10.13125/CH/4493
application/pdf
2533-1825
4493
special II
en
urn:nbn:it:unica-26455
Fabio Del Prete
https://creativecommons.org/licenses/by/3.0/
Critical Hermeneutics
Temporal location of events in language and (non) persistence of the past
Text.Serial.Journal
https://ojs.unica.it/index.php/ecch
4
Articles
2020-12-17
2020-12-17
2020-12-17
2020-12-17
25-68
1
Fabio Del Prete
2020/12/17
10.13125/CH/4493
25
Centre National de la Recherche Scientifique (CNRS) - France
2533-1825
special II
68
urn:nbn:it:unica-26455
Temporal location of events in language and (non) persistence of the past
https://ojs.unica.it/index.php/ecch/article/download/4493/4576
4
Critical Hermeneutics, special 2 (2020)                        Received: 15/9/2020
Biannual International Journal of Philosophy                   Accepted: 15/9/2020
http://ojs.unica.it/index.php/ecch/index                      Published: 17/12/2020
ISSN 2533-1825 (on line); DOI 10.13125/CH/4493




     Temporal location of events in language and (non)
                           persistence of the past


                                    FABIO DEL PRETE




Abstract
The article reviews some analyses of temporal language in logical
approaches to natural language semantics. It considers some
asymmetries between past and future, manifested in language, which
motivate the “standard view” of the non-reversibility of time and the
persistence of the past. It concludes with a puzzle about the changing
past which challenges the standard view.
Keywords: time, events, necessity of the past




1.    Introduction
Languages like Italian have tensed forms of the verb which, in interac-
tion with temporal adverbs, express the location of an event in time.
For example, the italicized verb forms in the Italian sentences (1a)-
(1c), in interaction with the temporal adverbs in parentheses, locate a
particular event in the past, the present and the future, respectively:


      (1)      a.      (Ieri) il presidente dell’UCI era a Bruxelles.
                       ‘The president of UCI was in Brussels (yesterday)’
               b.      (Questa mattina) il presidente dell’UCI è a Bruxelles.
                       ‘The president of UCI is in Brussels (this morning)’
               c.      (Domani) il presidente dell’UCI sarà a Bruxelles.
                        ‘The president of UCI will be in Brussels (tomorrow)’
Fabio Del Prete, Temporal location of events in language




The verb forms in question do this with respect to a reference point—
typically, the moment at which the sentence is uttered. The past, pre-
sent and future of (1a)-(1c) are, respectively, past, present and future
with respect to that moment, which we may call “the hic et nunc of the
utterance”. This can be seen as the “zero point” from which every event
is apprehended.
     The property just mentioned makes tense, by and large, an index-
ical category: to determine its contribution to meaning, we must first
identify the context of utterance. For example, suppose that you run
into an utterance of (1b) – maybe you see an inscription of this mes-
sage in a letter, or you foresee it through the powers of your imagina-
tion as a future utterance – but you are not aware of the hic et nunc of
it, so that you don’t know whether the sentence was uttered one year
ago or will be uttered in a century from now. Until you don’t identify
the hic et nunc of this utterance, you won’t be able to determine its full
meaning (being now September 1st 2020, does the utterance mean
that the UCI president was in Brussels in the morning of September 1st
2019? or does it mean that she will be in Brussels in the morning of
September 1st 2120?).
     Linguists have viewed the function referred to above as funda-
mental to tense. Accordingly, they have defined tense as the gram-
maticalised expression of location in time. Bernard Comrie expresses
this view in the following passage:


     [For grammatical categories, including tense, w]hat one finds
     most typically is the choice of the speech situation as the ref-
     erence point […]. As far as tense is concerned, then, the ref-
     erence point is typically the present moment, and tenses lo-
     cate situations either at the same time as the present




26
                                          Critical Hermeneutics, special 2 (2020)




    moment, or prior to the present moment, or subsequent to
    the present moment (Comrie 1985).


The location of events in time is fundamental to human experience.
Our lives happen in time, as successions of events. An important func-
tion of language is to represent the events making up our personal
lives and our public history by locating those events within an estab-
lished temporal frame and by determining temporal relations (before,
after, etc.) between them on the background of such a frame. In this
function, language does an invaluable service to memory – both to
“private” memory about events from our personal lives and to “public”
memory about events from our common history. In this article I con-
sider the subject of the temporal location of events from the perspec-
tive of natural language semantics. The more general question accom-
panying my inquiry is what we can learn about fundamental properties
of time from a consideration of linguistic phenomena. The specific
questions arising from my inquiry bear in particular on the (non-)re-
versibility of time and the (non-)persistence of the past.
    The article is structured as follows. I begin with a recollection of
analyses of temporal language in logical approaches to natural lan-
guage semantics (section 2). Then I consider some asymmetries be-
tween past and future that become manifest in language, which raise
the questions of reversibility and persistence, and I present the “stand-
ard view” of the non-reversibility of time and the persistence of the
past (section 3). Then I consider a puzzle about the changing past that
challenges the standard view (section 4). I conclude suggesting an
open-minded view on the fundamental questions.


2. Logical approaches to the semantics of temporal expressions
Arthur Prior is the philosopher who laid the ground to logical ap-
proaches to the semantics of tense, by founding modern tense logic



                                                                              27
Fabio Del Prete, Temporal location of events in language




(Øhrstrøm and Hasle 1995; Copeland 2020; Goranko and Rumberg
2020). Preliminarily, we are interested in Prior’s philosophical ideas
about time, which are particularly well-suited to think about history. It
is not an accident that the first modern treatment of so-called “histor-
ical modalities” (modalities such as “In 1932 it was possible for Great
Britain to avoid war with Germany; but in 1937 it was impossible”;
Thomason 1984), which were formalized by Richmond Thomason in
the ’70s and ’80s, sprang from Prior’s tense logic and from his views
about indeterminism and what was later called “branching time” (the
view that, at any moment in history, the world has only one past but
several possible futures branching off from that moment; see section
3.2.).
     Prior was a temporalist: he thought that human thoughts are fun-
damentally tensed and that the temporal notions of pastness, present-
ness and futurity are not expressible in the objectivist, atemporalist
terms of the notion ‘time instant t1 precedes / follows time instant t2 in
the series of times’. He was also a presentist: he thought of the present
as the fundamental perspective of human thought on reality, while he
conceived of the past and the future, derivatively, as “displaced pre-
sents”—the past is what has been present and the future is what will
be present (we’ll see shortly that this derivative conception of the past
and the future as displaced presents lies at the heart of Prior’s treat-
ment of the past and the future qua grammatical categories, i.e. gram-
matical tenses).
     In these respects, Prior’s ideas differed dramatically from those of
Willard Van Orman Quine. In his Word and Object, Quine writes:


     Our ordinary language shows a tiresome bias in its treatment
     of time. Relations of date are exalted grammatically as
     relations of position, weight, and color are not. This bias is of
     itself an inelegance, or breach of theoretical simplicity.



28
                                                  Critical Hermeneutics, special 2 (2020)




     Moreover, the form that it takes – that of requiring that every
     verb form show a tense – is peculiarly productive of needless
     complications, since it demands lip service to time even when
     time is farthest from our thoughts. Hence in fashioning
     canonical notations it is usual to drop tense distinctions
     (Quine 1960).


For Quine, tensed sentences such as (1a)-(1c) are a logically imperfect
way to convey certain meanings and should be improved by regiment-
ing the tensed expressions of everyday language in the objectivist
terms provided by the mathematical ordering of times (according to
the relation of precedence), accompanied by tenseless predications
about such objectively ordered times. For example, (1a) should be reg-
imented as (1a')1:


     (1)      a’.    The president is in Brussels at time t1 and t1 precedes
     the time t0 at which event e0 happens (and t1 is included by the
     day preceding t0).


Prior’s advice is radically different: we should take our tensed talk se-
riously for what it is, not trying to reduce it to something else. The use
of tensed forms, far from being logically imperfect, is a legitimate and
meaningful way of expression. Instead of regimenting our language to
avoid such forms, we should rather devise a new logic capable of for-
malizing their meaning.



1
  In Quine’s regimentations, the verb form “is” is to be taken as the tenseless present
of mathematics, as it shows up in eternally true statements such as “2 + 2 is equal
to 4”, while the specification “at time t1” makes explicit – once and for all – the
temporal reference which is left implicit by the logically imperfect sentences of our
ordinary language, thus making the propositions expressed by those sentences
eternally true or eternally false. The event e0 introduced in the regimentations
represents the event of their utterance.



                                                                                      29
Fabio Del Prete, Temporal location of events in language




        In the following sections I consider some logical approaches to
temporal language, starting from Prior’s approach, and then moving to
refinements of the latter which were motivated by certain limits inher-
ent to Prior’s tense logic.


2.1. Priorian tense operators
In this presentation I use the graphical device of a line oriented from
left to right to represent the temporal flow of events. The left part is
associated with the past, the right part with the future. A designated
point “t0” is associated with the present – the time at which the utter-
ance happens.


                                        t0
     Past                                                                 Future
                                  the present
       Fig. 1. The time line



Prior (1957) proposed a logical language containing two tense opera-
tors2: one for the past, one for the future. Syntactically, these opera-
tors, PAST (“it has been the case that …”) and FUT (“it will be the case
that …”), are prefixed to a proposition p; this yields another proposition
– a past tense proposition PAST(p), formalizing a sentence like (1a),
or a future tense proposition FUT(p), formalizing a sentence like (1c).
Prior’s idea, which he revived from Medieval Scholastics, was that a
proposition takes a truth value, True or False, at a time. The value of
a proposition at a time t1 may differ from its value at a different time
t2. For instance, proposition (1b) may be True at September 20th, 2020
but False at September 21st, 2020 (the reason being that the president



2
 Prior (1957) actually introduced other temporal operators. For our purposes it will
suffice to consider the operators described in the main text.



30
                                               Critical Hermeneutics, special 2 (2020)




may be in Brussels in the morning of the former but not of the latter).
Prior’s operators are defined below:


     1.       Prior’s tense operator PAST:


     •     PAST(p) is true at t if and only if p is true at a time t' in the
           past of t.


                          t'                           t


                          p                          PAST(p)
Fig. 2. Representation of the meaning of “PAST(p)”



     2.       Prior’s tense operator FUT:


     •     FUT(p) is true at t if and only if p is true at a time t' in the
           future of t.


                          t                            t'


                        FUT(p)                         p
Fig. 3. Representation of the meaning of “FUT(p)”



To exemplify, suppose you uttered (1a) on the 20th of August, 2020:


     (1)      a. (Ieri) il presidente dell’UCI era a Bruxelles


     The Priorian logical structure of (1a) is (2):


     (2)      PAST (the president of UCI is in Brussels)




                                                                                   31
Fabio Del Prete, Temporal location of events in language




     and (2) is evaluated as in (3):


     (3) is true at the time of August 20th, 2020 if and only if ‘the
     president of UCI is in Brussels’ is true at some time t' in the past
     of August 20th, 2020


So far, we have been implicitly assuming that the time at which a prop-
osition is evaluated is the present time t0. Though this is often the case,
it is not always so. The proposition to which a tense operator is prefixed
may be itself of the form PAST(p') or FUT(p'), so that the final propo-
sition may have one of the following forms:


     (4)      a.     PAST(PAST(p'))
              b.     PAST(FUT(p'))
              c.     FUT(PAST(p'))
              d.     FUT(FUT(p'))


Each of the formulas (4a)-(4d) may be associated to a particular tensed
construction from natural language. Relevant tensed constructions are
exemplified by the italicized parts of (4a')-(4d') (we read these sen-
tences as making up a historical narrative, uttered at 2 PM on the same
day as the reported events):


     (4)      a'.    At 9AM, the president had already arrived in
                     Brussels.
              b'.    He would give his speech at 10AM.
              c'.    By 6PM he will already have returned to Linate
                     Airport.
              d'.    He will be about to embark for Rome then.




32
                                            Critical Hermeneutics, special 2 (2020)




(4a') is the past of a past: the president’s arrival in Brussels is pre-
sented as past not just with respect to the present but to a past 9AM
time. (4b') is the future of a past: the president’s speech is presented
as future not with respect to the present but to that past 9AM time.
(4c') is the past of a future: the president’s return to Linate Airport is
presented as past not with respect to the present but to a future 6PM
time. Finally, (4d') is the future of a future: the president’s embark-
ment for Rome is presented as future not just with respect to the pre-
sent but to that future 6PM time.
     The discussion of (4a')-(4d') should clarify that the times at which
the innermost tense operators in (4a)-(4d) are evaluated are distinct
from the time of utterance: they are displaced either in the past or the
future of it by the outermost tense operators. While the broad temporal
aspects of the meanings of (4a')-(4d') highlight a nice feature of the
iteration of tense operators allowed in Prior’s tense logic, there are finer
temporal aspects of those meanings that lie beyond the reach of this
logic, thus showing its limits. One such crucial aspect is the reference
to particular time points, so common in natural language, which is typ-
ically achieved via time adverbials (see [4a']-[4d']).


2.2. Problems for the Priorian analysis of tense
Consider the following scenario (due to Barbara Partee). While driving
on the highway to go to the sea, you utter (5) as you remind that, at
the point in which you left home, you forgot to turn off the stove:


     (5) I didn’t turn off the stove!


     The sentence clearly refers to a particular time […] whose
     identity is generally clear from the extra-linguistic context,
     just as the identity of the he in [the sentence He shouldn't be
     in here] is clear from the context (Partee 1973).



                                                                                33
Fabio Del Prete, Temporal location of events in language




     Partee notes that there are two possible Priorian analyses of (5),
according to whether PAST takes scope above negation, i.e. (5’), or
below it, i.e. (5”):


     (5’)     PAST(NOT(I turn off the stove))
     (5”)     NOT(PAST(I turn off the stove))


Consider the evaluation of (5’) first. Assuming that you utter (5) at
5PM, the truth conditions of your utterance under analysis (5’) are as
follows:


     (6) (5’) is true at 5PM if and only if ‘I turn off the stove’ is false
     at some time t' in the past of 5PM


Notice that these truth conditions come down to requiring that some-
times in the past you did not turn off the stove. Turning now to (5”),
the truth conditions of your utterance under analysis (5”) are as fol-
lows:


     (7) (5”) is true at 5PM if and only if ‘I turn off the stove’ is true
     at no time t' in the past of 5PM


These truth conditions come down to requiring that never in the past
did you turn off the stove.
     The truth conditions predicted for your utterance under either one
of (5’), (5”) are both empirically inadequate. On the one hand, those
predicted under (5’) are too weak: there are lots of moments in the
past in which you did not turn off the stove and might so satisfy the
truth conditions in question; your utterance, however, is not about just
any such moment, but about a particular one among them. On the



34
                                           Critical Hermeneutics, special 2 (2020)




other hand, the truth conditions predicted under (5”) are too strong:
there are lots of moments in the past in which you turned off the stove;
however, your utterance is not meant to deny that there is any such
moment, but only to assert that you did not turn off the stove at a
particular moment in the past.
    The consideration of Partee’s case clarifies, even without consid-
ering a sentence containing a time adverb, that Prior’s tense logical
approach is hopeless in dealing with the phenomenon of reference to
specific times. We had anticipated the problem discussing the referen-
tial aspects of the narrative (4a')-(4d'): while Prior’s tense operators
allow one to move backward and forward in time (to evaluate proposi-
tions with respect to times displaced from the hic et nunc of the utter-
ance), they lack the power of targeting specific moments in the way
that time adverbials do. Therefore, if we want a satisfactory analysis
of temporal location in language, while keeping to Prior’s philosophical
attitude, we need to refine Prior’s logic so as to give his tense operators
“referential power”.


2.3. Hybrid Tense Logic
The following passage is from the entry Hybrid Logic of the Stanford
Encyclopedia of Philosophy:


    Hybrid [tense] logics are logics that result by adding further
    expressive power to ordinary [tense] logic. The most basic
    hybrid logic is obtained by adding so-called nominals which
    are propositional symbols of a new sort, each being true at
    exactly one [moment] (Braüner 2017; emphasis added by
    FDP).


Let’s illustrate what this means by applying it to Partee’s case. Let’s
suppose that “t*” (a nominal) is a very specific proposition, True at



                                                                               35
Fabio Del Prete, Temporal location of events in language




exactly one moment, i.e. that particular moment in the past of your
utterance in which you should have turned off the stove (in other
words, “t*” is a proposition that univocally describes the state of the
world at the moment in question). Given this property of “t*”, it follows
that the conjunction “t* & NOT(I turn off the stove)” is a proposition
True at at most one moment: if this conjunction is True at any moment,
it cannot but be True at the unique moment at which “t*” is True. In
Partee’s case, the meaning of your utterance of (5) can then be ana-
lysed along the lines of the logical paraphrase “it has been the case
that the state of the world is as described by t* and I do not turn off
the stove,” where “it has been the case that” is just Prior’s past tense
operator, “the state of the world is as described by t*” is the very spe-
cific proposition that is True only at the crucial moment in the past
referred to in your utterance, and “I do not turn off the stove” is the
proposition (probably True at many moments in the past) that your
utterance claims to be True at that same moment.
     The hybrid tense logical analysis of (5) is thus as in (5’’’), and the
resulting truth conditions of your utterance are as in (8):


     (5)      I didn’t turn off the stove!
     (5’’’)   PAST(t* & NOT(I turn off the stove))
     (8)      (5’’’) is true at 5PM if and only if ‘I turn off the stove’ is
     false at some time t* in the past of 5PM coinciding with the mo-
     ment the speaker is referring to (univocally described by the nom-
     inal “t*”).


These truth conditions can be depicted as follows (the green spot on
the time line represents the presupposed antecedent event of you turn-
ing on the stove and is added to have a complete pictorial representa-
tion of the situation, the red spot represents the event of you not turn-
ing off the stove at the crucial moment identified by the nominal “t*”):



36
                                                Critical Hermeneutics, special 2 (2020)




                                           t*                       t0 (= 5PM)


                                                                  Present time


     I turn on the stove                I do not turn off the stove


Fig. 4. “I didn’t turn off the stove”



In conclusion, the introduction of nominals – propositions that are True
at exactly one moment – endow Prior’s tense logic with the referential
power that this logic lacked.


2.4. Hybrid Tense Logic and Reichenbachian semantics of tense
An account of tense that is usually presented as an antagonist to Prior’s
is due to Hans Reichenbach, who proposed an apparently more com-
plex analysis of natural language tenses. A strong empirical motivation
for Reichenbach’s analysis comes from compound tenses, e.g. the Past
Perfect in (9), as opposed to the Simple Past in (10):


     (9)      [CONTEXT SENTENCE: Mary arrived at 3PM.] Peter had
              left.
              (Inference: Peter’s departure happens earlier than Mary’s
              arrival)


     (10)     [CONTEXT SENTENCE: Mary arrived at 3PM.] Peter left.
              (Inference: Mary’s arrival happens as early as Peter’s
              departure)


     In his Elements of Symbolic Logic, Reichenbach writes:




                                                                                    37
Fabio Del Prete, Temporal location of events in language




        “A particularly important form of token-reflexive symbol is
        found in the tenses of verbs. The tenses determine time with
        reference to the time point of the act of speech, i.e., of the
        token uttered. A closer analysis reveals that the time indica-
        tion given by the tenses is of a rather complex structure. […]
        From a sentence like [(9)] we see that the time order ex-
        pressed in the tense does not concern one event, but two
        events, whose positions are determined with respect to the
        point of speech. We shall call these time points the ‘point of
        the event’ and the ‘point of reference’. In the example the
        point of the event is the time when Peter [left]; the point of
        reference is a time between this point and the point of speech.
        In an individual sentence like the one given it is not clear
        which time point is used as the point of reference. This deter-
        mination is rather given by the context of speech” (Reichen-
        bach 1947; I added the emphasis).


        In this passage, Reichenbach draws his famous three-way distinc-
tion:


        • Speech point (S, time point of the token)
        • Reference point (R, the time of reference with respect to which
          the event is temporally located)
        • Event point (E, the running time of the event)


This seems indeed to introduce some complexities with respect to
Prior’s analysis. In particular, the notion of reference point does not
seem to correspond to any construct in Prior’s tense logic. However,
recall that Prior’s tense operators can be iterated (e.g. [4a]-[4d]); if
we add to this the referential power provided by nominals, the prima
facie difference between the two approaches might vanish.



38
                                                 Critical Hermeneutics, special 2 (2020)




     It has indeed been shown that Hybrid Tense Logic allows for a
unification of Prior’s and Reichenbach’s insights about tense. A contri-
bution in this direction comes from the work of Patrick Blackburn
(Blackburn 1993, 1994). More recently, Blackburn and Jørgensen
(2016) have argued “that Prior and Reichenbach are best viewed as
allies, not antagonists” and they’ve done so “by combining the central
insights of Prior and Reichenbach in the framework of hybrid tense
logic”. We illustrate how such a unification works via a couple of exam-
ples.
     For sentence (9), we have the following Reichenbachian analysis:


                 E       R                                           S
PAST                                                                         FUTURE


                                                                Speech point
    Peter leaves           contextually salient reference point
                                     (= Mary’s arrival)
Fig. 5. Reichenbachian analysis of “[Mary arrived at 3PM.] Peter had left”



     Using “r*” as a nominal describing the reference point R, we obtain
the Hybrid Tense Logic analysis (9’) for (9):


     (9’)     PAST(r* & PAST(Peter leaves))


That is: it has been the case in the past that r* is True – and this takes
us back to the time of Mary’s arrival – and it has been the case in the
past of this other time that Peter leaves. This gives us the correct tem-
poral order by which Peter’s departure precedes Mary’s arrival.
     For (10), we have the following Reichenbachian analysis (temporal
coincidence between the event point and the reference point is de-
picted as spatial contiguity of the respective spots on the time line):



                                                                                     39
Fabio Del Prete, Temporal location of events in language




                      E=R                                           S
                                                                         FUTURE


                  Peter leaves                               Speech point
Fig. 6. Reichenbachian analysis of “[Mary arrived at 3PM.] Peter left”



Again, using “r*” as a nominal describing the reference point R, we
obtain the Hybrid Tense Logic analysis (10’) for (10):


     (10’)    PAST(r* & Peter leaves)


That is: it has been the case in the past that r* is True – again, this
takes us back to the time of Mary’s arrival – and that Peter leaves. This
correctly gives us the coincidence between Mary’s arrival and Peter’s
departure.


2.5. Interaction between tense and temporal adverbs
Time adverbs are typically used to constrain the temporal location of
events (Dowty 1979). Consider (1a) again, repeated as (11):


     (11)     (Ieri) il presidente era a Bruxelles




40
                                                 Critical Hermeneutics, special 2 (2020)




                                   YESTERDAY




                          E (= R)                             S
PAST                                                                         FUTURE


            The president is in Brussels                     Speech point
Fig. 7. Semantic contribution of “yesterday”



Semantically, adding the temporal adverb to the tensed verb in (11)
comes down to constraining the temporal location of the event within
the boundary of a particular time in the past: that past interval which
corresponds to the day before the day of the utterance.


2.5.1. Operator-based analysis of temporal adverbs
David Dowty presents a problem for a prima facie plausible analysis of
temporal adverbs in terms of Prior-style tense operators. He considers
the following tentative analysis for the adverb “yesterday” (Dowty
1979):


     • YESTERDAY(p) is true at t iff p is true at some time t' in the
         past of t which is within the day before t


                              Day-before-the-day-of-t


                         t'                                     t
PAST                                                                         FUTURE
                         P                           YESTERDAY(p)
Fig. 8. Operator-based analysis of “yesterday”




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Fabio Del Prete, Temporal location of events in language




Let’s assume now that (11) has the logical structure in (12) below. This
formula then receives the truth conditions in (13):


      (12) YESTERDAY(PAST(The president is in Brussells))
      (13) “YESTERDAY(PAST(The president is in Brussells))” is true at
      t iff “PAST(The president is in Brussells)” is true at some time t'
      in the past of t which is within the day before t iff “The president
      is in Brussells” is true at some time t'' such that, for some time t'
      in the past of t which is within the day before t, t'' is in the past of
      t


These truth conditions can be depicted as in Figure 9:


                                                  YESTERDAY


                    t"                       t'                        t




 The P. is in Br.        PAST(the P. is in Br.)         YESTERDAY(PAST(the P. is in Br.))



Fig. 9. “YESTERDAY(PAST(The president is in Brussels))”



Clearly, this analysis does not work: it predicts that (11) is true now if
the president was in Brussels one year ago. In other words, the anal-
ysis in question predicts that (11) means the same as “At some point
within yesterday it was true that the president had been in Brussels in
the past of that point,” which clearly is not the case. The same problem
arises if we reverse the order of the operators PAST and YESTERDAY
in (12), as shown in (14) (Dowty 1979: 323).




42
                                           Critical Hermeneutics, special 2 (2020)




    (14)    PAST(YESTERDAY(The president is in Brussells))


This alternative analysis does not work either since it predicts that (11)
means the same as “At some point in the past it was true that the
president had been in Brussels on the day before that point,” which is
also true now if the president was in Brussels one year ago.
    In conclusion, we need to provide an account of the interaction
between tense and temporal adverb which does not run into the em-
pirical problem above – possibly keeping to Dowty’s idea to treat “yes-
terday” as a Prior-like temporal operator.


2.5.2. Temporal adverbs in Hybrid Tense Logic
Hybrid tense logic helps us out of the problem of the interaction of
tense and time adverbs. The crucial insight is twofold: (a) the past
tense and the temporal adverb both take scope over the nominal r*
representing the reference point, and (b) they do so independently
from one another. This scope and independence properties are shown
by the hybrid tense logical formula in (15), which is evaluated as in
(16):


    (15)    PAST(r* & the president is in Brussels) & YESTERDAY(r*)


    (16) (15) is true at time t iff
           (a)    ‘the president is in Brussels’ is true at some t’ in the
           past of t coinciding with the moment the speaker is referring
           to which is univocally described by r*;
           (b)    r* is true at a time t’ in the past of t which is within
           the day before t.




                                                                               43
Fabio Del Prete, Temporal location of events in language




The truth conditions in (16) correctly capture the temporal fact (in-
volved in the meaning of [1a]) that ‘the president is in Brussels’ is true
at some time t’ in the past of t which is within the day before t.
     To summarize, the present section has been essentially devoted
to presenting an outstanding formal approach to the semantics of
tense, keeping an eye to its historical development. For the sake of this
exposition, I have assumed the representation of time as a directed
line, largely used by linguists, without problematizing it. In the next
section I turn to some substantive questions regarding time as is rep-
resented in language.


3.   Directionality of time in language and branching futures
In this section I present linguistic data supporting the view of (a) the
directionality of time and (b) the asymmetry between the uniqueness
of the past and the plurality of the (possible) future(s).


3.1. Temporal asymmetries: polarised scalar adverbs
Having regard to the properties of time, some telling asymmetries ap-
pear as soon as we consider data such as the contrasts below (two
interrogative marks in front of a sentence indicate that this is seman-
tically anomalous):


     (17)     a. È già tardi.
               ‘It is already late’
              b. ??È ancora tardi.
               ‘It is still late’


       (18) a. È ancora presto.
               ‘It is still early’
              b. ??È già presto.
               ‘It is already early’



44
                                                 Critical Hermeneutics, special 2 (2020)




The so-called “phase adverbs” già ‘already’ and ancora ‘still’ display a
puzzling behaviour in their interaction with the gradable adverbs presto
‘early’ and tardi ‘late’: each one of the former can meaningfully modify
only one of the latter. Why so?
     Let’s characterize the contrasts above by drawing some pictures.
First, we associate the adverbs presto and tardi with two regions of the
time scale, separated by a transition point, i.e., a moment in time at
which it is not early anymore and it is not late yet; the region associ-
ated with presto is located to the past side, while the region associated
with tardi to the future side – obviously so, since what happens earlier
in time becomes past at a point at which what happens later is future.


                             transition point
  PAST                                                                    FUTURE
                presto                                 tardi
Fig. 10. Transition between the two regions presto – tardi on the time scale



The rationale behind the “pastward” orientation of the presto-arrow
and the “futureward” orientation of the tardi-arrow is simple: presto
has degrees that grow as you move from later times to earlier times,
while tardi the other way round.
     Next, we associate the adverbs ancora and già with two regions of
some scale (not necessarily the time scale, for reasons clarified below),
separated by a transition point, i.e., a point at which a certain property,
P1, does not hold anymore while the opposite property, P2, does not
hold yet; the region associated with ancora is located to the “low val-
ues” side of the scale while the region associated with già is located to
the “high values” side.




                                                                                     45
Fabio Del Prete, Temporal location of events in language




                              transition point
       P1                                                                P2
               ancora                                      già
Fig. 11. Transition between the two regions ancora – già on a relevant scale (asso-
ciated with gradable properties P1, P2)


It may not be obvious why ancora and già should be associated with
regions of the scale in this way. Here is why:


     • ancora indicates that some gradable property, P1, continues to
     hold as one proceeds to values on the scale that are ever closer
     to the Point of Transition, PT; starting from PT, P1 ceases to hold
     and a gradable property P2, opposite to P1, begins to hold;
     • già indicates that P2 has begun to hold and will moreover hold
     at all higher values on the scale.


Hereafter, I refer to ancora and già as “polarised scalar adverbs”: their
meanings are defined on some relevant scale (which may be the time
scale or other) and they are “polarised” since they are associated to
opposite poles on that scale.


3.1.1. Polarised scalar adverbs in non-temporal domains
Consider the following context:


     Context NT1. We are looking for tall persons for a certain task
     (say, to pick fruits from apple trees). The minimal height required
     to do the task is 1m80cm (the transition point). Two candidates
     come to us, Leo and Teo, whose heights are 1m85 and 1m75,
     respectively.




46
            (3a)    Leo è già alto.
                     una persona dell'altezza di Leo
                                            Critical    (che non special
                                                     Hermeneutics, è granché)  o più alta può esse
                                                                         2 (2020)



            (4a)Teo è ancora basso.
We can representtheunasituation  of ContextdiNT1
                         persona dell'altezza  Teovia
                                                   (cheanon
                                                         scale of height
                                                            è proprio poco) o più bassa n
measures, ordered from   smaller
                    ancora  sceltameasures (in a region of the scale that
we associate with the property ‘short’) to greater measures (in a region
           Inthat
of the scale  questo
                  wecaso, la scalawith
                     associate     di riferimento rispetto
                                       the property         alla quale gli avverbi "già" e "ancor
                                                      ‘tall’):
            interpretati è questa:

                                     transition point
                                        •        •
                                 Teo's height   Leo's height
            short                                                    tall

Fig. 12. The situation of Context NT1



     Now, consider (19), as uttered in Context NT1:


     (19)     Leo è 1m85, è già (abbastanza) alto. Teo è 1m75, è ancora
              (troppo) basso.
              ‘Leo is 1m85, he’s already (enough) tall. Teo is 1m75, he’s
              still (too) short’.


This sentence would be true in the envisaged situation. However, sen-
tence (20), as uttered in Context NT1, would be meaningless:


     (20)     Leo è 1m85, è ancora alto. Teo è 1m75, è già basso.
              ‘Leo is 1m85, he is still tall. Teo is 1m75, he is already
              short’.


     Let’s now consider the following alternative to Context NT1:


     Context NT2. We are looking for short persons for another task
     (say, to work in a room with a low ceiling). The maximal height
     allowed for this task is 1m80cm. Two candidates come to us, Leo
     and Teo, whose heights are 1m85 and 1m75, respectively.



                                                                              47
Fabio Del Prete, Temporal location of events in language




Again, we can represent the situation of Context NT2 via a scale of
height measures, but notice that this time the height measures will be
ordered from greater ones to smaller ones:


                                 transition point (1m80)


           tall               Leo’s height        Teo’s height     short


Fig. 13. The situation of Context NT2



If we now consider (20) again, but this time as uttered in Context NT2,
we can see that, far from being meaningless, (20) is now true. On the
other hand, (19), which was true as uttered in Context NT1, as uttered
in Context NT2 is meaningless!
     We interpret the observations above by noting the following prop-
erties of già and ancora (we are focusing here on their use in non-
temporal domains):


     • “Già” indicates upward persistence of a property.
        [In Context NT1: Leo’s height is enough and the same is true of
        any height following Leo’s on the relevant scale (Fig. 12); in
        Context NT2: Teo’s height is small enough and the same is true
        of any height following Teo’s on the relevant scale (Fig. 13)].


     • “Ancora” indicates downward persistence of a property.
        [In Context NT1: Teo’s height is not enough and the same is
        true of any height preceding Teo’s on the relevant scale (Fig.
        12); in Context NT2: Leo’s height is not small enough and the
        same is true of any height preceding Leo’s on the relevant scale
        (Fig. 13)].



48
                                              Critical Hermeneutics, special 2 (2020)




(Compare these properties with what was captured in Figure 11).


3.1.2. Polarised scalar adverbs in the temporal domain
Take the following context:


     Context T1. We are waiting for our friends, Leo and Teo, at a birth-
     day party. They are expected to arrive by 9PM. Leo arrives by the
     expected time, but at 9:10PM Teo still has to arrive.


     We can represent this situation via the usual time scale (where
times are ordered from earlier to later):
                                   9:10PM
 PAST                                                                    FUTURE
                      Leo’s arrival         Teo’s arrival
Fig. 14. The situation of Context T1



Suppose that at 9:10PM we utter (21):


     (21) Leo è già arrivato. Teo ancora non è arrivato.
            ‘Leo has already arrived. Teo still has not arrived’


This sentence is true in the envisaged situation. On the other hand,
sentence (22), as uttered in Context T1, would be meaningless:


     (22) ??Leo è ancora arrivato. Teo è già non arrivato.
            ‘Leo has still arrived. Teo has already not arrived’


Let’s focus on the left sentence of (21) (Leo è già arrivato ‘Leo has
already arrived’). Figure 15 depicts that part of its meaning –




                                                                                  49
Fabio Del Prete, Temporal location of events in language




contributed by già – that I characterize in terms of forward persistence
of a state (in time):


                                   9:10PM
     Past                                                         Future
              Leo’s arrival           e           e         e
                 [e = (state of) Leo having arrived]
Fig. 15. Forward persistence of Leo having arrived



The idea is simple: Leo arrived (at some point before 9PM), and from
that point onward it will be forever true that Leo arrived.
      Turning to the right sentence of (21) (Teo ancora non è arrivato
‘Teo still has not arrived’), Figure 16 depicts that part of its meaning –
contributed by ancora – that I characterize in terms of backward per-
sistence of a state (in time):


                                     9:10PM
     Past                                                         Future
                  e        e        e          Teo’s arrival
                 [e = (state of) Teo not having arrived]


Fig. 16. Backward persistence of Teo not having arrived (yet)



The idea, again, is simple: Teo has not arrived (yet) by some point
after 9PM, and moving to the past of that point it is always true that
Teo has not arrived (yet).
      We interpret the observations above by noting the following prop-
erties of già and ancora (this time we are focusing on their use in tem-
poral domains):




50
                                                 Critical Hermeneutics, special 2 (2020)




     • “Già” indicates forward persistence of a state in time; with a
        formula:
        t  I [(t) & t’  I [t < t’ → (t’)]]
        [Leo’s having arrived holds at 9:10PM and it also holds at any
        time following 9:10PM on the time scale]
     • “Ancora” indicates backward persistence of a state in time; with
        a formula:
        t  I [(t) & t’  I [t’ < t → (t’)]]
        [Teo’s not having arrived holds at 9:10PM and it also holds at
        any time preceding 9:10PM on the time scale]


Let’s now turn to the following alternative to Context T1 – this is in all
respects like Context T1, except that we are now trying to reverse the
time scale (via the “thought experiment” added in italics to the context
description)3:


     Context T2. We are waiting for our friends, Leo and Teo, at a birth-
     day party. They are expected to arrive by 9PM. Leo arrives by the
     expected time, but at 9:10PM Teo still has to arrive. We feel angry
     at Teo – he is always late! – and to defocus from our unpleasant
     feeling we imagine Teo’s arrival as being already there, to the fu-
     ture, as much real as Leo’s past arrival, and we imagine that we
     are moving through time from Teo’s arrival back to Leo’s arrival.


This time the situation is represented as follows (notice the peculiar
orientation of the time line from the future to the past, i.e. the ordering
of times from later to earlier):




3
 We want to see if we can rescue (22) by inverting the “natural” (earlier-to-later)
order of times. Recall that, in the passage from Context NT1 to Context NT2, we were
able to rescue (20) by inverting the order of the degrees of height.



                                                                                     51
Fabio Del Prete, Temporal location of events in language




                                       9:10PM
     Future                                                        Past
                      Teo’s arrival            Leo’s arrival
Fig. 17. The situation of Context T2



Crucially, (22) continues to be meaningless, even if considered as ut-
tered in Context T2 – hence, against the reversed time scale of Fig. 17.
On the one hand, the left sentence of (22), if it could ever mean any-
thing, would mean the same as ‘at 9:10PM, Leo is still (in the state of
having) arrived;’ this doesn’t seem to be a meaningful thought to be
ever expressed! On the other, the right sentence of (22), if it could
ever mean anything, would mean the same as ‘at 9:10PM, Teo is al-
ready (in the state of having) not arrived;’ this, too, doesn’t seem to
possibly make any sense!
       The moral of this section concerns a fundamental difference be-
tween time versus other types of scales. The different behaviour of the
adverbs ancora / già in the non-temporal contexts NT1 - NT2 and in
the temporal contexts T1 - T2 suggests that the natural ordering char-
acterizing time cannot be reversed in the same way as the smaller-to-
greater relation characterizing the scale of degrees of height (we chose
the pair of predicates alto - basso but we could have made our point
by picking a different pair of non-temporal antonyms).


3.2. Asymmetry between past and future
Section 3.1. has shown some evidence that time is represented as di-
rectional in language: unlike other kinds of scales that natural language
meanings rely on, time is characterized by a “natural” ordering that is
not reversible. We consider now whether there are other properties of
time, revealed by linguistic data, that may have a relation to this di-
rectionality property. It turns out that there is another one, on which



52
                                         Critical Hermeneutics, special 2 (2020)




an abundant literature on the asymmetry between the linear past and
the branching future has flourished.


3.2.1. Many futures, one past
There are data suggesting that the traditional linear representation of
time is too simplistic – this representation may be useful for the pur-
pose of analysing certain temporal aspects of natural language mean-
ing, but it is limited when one comes to the analysis of more subtle
data at the crossroads of temporality and modality.
    Consider the contrast between (23a) and (23b):


    (23)      a. The meeting will take place in Room C, unless the
              management makes the Aula Magna available;
              b. The meeting took place in Room C, unless the man-
              agement made the Aula Magna available.


On the one hand, (23a) expresses a condition for the future occurrence
of the meeting in Room C, namely that the management will not choose
the Aula Magna instead. The “unless” clause in this sentence introduces
this condition without making it so that the main clause in the future
tense (“The meeting will take place in Room C”) is not asserted – the
latter is asserted in spite of the “unless” clause, which only has the
effect of qualifying the assertion (Condoravdi 2003). In (23b), on the
other hand, the “unless” clause has a different effect: it makes it so
that the main clause in the past tense (“The meeting took place in
Room C”) can no longer be seen as asserted, once the “unless” is pro-
cessed.
      Another relevant contrast is that between (24a) and (24b):


    (24)      a. The management made the Aula Magna available
                   before the meeting took place in Room C;



                                                                             53
Fabio Del Prete, Temporal location of events in language




                 b. The management made the Aula Magna available af-
                     ter the meeting took place in Room C.


On the one hand, in (24a) the meeting taking place in Room C is still
future with respect to the management making the Aula Magna avail-
able and the very fact that the management made the Aula Magna
available may well have had the effect that the meeting didn’t take
place in Room C after all (because it probably took place in Aula Magna
instead). On the other hand, in (24b) the meeting taking place in Room
C is already past with respect to the management making the Aula
Magna available, and the fact that the management made the Aula
Magna available cannot possibly have had the effect that the meeting
didn’t take place in Room C – what is past cannot be canceled.
     Let’s consider one final contrast, the one between the Question-
Answer pairs in (25a) and (25b):


     (25) a.      Q: Where will the meeting take pace?
                  A: The ministers have two places available. It may take
                  place in Room C or in Aula Magna’;
           b.     Q: Where did the meeting take pace?
                  A: The ministers had two places available. It may have
                  taken place in Room C or in Aula Magna.


Only in (25b) does the modal mean that the speaker does not know
which room, while the issue is objectively settled. In (25a) the modal
does not (at least, not necessarily) mean that the speaker does not
know which room and it means instead (at least, under a very plausible
reading of the sentence) that the issue is objectively open.
       The general idea brought to salience by such linguistic contrasts
is an old and venerable idea: the past is fixed and determinate, the




54
                                          Critical Hermeneutics, special 2 (2020)




future is open and indeterminate (Aristotle 1984, Prior 1967, Thom-
ason 1984, Belnap et al. 2001, Condoravdi 2003).




3.2.2. “Branching time” approaches to the past-future asymmetry
At this point, the Priorian attitude toward temporal language shows up
again. A little bit more formally, the idea is that our world, considered
from the perspective of any moment m0 in its history, has a unique
actual past and present – the actual past and the actual present at m0
– but many metaphysically (not just epistemically) possible futures –
the possible futures at m0. A very natural way to represent this view
diagrammatically, and to translate it next into a formal model, is the
following:
    a)   represent the unicity of the past at m0 as a single oriented
         line (usual left-to-right orientation) that ends at m0 (see the
         green line in Figure 18);
    b)   represent the plurality of the future at m0 as a manifold of
         oriented lines branching off from m0 – all such lines begin at
         m0 and proceed rightward, possibly breaking into different
         lines at subsequent moments (see the red lines in Figure 18);
    c)   represent the world itself, as considered from the perspective
         of moment m0, as the cluster of all histories passing through
         m0 – where by “history” it is meant a complete linear path
         made up of moments temporally connected with each other
         (Figure 18 shows four such histories, h1-h4).




                                                                              55
Fabio Del Prete, Temporal location of events in language




                                                                                h1
                                                    m'


                                                                                h2

                              m0                                                h3


                                                    m''
                                                                                h4
Fig. 18. “Branching Time” representation of our world from the perspective of
moment m0



The resulting model has been known as “Branching Time” (Prior 1967,
Thomason 1984, Belnap et al. 2001).
     Let me illustrate the basic concepts of Branching Time by
discussing the structure of Figure 18. This has four histories: h1, h2, h3
and h4. Moment m0 belongs to all four. It can thus be said that there
are four possible futures at m0: the four paths that our world can take
after m0, following one or the other of h1-h4. Moment m' only belongs
to h1 and h2. It can thus be said that m' only has two possible futures,
corresponding to h1 and h2, while h3 and h4, which were possible
futures at m0, are no longer possible futures at m'. Similarly, moment
m'' only belongs to h3 and h4 and can then be said to only have two
possible futures (in general, futures shrink as we move forward in time;
we come back to this shortly). Regarding the ordering of moments via
the earlier-to-later relation, not all moments are temporally connected
with each other: while m0 is in the past of both m' and m'' (and is so
connected with both), m' is not in the past of m'' nor is m'' in the past
of m' (thus, m' and m'' are not connected with each other). The fact is



56
                                          Critical Hermeneutics, special 2 (2020)




that m' and m'' are moments lying on alternative futures; each of these
futures may end up becoming actual, but, crucially, they could not
become both actual (though many alternative courses of events may
be possible at a given point, history always ends up realizing only one
of them).
    Notice that the Branching Time model lends itself naturally to a
“growing block” view of the past: the past of our world “grows” as we
move forward in time, for instance from m0 to m' (the past at m' is a
“larger block” than the past at m0). This is a sense – the only sense –
in which the past can be said to “change”. In all other respects, it is
immutable. In particular, what is past at a moment mi continues to be
past at any later moment mj; in this sense, there may be no loss of
past as time goes by. One thus finds a sharp contrast with the future:
what is a possible future at a moment mi may no longer be a possible
future at a later moment mj; in this sense, there may be loss of possible
futures as time goes by.
    The Branching Time model allows us to account for the
asymmetries observed in the interpretation of (23a,b), (24a,b) and
(25a,b) above. To prove this, I should provide formal analyses in
Branching Time of the relevant linguistic constructions featuring in
those sentences. For reasons of space, I’ll confine myself to discussing
the before / after contrast in (24a,b), against the temporal structure of
Figure 18. Suppose that (i) the management makes the Aula Magna
available at m0, (ii) the meeting takes place in Room C at m' but not at
m" (notice that supposition (ii) is coherent since m' and m" are on
alternative futures for m0, and what happens in one future may not
happen in the other). Suppose further that, (iii) right after m0, the
world takes the path of history h4, thus going through the moment m"
in which the meeting does not take place in Room C. Given (i)-(iii), an
utterance of (24a) made right after m0 would be True: the Aula Magna
is made available at a moment, m0, at which the meeting taking place



                                                                              57
Fabio Del Prete, Temporal location of events in language




in Room C has not occurred yet and the latter event occurs at a
moment, m', in a possible future of m0; however, the event in question
does not occur in a different future of m0, i.e. h4, which ends up
becoming the actual future.
     Suppose now that (a) the meeting takes place in Room C at m0,
(b) the management makes the Aula Magna available at m', and (c)
right after m0, the world takes the path of history h1, thus going
through the moment m' in which the management makes the Aula
Magna available. Given (a)-(c), an utterance of (24b) made right after
m' would be True: the Aula Magna is made available at a moment, m',
at which the meeting taking place in Room C has already occurred,
since the latter event occurs at a moment, m0, in the past of m'; since
m' has only one past, it is not possible that the meeting taking place in
Room C does not occur in a different past of m' (once this event has
occurred, there is nothing you can do which could make it not have
occurred!).
     The two reasonings above are just a sketch of an account of how
A before B can be true in a history without B ever being true in that
history and how A after B can be true in a history only when B is also
true in that history4.


3.2.3. Formal analyses of the past and the future tenses in Branching Time
As we consider the future tense, the Branching Time model offers us
different options to formally analyse it. The availability of different
options is expected, given the complexity of the future dimension that
is captured by this model.
     One important option is the so-called “Peircean future” (Prior
1967):


4
 These properties are known as the “non-veridicality” of before (the truth of A before
B does not entail that B is true) and the “veridicality” of after (the truth of A after B
entails the truth of B). See Beaver and Condoravdi 2003.



58
                                             Critical Hermeneutics, special 2 (2020)




     • “FUT(p)” is true at m0 if and only if “p” is true at a moment
       following m0 in every history passing through m0


                                                            p             h1
                                        m0
                                                                p           h2
                                      FUT(p)                    p
                                                                          h3
Fig. 19. “Peircean” future



On the Peircean solution, future tensed sentences are essentially
necessity modal sentences. This solution thus predicts that the future
contingent statement (FC) is equivalent to the necessity modal
statement (NF):


     (FC)     There will be a sea battle tomorrow.
     (NF)     It is now necessary that a sea battle will occur tomorrow.


     This can be criticized as an undesirable outcome of the solution in
question.
     Another notable solution is known as the “Ockhamist future” (Prior
1967):




                                                                                 59
Fabio Del Prete, Temporal location of events in language




     • “FUT(p)” is true at m0 if and only if “p” is true at a moment
       following m0 in the history h* that will be actual (Prior 1967)


                                                           p      h*
                                             m0
                                                                   h2
                                            FUT(p)
                                                                  h3
Fig. 20. “Ockhamist” future



The Ockhamist solution is based on the idea that, although there are
many possible futures at m0, only one of these will be actual (the one
corresponding to h* in Figure 20) and a future tensed statement made
at m0 targets this only future. This solution has the following
consequence: if I assert at m0 “there will be a sea battle tomorrow”
and on the day following the day of m0 (in the history that becomes
actual) there happens (not) to be a sea battle, then my assertion is
(not) True, regardless of what happens in the other histories that were
possible futures at m0. This consequence has some intuitive appeal –
we do look at what actually happened when we have to assess past
utterances of future tensed sentences for truth (MacFarlane 2003).
Besides this, the Ockhamist solution (unlike the Peircean) preserves
the contingent character of (FC) above, as distinct from the necessity
modal statement (NF). I’ll leave it open what is the empirically most
adequate analysis of the future tense in Branching Time.
     Let’s turn to the past tense. It should be obvious that Branching
Time does not provide us with several options in this case – for a
“backward looking” tense operator (like PAST), it does not make any
difference whether the temporal structure is the traditional linear
structure, or whether it is the tree-shaped structure of Branching Time:
as long as we look backward in time, we always face a linear path. The



60
                                              Critical Hermeneutics, special 2 (2020)




past tense operator can thus be defined in the following straightforward
way (making no reference to any particular history):


     • “PAST(p)” is true at m0 if and only if p is true at a moment m'
       preceding m0


                                                                           h1
                        m'               m0
                                                                             h2
                          p            PAST(p)
                                                                           h3


Fig. 21. The past in Branching Time



Since there is a unique history (or, more precisely, a unique path) going
backward from moment m0, the past tense does not raise a problem of
definition in the same way as the future tense does. We only need to
look at that unique past history (path) and check whether it contains a
moment at which p holds or not.
     Given Branching Time, there is a sense in which PAST(p), unlike
FUT(p), when true, is not just contingently true but true by necessity:


     • If p is now past, then it is now necessary that p is past (thesis of
       the “necessity of the past”).


The relevant notion of necessity is what has been called historical
necessity (Thomason 1984); taking the symbol “NEC” to denote
historical necessity, this notion can be defined as in (HN) and the above
thesis of the “necessity of the past” can be formulated as in (NP):


     (HN)    “NEC(p)” is true at m if and only if “p” is true at m in every



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     history passing through m


     (NP)     PAST(p) → NEC(PAST(p))


In conclusion, Branching Time provides for a sense in which the past is
necessary. This is the way in which this model formally captures the
standard view of the non-modifiability (or persistence) of the past. In
the next section I introduce a puzzle that challenges this view.


4.   The Puzzle of the “Changing Past”
Barlassina and Del Prete (2015) (hereafter, B&DP) present the
following    puzzle    about    the    past.    Preliminarily,   some   technical
vocabulary:


     • People utter sentences at contexts, represented as pairs <w, t>
       of a world and a time (the world and the time of the utterance).
     • Sentences express propositions at contexts.
     • A sentence S is temporally specific if and only if, for any context
       c, the proposition expressed by S at c is about a specific time.
     • A sentence S is about the past in a context c if and only if the
       proposition expressed by S at c is about a time that precedes c.
     • A temporally specific sentence S that is about the past in a con-
       text c is true in c if and only if the time the proposition p ex-
       pressed by S in c is about has, relative to the past of c, the prop-
       erty that p ascribes to it.
     • A context c' is a successive same-world context to context c if
       and only if:
       the world of c' is the same as the world of c,
       the time of c' follows the time of c.
     • A sentence is context-insensitive if and only if it expresses the
       same proposition at all contexts.



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Their starting point is what they take to be a platitude: we say true
(false) things about the past and the truth (falsity) of what we say
depends on how the past is. This is made formally precise as follows:


    • Truth About the Past (TAP)
      Let S, c, p, Q, t be such that: S is a temporally specific sentence
      that is about a past time in context c, p is the proposition ex-
      pressed by S at c, and Q is the property that p ascribes to the
      specific time t. Then, S is true in c if and only if t has property Q
      relative to the past of c.


To see how TAP works, consider sentence


    (26)    Barack Obama was born in 1961


as uttered in context <@, 23rd May 2019> – this consists of our actual
world @ and time 23rd May 2019; (26) is temporally specific (it is about
the year 1961), it is about the past (the year 1961 is in the past of 23rd
May 2019), and the proposition it expresses at <@, 23rd May 2019>
(i.e., that Obama was born in 1961) ascribes to the year 1961 the
property of being a time in which Obama was born. By TAP, (26) is true
in <@, 23rd May 2019> since, relative to the past of <@, 23rd May
2019>, the year 1961 has indeed the property of being a time in which
Obama was born.
    B&DP ask us next to consider the following story (almost true –
apart from the fictional character of Frank):


    “It is the 23rd of July 2000. Being the rider with the lowest
    overall time at the end of the last stage, Lance Armstrong is
    declared the winner of the Tour de France by Union du



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     Cyclisme Internationale (UCI). On <@, 25th December 2002>
     (hereafter, Context A), Frank utters [(27)]:


     [(27)] Lance Armstrong won the Tour de France in 2000.


     There is a clear intuition that Frank said something true. Time
     goes by. Having discovered that Armstrong made use of
     banned substances, on the 22nd of October 2012 UCI
     withdraws all of Armstrong’s wins at TdF. As Frank is not
     aware of this fact, he utters [(27)] again at <@, 25th
     December 2012> (hereafter, Context B). This time, it seems
     that Frank said something false”.


Based on this story, they present the following reasoning, leading to
the paradoxical conclusion in F:


     (A) (27) is a temporally specific sentence: for any context c, the
           proposition expressed by (27) at c is about the year 2000;
     (B) (27) is about the past in both Context A and Context B;
     (C) (27) is context-insensitive (it does not contain any context-
           sensitive element – demonstratives, indexicals, or the like),
           hence it expresses the same proposition at both Context A
           and Context B, namely, that Armstrong won the TdF in 2000;
     (D) (27) is true in Context A, hence it follows from TAP that, rel-
           ative to the past of Context A, the year 2000 has the property
           of being a time in which Armstrong won the TdF;
     (E) (27) is false in Context B, hence it follows from TAP that, rel-
           ative to the past of Context B, the year 2000 does not have
           the property of being a time in which Armstrong won the TdF;
     (F) Context B is a successive same-world context to Context A
           (Context A and Context B are located in the same world, @),



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         hence in moving from Context A to Context B the past (of the
         actual world) has changed: the year 2000 had a certain prop-
         erty on Christmas 2002, but did not have that property on
         Christmas 2012 any longer.


B&DP consider two objections to the puzzling conclusion in (F). The
first one contends that there is no truth value change for (27), hence
questioning the joint truth of (D) and (E). One variant of this objection
consists in claiming that (27) was already false in Context A because
Armstrong got the lowest time only by cheating. The other variant
consists in claiming that (27) was still true in Context B because sincere
and informed speakers assert (27), or sentences implying (27), after
the revocation of Armstrong’s titles (for instance, they assert true
historical sentences such as “Armstrong won the TdF seven times from
1999 to 2005. He was later stripped of those titles for doping” …). The
second objection contends that (27) has some hidden context-
sensitivity (due to the verb phrase ‘win the TdF in 2000’), against
assumption (C): in Context A, (27) would express the proposition that
Armstrong won the TdF in 2000 according to the declaration of Context
A, but in Context B, it would express the different proposition that
Armstrong won the TdF in 2000 according to the declaration of Context
B. B&DP reply to each objection with detailed linguistic arguments that
I cannot recall here. Notice that, if they are right, there might be other
cases in which our past can change and this would force us to try to
make sense of this.


5.   Conclusion
We reviewed some classical approaches, from logic and philosophy, to
temporal meaning in natural language, beginning with the subject of
temporal location of events in language and moving then to general
properties of time as may be revealed by semantic analysis.



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Throughout the article, the analytical attitude toward temporal
language has been inspired by the sort of logical approach to time and
tense that Prior developed in the 1950s and ’60s. Building on previous
work on historical modalities, we introduced the asymmetry between
closed past and open future, showing some linguistic correlates of it,
and presented the Branching Time model as a formal tool to capture
this asymmetry and to build enlightening semantic analyses of a
number of linguistic contrasts. Finally, we considered a paradoxical
argument whose conclusion challenges the traditional view of the
persistence of the past. If its proponents are right, we should stop
asking whether the past can change and start to think how this could
be. One might notice that the argument is based on a special property
of winning events, namely their annullability, and on this basis might
contend that the puzzle is not generalizable to other sorts of events
that are not annullable in the same way – for instance: though it was
possible for UCI in 2012 to make it the case that Armstrong did not win
the TdF in 2000, how could it be possible for anyone after the 2000
TdF to make it the case that Armstrong did not have the lowest overall
time at the end of the last stage or that he did not ascend the Hautacam
on the 10th of July? It seems hard to erase events of the latter sort
from history. These speculative remarks raise the question of a
distinction between two sorts of events, with events such as winning
the TdF being of one sort and events such as ascending the Hautacam
on   a   bicycle    being    of   the   other    sort.     Providing   an   explicit
characterization of the two sorts of events – one which would allow for
a neat separation, among the events reported in our historical
narratives, between events of one sort and events of the other sort –
might prove to be a difficult task.


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