Time & Cross-Temporal Relations

107 Pages·2008·6.446 MB·English

by  Guiliano Torrengo

GIULIANO TORRENGO
TIME
AND CROSS-TEMPORAL
RELATIONS
MIMESIS
INTERNATIONAL
NOTE TO THE SECOND EDITION CONTENTS
The first edition of "Time and Cross-Temporal Relations" came out in 2008; a few
months after I got my PhD with a dissertation on the same topic.Although many articles
and books that are relevant to the discussion on cross-temporality have been published
since then, I have decided to limit the changes in the text to adding a few important
references. A complete update of the discussion would have implied writing an almost
entirely different book, and I think that whoever shares an interest in the subject matter
of it can still take advantage of the text in its original version.
p. 11
INTRODUCTION
I. Time and Relations 11
I.I Changes, Comparisons, and Cross-Temporality 11
I.2 Do We Need Cross-Temporality? 14
1.3 The Expressibility Problem 18
I.4 Temporal Parts Analysis of Cross-Temporality 20
II. Detecting Cross-Temporality 21
II.1 What You See Is Not What You Get 22
II.2 What You Get Is Not What You See 22
III. Plan of The Work 23
CHAPTER 1. TENSES AND CONTEXT 27
I. The General Semantic Framework 27
I.1 Formal Semantics 29
I.1.1 The Model 31
I.1.2 Semantic Rules and Intensional Operators 33
I.1.3 Indexicals and Parameters 36
I.1.4 Parsing and Evaluating 41
1.2 Context and Circumstances:
Two Roles of the Parameters 43
II. Context and Time 46
II.I Propositions 46
© 2014-Mimesis International II.2 Relativized Propositions and Relativized Evaluations 48
www.mimesisinternational.com II.3 Tensed Propositions and Tenseless Propositions 49
e-mail: [email protected] II.4 Time Focus and Kernel Propositions 56
III. Truth-Conditions and Time 60
Book series Philosophy, n. 4
III.I Tenseless Truth-conditions 61
Isbn: 9788857523903
III.1.1 A Remark on Tenses and Indexicals 65
© MIM Edizioni Sri III.2 Tensed Truth-Conditions 67
P.l. C.F. 0241937030 IIl.3 Multiple Temporal Focus 70
III.4 Cross-Temporal Claims CHAPTER 4. TIME 143
and the "No-splitting" Problem 73 I. Introduction 143
76 1.1 Introductory Remarks 143
IIl.5 The Scope of Tenses
1.2 Factive Realism 145
79 II. Realism and Anti-Realism about Tenses 148
CHAPTER 2. THE TEMPORAL PARTS APPROACH
79 II.l The Debate 148
I. Introduction
II. Realist and Anti-Realist View About Persistence 81 Il.2 Perspectival Contexts 154
11.l Three-Dimensionalism and Four-dimensionalism 81 II.3 "No-splitting" Problem Revisited 159
85 11.3.1 The Problem / 159
II.2 Persistence and Exemplification
11.3 Temporal and A-temporal Predication 88 Il.3.2 The Received Views 163
II.4 Temporal Predication and the Articulation of Content 91 II.3.3 Alternative Solutions 164
II.3 .4 Cross-Temporally Tensed Relations 168
II.5 Relativization of the Predicate, Copula Tensing,
92 11.4 The "No-Cohesion" Problem 173
and Adverbial ism
III. The Grounding Problem 178
II.5.1 Relativization of the Predicate
and Relativization of the Term(s) 93 111.1 Presentism Again 179
95 III.2 Presentism and Truth-Value Links 181
Ill. Cross-Temporal Instantiation
95 III.3 Presentism and "Ontological Cheat" 191
IIl.1 Instantiating Relations
III.2 Temporal Relations and Temporal Parts 96 IV. The Myth of Simultaneity 198
97
III.3 Cross-Temporal Relations
BIBLIOGRAPHY 203
103
CHAPTER 3. ALTERNATIVE APPROACHES
103
I. Introduction
104
II. Realism and Anti-realism about Time Dimensions
II.l The Present, the Past, and the Future 104
II.2 Ontological and Metaphysical Realism 105
110
II.3 Presentism
ll.3.1 Presentism Explained 110
II.3.2 Ontic and Factive Presentism 112
112
11.4 Presentism and Relations
116
III. Eliminativism
116
III.1 Biting the Bullet
117
III.2 Presentism and Moorean Evidence
III.3 Van Inwagen and Identity across Time 119
123
III.4 "Internalism"
III.5 Quasi-Truth and Humean Supervenience 126
III.6 The Sentential Connective Account 130
134
IV. Non-EliminativistApproaches
134
IV.1 The Relativization Strategy
139
IV.2 Relational Properties
"We transcend tense by escaping into
the fourth dimension".
w.v.o QUINE, Quiddities, p. 198.
INTRODUCTION
"Oh, but I was so much older then, I am younger than
that now".
Bos DYLAN, My Back Pages
I. TIME AND RELATIONS
I was once a child, now I am a man. Many things about me can be
said to have changed, if I compared myself as I am now to myself as
I was once. For instance
(1) I am now taller than I was once.
On the face of it, expressions such as these are about relations one
entertains with oneself through time; they are, as we shall say cross
temporal claims. The central tenet of this book is that such claims
express relations that are cross-temporally exemplified. I will start,
then, by introducing the notion of cross-temporal exemplification.
I.I Changes, Comparisons, and Cross-Temporality
Cross-temporal claims are sometimes taken as familiar ways of
talking about how ordinary things-such as persons, tables, and
apples-change over the course of time. For instance, I may utter
(1) to say that I have changed through time-I have grown taller.
However, there are cases in which cross-temporality and change
part company. For instance, consider
(2) I am now taller than my cousin was.
12 Time and Cross-Temporal Relations Introduction 13
Here, there is no change at all, we are merely comparing different situation urges us to elaborate a more refined answer. Firstly, Jet us
things at different times, regardless of which changes they may, or see if we manage to elaborate an answer using ordinary English. Jn
may not, have undergone. ordinary speech, we may either say
Thus, on the one hand, claims such as (1) involve change: I could (H) A relation R holds at a time t between x .•. xn,
1
not be taller than I was once if I were not changed in the meanwhile;
on the other hand, they share their general temporal structure with or
sentences such as (2): both sentences focus on two times, one for
each of the two "sides" of a (binary) relation. If change is implied in (E) The terms x1 ••• xn enter into a relation R at t ... t" respectively.
(1), then, it is not in virtue of its temporal structure (alone), but rath
Roughly, all we can say in the "hold" vocabulary can be recast in
er in virtue of the fact that in (1) we are comparing an object with
terms of the "enter" vocabulary, but not the other way around. When
itself, whereas in (2) we are comparing two different objects. (2)
shares this feature with simultaneous (and thus non cross-temporal) we say that a relation R holds at t between x ... x , we are necessar-
1 n
ily focusing on the time of exemplification of R. Whereas, when we
comparisons, such as (3):
say that x x" enter the relation R, we are not constrained to focus
1 •••
(3) I am now taller than my cousin. on one time only: we can focus on many times, one for each term
entering R.
Now, there are two are primafacie obvious considerations about
(3), which seem to hold also for (2): It looks like the problem we had in answering (Q) arose because
we were formulating the question with "unsuitable" vocabulary. The
(a) The relation involved in (3)/in (2) is being taller than. right question is not when my cousin and me exemplify the taller
(b) The subjects of exemplification in (3)/(2) are me and my cousin. than relation, namely when does this relation hold between us. Rath
er, the question is when my cousin and I, respectively, enter such a
However, while (a) and (b) seem to be innocuous as applied to relation. And the answer is that I enter it at the present time and he
(3), they turn out to be puzzling once we apply them to (2). Consider enters it in 1984. In other words, in the "hold" vocabulary we can
the question: express only relations that are simultaneously exemplified; whereas
in the "enter" vocabulary we can define cross-temporal exemplifica
(Q) When do my cousin and I exemplify the being taller than rela tion as follows:
tion?
(D) A relation R is cross-temporally exemplified by x xn if and
•••
The answer is utterly trivial if we focus on (3). If (3) is true, we only if each x; enters R at a different time than some x .. 1
exemplify it now, at the present time. And, more generally, we will }
exemplify it every time at which (3) is true. But if we focus on (2), Serious cross-temporality is the thesis that certain relations are
the correct answer turns out to be far less apparent. It is not now that cross-temporally exemplified, according to the definition given in
my cousin and I exemplify the being taller than relation, because (D).
it is possible that now I am not taller than my cousin, even if (2)
is true. Is it in 1984, then? No, because it is again possible that I (SC) There are cross-temporally exemplified relations.
was not taller than my cousin at that time, even if (2) is true. Is it
during the lapse form 1984 to the present time? No, again. Having We can state now more exactly the differences and analogies be
been taller than my cousin during all these years is not a sufficient tween (1) - (3). On the one hand, (3) focuses on the time at which
condition for me to be now taller than my cousin was in 1984. The a relation holds between its terms: it expresses a simultaneous rela-
Time and Cross-Temporal Relations Introduction 15
14
tion. On the other hand, (1) and (2) focus on the different times at W.hat ar.e we g?i~g.to lose in this .paraphrase? It is tempting to an
swer. nothing, (2 ) 1s JUSt a more articulated way of expressing what
which each term enters into the relation of being taller than, and,
(2) expresses. After all, what else is a comparative relation between
thus, they express cross-temporal relations. Among the. com~arisons
my cousin and me in (2), if not a difference in the heights we exem
that are cross-temporally exemplified there are some implymg that
plify at different times. Note that the only relational aspect in (2') is
a change takes place through time: those comparing the same entity
in the last conjunct, and-unarguably-the last conjunct has noth
through time, such as (1). In other terms, the necessary and suffi
ing temporal whatsoever; it is just a relation between quantities, i.e.
cient conditions for a comparative claim to imply a change are that
numbers. Then, appearances notwithstanding, (2) does not express
(i) it expresses a cross-temporal instantiation, and (ii) there is only
a cross-ten:poral exemplification of a relation. The only temporal
one term of comparison.
referen~es in (2) concern only exemplifications of properties at dif
ferent times, a phenomenon which sounds much more familiar-not
1.2 Do we need Cross-Temporality?
just to the scholar, but probably to whoever has not been trained in
the philosophy of language as well.
Now, if (a) and (b) are true, and if sentences such as (2) are some
times true, we can formulate an argument to the effect that (SC)
is true. Firstly, note that if (a) and (b) are true, we cannot state the Still, if we aim at maintaining that relations are never cross-tem
necessary and sufficient conditions for (2) to be true in the "hold" ~orally exemplified- according the sufficient and necessary condi
tions (D)-we need to. check whether the strategy can be applied
vocabulary. It is easy to see why: the being taller than relation may
across the board. Consider (4), a sentence similar to (3) both with
hold at no time between my cousin and me, while being true that in
respect to the comparative and the cross-temporal aspect:
2007 I am taller than my cousin was in 1984. Secondly, while the
"hold" vocabulary is useless to state necessary and sufficient condi
(4) John looks like Grandpa at 20.
tions for (2) to be true, the "enter" vocabulary is not. In the "enter"
vocabulary we can state that (2) is true if and only if I enter the rela
. The properties that John and his grandfather exemplify now and
tion being taller than at the present time, while my cousin enters the
m the past .<respectively), which are relevant for paraphrasing (4),
very same relation in 1984. Thus, if (2) is true, my cousin and I enter
ar~ properties concerning features of their look. Here the analogy
the same relation at different times, and analogously for analogous
with (2) at least partly breaks down: quite obviously, the relation
true sentences. Therefore, (SC) is true.
between these properties that shows up in the paraphrase will not
be a quantitati~e relation. Nonetheless, we are not yet compelled to
I grant this is not a compelling argument in favour of (SC). How
read (4 ) as saymg that John and his grandpa enter into a relation at
ever whoever denies (SC) must give us an account of what's wrong
differ~nt times. For instance, we may take similarity between John
in it' and this is not at all a trivial deed. A prima facie promising
and his grandfather as amounting to similarity (or identity) between
strat~gy is to deny that claims such as (1) and (2) express relations
the class of features they exemplify at different times:
between Michael and John. Let me explain the alternative picture
that I am attributing (not arbitrarily1 to my opponents. Suppose, we
) (4 ,') John now has features f's, his grandpa at 20 had features g's, and
rephrase (2) as (2'): the f s are s1m1lar (or identical) to the g's.
(2) I am now taller than my cousin was. However, note that, while this is a proposal that some philos
ophers may be happy to endorse, it is somewhat more "artificial"
(2') I am now n units tall, my cousin was m units tall, and n > m.
than par~phr~sing (2) with (2'). Moreover, and more importantly,
whether m (4) a cross-temporal exemplification is involved or not,
See, for instance, Bourne 2006, van Inwagen 2001 and Salmon 2005.
Time and Cross-Temporal Relations Introduction 17
16
temporally exemplified cannot simply be dispelled on the orounds
depends on what we take feature_s-an~, ge~erally s~eaki~g, the 0
of an ad hoc assumption to the effect that (SC) is false.
terms of the relation that shows up 111 the relational conjunct of the
paraphrase-to be. Features are certai~ly not _nu~~ers, and if they
"behave" with respect to space and ttme as 111d1v1duals-such as (II) ~1ore~ver, whether there actually are cases of cross-temporal
exemphficatt_on or not is at least partly an empirical question to be
John and his Grandfather-"behave" with respect to space and time,
solved by science, rather than an a priori question to be addressed
we have not managed to paraphrase away serious cross-temporality
in philosophy. Theories of physics provide us reasons to think that
in any case.
~e need a '.11odel of the world that encompasses cross-temporal rela
F?:
As we will see, there are cases in which "eliminating" cross-tem t~ons. 111stance: as Theodore Sider has argued, comparing spa
tial pos1t1ons of things through time is crucial to science, because
porality leads us to even more "fishy" manoeuvres. I do not have
knockdown arguments against the idea that relations are never cross it is co_nst~tutive ?f. central notions of physics like velocity and ac
temporally exemplified, and proving (SC) to be true behind any rea celer~t10~ . And 1t is not clear whether we can paraphrase physical
theones 111 a way that does not imply that relations are sometimes
sonable doubts. However, several reasons to resist the rejection of
serious cross-temporality will be provided in the course of this work, cross-temporally exemplified3.
so that it is fair to say that, eventually, it would appear that (SC) is at
(II!) Lastly, if_ we do not admit serious cross-temporality we are
least as much as plausible as its negation. To anticipate:
at ~ams to pr_ov1de t~uth-makers4 for many, if not all, perceptual
(I) We do have primafacie linguistic evidence, from the surface claim~. Even 1f we th111k of comparisons through time as not prob
form of sentences such as (1)-(4) to maintain that relations are l~mat1c, ~erceptual r~lations have little in common with compara
tive relations. In particular, perceptual relations are "external rela
sometimes cross-temporally exemplified. We can construe temporal
tions'', name!y they do not involve any qualitative or quantitative
qualifications in relational statements such as (1)-(4) as specify
ing the times at which each term enters in relation with the oth as~ect of ~heir terms. Moreover, their terms (a perceiver and a per
ceived object) always enter the relation at distinct times. Thus, it is
ers. Indeed, the "serious" reading, I will argue, is suggested both by
h_ard to see how there could be a case of perception involving only
the way we understand those claims, and by what we know about
simultaneously exemplified relations. And note that, if this is true,
the things we are ascribing relations to. Cross-temporality is sure
ly a notion within our grasp; therefore, whoever denies (SC) must ~ross-te_mpor~I relations turn out to be very common in our ordinary
111teract1on with the world. To be sure, there are alternative accounts
provide a reason to maintain that in our ordinary idea of tempo
of what t?e truth-makers for sentences ascribing perceptual relations
ral reality there is always an implicit "assumption of simultaneity".
are. For 1_nstance, we may maintain that claims concerning percep
In other words, she has to explain why she treats cross-temporal
tual relations are made truth by chains of causes, whose members
exemplification as it were just an "illusion". Her burden is indeed
are pair wise linked by simultaneous relations. But, as I will argue,
urgent, since none of the central tenets of the different positions in
the cross-temporal truth-makers alternative is most promising.
the contemporary philosophy of time-not even presentism-rule
out cross-temporality. Presentism is the thesis according to which
only the present exists. If presentism is true, there are no relations
between presently existing objects and objects that have ceased to 2 Sider 2001: 28.
exist (putting aside "intentional" relations such as thinking), but not 3 Bourne 2006 argues that presentism is compatible with theories that
all (and not only) cases of cross-temporal exemplification are of this ascribe (seeming) relations between presently existing entities and non
presently existing entities. However, even if he is right, not all cases of
sort. Thus, even if presentism is true, we still need further arguments
cross-temporal exemplification are of this sort-as I emphasized before.
to do away with serious cross-temporality. The pre-theoretical rea
4 On the notion of truth-maker see Mulligan&Smith&Simons 1984, and
sons we have to take (1)-(4) as ascribing relations that are cross- Beebee&Dodd 2005.
Time and Cross-Temporal Relations Introduction 19
18
(5") There is a time t earlier than the present, such that at t: I am
I.3 The Expressibility Problem
a boy.
(6") There is a time t identical with the present, such that at t: I
Along with the question whether (SC) is tru~ or not,~ will investi am a man.
gate which theses-both in the philosophy of time an~ in_ the ~eman­ (7'') There is a time t later than the present, such that at t: I am a
tics of temporal expressions-serious cross-temporality implies. By corpse.
endorsing (SC) we soon run into a certain number of problems. The
most apparent of these problems, and someho': ~~e problem at the If the verb expresses a relation, the syntactical form will be richer,
very heart of the matter, is a problei_n of express1b1llty. Ver~ roughly, since it will contain a further element X that together with the tensed
cross-temporal claims cannot be interpreted as expressing cros~­ verb forms a verb phrase. For instance, the syntactical structure of
temporally exemplified relations by resorting the s_tandard semantic (3) is showed in (3")
models for languages containing temporal expressions.
(3) I am now taller than my cousin.
Let us focus on tenses, in order to illustrate the idea, and keep (3 ') [I [IP PRES [1.r be now taller [x than my cousin]]J]
considerations concerning other temporal expressions for. later
It is not important here to determine what syntactical role [ than
chapters. Syntactically, tenses are inflections that, together w1th_an
my cousin] plays. What we need to emphasize is that relational sen
un-tensed Verb Phrase (VP), form an Inflection Phrase (IP), which
5 tences are interpreted by resorting to quantification over the times at
together with a Noun Phrase (NP), in turn, form a Sentence Con-
•
which the relation holds. More precisely, (3) will be interpreted as
sider, for instance:
(3") There is a time t identical with the present, such that at t: I am
(5) I was once a boy.
taller that my cousin.
(6) I am now a man.
(7) I will be a corpse.
But, then, the ordinary semantic means of regimenting the inter
These sentences have (simplifying a bit) the following syntactical pretation of temporal expressions seem to fall short of expressing
cross-temporal exemplification. If we take temporal expressions as
structure:
referring to the time at which a relation holds, rather than the time
at which one or more of the terms enter it, we are doomed to let out
(5') [I [IPPAST [VP be a boy])]
(6') [I [P PRES [vp be a man11] of the picture all those cases in which we talk of possibly different
(7') [I [I1P FUTURE [vp be a corpse]]] entities as entering the same relation at different times. Consider
again (2), whose syntactical structure is (2"):
(Where PAST, PRES and FUTURE stand for th~ correspondent tense
inflections, square brackets show the syntactic struc~ure, and sub (2) I am now taller than my cousin was.
scripts mark the type of phrase). In stan~ard semant1~s th~se syn (2") [I [JPPREs [vrbe now taller] [x than [IPPAST [vrmy cousin be]]]]]
tactic structures are interpreted by resorting to quant1ficat1on_ over
the times at which the property expressed by the verb phrase is ex- If we take the present tense in (2) as referring to the time at which
the relation of being taller holds between me and my cousin, the
. emplified6
:
further temporal qualification-'was'-is left unexplained.And the
same happens with the present tense if we take 'was' as referring to
More technically, tenses are heads of inflection phrases (IP) that have verb
5
phrases (VP) as complements. .
Higginbotham 2002, Parsons 1990, Kamp&Ryle 1993, Larson&Segal
This is not true just of the sentential operator account of Montague 1974,
6 1995, and Ludwig&Lepore 2003
and Kaplan 1989, but also of otherwise different approaches such as
20 Time and Cross-Temporal Relations Introduction 21
the time of exemplification. In both cases our analysis would yield (6"') There is a time t identical with the present, such that: I-at-t
a wrong interpretation of what is meant by (2), since it may be false am a man.
that I am taller than my cousin now, or that in the past I was taller (7'") There is a time t later than the present, such that: I-at-tam a
corpse.
than my cousin, while being true that I am now taller than my cousin
was. Neither is of help considering the temporal qualifications as
embedded one in another. If we take the past tense as embedded According to this analysis a cross-temporal claim such as (2) will
be construed as follows:
in the present tense, (2) would say that it is now the case that in
the past I was taller than my cousin. If we take the present tense as
(2) I am now taller than my cousin was.
embedded in the past tense, (2) would say that it was the case that I
am presently taller than my cousin. Again, these interpretations are
(2'") There is a time t such that is identical with the present, and a
not correct.
time t' earlier than the present, such that: I-at-tam taller that my-cousin
at-t'.
The problem, thus, lies in the interpretation of cross-temporal
sentences, and more precisely, in the underlying models used to in This analysis allows us to specify at what time each term enters
terpret tensed sentences. In each model, for every time instant (or in relation with the other(s), and thus, breaks with the "simultaneity
lapse) t, we "find" properties possessed at (or over) t by objects, and constraint". But what kind of entity is me-at-t' or me-at-t? Indeed,
relations that hold at (or over) t between objects, but not relations one reason why this analysis is not popular is that talking of 'me
between objects at different times. In other words, in the standard in the morning' or 'the book in the evening' sounds quite artificial
models all relations are simultaneously exemplified: for every R, after all8. However, the intelligibility of the analysis is warranted
there are no entities in the domain that enter R at a time that is dif by the notion of temporal part of an object, which is to be found in
ferent from the time at which some of the other terms enter R. This the contemporary debate on the metaphysics of persistence. Once
"simultaneity constraint" reflects the intuition that we use tenses and we interpret tensed sentences by resorting to models in which the
other temporal expressions to express when a certain relation holds, entities of our domain of discourse have temporal parts, expressing
or a certain property is exemplified7. cross-temporal exemplification becomes something unproblematic:
a relation is cross-temporally exemplified just in case it is exempli
1.4 Temporal Parts Analysis of Cross-temporality fied by non-simultaneous temporal parts of its terms.
The sort of semantic analysis of tense and other temporal expres
sions I have in mind differs radically from the standard analysis. II. Detecting Cross-temporality
I propose to interpret tenses as qualifying the objects and events
we are ascribing properties and relations to, rather than qualifying It is important to distinguish cases of cross-temporal relations
the exemplification of properties and relations. Sentences (5) - (7) from cases that seem similar (and have sometimes been treated as
should be parsed as: similar) when in fact their treatment does not give rise to any special
problems, or gives rise to problems of a different sort. And it is also
(5"') There is a time t earlier than the present, such that: I-at-tam important to realize that in some cases a cross-temporal relation is
a boy.
at work even though it does not show in the surface grammar (or in
the primafacie logical form) of our statements.
7 The same problem arise also within approaches such as Prior 1967,
Larsons&Segal 1995, Ludlow 1999, and also in the event approach such as
Parsons 1990, and in the discourse representation approach (Kamp&Ryle
1993). See also Cresswell 1985, and van Benthem 1980. 8 See van Inwagen 2000.