REFERENCE TO THE PAST AND FUTURE

by Quentin Smith

Western Michigan University

 

Will be published in: Time, Tense and Reference (eds. A. Jokic and Q. Smith). M.I.T. Press,  forthcoming.

 

1. The Presentist and the Maximal Tensed Theories of Time

      There is a certain version of the tensed theory of time, sometimes called the presentist theory, that claims that only the present exists (in any sense of "exists") and that there are no exemplified properties of being future or being past. (This is a different sense of “presentist” than I used in Language and Time.) A. N. Prior is often identified as the founder of contemporary presentism, but most of his work aimed to developed a tense logic that could be used to express presentist ideas. The two most developed ontologies for a presentist theory are Peter Ludlow’s in Semantics, Tense, and Time, and William Lane Craig’s in The Tensed Theory of Time. Their ontologies differ greatly, however, and (before I discuss their particular ontologies) I shall concentrate at the outset on some general themes of presentism.

    The presentist theory implies that there are no past or future particulars, and thus no things or events that have properties of pastness or futurity. What exists are the things, with their properties and relations, that can be mentioned in certain present tensed sentences. If the sentence-token "Jane is walking" is true, there is a thing, Jane, which possesses the property of walking. The sentence-token, "Socrates was discoursing", even if true, does not contain a name that refers to a past thing, Socrates, since there are no past things. The ontological commitments of past and future tensed sentence-tokens are merely to presently existing truth-vehicles, that is, either the sentence-tokens themselves or the propositions they express (whether only one or both of these are truth-vehicles can be left open at this point). According to the presentist theory, there is no such thing as reference to the past or future since there exists no past or future items that could serve as referents (of names, definite descriptions, individual variables, etc.).

Another version of the tensed theory of time is the maximalist tensed theory of time (which is sometimes called "the mixed A-B theory"). This theory implies that there are past, present and future things and events, that past items possess the property of pastness, present items possess the property of presentness, and future items possess the property of being future. "Socrates was discoursing" involves a reference to a past thing, Socrates, and implies that the event of Socrates discoursing has the property of being past. According to the maximalist tensed theory of time, there is reference to the past or future since there are past and future items that can serve as referents of singular terms.

      I shall argue in this paper that if the correspondence theory of truth (as distinct from the eliminativist, coherentist, etc., theory) is true, there is no logically viable form of the presentist theory, and that the maximalist tensed theory of time is viable and thereby preferable to the presentist theory. In the entirety of this paper, I adopt the correspondence theory of truth.

 

2. Explaining The De Dicto Presentist Theory

 

       The de dicto presentist theories imply that there are true past tensed sentences (and some versions allow true future tensed sentences), but that the only ontological commitments of these truths are to certain "dicta", viz., propositions, sentence-types or sentence-tokens. Past and future tenses, it is said, convey information about or pertain only to dicta, not to any res (thing) or event that is past or future.

      Most philosophers who hold a tensed theory of time hold a de dicto presentist theory. But (up until the 1999 and 21^st century works of Ludlow and Craig, which I shall discuss later) very little has been said to explain the meaning of this theory. Philosophers such as Christensen, Loyld, Plumer, Zimmermann, Chisholm, Levison, Wolterstorff, C.J.F. Williams, Bigelow, Markosian and many others hold this view but typically they do not explain exactly what it means, apart from the general slogan that "only present objects exist and possess properties". (Perhaps Bigelow and Markosian have said more than the others mentioned.) Most of them refer to A. N. Prior, and they convey the impression that Prior has somewhere explained the theory. Prior has, in fact, not explained the theory; his focus is on the syntactics of tense logic and he has little to say about the semantic content of tensed sentences or the ontology implied by a presentist theory. Nonetheless, the tidbits of information from Prior are the largest fare that any presentist has yet managed to offer and in a sense current presentist theories are not in any significant sense original theories but are mere "footnotes to Prior". But the tidbits of information offered by Prior are not enough to prevent starvation, and so I shall begin by formulating some of the basic ideas of a general presentist theory in order to have some ideas to discuss.

     Since Prior concentrated almost exclusively on logic rather than ontology, it is best to begin with his basic tense logic notions. The first significant presentation appears in his Time and Modality. Sentential tense logic, in its simplest form, adds to classical sentential logic two tense operators, P ("It was true that") and F ("It will be true that"). The sentential variables p and q take present tense sentences (e.g., "Plato is thinking") as their values. The sentence "Plato was thinking" has the symbolic form Pp, which translates as "It was true that Plato is thinking". The basic idea of sentential tense logic is to analyze past and future tenses ("was", "will be") in terms of sentential operators ("It was true that" and "It will be true that") that are attached to present tensed sentences. Present tensed sentences do not need present tense operators, since "It is true that Jane is walking" is equivalent to "Jane is walking".

A semantics for tense logic is the interpretation of the meaning of the syntactic symbols, such as Pp or Fp. Translating the symbols into English is merely a preliminary to a semantics for tense logic; we may translate "P" as "It was true that" or equivalently "It was the case that" but we still have the question of the meaning of "It was true that". Unfortunately, this translation has virtually all that has been done in the attempts by presentists to provide a semantics.

    The Prior-type version of the presentist theory may be aided and abetted by interpreting sentences in terms of a de dicto/de re contrast. If a tense occurs de dicto, it follows (we shall say) that the tensed expression ascribes a temporal property to a dictum, a proposition. (Of course, literally "dicta" are speech items but I am here using it more broadly to include propositions expressible by sentence-tokens). The sentence "It will be true that the sun is exploding" involves a de dicto occurrence of "will be" since "It will be true" ascribes a temporal property to a proposition. The property, having future truth, is ascribed to the proposition expressed by "the sun is exploding".

If a tense occurs de re, it follows that the tensed expression ascribes a property to a thing (the res) or event. The sentence "the sun will explode" involves a de re use of "will" since the tensed expression, "will explode" ascribes the temporal property, exploding in the future, to the sun.

The semantics for tense logic favored by de dicto presentists is based on the idea that all occurrences of past and future tenses are de dicto (even though some occurrences might appear to be de re) and thereby can be represented by sentential operators, such as "It was true that". According to this theory, the sentence "the sun will explode" might appear to ascribe a temporal property to the sun, but in reality it does not; it ascribes a temporal property to a proposition. "The sun will explode" means the same as "It will be true that the sun is exploding".

The de re/de dicto distinction also appears in the presentist' approach to quantified tense logic, which is about valid reasoning patterns involving tensed sentences that include the quantifiers "some" or "any".

Quantified tense logic may be formulated in at least two ways. A presentist way is based on the idea that quantifiers ("any", "some") occur only within the scope of tense operators. In the sentence, "some thing will fly to Mars", the quantifier "some" does not occur within the scope of a tense operator. But it does occur in this way in "It will be true that some thing flies to Mars".

The de dicto presentist holds that quantification over past or future particulars should occur only in the scope of tense operators. Consider the sentence "some person did exist who authored The Republic". The presentist will take this to express the same proposition as "It was true that some person authors The Republic", which has the symbolic form P($x)Gx. The quantified expression "some person" occurs within the scope of "It was true that"; this implies that "some person" does not now refer to anything (there are no past people for it to refer to), but used to refer to something, to a person that existed at the time the proposition was true.

The assumption of the de dicto presentist that temporal properties should be ascribed only to propositions also appears in the treatment of quantification over present particulars. The sentence "Some person is presently writing a book" is not interpreted as ascribing the temporal property, presently writing a book, to a person. Rather, it is taken to mean the same as "It is true that some person is writing a book", which has a present tense operator. This sentence ascribes the property of being presently true to the proposition, some person is writing a book. This de dicto interpretation of quantification is exemplified in Prior's remark in Past, Present and Future (p. 144): ". . . a quantifier preceding any such operator [i.e., any tense operator] is naturally taken to be governed by the 'It is the case that-', which is prefixable to anything we say, and therefore to range over what now exists." Thus Prior takes "somebody, about whom it is true that she is a musician, is now composing a song" to mean the same as "It is true that somebody, about whom it is true that she is a musician, is now composing a song".

The maximalist tensed theory of time, by contrast, allows quantification over past, present or future particulars to occur outside the scope of tense operators. The expression "some person" in the sentence "some person existed who authored The Republic" quantifies over all past, present and future persons. This reflects the assumption that some people exemplify pastness, some exemplify presentness and some exemplify futurity.

The maximalist theory implies a de re use of the symbols P and F. Traditional tense logic (following A. N. Prior) uses P and F only in a de dicto manner, to mean "It was true that" or "It will be true that". ("N" is often used for the present tense operator, "It is true that" or "It is now true that".) But in an expression of the symbolic form ($x)Px, "P" does not mean "It was true that" but stands for a property of x, the property of pastness. The expression translates as "Something is past". Since "P" is not here used as a sentential operator, but as a predicate, this should be marked in our symbolic notation. We may put an asterisk after P to mark the use of this symbol as a predicate. Thus we should say ($x)P*x.

    The symbol P is also used in a de re manner in ($x)[PG]x. Here the symbol P operates on the predicate G to form a more complex predicate, PG. This translates as "Something exemplifies past G-ness" or, equivalently, "Something's exemplification of G has pastness". In PG, P is used as a predicate operator. To mark this distinctive use of P, we can italicize P, so that we say ($x)[PG]x.

According to the maximalist tensed theory of time, an adequate quantified tense logic must use P (a sentential operator), P* (a predicate) and P (a predicate operator). Given these symbolic distinctions, the maximalist can allow that P is used only de dicto, since the maximalist has P* and P to express de re occurrences of the past tense.

     The distinction between de dicto and de re occurrences of tense logic symbols is partly analogous to the distinction between de dicto and de re uses of o in modal logic. The box is used de dicto in oA, where it means "It is necessarily true that A", where A is some proposition. The box is used de re in ($x)oFx, which means something is necessarily F.

A.N. Prior's rejection of the maximalist tensed theory of time is analogous to Quine's position regarding quantified modal logic. Much as Quine found problematic de re occurrences of "must be", so Prior found problematic de re occurrences of "was" and "will be". Quine objected to the realism about essential properties associated with constructions of the form ($x)oFx  (something exemplifies being necessarily F) and Prior objected to the realism about properties of pastness, futurity and presentness associated with constructions of the form ($x)P*x (something exemplifies being past).

    In Prior's case, the rejection of the realist position is in part due to his categorization of pastness, presentness and futurity as activities. Prior suggests that these temporal properties of events (if there were such properties) belong in the same ontological category as activities done by things. Prior denies that there are events "momentarily doing something called 'being present' and then doing something else called 'being past' for much longer" (p. 18, Past, Present and Future). Prior may be interpreted as suggesting that it is a mistake to categorize presentness and pastness along with such activities as running or talking, and then say that presentness and pastness (if there are such properties) are activities performed, not by things, but by events.

The maximalist may grant this point to Prior, but argue that presentness and pastness need not be categorized as activities performed by events. The maximalist may argue that "events possess temporal properties of being present or being past or being future" does not entail "presentness, pastness and futurity are activities done by events". These temporal properties, like such properties as existence or self-identity, are unusual kinds of properties and should be placed in an ontological category by themselves.

 

3 "Circumstances of Evaluation" in the De Dicto Presentist Theory

 

3a A Paradox for the De Dicto Presentist

The de dicto presentist theory of time is false if there are some true sentences whose de dicto interpretation turns them into logical contradictions. It appears there are such sentences. It is logically possible that 10 billion years ago, before any intelligent organisms evolved, there were no languages or propositions and thus no truths or falsehoods. Consider the sentence, "It is logically possible that there was a time t at which there were no truths". If "there was" and "there were" are de dicto occurrences of tenses, then this sentence says the same as "It is logically possible that it was true at time t that there are no truths", which is a logical contradiction. According to the maximalist, the sentence must instead be taken to mean that it is logically possible that some time t exemplifies pastness and having contained no truths.

It may be objected by the presentist that platonic realism is true and thus that it is necessary that there be truths at all times. The maximalist may respond that the truth of platonic realism and the falsity of nominalism are determined by metaphysics, not by logic. "Platonic realism is true" is not a logical theorem and "there were no truths 10 billion years ago" is not a logical contradiction. Thus, a purportedly valid system of logic that implies these sentences are logical truths or falsehoods is not in fact valid.

The presentist may have a second response, namely, that the sentence, "It is logically possible that it was true at time t that there are no truths", does not imply that there are truths at time t. The proposition, there are no truths, exists at present and the tense operator "it was true at time t that" does not imply that this proposition existed at time t. Rather, it implies merely that the time at which the presently existing proposition should be evaluated for truth or falsity is the past time t, and that the proposition possesses truth at this time. The past time is the circumstance of evaluation (in respect of which the proposition possesses truth or falsity) but the proposition exists in the context of its utterance, the present time.

The maximalist will say that this response depends on the intelligibility of the thesis that the proposition, there are no truths, possesses at time t the property of being true and yet does not exist (in any sense of "exist") at this time. How can a nonexistent (at time t) possess a property (at time t)? Can the familiar notion of a "circumstance of evaluation" resolve these problems?

 

3b Possible Interpretations of "Circumstances of Evaluation"

  What does it mean (semantically and ontologically) to say that the proposition, there are no truths, is evaluated as being true at time t? Does it mean that this proposition now corresponds to the situation that existed at time t? Or does it mean that this proposition does not now correspond to the situation at time t, but corresponded at the time t to the situation that existed at time t? Or does it mean something else altogether?

It cannot mean that it now corresponds to time t. For the proposition there are no truths (which is expressed by a present tensed sentence) is about the present situation, and time t is past. The proposition states that the situation of there being no truths is present, and the situation at time t is not present.

Does it mean that it does not now correspond to time t, but used to correspond to time t, that is, corresponded to time t at time t? This would mean that it exemplified the relational property, corresponding to time t, at time t. Thus the proposition's exemplification of this correspondence relation is itself part of the total situation that existed at time t. But if the proposition is true, the proposition is not a part of this situation; the proposition did not exist at time t. When time t was present, no truth and thus no true proposition existed. Consequently, when time t was present, the proposition did not exemplify the relation of corresponding to the situation at time t, since there was then no proposition to exemplify such a relation.

It appears, then, that the presentist is committed to saying that the proposition's having corresponded to time t first came into existence after time t was past. But this amounts to the coming into existence of a past event, an event that never was present. (We may use "event" or "state" in a broad sense to encompass abstract objects' exemplification of properties as well as concrete objects' exemplification of properties.) Thus we have an event E, such that E is past but never was present. But that is an implicit logical contradiction, since "is past" is synonymous with, and expresses the same concept as, "was present".

   Furthermore, we are committed to past events on this analysis, which is precisely what the presentist wants to avoid. The proposition's standing in the relation of correspondence to time t is a past, abstract event. According to J. Kim, an event is an object exemplifying a certain monadic or relational property at a time. Kim had in mind concrete objects, but there can be abstract events if there are abstract objects that change their properties or relations at different times. Accordingly, we do not have a presentist theory.

   It may be said we still have a concrete presentist theory, namely, that the only concrete items that exist are present, and that this may be sufficient to satisfy the presentist. But even this is not true, since correspondence is a relation between a relevant proposition and the concrete state of affairs it is about. If the state of affairs the proposition is about is time t and if the correspondence relation obtains at time t, then the relatum, t, also exists. Since t is past, we have a concrete state of affairs that exemplifies pastness.

 

3c. Indexed Propositions

   So far I have argued that de dicto presentism is unable to deal with an unusual sort of case, namely, the logical possibility that there was a time t at which there were no truths. But if presentism is false, surely it can be refuted without having to resort to esoteric paradoxes of this sort. Presentism should break down for any normal proposition. Let us pursue this new line of criticism.

   The line of criticism can be developed if we give a precise analysis of the phrase "evaluating a proposition at a circumstance". Let us first consider the analyses that ought to be given to the phrases "circumstance of evaluation" and "context of utterance" in the semantic interpretations of modal logic. If David Kaplan utters "I am here now" in a certain context, he expresses the proposition (ignoring the tense), David Kaplan is in Santa Barbara in 1997. This is a singular proposition; if we accept Kaplan's account of singular propositions, we may say this proposition includes Santa Barbara, 1997 and David Kaplan as constituents. But suppose we evaluate it in a possible circumstance in which Kaplan does not exist. According to Kaplan-type theories, this should not mean that the proposition exists in that circumstance and is false. If the proposition exists in that circumstance, Kaplan exists in that circumstance, since he is a part of the proposition. But that contradicts the supposition that Kaplan does not exist in that circumstance. But if the proposition does not exist in that circumstance, what does it mean to say that the proposition is evaluated as false in or at that circumstance?

      I believe the modal logician is considered a modally indexed proposition, viz., Kaplan exists in Santa Barbara in 1997 in a merely possible world W. This proposition exists in the actual world and is false, since (we are supposing) Kaplan does not exist in the world W. Further, it is necessarily false, since world-indexed propositions have their truth values necessarily.

 We need a concept of an indexing evaluation, which is a relation between an non-indexed proposition and an indexed proposition. If we take, Socrates is talking, we can index it temporally and evaluate the resulting indexed proposition, Socrates is talking at time t. And if we evaluate the modally non-indexed proposition, Kaplan exists in Santa Barbara in 1997, we consider the different proposition that contains the modal index in which we are interested, e.g. the world W, and we consider Kaplan exists in Santa Barbara in 1997 in W.

   This enables us to explain the metaphorical statement that the proposition is true "in" or "at" the circumstance of evaluation, even though the proposition does not exist in the circumstance. On page 495 of THEMES FROM KAPLAN, Kaplan says:

 

"(3) I do not exist.

 

Under what circumstances would what I said [the singular proposition expressed by the sentence-utterance] be true? It would be true in circumstances in which I did not exist."

 

Likewise, Joseph Almog says: "only after the proposition gets off the ground can we go on to evaluate it, find its truth value, in various loci of evaluation." (Journal of Philosophy, April 1986: p. 220.)

 

   How can the proposition be true in the circumstances of evaluation if it does not exist in these circumstances? If a proposition does not exist in the world W, but nonetheless is true in W, then in W a nonexistent (the proposition) possesses a property (being true). But how can a nonexistent possess a property?  It can't. So it may then appear that Kaplan, Almog and others are committed to holding the proposition exists in the circumstances. In fact, however, that is not their view ((contra my mistaken interpretation of Kaplan in Ethical and Religious Thought in Analytic Philosophy of Language, Yale University Press, 1997, in which I argued that Kaplan's theory implied that propositions exist in the circumstances of evaluation.) Kaplan holds that the proposition does not exist in the circumstance of evaluation, or at least need not exist in the circumstance (Kaplan, personal communication). Kaplan's view on this matter is most clearly expressed in a passage in his 1989 essay "Afterthoughts". He writes there is a distinction

 

"between what exists at a given point and what can be 'carried in' to be evaluated at that point, though it may exist only elsewhere. My 'Circumstances of Evaluation' evaluate contents that may have no native existence at the circumstance but which can be expressed elsewhere and carried in for evaluation". (Themes from Kaplan, p. 613).

 

I suggest that Kaplan's spatially metaphorical talk of a content being "carried in for evaluation" at a circumstance should be literally analyzed as meaning that the content p is "carried in" to the circumstance C in the literal sense that we turn our attention from that content p to a different content p* that is p as indexed in terms of C. In other words, we turn our attention from p to p-at-C (where the content p* is p-at-C) and evaluate the truth value of p-at-C. If C is a possible world, then p is modally indexed and p-at-C is in every case a necessary truth. Each world-indexed proposition, such as Hume dies in childbirth in the world W2, is necessarily true. This is not the familiar theory of context of use/circumstance of evaluation that is widely employed and I am not suggesting that this is what Kaplan had in mind. Rather, I am suggesting it is most plausible way of literally explaining "evaluating a proposition at a circumstance". Given this, the standard symbolism needs to be different. Where F is the true value of false and V the evaluation function, we have, instead of V(p,w) = F, the symbolic formula V(p*) = oF, where p* is the proposition formulated by world-indexing the proposition p.

    The context of use/circumstance of evaluation distinction must be analyzed in cases of temporal evaluations in different ways to my analysis of modal evaluations. Consider the singular proposition Kaplan has not yet written "Demonstratives", which is transiently false. Suppose we want to evaluate this proposition at the year 1864. It comes out as true. But this means that a different proposition, a tenseless proposition, Kaplan had not yet written "Demonstratives" in 1864, is intransiently true. This is the same proposition as Kaplan's writing "Demonstratives” is (tenselessly) neither simultaneous with nor earlier than 1864. Just as modally indexing a contingently truth-valued proposition turns it into a different, necessarily truth-valued proposition, so temporally indexing a tensed, transiently truth-valued proposition turns it into a different, tenseless and intransiently truth-valued proposition.

       But there is an important different between modal and temporal indexing evaluations, since a tensed proposition can be indexed in a tensed way, so that it is turned into a different but tensed and transiently truth-valued proposition. The tensed proposition Kaplan has not yet written "Demonstratives" can be indexed in a tensed way when it is evaluated for truth or falsity in 1864. There is an evaluation of a temporally indexed proposition, namely, It was 1864, 133 years ago, and at this time Kaplan had not yet written "Demonstratives". This proposition is now true.

  Once we analyze the phrase "circumstance of evaluation" in terms of an "indexing evaluation", we can see clearly how the presentist theory collapses. We now evaluate the temporally indexed proposition, It was 1864, 133 years ago, and at this time Kaplan had not yet written "Demonstratives" and find it is now true. It corresponds to a concrete state of affairs one of whose parts is the past year 1864. On a relational theory of time, this year is a set of events; the concrete events included in this set are concrete parts of the temporally indexed proposition. On a substantival theory of time, this year is a substance or concrete particular that is contingently occupied by the events in this set.

    If 1864 is both past and a part of a concrete state of affairs to which the temporally indexed proposition now corresponds, then 1864 exists in some sense; it now belongs to the past. It exists at least in the sense that it presently has the property of being past by 133 years; this year did not formerly have the property of being 133 years past, and it will not have this property in the future; rather it now has this property. Further, this year presently has the property of standing in part of a correspondence relation to the true proposition. It follows that the de dicto presentist theory is false.

    The same applies for general propositions, which do not include concrete things as constituents. Suppose "1864" expresses a sense (the year that is 1,863 years after Jesus's birth) and that "Kaplan" expresses the sense, the author of "Demonstratives". In this case, the phrase "It was 1864, 133 years ago" means that the descriptive sense, the year that is 1,863 years after Jesus's birth, was satisfied 133 years ago. But this affects nothing essential in my critique of the presentist, since it is still the case that this proposition (which exists now) corresponds now to a concrete state of affairs that existed 133 years ago and that includes the year 1864 as one of its parts. The point is that the temporally indexed proposition corresponds to a past concrete state of affairs. It is logically irrelevant if there are singular propositions that include past or future concrete existents as parts. All that is relevant is what stands in a correspondence relation to a proposition, be the proposition singular or general. Even if we assume nominalism and hold there are no propositions but merely sentence-tokens and the truth-makes of these sentence-tokens, the critique remains unchanged. Let us consider only the true, tensed sentence-token, "It was 1864, 133 years ago, and at this time Kaplan had not yet written 'Demonstratives'". This sentence-token corresponds to a state of affairs that includes past concreta as parts. Thus, the criticism of the presentist theory is logically independent of the theory of singular propositions and even of the theory propositions of any sort, since it suffices to state the case in terms of a present sentence-token correspond to a concrete state of affairs that includes past concreta.

 

3D. A Presentist Theory Based on Plantingian "States of Affairs"

   Note that I am using "state of affairs" in the sense explained in Language and Time, where I distinguished it from Plantinga's use of "state of affairs". For Plantinga, a state of affairs is a permanently existing abstract object that is similar to a proposition in its structure and parts. It contains no concrete objects among its parts. A Plantingian state of affairs exists and obtains or else it exists and does not obtain (e.g., Spiro Agnew's being president exists but does not obtain). This is analogous to a proposition, which exists and is false or exists is true. A tensed state of affairs permanently exists, but obtains transiently. Plantinga's theory of tensed states of affairs is developed in Craig’s ontology for presentism in Craig’s book The Tensed Theory of Time (Kluwer, 2000).

    By contrast, I use "state of affairs" to mean something that (in the relevant cases) consists of a concrete particular or particulars as exemplifying some n-adic property. Perhaps "situation" or "complex event" could be substituted for my usage of "state of affairs". In Language and Time (pp. 156-158) I argued that Plantinga's "states of affairs" are indiscernible from his "propositions" and are identical with them.

   William Lane Craig accepts and develops Plantinga's theory of abstract states of affairs and their (alleged) distinction from propositions. I have argued that the Plantinga-Craig theory of abstract states of affairs is false (see Smith, Ethical and Religious Thought in Analytic Philosophy of Language: New Haven, Yale University Press, 1997, Part Two). But if we suppose, counterlegally, that there is a proposition/state of affairs distinction of the Plantinga-Craig sort, would that allow for a logically coherent presentist theory?

   If we adopt the Plantinga-Craig theory, we may say that the sentence-token "Hegel used to be alive" expresses the true proposition Hegel used to be alive, and relates in a relevant way to the obtaining state of affairs Hegel's having been alive. This Plantingian-Craigian state of affairs is an abstract object and consists only of abstract objects, namely, Hegel's individual essence, the property of being biologically alive, and perhaps something else.     But what else? There's the rub. If it consists of nothing else, this state of affairs is a tenseless state of affairs, namely, Hegel's [tenselessly] being alive, and its obtaining is not sufficient for the past tensed sentence-token, "Hegel used to be alive" or the proposition it expresses, Hegel used to be alive, to be true. If the tenseless state of affairs obtains, it obtains intransiently and thus at times when the past tensed proposition is false (e.g., before Hegel was born or while he is still alive).

   The Plantingian-Craigian state of affairs thus must include some temporal component that makes it a past tensed state of affairs. What could this be? The only candidate that comes to mind is the property of being past, such that the state of affairs is Hegel's being alive having the property of pastness. But if this past tensed state of affairs now obtains, what concreta suffice to make it obtain? If there is nothing sufficient to make it obtain, and it obtains nonetheless, we have a contradiction; if nothing suffices to make it obtain, that fact suffices to make obtain the negation of this state of affairs. Analogously, if there are no concreta that are the truth-makers of the proposition Hegel used to be alive, then this proposition is true with nothing sufficing to make it true; this is an implicit contradiction, since the absence of a truth-maker suffices to make true it is not true that Hegel used to be alive.

    It may be said that the concreta consisting of Hegel's bones suffice to make presently obtain the state of affairs of Hegel's being alive having the property of pastness. These bones would presumably also be the truth-maker of the proposition, Hegel used to be alive. But this cannot be the case, since the state of affairs and proposition would still obtain or be true if the bones ceased to exist. Furthermore, the issue of truth as correspondence remains unsolved, since Hegel used to be alive does not correspond to a present situation consisting of a few bones. Such a proposition is there presently are bones that used to belong to Hegel. The proposition is about Hegel, not his bones. If truth is correspondence, then truth-makers are correspondents of propositions.

   If it is said that only what presently exists makes this state of affairs obtain or the proposition true, then it is false that the proposition corresponds to something past and it is false that the state of affairs obtains by virtue of something past. Rather, the proposition corresponds to something present. But if it corresponds to something present, it is about something present, and thus is not about something past, namely, the formerly alive person Hegel. Likewise, if the state of affairs obtains by virtue of something present possessing some property, then the state of affairs does not bear an obtaining-making relation to anything past and is not a past tensed state of affairs. It is a present tensed state of affairs.

  Furthermore, the proposition Hegel used to be alive cannot be about a present abstract object. If it is said that the proposition corresponds to the presently existing and obtaining abstract state of affairs, Hegel's having been alive, then the proposition is about this state of affairs and is not about Hegel. That is, it is about an abstract object, a Plantingian-Craigian state of affairs, and is not about a concrete object, Hegel, and his being biologically alive. But manifestly "Hegel used to be alive" is not about an abstract object, but a person, a concrete object.

    The proposition about the presently existing and obtaining abstract object is the proposition, the presently existing abstract state of affairs, Hegel's having been alive, presently obtains. But this is different than the proposition Hegel used to be alive, which is not about a presently existing object.

   If the proposition is now true and is about Hegel, and truth is correspondence, then there must be a correspondence relation to a past concretum, namely, Hegel and his past possession of the property of being biologically alive. The same holds for the Plantinga-Craig state of affairs; the abstract state of affairs bears an obtaining-making relation (analogous to the truth-making relation) to whatever it is that makes it obtain, and what makes it obtains is some past concretum, Hegel, having possessed the property of being alive. It follows that the presentist theory is false if the Plantinga-Craig theory of states of affairs is true.

          In any case, this discussion in a sense is otiose, given what I have argued in Language and Time and Ethical and Religious Thought in Analytic Philosophy of Language, namely, that there can be no such thing as an abstract state of affairs in the Plantinga-Craig sense and that the concept of such a state of affairs, and of its distinction from a de dicto proposition, is logically incoherent.

   I conclude that for these several reasons, Craig’s version of the presentist theory does not succeed. (Plantinga appears to hold a tensed theory of time, but appears noncommittal about whether he holds a presentist or maximalist version.)

 

4 De Dicto Occurrences of Tenses Imply De Re Occurrences

A characteristic feature of the de dicto presentist theory, espoused by Prior, Craig and others, is that it denies not only the existence of the past and future, but also claims that there is no monadic property of presentness that is exemplified by anything concrete. The de dicto presentist may allow that there is a monadic property of presentness, but he will insist it is a second order property, belonging to presently true propositions.

      A demonstration of the falsity of this idea will lead us to another argument for the concrete existence of the past and future.

  The idea that all occurrences of tenses are de dicto leads to a certain  semantic interpretation of such present tensed sentences as "the moon is bright". According to the de dicto interpretation, this sentence does not report that an event, the moon's exemplification of brightness, has presentness. There is no first order property of presentness and no event; there is only the thing, the moon, exemplifying brightness, and the proposition, the moon is bright, exemplifying being presently true.

This presentist balloon deflates as soon as we ask: when does the moon exemplify brightness? If "exemplify" is tenseless, then there is no answer, and the analysis is faulty, since the present tense sentence "the moon is bright" implies the moon is now exemplifying brightness. The sentence, "the moon is (tenselessly) bright" stands on a par with "There are (tenselessly) dinosaurs" in terms of its temporal information, namely, there is no temporal information.

   But if "exemplify" is present tensed, then we must ask: what is the semantic content of the present tensed aspect of this verb? The present tense must have some semantic content or meaning, since the present tense conveys some temporal information and thus is not a meaningless syntactic device like "It" in "It is raining". Further, to what ontological category does this temporal information belong?                

According to the de dicto theory of tenses, the semantic category of the present tense is "Sentential Operator" (the present tense has the same semantic content as "it is true that") and the relevant ontological category is "Second Order Property"; the present tense ascribes the property of being presently true to a proposition. Of course, no presentist has actually said this, but this is because presentists are mum when it comes to any details about their ontology. (If one says nothing, one can't be refuted. The only problem is that one then has no theory. I am here motivated by the spirit of charity to try and supply the de dicto presentist with the minimum essentials of an ontology.)

    This presentist theory implies that if the sentence "the moon is bright" is true, we are ontologically committed to (a) the proposition, the moon is bright, (b) the proposition's exemplification of the property, being presently true, (c) the thing, the moon, and (d) this thing exemplifying a property of brightness.

The maximalist may well object to this theory that "exemplifying" in (d) is present tensed, reflecting the fact that the thing presently exemplifies a property of brightness. According to the maximalist, the thing's present exemplification of brightness (rather than a timeless, past or future exemplification of brightness) is the ground for the proposition's being presently true. It is the concrete state of affairs that makes the proposition true. (Here I am again using "concrete state of affairs" in my sense, to refer to a concrete object's [e.g., a moon's] exemplification of an n-adic property or properties.)

The presentist cannot say that "exemplifying" in (d) is tenseless, since the moon's (tenselessly) being bright is not a sufficient condition of the moon now being bright. The moon's tenseless brightness implies only the moon is bright at some time; that time need not be the present time.

But if the presentist admits that "exemplifying" in (d) is present tensed, her analysis is circular. She is analyzing the ontological commitments of "The moon is bright" as the (concrete state of affairs consisting of) moon being bright, where "being" is present tensed. This does not yet give us a semantic or ontological analysis of the present tense.

Perhaps the presentist will say that the present tense of "exemplifying" in (d) has the semantic content of "It is true that". This could mean that the semantic content of the present tense of "exemplifying" is the property of being presently true possessed by the proposition, the moon is bright. But this cannot work for two reasons.

First, it would make the first level existents (the thing and its first order property), consists of a thing and an exemplification relation to brightness, such that this relation does not contain or possess anything that corresponds to the present tense. This relation is named by a tenseless use of "exemplification". But this means we are left, on the level pertinent to first order properties, with a thing and its tenseless exemplification of brightness, and we have seen that this cannot be the truth-maker of "the sun is bright".

Thus the de dicto presentist theory appears to be implicitly self-contradictory. It claims that propositions that can only be made true by present first order states of affairs are made true by first order states of affairs that are not present.

The second problem with the de dicto analysis of the ontological commitments of "the moon is bright" is its analysis of the proposition and the second order property of being presently true. The proposition, the moon is bright, exemplifies the property of being presently true. But what does "exemplifies" mean? Surely, it is present tensed. If so, it would mean "it is true that". Thus, the analysis of "the moon is bright" ends up with the proposition, It is true that it is true that the moon is bright. Since this proposition exemplifies being presently true, we have an infinite regress.

   But this regress is benign and I see no problem with it. (Even apart from considerations of time, for any proposition p, there is a benign regress of the form ". . . it is true that ... it is true that it is true that p").

The second problem is instead this: if an abstract entity, a proposition, can exemplify a temporal property, why cannot a concrete item, such as a thing or event, exemplify a temporal property? There is no relevant difference between abstract and concrete items that makes the former alone capable of exemplifying temporal properties. Indeed, the metaphysical tradition since Plato have argued just the opposite: abstract objects do not have temporal properties (they exist timelessly) and only concrete items have temporal properties. The presentist has pointed to no relevant difference between abstract and concrete objects that makes the former alone capable of exemplifying temporal properties. This second problem with the idea that presentness is not a first order property is in essence one of logical arbitrariness; the first problem with this idea is one of implicit self-contradiction.

    At this point I have argued that there are concrete items in the past or future to which some propositions correspond (which refutes the "presentist" aspect of de dicto presentism) and I have argued that temporal properties such as presentness are first order properties (which refutes the "de dicto" aspect of de dicto presentism). The next step is to clarify the implications of this criticism of de dicto presentism, namely, that there exist past, present and future concrete things and events.

 

 

5. Is it a Contradiction that: There exists what no longer or not yet exists?

 

     According to the de dicto theory, the ontological commitments of the sentence "Plato had been alive" are merely the proposition, Plato is alive, and the proposition's property of having been true. The maximalist tensed theory of time requires further ontological commitments from the sentence "Plato had been alive". This sentence commits us to a past thing, viz., Plato, and a past event or state, namely, Plato's being alive. This maximalist conclusion is based on the correspondence theory of truth.

    Correspondence is a symmetrical property. (It is a dyadic property and thus a relation.) If the proposition, Plato is alive, had been true, then this proposition exemplifies past correspondence to Plato's being alive. Since correspondence is a symmetrical relation, this implies that some event, Plato's being alive, exemplifies past correspondence to the proposition, Plato is alive. The reason this event exemplifies past correspondence is that the event exemplifies pastness. Since Plato is a part of this past event, Plato exemplifies pastness. It follows that some events and things are past.

This maximalist conclusion implies that the temporal property pastness is de re, since it is a property of a thing, Plato, and of an event, Plato's being alive. There was something, Plato, over which we can now quantify; it is the case that ($x)P*x. The same results hold for propositions that will correspond to something exemplifying some property.

Presentists seem to find troubling or even abhorrent the idea that past or future things or events presently possess properties. Is this due to metaphysical angst or logical insight?

     Consider the formula ($x)P*x. Does not ($x) in this formula convey that there presently exists an x? And does not P*x mean that this x is not presently existing but is past? If so (the presentist may argue), the symbolic representation of de re occurrences of tenses turns true sentences into contradictions.

But the maximalist may respond that ($x) has at least three different meanings in an adequate quantified tense logic, corresponding to three different senses of "exists".

 

(1) If "exists" is present tensed, it can have one of two senses. In one sense, it is logically equivalent to "has the property of presentness", so that "Mount Everest exists" is logically equivalent to "Mount Everest has the property of presentness".

 

(2) If "exists" is present tensed, it can also be equivalent to "presently possesses some property". Something that is past or future exists in this present tensed sense, since if something is now past, it presently possesses the property of pastness. Likewise, if Jones now has the property of having been born 500 years ago, Jones presently possesses the property of having been born 500 years ago. Jones exists in this second present tensed sense of "exists", but he does not exist in the first present tensed sense of "exists".

 

(3) If "exists" is tenseless, it is in effect disjunctively tensed; that is, it is equivalent to "has existed, exists or will exist", where the middle "exists" is equivalent to "has the property of presentness". If we say "Socrates exists", we mean that Socrates either has existed, or exists (presently), or will exist. The phrase "has existed" is logically equivalent to "was present" and "will exist" is logically equivalent to "shall be present".

The maximalist argues that this threefold distinction shows that there is no logical difficulty in the idea that some past or future item presently possesses a property.

   For example, the maximalist may note that "some past thing presently has the polyadic property of being remembered" is not a logical contradiction. Nor can it be turned into a logical contradiction by substituting synonyms for synonyms. Indeed, the maximalist continues, an analysis of the concept expressed by "remembering" implies the presentist theory is false. Remembering is not a relation between a present person and a present image. If it were such a relation, it would follow that what is being remembered is in every case an image that exists simultaneously with the act of remembering. But this is an analytic contradiction, since it is a part of the logic of "remembers" that what is remembered exists earlier than the act of remembering. Remembering a thing is a three-termed relation: a person remembers a past thing by forming a present image of that past thing. The "of" expresses a relation in which the present image stands to the past thing. (Note that "x remembers y" expresses a different concept than "x seems to remember y". "x seems to remember y" is consistent with "y never existed and what seems to be the case to x is not (or never was) the case". The verb "remembers" is a verb of success and "x remembers y" is equivalent to "x seems to remember y and this seeming is true".)

    The maximalist may elaborate that there will appear to be a difficulty about non-present items presently possessing properties if one is mistaken about the sorts of properties a past or future item can possess. Since Plato does not now exist, Plato does not now possess the properties of walking, breathing, writing, thinking, etc. These properties can only be possessed by Plato when he is present. But Plato now possesses the properties of being past, of being referred to by the name "Plato", of being thought about, of being located earlier in time than Descartes, etc. Further, Plato now possesses the properties of having walked, having written The Republic, having been alive, having been a human, etc., all of which can be expressed in a symbolic notation of the form ($x)[PG]x, where (Ex) can be taken as tenseless or as present tensed in the second sense distinguished by the maximalist.

   Wolterstorff, Craig, Levison, Prior, Christensen and many other presentist theorists have argued that it is plausibly or obviously true that "only what presently exists possesses properties". Each of their attempts to make this slogan seem plausible, however, is based on a multiple equivocation upon "exists", switching from "exists" in one of its present tense senses to "exists" in the other of its present tense senses to "exists" in the tenseless sense.

  

6. Oaklander and McTaggart's Paradox

Is there a paradox lurking here for the maximalist version of the tensed theory of time? Both presentists and tenseless theorists think an argument involving McTaggart's paradox suffices to refute the maximalist tensed theory. But they are wrong, since all extant arguments of this sort are based on a premise the maximalist theory rejects, namely, that events simultaneously or timelessly are past, present and future. Not a single proponent of the "McTaggart's paradox argument" against the maximalist theory has ever succeeded--or even attempted--to deduce a contradiction from any thesis that actually belongs to the maximalist theory. (I provided textual evidence for this claim in Language and Time, pp. 169-178.)

   There is an exception to this tradition. L. Nathan Oaklander has recently endeavored to deduce a contradiction from theses actually espoused by tensed theorists. In one of these articles, his 1996 article in Synthese, "McTaggart's Paradox and Smith's Tensed Theory of Time", he endeavors to deduce a contradiction from the theory espoused in Language and Time, and in my essays in Oaklander and Smith (eds.), The New Theory of Time. I shall examine Oaklander's interesting argument.

      L. Nathan Oaklander claims my account is implicitly self-contradictory.  Oaklander argues as follows:

If events are present, past or future, then (to avoid McTaggart's paradox) the events must have these properties successively. It is the case that

 

(1) E is present, will be past and has been future, or

    E is past, and has been future and present, or

    E is future and will be present and past.

 

Oaklander notes that (regarding the second disjunct) the attribution of futurity and presentness to E in the past is a contradiction, unless it is specified that they have them successively or at different times in the past. This is correct; the second disjunct should be taken as meaning that "E is past and has been future and later was present". (It is not part of my theory to analyze later or other B-relations in terms of tensed properties.) This could be put more complexly by distinguishing different degrees of pastness and futurity. For example, it may be true that (using subscripts to indicate different cases of the inherence of a property):

 

(2) Being one hour past presently inheres₀ in E, and being two hours past presently inheres₁ in the inherence₂ of futurity in E, and being one hour past presently inheres₃ in the inherence₄ of presentness in E.

 

Oaklander says the following: "For if E was future earlier than E was present, then on Smith's analysis that would imply that, say, being past by two hours presently inheres₁ in the inherence₂ of futurity..." (I have substituted my subscripts).

 

Oaklander claims this implies that:

 

(3) The state S₁ (being past by two hours presently inhering₁ in the inherence₂ of futurity of E) is EARLIER THAN the state S₂ (being past by one hour presently inhering₃ in the inherence₄ of presentness in E).

 

Oaklander says this contradicts my claim that the relation of earlier can obtain between two events only if at least one of the events is not present. However, (2) does not imply (3) and (3) is no part or implication of the tensed theory of time I defended. (3) is Oaklander's invention. The theory I espoused implies that states S₁ and S₂ are SIMULTANEOUS. When E's futurity is two hours past, E's presentness is one hour past. If E was present one hour ago, then E was future two hours ago; presentness inheres in E's being one hour past and (simultaneously) presentness inheres in E's being two hours in the future.

Phrased in terms of (3), we substitute "SIMULTANEOUS WITH" for "EARLIER THAN".

Oaklander's argument rests on an invalid inference. The valid inference from (2), about the relation of being earlier than, is instead to conclusions such as this: The relation of earlier than obtains between S₃ (being past by one hour presently inhering₀ in E), and S₄ (being past by two hours presently inheres₄ in E). Equivalently, the presentness of E's being past by two hours is a state that obtains one hour later than the state of the presentness of E's being past by one hour.

Oaklander's second objection is that if an inherence of a property F in something (perhaps another inherence relation or tie) exists now, then there must also exist now a term in which the property F inheres. But this principle, accepted by many philosophers, including many defenders of presentist theories, is false. It is based on a fallacy of equivocation of "exists". If "exists" is used tenselessly, it means "existed, exists or will exist [or has timeless existence]". In this tenseless sense, something must exist in order to possess a property, for if it does not exist, there is literally nothing there to possess a property. But if "exists" means "is present", the principle is immediately implausible. It is true that the events of the year 1996 are earlier than the events of the present moment; this implies that the 1996 events presently exemplify the relation of being earlier than the events that are now present. But the 1996 events are now past; they no longer exemplify presentness. But it is precisely because these events do not now exemplify presentness (or "existence" in the present tensed sense) that they now exemplify being earlier than the events that do now exemplify presentness. Further, it is precisely because events do not "exist" in the present tense sense that they can stand in the relation to me of being remembered by me.

In sum, "only what exists can possess properties" is plausible if "exists" is used in a tenseless sense, but it is implausible if "exists" is used in a present tensed sense.

    I will conclude that the different notions of existence implied by the maximalist tensed theory of time allows the long-discredited theory of "degrees of existence" (espoused by philosophers from Plato to the British Idealists of the late 19th and early 20th century) to be revived, although with a different sense given to the phrase "degrees of existence".

    Being presently present is the highest degree of existence. Being presently past and being presently future by a merely infinitesimal amount is the second highest degree of existence. Being presently past by one hour and being presently future by one hour are lower degrees of existence, and being presently past by 5 billion years and being presently future by 5 billion years are still lower degrees of existence. The degree to which an item exists is proportional to its temporal distance from the present; the present, which has zero-temporal distance from the present, has the highest (logically) possible degree of existence. These degrees are quantifiable in terms of their inverses, degrees of nonexistence. The present has a zero degree of nonexistence. What is one second past has a one second degree of nonexistence, and what is two seconds past has a greater degree of nonexistence, namely, a two second degree of nonexistence. This theory is coherent unless one misinterprets it by assigning a different meaning to "degree of nonexistence" than I have assigned it.

   That existence is degreed explains our phenomenological experience.

There is a difference of degree and not of kind between the present and what is no longer present or not yet present. This is evinced by the fact that our present mental state includes temporal parts that are past by 1/millionth of a second, etc., and this small degree of pastness is such a high degree of existence that we cannot experientially distinguish it from present existence, 100% existence. It is arguable that these degrees of existence are immediately given in our phenomenological experience, which is evidence for them apart from the semantic and ontological arguments I have given here and elsewhere.

 

7. Peter Ludlow’s Reductive Theory of Presentism

    Peter Ludlow advances a reductive theory of presentism in Chapter Ten of his Semantics, Tense, and Time [1999]. This reductive theory eliminates the problems of the de dicto theory and other versions of presentism I discussed in earlier sections. However, before I examine Ludlow’s reductive theory, I shall first discuss his preliminary theory, the theory of de dicto presentism (not Ludlow’s term) in Chapter 7 of his book, and show how his reductive presentism can resolve the problems with this and other theories of de dicto presentism.

      Ludlow outlines a certain version of what I have generally called “de dicto presentism”. Ludlow writes:

 

  “ . . .  the A-theory can treat PAST as an indexical predicate that holds of a proposition-like object, effectively displaying the indexical sense of the past-tense morpheme on the right side of the T-theory axiom:

(1)

(a). Val(x, PAST) iff x was true.” [p. 97]

 

By a “proposition-like object” Ludlow means a proposition that changes or can change its true value. The x in (1a) is a proposition and it has the “indexical predicate” that Ludlow calls “was true”. So far, this is a version of de dicto presentism. Note that “was true” is considered as a predicate of propositions. This conforms to my earlier statement that Prior’s operators, “It was the case that” (which means“ It was true that”) are logically equivalent to alethic properties of sentences or propositions. Consider the analogy with the modal case: “It is necessarily true that four equals two plus two”. Here the modal operator “It is necessarily true that” is equivalent to a predicate of the proposition expressed by “four equals two plus two”, the predicate “is necessarily true”. Thus “It is necessarily true that four equals two plus two” is logically equivalent to “Four equals two plus two is necessarily true”. (Of course we are here talking about the de dicto modalities; it is now a commonplace in modal logic that de dicto modalities are not equivalent to de re modalities, which I have not been discussing in the above sentences.) Likewise, we can agree with Ludlow, who gives a semantics for Prior’s tense logic “that is consistent with Priorian metaphysics” [199: 100] that the predicate “was true” is equivalent to the operator “It was true that”. In other words,  “It was true that Alice is sitting” is logically equivalent to “Alice is sitting was true”. This is how the de dicto presentist analyses “Alice was sitting”. We agree with Ludlow that “was true” is a predicate of propositions. Ludlow symbolizes this as follows: “Val (x, PAST) iff x was true” [1999: 100] The important point to notice here is that x is the proposition expressed by a token of “Alice is sitting” and ”was true” is a predicate that applies to this proposition. Ludlow holds that predicates, which are linguistic items, associate tokens of properties with the “semantic values” of the predicates, in this case the proposition x, so that “was true” associates a property-token with the proposition expressed by “Alice is sitting”. Before I explain Ludlow’s theory in more detail, let me pause to make a few general observations.

 The de dicto presentist theory may be construed as holding that either properties or tokens of properties expressed by “was true” are exemplified by propositions. What is expressed by “Alice is sitting” is an operand for the operator “It was true that” and is truth-vehicle that has the predicate “was true”. (Some presentists may wish to say, and sometimes do say, that the sentence-token “Alice is sitting” is the operand or truth-vehicle, rather than the proposition expressed by a sentence-token.) Note that there are no further candidates for operands other than propositions or sentence-tokens. For example, it violates the logical law of the indiscernability of identicals to claim that there are “facts” or “states of affairs” (conceived as abstract objects) in addition to propositions, for such abstract states of affairs are indiscernable from propositions, as I argue in [1993: 156-158]. This is a criticism of Plantinga [1974] and Craig [2000a]; Ludlow does not adopt an “abstract state of affairs” versus “proposition” distinction and holds a view that is similar in this respect to my own.

Let us see now why Ludlow’s preliminary version of presentism, a de dicto presentism, motivates a move to Ludlow’s subsequent reductive presentism in Chapter 9 of his book. If “was true” and “will be true” express or refer to property-tokens of propositions, then our discussion of de dicto presentism would apply to this theory. This can be seen if we distinguish what Ludlow calls “the semantic value” of a linguistic predicate from its sense. The semantic value of "is red" as tokened in a sentence-token is not the class of red things but the particular that is attributed the predicate in that sentence-token. The sentence-token "This blanket is red" is such that the semantic content of "is red" is identical with this particular blanket. The use of the phrase “semantic value” may seem to some that Ludlow is saying that predicates refer to their extensions, such as this blanket. But this is not Ludlow’s position. Ludlow distinguishes the sense of a predicate from its referent. Let us consider the predicate (or at least the verb phrase) "is bald". Ludlow makes three points about predicates in general that I shall apply to this verb phrase:

 

1. When I say, "Shelly is bald" the semantic value of "is bald" is Shelly.