain. Let us remember that our object was to explain persistence in spite of change: how it is that an object can be φ at t and not-φ at t'. However, according to theory outlined above, it is not possible for an object to be φ at t unless t is present. The object only possesses its present properties, it no longer possesses those it had in the past nor yet those it will have in the future. But then, the object neither persists nor changes. Nothing is (simpliciter) φ at t, when t is past or future. Unless the object is a substrate, if it does not possess its past or future properties, then the object does not exist in the past or in the future, so it does not persist. If it does not persist, it does not change: change implies that there is a persisting object that has complementary properties at different times. If objects do not change, then obviously the problem of temporary intrinsics vanishes. But at the cost of many other vanishings whose legitimacy is highly dubious.
A rapid way of providing a defence against the above criticism would be to say that, simply, the persistence of an object consists in that it existed at certain times, it exists now and it will exist in others. If this is to accept persistence, then no one can deny it. This answer trivializes the theory, in what Lewis considered the accepting that, in one way or another, things persist. Merricks'claim that only the present exists may be interpreted in at least two ways. According to the first, `to exist' must be interpreted as `to-exist-at-the-same-moment-as-the-utterance-of-the-sentence'. If this is the reading that Merricks makes of (*) `only the present exists' then the sentence expresses a tautology, the same expressed by `only the present is present'. Another reading of (*) is to assume that `to exist' means `to be real', in the same sense in which we say that the world is the set of real events. This interpretation commits Merricks to a parallelism between worlds and times that is highly debatable, namely, that the real world is to possible worlds what the present is to past and future times. Merricks declares himself to be an actualist (on p.77, n.15 he says that he understands possible worlds in the same sense as Plantinga, not in that of Lewis) and a presentistFoot note 4_14 (he states that, since the modal question is analogous to the temporal question, the real world is to the present what the possible worlds are to the past and future). His position consists in treating possible worlds as constructed from the real world, a theory which is entirely respectable. However, with times the matter is not so straightforward: the future and the past do not appear to be constructed on the basis of the present, or at least, it is by no means clear how we may understand such a «construction».Foot note 4_15 In the last analysis, the future (or the past) does not appear to be on the same ontological level as a possible world: my expectations are not frustrated if I fail in a possible world, but this is the case if I do in the real future. In certain parts of his paper, (such as, for example, on p. 180) the author appears to commit himself to the first of the interpretations given above. But, what interest can such an assertion have? A tautology is implied by every theory, so a four-dimensionalist could also accept Merrick's viewpoint. When Merricks explains why a four-dimensionalist could not accept his theory (p.181) he seems, however, to be committing himself to the second interpretation which I have given above. And this, as I have said, is highly debatable: it does not appear to explain what persistence and change consist in.
However, all things considered, perhaps this theory may be able to account for persistence and change in a non-trivializing manner. We simply have to find the correct way to reformulate them. An object O persists from t to t' if `O exists-now' is a true utterance at t and at t'.
Secondly, let us recall that both the relative property theory and that of relative instantiation rule out, very reasonably, the possibility that the same object possesses complementary properties at the same moment in time. However, the theory of present possession of properties only rules out the possibility that an object possesses complementary properties now, not that it possesses them in the past or future. Nevertheless, white and not-white are just as complementary in 1990 as they are in 1995. The supporter of the present possession of properties theory would appear to claim that the ontological status of the past and the future is substantially different from that of the present. Beneath this theory there appears to lie a conception based on the typical `myth of the passage of time'Foot note 4_16, according to which time itself passes or changes by taking objects from the past to the present and thence to the future. Objects, however, do not change by ceasing to be past and becoming present or future. Whether they be past, present or future is a matter essentially relative to the speaker.Foot note 4_17
The third drawback is the inability of this theory to establish a metaphysical distinction that I consider unavoidable. To affirm in a neutral sense with respect to time that φ(O) means that O in the real world was, is, or will be φ. To reject this neutral sense of the sentence is an impediment to distinguishing the real course of events from the course of merely possible events. According to this theory, φ(O) is true if and only if O is now φ, and is false whether O was or will be φ as much as if O never was φ, is φ or never will be φ. However, it is obvious that there is a difference which must be accounted for between the real pasts and futures and those which are merely possible: if the real future does not exist, it is a non-existence of a different order from the non-existence of a future which is a mere possibility. This latter will not have any bearing on the decisions taken by someone who deals on the stock exchange.
Now let's move on from the metaphysical question to a matter which arises naturally from the remarks made in this first section. In the preceding pages I approached the problem of temporary intrinsics as a metaphysical problem for continuants theorists: to explain how an object may persist in spite of the alteration of its intrinsic properties. But it is clear that this is linked to a semantical issue: how to give the logical form of sentences which attribute temporal properties in such a way that no contradiction arises by attributing complementary properties to the same object.Foot note 4_18 For Lowe, such problems must be resolved separately: a theory which set out to solve them simultaneously would fail to provide satisfactory answers to any of them. In my opinion, however, the situation is precisely the opposite. The sine qua non of any solution to the metaphysical problem is its contribution to the providing of elements for a solution to the semantic problem (the entities which we will be committed to must function as referents of certain linguistic terms). This is also true in reverse, if we interpret a sentence that attributes temporal properties to a persisting object as one that quantifies over certain entities, we must be sure that our ontology provides us with the appropriate category of entities to serve as the corresponding referents. Any attempt to resolve the two problems separately will inevitably fail. A semantic theory must be able to justify its ontological commitment; one cannot offer it as a mere strategy for «saving the phenomena». If a property is analyzed in semantic terms as a relation to a time, the analysis must be justified in metaphysical terms. If such a justification were not necessary, then any semantic theory which could account for events and linguistic inferences would be acceptable, regardless of any metaphysical consideration. But this is not the case. Lowe himself welcomes the semantic thesis of the relative instantiation theory because it seems to him to be «the least revisionary with respect to our common-sense talk of persistence through change».Foot note 4_19 If we believe that it is appropriate to respect this way of speaking it is because we believe that the metaphysics that supports it is the correct one, or the least problematic.
Before going through the semantic proposals for the analysis of sentences of the type `O is φ at t', it is helpful to mark out the territory in which they are developed and to signpost the general framework in which they are inserted.
Traditionally -- according to the ideas of Prior (1968) -- temporal semantics has worked in close parallel with modal semantics. Sentences of the type: `modal operator [φ]' have served as a semantic model for sentences of the type `temporal operator [φ]': `it happened that' would express, in the same way as `it is possible that', a function from indices to truth values (the indices would be times in the case of the temporal operator and possible worlds in the case of the modal operator) In the same way that the semantic value of a modal sentence is constructed starting from the semantic value of an expression which speaks of the real world (`it is possible that [Richard Nixon resigned]'), the semantic value of a sentence in the future or in the past is constructed on the basis of the semantic value of an expression which speaks of the present world (`it happened that [Richard Nixon resigned]'). The justification for the temporal case is that we can intuitively evaluate the truth value of the sentence in the past, `P[φ]', or in the future, `F[φ]', in the following way: `P[φ]' is true at t, if there is a t'<t with respect to which `φ' is true. `F[φ]' is true at t, if there is a t'>t with respect to which `φ' is true. The specifying of the truth conditions of temporal sentences is more or less complex depending on the type of temporal operator: it may be a general operator (`always', `sometimes'), a specific operator (`in 1456', `yesterday') or an operator in the simple past or future (`she listened', `it will rain'). Henceforth, given the global nature of the remarks I intend to make, I shall use the letters `P' and `F' to designate the temporal operator for the past and for the future, respectively, without taking into account the difference between the types of operators mentioned.
If the analogy with modal semantics is valid, the evaluation of temporal sentences will therefore vary with time, as the evaluation of modal sentences will vary depending on the possible world under consideration. We shall say that:
(1) The ruling of the Supreme Court induces Richard Nixon to resign.
is true as of August 8th, 1974, but false on the previous day, analogously to its truth in the real world but not in other possible worlds. As long as accepting this analogy does not require us to place the ontological status of the real world on the same level as the present,Foot note 4_20 I have no objection to adopting it, as it accounts for our usual methods of evaluating sentences. The fact that our evaluations differ depending on time reflects in a technical sense the idea that what we say may be true in one time, but false in another: taking a sentence of the type`temporal operator [φ]', the truth value of `φ' depends in part on the moment of time to which the operator refers.
So what is the semantic and syntactic category of `φ'? If its syntactic character is declarative (if it possesses as a semantic value a proposition or function from possible worlds to truth values), then in no coherent sense can we say that `what we say' therewith varies in terms of its truth value depending on time, since every proposition, in so far as it contains information, is eternal. Supposedly, some stoic and scholastic theories tried to reconcile the idea that a sentence that is neutral with respect to time could express a proposition whose truth value would vary when the sentence (not the proposition) was completed with a time reference. All the same, to claim that a proposition is an incomplete informational content or that it is one which requires semantic determination is simply a contradictio in terminis. M. Richard (1980, 14ff) maintains that our attributions of common-sense belief may only be analyzed correctly if we understand the contents of belief to be eternal propositions. Let us consider the following pair of sentences:
α. In 1973 Helen believed that Richard Nixon was the President of the United States.
β. Helen still believes what she believed in 1973.
What is the content of Helen's belief? If the object of Helen's belief at α were the temporalized proposition expressed as `Richard Nixon was the President of the United States in 1973', while at β her belief would correspond to the temporalized proposition expressed as `Richard Nixon is the President of the United States in 1997', then from α and β would follow the proposition þ:
þ: Helen believes that Richard Nixon is the President of the United States in 1997.
However, it does not appear to be reasonable to attribute this belief to Helen because of α and β. If, on the other hand, instead of believing that a sentence expresses an incomplete proposition which becomes complete when it is temporalized by the context, we believe that a sentence always expresses the same proposition, in this case, that which corresponds to `Richard Nixon is now the President of the United States', our analysis of belief-attributing sentences will produce the appropriate results. From α and β follows the reasonable proposition þ':
þ': Helen believes that Richard Nixon was the President of the United States in 1973.
But then, if `φ' expresses a (complete) proposition, i.e. if it already contains an implicit reference to the time of its evaluation, then the temporal operators become superfluous. If (1) contains an implicit reference to 08/08/74, then what function will the operator `08/08/74' perform when it appears explicitly in the sentence? Syntactically, the operator would be an adverbial-type expression (of the type <t,t> in Montague's semantics, an expression which, when applied to a sentence, yields another sentence as a value).Foot note 4_21 Semantically, however, it would provide no more information than what was already assumed.
One of the questions in dispute concerning temporal semantics is, as can be seen, whether or not sentences that lack an explicit temporal reference contain an implicit reference to the time at which they are to be evaluated. Eternalist semanticsFoot note 4_22 maintains that a sentence like (1) expresses different propositions according to the implicit reference to a time that it contains. According to temporalist semanticsFoot note 4_23 this sentence always expresses the same proposition (temporally neutral) whose truth value varies according to the time in which it is evaluated (such a proposition would be a function assigning to each possible world the set of times in which the proposition is true in it). This latter semantics explains in this way the function of the temporal operator: the embedding of the temporal operator in the temporally neutral proposition expressed by `φ' would produce a temporally definite proposition. Nevertheless, this notion of a `temporally neutral proposition' is something we have already seen to be somehow suspect.
Besides, the syntactic category of `φ' may not, after all, be enunciative. If `φ' has a predicative category (if it possesses as its semantic value a function from possible individuals to truth values), then maybe we will be able to reconcile the two theses which so far seemed incompatible, namely, (i) that `what we say' is complete and determined with respect to every index, i.e., it has an eternal value, and (ii) that `what we say' is sensitive to the time of reference. Evans (1985b) presents a theory, which he calls `T3', in which `φ' in `P[φ]' has a predicative value,Foot note 4_24 which is completed with a reference to the time of the utterance indicated by the temporal operator. So, `P[φ]' is true at t if and only if there is a t'>t such that the utterance of `φ' at t' were true (or to put it another way, if and only if `now φ' were true at t'). However, this theory cannot account for all linguistic phenomena. N. Salmon (1989) has shown that theories of this type are unable to discern the difference in truth conditions between the following sentences:
(2a) On 08/08/1973, a fortune-teller predicts that the ruling of the Supreme Court will induce Richard Nixon to resign the following day.
(2b) On 08/08/1973, a fortune-teller predicts that the ruling of the Supreme Court will induce Richard Nixon to resign tomorrow.
If I utter (2a) and (2b) on 07/08/1974, the proposition corresponding to the fortune-teller's prediction in (2a) is false, whereas that which corresponds to (2b) is true. However, according to Evans' theory T3, the premonitory sentences (2a) and (2b) would be true if and only if:
(2a') `now the ruling of the Supreme Court will induce Richard Nixon to resign the following day' were true on 08/08/1973.
(2b') `now the ruling of the Supreme Court will induce Richard Nixon to resign tomorrow' were true on 08/08/1973.
so that, inevitably, as the operator `now' always has wider scope, the extension of `on the following day' will be the day following that of the utterance and not, as one might have expected, the day following the temporal parameter of the context to which the propositional stem refers. The theory in question is analogously deficient with respect to all types of temporal indexicals. A further example is provided by the following pair of sentences:
(3a) Twenty-five years ago nobody would have believed that the ruling of the Supreme Court would induce the President of the United States to resign.
(3b) Twenty-five years ago nobody would have believed that the ruling of the Supreme Court would induce the actual President of the United States to resign.
where the proposition corresponding to the content of the belief expressed in (3a) is true, whereas one would expect the proposition corresponding to (3b) to be false. According to Evans' theory, on the other hand, both propositions would be of type `now[P[φ]]', and therefore would not be able to account for the truth conditions of (3a).
Salmon's proposal is based on the necessity of a double indexing: that of the extensions of the expressions to the time of actual utterance, on the one hand, and to other times according to the temporal operators that occur in the sentence, on the other.
It is, in short, a question of recognizing that the semantic value of expressions is sensitive as much to the time of the context of the utterance as to the time marked by the temporal operator. The difference between the truth conditions (2a) and (2b) lies in the fact that the extension of the temporal indexical must be relativized to the time of the temporal operator + 1 in (2a), whereas in (2b) it must be relativized to the context + 1. For Salmon, temporal operators are neither extensional (like the connectives of the language of propositional logic) nor intensional (like modal operators). That they are neither extensional nor truth-functional expressions is demonstrated by the fact that, for example, although relative to 08/08/1973 both `Richard Nixon resigns' and `26=2' express false propositions, a sentence such as (4):
(4) On 08/08/1974 Richard Nixon resigned.
expresses a true proposition, whereas `on 08/08/1974 26 = 2' expresses a false one. It can be shown that the propositions are not intensional either if we consider that, for example, although `The President of the United States' and `The actual President of the United States' express the same intension, nevertheless, with respect to 08/08/1974, `The President of the United States resigned' expresses a true proposition, whereas `the actual President of the United States resigned' expresses a false proposition. Salmon's theory assigns to `φ' at `complete temporal operator [φ]' a predicative value and analyzes (4) by segmenting it into the incomplete temporal operator `on 08/08/1974 [x]' and the temporal sentence `Richard Nixon resigned', the result of applying the operator `P[x]' to the propositional stem `Richard Nixon resigns'. For Salmon, non-general temporal operators are incomplete expressions that are applied to temporal sentences just as singular terms are applied to monadic predicates. In this way, (4) may be seen as the result of applying the incomplete`on 08/08/1974 [x]' to the temporal sentence `Richard Nixon resigned', which, in turn, is the result of applying the complete operator `on 08/08/1974 + past' to the temporally neutral propositional root `Richard Nixon resigns'. Complete temporal operators are, in fact, superintensional operators,Foot note 4_25 functions from propositional matrices (Salmon's terminology), neutral with respect to time, to truth values. In this way theses (i) and (ii) are justified: the idea that propositions are eternal is maintained (since `φ' is not an expression whose semantic value is a proposition, but is rather an attribute, since it is a propositional root) and the different evaluation of our sentences according to the time is accounted for (since the truth value assigned will depend on whether, given a certain time, t, φ(t) holds true or not): `what is said' in (1) on 07/08/1974 and on 08/08/1974 is, in some sense, the same content.
Having identified the context of semantic issues which a sound analysis of sentences of the type `O is φ at t' must face, I shall move on to consider the concrete theories derived from the metaphysical theories analyzed in section I. There are basically four possible analyses of sentences of the type `O is φ at t':
(1) φ (t/O)
(2) (t/φ) (O)
(3) (t/is) (O, φ)
(4) (t/is-now) (O, φ)Foot note 4_26
The supporters of a four-dimensionalist metaphysics of temporal parts propose (1), according to which it is the singular term which is modified by the time adverbial. The friends of continuants may propose any one of the remaining three. Those who propose (2) maintain that properties are relations to times; (3) is the analysis offered by those who believe that it is the instantiations of properties that are relative to moments of time, and (4) would be the analysis corresponding to the theory of the present possession of properties. Strictly speaking, none of these analyses contains a suggestion as to how to tackle the question of temporal indexicals, but there is no reason to suppose that that they could not incorporate one. The only indication of difficulty may be found in the analysis corresponding to (4), in so far as it is related to Evans' theory T2, which is semantically unsatisfactory for the reasons already given.Foot note 4_27
The four analyses deny the apparent incompatibility of a, b and c:
a. O is φ at t
b. O at t is O at t'
c. O is not-φ at t'
(1*) The semantic value of `O' varies according to t
(2*) The semantic value of `φ' varies according to t
(3*) The semantic value of `is' varies according to t
(4*) The semantic value of `is-now' varies according to t.
All the above can account for the fact that different utterances of the same type, `O is φ', have different semantic values at different times. None of them implies, however, that the evaluation of the sentence varies with the time, that is, none of them accepts (5):
(5) The semantic value of `true' varies according to t.
To accept (5) would mean rejecting the notion of «true simpliciter», admitting only relative notions of the type «t/true», analogous to «W/true», «true at the possible world W». Such a theory would commit itself either to modal and temporal possibilism B la Lewis (according to whom «true simpliciter», is like _ true@), or to modal actualism and presentism B la Merricks (according to whom «true simpliciter» is like «true now»).Foot note 4_28 At least the analyses offered by (1), (2), and (3) are perfectly compatible with a modal actualist and temporal realist position, which, unless some convincing metaphysical argument comes along to demonstrate the contrary, is the most appealing theoretical position from my point of view. (4), on the other hand, while it is compatible with modal actualism, is not compatible -- as I understand it -- with temporal realism.
The relativized terms for each of the theories and their respective syntactical and semantic categories would be as follows:
syntactic categorysemantic category
(2**) t/φ <e,t> function from possible individuals to truth values (set of possible individuals which are φ at t)
(3**) t/is <<e,<e,t>,t> function from possible worlds to truth values
(or tly <t,t>) (set of possible worlds in which some object has some property at t)
(4**) t/is-now <<e,<e,t>,t> function from possible worlds to truth values (set of possible worlds in which some object has some property at t)
We may note that none of these theories -- except, perhaps that which corresponds to (1) -- will admit in its semantics expressions that take moments of time as arguments, since expressions relativized to moments of time are considered to be primitive.
The theories which offer the analyses (1) and (4) are the only ones that provide a specific semantics for `O at t':
(1***) `O at t' refers to the temporal part of O that exists at t
(4***) `O at t' refers to the object O which exists at t when t is present
The expression `O at t' is a component which may be segmented without syntactic or semantic violence from `O is φ at t', as is shown by our everyday usage with reference to certain objects in given circumstances or at given moments, identifiable regardless of the theory of persistence that we choose to adopt:
a. Emily at the time was very naive.
b. When Fred gets drunk (drunken Fred) he always gets weepy.
c. You'll love the taste of this piece of newly-baked bread.
d. John Major in 1992 had more supporters than John Major in 1997.
All of these sentences can be easily analyzed using the semantic theory that corresponds to the four-dimensionalist theory, but there are other possible analyses compatible with the theory of continuants that could account for them perfectly well. The semantic theory of temporally indexed objects is able to analyze this type of sentences, in terms of expressions of the type `t/O', as well as this other type of sentences, in terms of non-relativized `O':
e. Emily is a human being.
f. This piece of bread is leavened flour.
Nevertheless, we must explain what the relation is between `O at t' and `O'. Quine (1992, 172) proposes analyzing `O at t' as denoting the common element of O and t, where `t' refers to the four-dimensional fragment (heterogeneous and discontinuous, if ever there was one) of the material world which exists at that time and `O', in its turn, refers to a certain four-dimensional object. His treatment would be analogous to that of `white flour', which would refer to the common element that exists between being white (or the set of white objects) and «flourness». Quine's analysis also permits us to analyze expressions of the type `the intellectuals of the 18th century' or `wine of the vintage of 66', which refer to classes, as classes of temporal parts of objects. Thus, `the intellectuals of the 18th century' would be analyzed as: the y: >x (y =18th cent./x v x is an intellectual). In general, `the z at t' would refer to the y: >x (y = t/x v x, z). Quine's proposal may be accommodated if desired by discarding his materialist ideas, which restrict the reference of the terms to the material world, along with his extensionalism, adopting instead an intensional semantics that includes the content of predicates, singular and general terms, and sentences.
The semantics put forward by the four-dimensionalists is fully coherent with its ontology. In (1), the modifying of the singular term by the time adverbial is justified because the object from which a property is predicated is a temporal part. In case (2), the ontological counterpart of the expression `t/φ' would have to be a relational property, a different one whether `φ' referred to a property possessed by different objects, or in the case whereby t varied (an analysis which, although metaphysically questionable, does not appear to me to be open to semantical objections; mutatis mutandis for case (3)).
Four-dimensionalist semantics, with its temporally indexed subjects, would appear at first sight to present a serious drawback. Apparently, it must establish two possible types of references for singular terms. On the one hand, a proper noun may refer to the maximal sum of the temporal parts of an object, as in the case of the proper noun of this sentence:
g. Peter is a person
or it may refer only to one or several of its temporal parts, as in the case:
h. Peter was blond in 1970,
a «transparent» reading of which would be: `Peter-in-1970 is blond'.Foot note 4_29 In general, the first case would apply when the predicated property is expressed by a sortal term of substance (such as `human being', `house', `tiger') or by a term applicable to the entire temporal course of an object (such as `to be the son of', `to be younger than'); the second case would apply when the predicate is a phase sortal or other predicate of temporally restricted application (such as `to be seated', `to be an adult', `to paint a picture'). So then, to what extent does this constitute a stumbling-block for the four-dimensionalist semantic theory? If it were unavoidable for this semantic theory to fix two types of referents for different tokens of the same singular term, then there would be a clear mismatch between the semantic theory and the way in which natural language functions in terms of usage: the linguistic data do not appear to point to any such systematic ambiguity of singular terms.
In fact, it is not necessary to postulate such an ambiguity for a four-dimensionalist semantics. We may say that singular terms always refer to maximal sums of temporal parts, although their reference must necessarily be fixed by means of a temporal part, since the sum is epistemologically beyond our reach due to the excessive «length» of the space-time region it occupies. Language, according to the four-dimensionalist, would be essentially metonymic: we name the whole by pointing to one of its parts. A sentence of the type `O is φ at t', although it has to do always with the sum total of temporal parts of a certain type, is a sentence which may be analyzed as `O has a temporal-part-at-t which is φ'. Thus, `Peter was blond in 1970' would be analyzed as `Peter has a temporal-part-at-1970 that is blond'. Sentences like g or h, therefore, deal with or quantify upon persisting objects, as one would have expected. The difference between one with respect to the other may be seen as the consequence of the scope of application of the corresponding predicates (in g the predicate applies to the object at all times, whereas in h only at certain times). The «transparent» reading in each case would be as follows:
g'. There is an x such that P(t/O, x) and, for every time t, if t/O exists, then there is a property φ (=to be a person), such that φ (t/O).
h'. There is an x such that P(t/O, x) and there is a time t=1970 and a property φ (=to be blond) such that φ (t/O).
A clear exposition of the metonymic character of language may be provided by the analyses of the following identity sentences:
i. Borges is the author of Fictions.
j. The baby in the photograph is the present managing director of the firm.
k. This statue is this piece of clay.
whose truth conditions would be expressed by:
i'. The four-dimensional object to which, perceiving one of its temporal personal parts, the name `Borges' was given, consists of the same maximal set of temporal personal parts (= is the same) as the four-dimensional object one of whose temporal parts wrote Fictions.
j'. The four-dimensional object to which I refer as `the baby in the photograph' by pointing out to one of its temporal parts consists of the same maximal set of temporal personal parts (= is the same) as the object to which I refer as `the present managing director of the firm' pointing out to one of its temporal parts.
k'. There is a four-dimensional object such that the temporal part thereof to which I refer as `this statue' is the same as that to which I refer as `this piece of clay'.
The advantage of analyzing everyday language as a metonymic language which quantifies over persisting objects and not over temporal parts is that we can retain the common-sense belief that identity sentences such as i or j may be true identity sentences in certain circumstances, and not systematically false, as they would be if their corresponding singular terms were interpreted as referring to temporal parts. Clearly, j would then be a false identity sentence, since the temporary part named as `the baby in the photograph' could not be identical (but rather gen-identical) to that named as `the present managing-director of the firm'.
Apparently, the semantic theories derived from the continuants theory do not have the same problems of mismatch with everyday language. There are no temporal parts of objects to refer to, but instead different occurrences of the same complete object. Nevertheless, I think that the continuants theorist is ontologically committed to certain core-continuants, commitment which would suppose certain problems of mismatch with everyday language. But, to see what is involved here we would need to go back to the metaphysical debate, which would define a subject for a different paper.
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