THE INFINITE REGRESS OF TEMPORAL ATTRIBUTIONS by Quentin Smith

Originally Published in: The Southern Journal of Philosophy (1986) Vol. XXIV, No. 3

The idea that presentness, pastness and futurity are attributes of events is supposed to entail a vicious infinite regress of tenseless predications. This belief is not only held by McTaggart, its first advocate, but also by most 20th century philosophers of time, including both tensers and detensers. The widely adopted solution to this problem is to deny the premise that presentness, pastness and futurity are attributes of events. The tensers argue that time does consist of presentness, pastness and futurity, but that these are not attributes of events.[1] The detensers deny that presentness, pastness and futurity are real aspects of time, and maintain that time consists only of relations of simultaneity, earlier than and later than.

The purpose of this paper is to challenge this dogma of 20th century philosophies of time and to show that the idea that presentness, pastness and futurity are properties does indeed entail an infinite regress, but that this regress is neither vicious nor constituted of tenseless predications (cf. Section One). I then argue that the various attempts to show that presentness, pastness and futurity are real but are neither attributes nor regressive are unsuccessful (cf. Section Two). Finally, I indicate that temporal attributes are not unique but share their infinitely regressive character with other reflexive properties (cf. Section Three).

1. Mc Taggart s’ Paradoxical Interpretation of the Infinite Regress of Temporal Attributions

“McTaggart’s paradox” is not in truth the infinite regress of temporal attributions, but his (and his critics’) interpretation of this regress. That the regress in reality is logically unproblematic can be made apparent through an examination and critique of McTaggart’s theory.

The following levels of temporal predication are implied in McTaggart’s theory.[2] (Tenseless copulas are indicated by parentheses.)

The first level of temporal predications applies to events; every event (is) present, past and future. Since presentness, pastness and futurity are incompatible predicates, they cannot belong to the same event simultaneously, but successively. In tensed language, this means that the event is present, will be past and has been future, or that it is past, and has been future and present, or that it is future and will be present and past. The import of these sentences is made explicit in more complicated tenseless sentences; for example, the statement that ‘the event is present, will be past and has been future’ means that ‘the event (is) present at a moment of present time, (is) past at some moment of future time, and (is) future at some moment of past time’. It is tenseless sentences of the latter sort that make explicit the nature of temporal predications on the first level.

The second level predications can be specified if it is pointed out that each of the moments of time introduced on the first level (is) present, past and future. For example, in the statement, ‘the event (is) present at a moment of present time’, the moment of time referred to (is) not only a present moment, but (is) also a past and future moment. Since it is contradictory to assert that the moment (is) present, past and future simultaneously, it must be asserted instead that the moment (is) present at some higher level present moment, (is) past at some higher level future moment, and (is) future at some higher level past moment.

The third level temporal predications are introduced through explicating the characteristics of the second level moments. Each of the second level moments (is) present, past and future, not simultaneously, but at different third level moments. A second level moment (is) present at some third level present moment, (is) past at some third level future moment, and (is) future at some third level past moment.

And the same applies to each of these third level moments, and so on infinitely.

McTaggart believes this infinite regress is vicious, which he explains as follows:

Such an infinity is vicious. The attribution of the characteristics past, present, and future to the terms of any series leads to a contradiction, unless it is specified that they have them successively. This means, as we have seen, that they have them in relation to terms specified as past, present, and future. These again, to avoid a like contradiction, must in turn be specified as past, present, and future. And, since this continues infinitely, the first set of terms never escapes from contradiction at all.[3]

These remarks are paradoxical. McTaggart is indeed correct that the attribution of presentness, pastness and futurity leads to a contradiction

unless they are attributed successively. However, in each case it is specified that the terms to which they are attributed have them successively. For example, on the first level, it is specified that each event (is) present, past and future, not simultaneously, but at different moments of time, and on the second level it is specified that each moment has these attributes at different higher level moments of time. It seems to follow from this that none of the attributions of presentness, pastness and futurity lead to a contradiction. But McTaggart concludes that since there are infinite levels of predication, ‘the first set of terms never escapes from contradiction at all’. How could it never escape from contradiction if it never was contradictory? The first set of terms, the events, are contradictory only if it is not specified that these terms have presentness, pastness and futurity successively. But it is specified that they have them successively!

McTaggart seems to believe that the first set of terms is contradictory because he infers from

(1) The attribution of the characteristics past, present, and future to the terms of any series leads to a contradiction, unless it is specified that they have them successively

(2) The attribution of the characteristics past, present, and future to the terms of any series leads to a contradiction, which is subsequently resolved by specifying that they have them successively.

This is an invalid inference, for a statement of the form, A, unless B does not entail a statement of the form, A and B.

If this inference were valid, the levels of predication would be increased, so as to include before each of the levels represented on the previous pages another level or sublevel consisting of contradictory predications. The hierarchy would be represented so:

(4a) Each event (is) present at a present moment, past at a future moment, and future at a past moment.

(5a) Each moment (is) present at a higher level present moment, past at a higher level future moment, and future at a higher level past moment.

(5b) However, each of these higher level moments (is) present, past and future simultaneously.

The three simultaneous predications (on the first level and sublevels (4b) and (5b)) are superfluous. Their presence in the hierarchy is unnecessary and unjustified, introduced only as a consequence of the tacit and fallacious inference from the assertion (1) to the assertion (2). Just because the temporal predicates would be predicated in consistently if predicated simultaneously does not imply that on each level they are so predicated, such that the contradiction this involves must be resolved by a new successive predication of them. It is as if every time I predicate blackness and whiteness to something, like a zebra or newspaper, I must first predicate blackness and whiteness in the same respect, and then resolve this contradictory predication by a new consistent predication, wherein blackness and whiteness are predicated in different respects.

Introducing these contradictory temporal predications leads to a misrepresentation of the relation that the genuine and necessary levels of temporal predication have to each level. Each higher level does not in truth stand to the immediately lower level as a resolution stands to a contradiction, but as an analysans stands to an analysandum. If we remove the superfluous contradictory statements, then the first two levels are (4a) and (5a) (corresponding to the first two levels represented on pages 2-3). (5a) makes explicit what is implicit in (4a), namely that the first level moments are present, past and future at higher level present, past and future moments. (5a) is an analysis of the meaning of the statement that the first level moments are present, past and future, a meaning that is not made explicit in (4a) itself.

These considerations support the contention that the infinite regress of genuine and necessary temporal predications is a regress of analysandum and analysans, not of contradictions and resolutions, and consequently lacks the viciousness McTaggart attributed to it.

There is a second unnecessary assumption made by McTaggart, that there is a hierarchy of levels of moments. He assumed that in order for a moment to be present it must occupy a higher level present moment, such that the answer to the question “when does presentness inhere in the first level moment?” is “at a second level moment which (is) present”. But a more parsimonious answer can be given to this question, namely that “presentness inheres in the first level moment at present”, this answer meaning that the inherence of presentness in the first level moment is itself present, i.e. presentness not only inheres in the moment but also in its own inherence in the moment. To the question, “and when does presentness inhere in its own inherence in the moment?” a similar answer is given, “at present”, i.e. presentness not only inheres in its inherence in the moment, but also in its inherence in its inherence in the moment. This regress of the inherences of presentness in its inherences

continues ad infinitum. Accordingly, instead of representing the infinite regress of attributions of presentness as

(6) E (is) present at a moment which (is) present, and this moment (is) present at a second level moment which (is) present, and the second level moment (is) present at a third level moment which (is) present, and so on infinitely

(6a) E (is) present at a moment which (is) present, and the (being) present of this moment (is) present, and the (being) present of the (being) present of the moment (is) present, and so on infinitely.

(6a) is more parsimonious than (6), for instead of postulating an infinite number of levels of moments and predications of presentness, it postulates only one level of moments and an infinite number of predications of presentness.

A third unnecessary assumption can now be eliminated from McTaggart’s conception of the regress, that events occupy moments. It is possible to do away not only with the levels of moments above the first level, but also with the first level itself. Although it is arguable that the facts of immediate experience[4] and science[5] suggest that events in fact occupy moments, it is not logically necessary that they do. There is no contradiction in the idea that presentness inheres in an event, and in its own inherence in the event, and so on infinitely. Accordingly, the regress of attributions of presentness is most parsimoniously represented as

(6b) E (is) present, and the (being) present of E (is) present, and the (being) present of the (being) present of E (is) present, and so on infinitely.

A fourth and final assumption of McTaggart’s that can be rejected is that the temporal predications are predicated by tenseless copulas. This assumption is incompatible with the goal of providing an analysis of tensed predications. If (6b) is to be the complete analysans of the present tensed sentence “E is present”, it must convey all the information that the latter conveys. But it does not. “E is present” conveys the information that E is now present, rather than was or will be present, but (6b), through predicating presentness tenselessly, does not convey this information. For example, the first conjunct of (6b), “E (is) present”, does not indicate when E has the property of presentness; it does not indicate whether E was present, is now present, or will be present. Analogous considerations hold for each of the other conjuncts of (6b). Consequently, (6b) cannot be the complete analysans of “E is present”.

(6c) E is present, and the being present of E is present, and the being present of the being present of E is present, and so on infinitely.

(6c) clearly conveys all the information that “F is present” conveys, namely that E is now present rather than was or will be present, and thereby can function as the complete analysans of “E is present”.[6]

But it maybe wondered if the elimination of the tenseless copulas also eliminates the need for a regress. A complete analysis of the first conjunct of (6c) shows that this is not the case. In the sentence “E is present”, “E” stands for an event, “present” stands for the property of presentness, and the present tense copula stands for the present inherence of the property of presentness in the event. “E is present” means

But (7a) does not make the sense of ”E is present” fully explicit. If “E is present” is true, then the inherence of presentness in its own inherence in F cannot be past or future; it must be present, so that

(7b) Presentness inheres in F, and in its own inherence in E, and in its inherence in its inherence in E.

It can easily be seen that this inherence of presentness in its own inherences goes on infinitely.

it should be observed that “inheres” and “inherence” as they appear in (7), (7a) and (7b) must be tensed, for if they were not these sentences would not convey the same information as “E is present”. For instance, if the “inheres” in the first conjunct of (7b) were tenseless, this conjunct would not convey that presentness now inheres in E, and thus it, along with the remaining conjuncts of (7b), would fail to convey what “E is present” conveys. The “inheres” in the first conjunct of (7b) must be present tensed, such that it designates what the second conjunct more explicitly designates, that presentness inheres in its own inherence in E.

These remarks about “inheres” and “inherence” show that the relation between “E is present” and (7), (7a) and (7b), and the relation between “E is present” and its infinite analysis in (6c), is one of logical equivalence, but is not one of referential identity. That is, “F is present” and (6c), to take two of these sentences, entail each other, but they do not explicitly refer to the same items. Let us say that a sentence explicitly refers to an item if there is a word or phrase in the sentence that stands for it. An item is implicitly referred to by a sentence if there are no words or phrases in the sentence that stand for it, but there is a

difference sentence with such a word or phrase that is logically equivalent to the sentence in question. Thus “the triangle (is) three- sided” explicitly refers to the triangle, the property of three-sidedness, and the inherence of this property in the triangle, and implicitly refers to the property of being three-angled, and the inherence of this property in the triangle, for “the triangle is three-sided” entails and is entailed by “the triangle is three-angled”.[7] Two sentences are referentially identical if and only if they explicitly refer to the same items.

We can thus understand how “E is present” and (6c) are logically equivalent but not referentially identical. The former sentence explicitly refers to an event E, the property of presentness, and the present inherence of this property in E. It implicitly refers to the infinite regress of inherences of presentness in its inherences that stems from the inherence of presentness in its inherence in F, for there are no words in this sentence standing for these infinite inherences of presentness and yet this sentence entails and is entailed by a sentence, (6c), in which there is a phrase (“and so on infinitely”) standing for these infinite inherences.

To clarify this notion, the difference between real and merely apparent referential distinctness must be noted. Two sentences merely appear to be referentially distinct if one of the sentences, S₁, has words or phrases in addition to those of the other sentence, S₂, such that these words or phrases do not succeed in explicitly referring to anything to which explicit reference is not made in S₂. The two sentences

have a merely apparent referential distinctness. Each “F is present” in (9) explicitly refers to the same items, viz., the present inherence of presentness in E. There is not an infinite number of distinct items to which (9) explicitly refers, but the same few items, items that are referred to over and over again an infinite number of times. Thus no item is explicitly referred to in (9) to which explicit reference is not made in(8).

(6c), on the other hand, is really referentially distinct from (8), for it explicitly refers to an infinity of items to which explicit reference is not made in (8). It is not the case that each explicit predication of presentness in (6c) is a predication of presentness of E or of the inherence of presentness in F; rather, each explicit predication of presentness predicates presentness of a different item; the first conjunct of (6c) predicates presentness of the event E and each of the remaining conjuncts predicates presentness of a different inherence of presentness; the second conjunct predicates presentness of the inherence I of presentness in F, the third conjunct predicates presentness of the inherence₂ of presentness in its inherence₁ in E, and so on.

Besides being logically equivalent to and really referentially distinct from (8), (6c) has a third relation to (8); it is its complete explication. It

explicitly refers not only to what (8) explicitly refers, but also to what (8) implicitly refers. (By contrast, “the triangle is three-angled” is logically equivalent to and referentially distinct from “the triangle is three- sided”, but is not its complete explication, since it does not explicitly refer to every item to which the former sentence explicitly refers.

What are the complete explications of “E is past” and “F is future”? They are not to be understood on the analogy of(6c); the explication of “E is past” is not

(8) E is past, and the being past of E is past, and the being past of the being past of E is past, and so on infinitely.

(8) implies that the being past of E is itself past, which is false. Events are not past in the past, but in the present; the events of a minute ago are not past a minute ago, but in the present minute. The answer to the question, “when does pastness inhere in events?” is “at present”. The same is true for the future. Hence, not only is it the case that present events are present at present, but also that past and future events are past or future at present. The correct explication of “E is past” is

(8a) E is past, and the being past of E is present, and the being present of the being past of E is present, and so on infinitely.

It is the standard view of the tensers that the elimination of the tdnseless copulas in McTaggart’s regress also eliminates the regress itself. This belief was first expressed by C.D. Broad,[9] and was later adopted or developed by G.J. Whitrow,[10] A.N. Prior,[11] F. Christensen,[12] G. LLoyd,[13] and others. The idea is essentially that tensed sentences imply no regress, and that a regress ensues only if an attempt is made to analyze these sentences in terms of tenseless predications of presentness, pastness and futurity.

I have already argued that tensed sentences like “E is present” do entail an infinite regress, a regress of temporal properties inhering in their own inherences. In this section, 1 will defend this argument against a theory espoused by many of the abovementioned tensers, that a view such as mine is based on the mistaken assumption that the grammatical predicates of sentences like “E is present”, “E is past” and “E is future” refer to properties of presentness, pastness and futurity. If this assumption is rejected, the theory implies, it will be seen that tensed sentences do not refer to temporal properties and a fortiori that they do not refer to infinitely regressive properties. The infinite regress is eliminated with the elimination of the temporal properties.

The theory in question maintains that “present” “past” and “future” are merely grammatical predicates, and that their role in a sentence is

most clearly brought out by translating the sentences with the temporal predicates into sentences without them. “The leaf’s falling is past”, according to this view, is translated as ‘The leaf was falling’, thereby eliminating the apparent reference to a property of pastness.

An analysis of this sort raises more questions than it answers. in particular, one is left baffled about the status of the referent of the analysans. In the above example, it is clear that ‘the leaf’ refers to a thing, and ‘falling’ to a property possessed by this thing; but what about the referent of ‘was’? The ‘was’ in part serves as a copula, and refers to the inherence of the property of falling in the leaf. But surely ‘was’ as a past tensed copula has an additional function, that of indicating the pastness of the inherence of the property of falling in the leaf? And what could this pastness be, if not a property of the inherence of falling in the leaf?

Perhaps ‘was’ does not refer to pastness at all. In that case, all that is referred to by ‘The leaf was falling’ is the leaf, falling and the inherence of falling in the leaf. Likewise, the present and future tensed sentences, ‘The leaf is falling’ and ‘The leaf will be falling’, do not refer to presentness or futurity but simply to the leaf, falling and the inherence of falling in the leaf. But this implies that the past, present and future tensed sentences have the same referent, a referent that is devoid of temporal status. And such an implication is incompatible with a tenser’s view of the world.

No illumination about the reference of ‘was’ is achieved if ‘The leaf was falling’ is analysed as ‘the leaf is falling’ prefixed by the sentential operator, ‘It was the case that’, so that we have ‘It was the case that the leaf is falling’.[14] Depending upon how the sentential operator is interpreted, it is either about the sentence upon which it operates, ‘the leaf is falling’, or about the referent of this sentence. If the former, the operator indicates that the sentence, ‘the leaf is falling’, was true, it used to refer. This entails that there was a referent of the sentence, there was a falling of the leaf. But what could this mean but that the property of falling formerly inhered in the leaf? And if this is not interpreted as the inherence of the property of pastness in the inherence of falling in the leaf, how is it to be interpreted?

If the operator is instead interpreted as being about the referent of the sentence upon which it operates, it is about the state of affairs, the leaf is falling;[15] it indicates that this state of affairs was. An analogous question arises here about the pastness of this state of affairs; if not a property of the inherence of falling in the leaf, what is it?

Ferrel Christensen’s version of this theory provides some sort of answer to these questions. He begins by indicating that tenses

perform a very different sort of task from telling what the nature or properties of an individual are: they tell when it has its properties. That is to say. they tell whether it once did, or does now, or will yet possess such-and-such characteristics (or bear such-and-such relations), and also simply whether it did, does or will exist. Indeed, it is precisely because the kind of information they carry is so different from that which is conveyed by predicates that the tenses have such a different logical form: to tell when the individual named in a sentence has the property (Or relation) predicated of it, the tense operator acts in a special way upon both terms together.[16]

According to Christensen, terms standing for present, past and future positions are “A-terms”; A-names (e.g. “the past”) and A-predicates (e.g. “is past”) are reducible to A-adverbs, the tensed element of copulas (such as the past tensed aspect of the “was” in “the leaf was falling”). He contjnues:

To assert that the A-names and A-predicates are reducible to the A-adverbs is to say that there are no such individuals or particulars as the past, the present and the future, and no such properties as pastness, presentness and futurity.[17]

The referents of A-adverbs are not items in “an ontology of individuals and their properties and relations”.[18] Christensen does not give a name to these referents, but it will be convenient to call them “A-adverbs” in the ontological sense, i.e. referents of “A-adverbs” in the grammatical sense of this term,

I think it can be proven that these ontological A-adverbs really are properties. Christensen rightly says that grammatical A-adverbs “tell when the individual named in a sentence has the property (or relation) predicated of it”.[19] If so, there is a distinction between the ontological A-adverb per se and its being of some individual’s possession of its properties. In a tensed predication, it is said when this individual possesses its properties, implying that the ontological A-adverb designated is an adverb of this individual’s possession of its properties and not of some other individual’s possession of its properties. If the A-adverb’s being of some individual’s possession if its properties is not distinguishable in some sense from the A-adverb itself, and the A-adverb itself is all that is designated by the tense of the copula, then it would be false that the past tense of the copula in “the leaf was falling” referred to an A-adverb of the leaf’s falling. It would instead be the case that this past tense designated an A-adverb simpliciter, an A-adverb that stood by itself, unattached to anything, an A-adverb that is not of the leaf’s falling or anything else.

But what of this of? What else could it be but the A-adverb’s modiflcation of, characterization of; qualification of inherence in the leaf’s falling? And so the ontological A-adverb after all is a property, for a property by definition is just that which inheres in (modifies, characterizes, qualifies) some item.

If Christensen nevertheless insisted that these were not properties that inhered in an individual’s possession if its properties (perhaps because he has decided to use the word “properties” in some especially restricted sense), but ontological A-adverbs that inhered in (or modified) the individual’s possession of its properties, I could for the sake of argument concede this point and prove that these A-adverbs nonetheless entail an infinite regress.

Take the ontological A-adverb designated by the past tense of the copula in “the leaf was falling”. When does this ontological A-adverb modify the leaf’s falling? It cannot modify it in the future, for if it did it would not yet be true that “the leaf was falling”, It cannot modify it in the past, for then it would no longer be true that “the leaf was falling”. It cannot modify it Permanently, for if the leaf was falling then at some earlier time it is the case that the leaf is falling. So the ontological A-adverb must modify it at present. If all A-positions are ontological A-adverbs, then “at present” here refers to an ontological A-adverb that modifies the modification of the leaf’s falling by the A-adverb referred to by the past tense of the copula in “the leaf was falling”. And when does the present A-adverb modify the past A-adverb’s modification of the leaf’s falling? By the same reasoning it must be concluded that it modifies it at present—and so on infinitely.

Perhaps a way to eliminate such infinite regresses is to conceive of A-positions as individuals in their own right, as individual events or entities. Instead of saying “the leaf was falling” or “the leaf’s falling is past”, we can say “the leaf’s falling occurred in the past”, where “the past” stands for an event or entity of a special sort.

Such a view has been developed by Ian Hinckfuss, although he believes it to be valid only if simultaneity is not relative to a reference frame. “The Present” Hinckfuss suggests, is an “event”[20] or “entity”[21] the coincidence with which explains the presentness of other events or entities. This implies that each present event E is related to The Present through the relation of coincidence, and by virtue of being so related, acquires the relational property of standing in a relation of coincidence with The Present. The question naturally arises, when does this relational property inhere in E? If E is coincident with The Present, the answer must be “at present”, i.e. that the inherence of the relational property in E itself stands in a relation of coincidence with The Present, and by virtue of so standing acquires the relational property of standing in this relation. And this second relational property must inhere in the inherence of the first relational Property in E at present, and so on infinitely. Consequently, the theory of The Present, The Past and The Future as individual events or entities fails to eliminate the regress. Moreover, this theory is less preferable than the theory that A-positions are properties, for it is less parsimonious: it postulates A-events or A-entities of a special sort, an infinite number of relations to these A-events or A-entities, an infinite number of relational properties, and an infinite number of inherences By contrast, the theory that A-positions are properties Postulates only these properties and an infinite number of inherences

I have not in this section discussed the detenser theories that tensed sentences are analysable into or at least have the same reference as certain tenseless sentences and that time consists merely of relations of simultaneity, earlier and later than, and not of A- If these theories were correct, there would of course be no regressive A- positions.

However, I have argued in other writings that the detenser theories of time are mistaken, that tensed sentences possess an ineliminable reference to A-positions, and that A-positions are essential and mind-independent elements of time.[22]

Properties are reflexive or nonreflexive; reflexive properties inhere both in terms and in their own inherence in terms; moreover, they also inhere in their inherence in their inherence in terms, and so on infinitely. Presentness is reflexive, because if some event is present, then the being present of that event also is present, and so on.

Identity and difference, understood as first-order properties, are also reflexive. If the property of self-identity inheres in some thing, it also inheres in its own inherence in that thing. For the inherence of self- identity in the thing is (identical with) the inherence of self-identity in the thing. if this inherence were not identical with itself, then it would be true that the inherence of self-identity in the thing is different from the inherence of self-identity in the thing, which is contradictory. By the same token, it is also the case that the inherence of self-identity in its own inherence in the thing is (identical with) the inherence of self- identity in its own inherence in the thing, and so on ad infinitum. Likewise, if a thing T₁ is different from another thing T₂, the inherence of the dyadic property of difference in T₁ is also different from T₂, and so is the inherence of d in the inherence of difference in T₁ and so on without end.

If oneness is understood as a first-order property of individuals, rather than as a property of concepts, then it too must be understood as reflexive. Some thing or event is one thing or event, and the inherence of oneness in the thing or event is one inherence, and the inherence of oneness in this inherence is itself one inherence, and so on endlessly.

Individuality is also a reflexive property. To be an individual is to be a bearer of properties, to be that in which properties inhere.[23] Not only is a thing or event individual, but the inherence of individuality in the thing or event is individual, for this inherence, like every inherence, is one, self-identical, and different from other items. For any individual, I, it is true that

(14) I is individual, and the being individual of I is individual, and the being individual of the being individual of I is individual, and so on without end.

Truistic properties, like round or nonround or extended or unextended, also are reflexive. A thing is round or nonround, and its being round or nonround is round or nonround. indeed, the inherence round or nonroundin a thing is round or nonround, for this inherence is

nonround, and if it is nonround then it is round or nonround And the same applies to the inherence of round or nonround in this inherence, and so on to infinity

By no means all properties, however, are reflexive. John is walking, but the inherence of walking in John is not walking; the sun is yellow, but the sun’s being yellow is not yellow.

The above accounts aims to show that presentness belongs to the class of reflexive properties, along with difference, self-identity, oneness, individuality and the truistic properties, to name a few. The regresses entailed by these properties are benign. A “benign” regress in the sense relevant here is one described by a regress of analysandum and analysans, an analysans being a sentence that makes explicit something implicit in the analysandum. For each regress there is a complete analysans, a sentence which explicitly refers (by means of a phrase like “and so on infinitely”) to all of the stages of the regress. This complete analysans is the complete explication (in the sense defined on pp. 389-390) of the original sentence (e.g. “E is present” or “I is individual”) that generates the regress; that is, it explicitly refers not only to what the original sentence implicitly refers, but also to what it explicitly refers. The complete explication is logically equivalent to but really referentially distinct from the original sentence.

There is no reason why these benign regresses cannot exist in reality. The concept of such a regress is not self-contradictory and hence is able to have real instances. The belief that the notion of an actual infinity is self-contradictory or somehow inapplicable to reality I have criticized elsewhere.[24]

* Quentin Smith is a full-time philosophy writer who lives in Charleston, South Carolina. His most recent publications include The Felt Meanings of the World (Purdue University Press, 1986) and articles in Nous, Philosophical Studies, Australasian Journal of Philosophy, Philosophy of Science, and The Philosophical Quarterly. [This is the original note from the 1986 paper.]

Y *Co of 1984 Rockefeller Award for best work in Philosophy by a non- academically affiliated philosopher Some revisions have since been made on the basis of comments by Brian Loar, William F, Vallicella, and two referees for The Southern Journal of Philosophy.

[1] There are some exceptions to this among the tensers for example Richard Gale, who believes that pastness, presentness and futurity are nonsensible properties of events. See his The Language of Time (New York: Humanities Press, 1968), esp. Ch. V. However. Gale does not realize the implications of this view, that there must be an infinity of temporal attributions

[2] Cf. J.M.E. McTaggart, The Nature of Existence Vol. 11 (Cambridge, 1927); the relevant portions of McTaggart’s theory are reprinted in The Philosophy of Time, ed. R.M. Gale (Garden City, N.Y., 1967), pp. 86-97.

[3] The Philosophy of Time, op. cit.. p. 96.

[4] Cf. Quentin Smith, The Felt Meanings of the World (West Lafayette: Purdue University Press, 1986), Chapter IV.

[5] See for example Michael Friedman’s Foundations of Space-Time Theories (Princeton, N.J.: Princeton University Press, 1983).

[6] I am using “complete analysis” in this paper to mean complete explication (which is defined on pp. 389-390, 395), and therefore lean allow the analysandum ‘ is present”, to appear in the complete analysans (6c).

[7] Note that lam using “refers” in a broad sense, to indicate any relation of a word to the item it stands for. Species of reference in this broad sense include reference in the narrow sense (as when it is said that names and definite descriptions “refer” but predicates and copulas do not), expression (predicates express properties), and predication (copulas predicate properties of things or events by standing for the inherence of the property in the thing or event).

[8] I do not have the space to show this here, but my arguments in this section suffice to refute not only McTaggart’s arguments for the thesis that attributions of presentness, pastness and futurity entail vicious infinite regresses, but also the recent defences of McTaggart’s thesis by Mellor, Oaklander, and Shorter. Vide, D.H. Mellor, Real Time (Cambridge: Cambridge University Press, 1981), Chapter 6; L. Nathan Oaklander, Temporal Relations and Temporal Becoming (Lantham: University Press of America, 1984), Chapter 2; J.M. Shorter, “The Reality of Time”, Philosophia, Vol. 14, Nos. 3-4, December, 1984, pp. 321-339. For a very different but nonetheless sound criticism of Mellor’s argument, see David Sanford’s “Infinite Regress Arguments”, in Principles of

Philosophical Reasoning, ed. James Fetzer (Rowman & Allanheld, 1984), pp. 93-117.

[9] CD. Broad, An Examination of McTaggart’s Philosophy, Vol. II (Cambridge: Cambridge University Press, 1938), Part I. The relevant portions are reprinted in Gale’s The Philosophy of Time, op. cit., 117-142. See especially pp. 139-142.

[10] G.J. Whitrow, “ ‘Becoming’ and the Nature of Time”, in Boston Studies in the Philosophy of Science, Vol. XXII, eds. R.S. Cohen and M.W. Wartofsky (Dordrecht Holland: D. Reidel, 1976), pp. 525-532.

[11] A.N. Prior, Past, Present and Future (Oxford: Clarendon Press, 1967), Ch. I.

[12] °F. Christensen, “McTaggart’s Paradox and the Nature of Time”, The Philosophical Quarterly, Vol. 24, No. 97, October, 1974, pp. 289-299.

[13] ‘AG. Lloyd, “Time and Existence”, Philosophy, Vol. 53, 1978, pp. 215-228, and “Tense and Predication”, Mind, Vol. 86, No. 343, July, 1977, pp. 433-438.

[14] The theory that ordinary tensed sentences are to be analyzed into tensed sentences prefixed by temporal sentential operators is developed by A.N. Prior in Time and Modality (Oxford, 1957), Past, Present and Future, op. cit., and Papers on Time and Tense (Oxford, 1968).

[15] By a “state of affairs” I do not mean a proposition or an abstract object, but a concrete thing or event qua possessing some property, e.g. the leaf qua possessing the property of falling.

[16] F. Christensen. op. cit., p. 297.

[17] Ibid.

[18] Ibid., p. 299.

[19] Ibid., p. 297.

[20] Ian Hinckfuss, The Existence of Space and Time (Oxford: Clarendon Press, 1975), p. 98.

[21] Ibid.

[22] Cf. “The Mind-Independence of Temporal Becoming”, Philosophical Studies, 47 (1985), pp. 109-119, The Felt Meanings of the World, op. cit., Ch. IV, and “Sentences About Time”, The Philosophical Quarterly, forthcoming in January 1987.

[23] I am here using “individual” in the wide sense. In the narrow sense of the term, an individual is an entity (substance) or event, like a cloud or a storm.

[24] Cf. “Infinity and the Past”, Philosophy of Science, forthcoming.