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Review of  Semantics, Tense, and Time

Reviewer: Görel Sandström
Book Title: Semantics, Tense, and Time
Book Author: Peter Ludlow
Publisher: MIT Press
Linguistic Field(s): Semantics
Issue Number: 11.1813

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Peter Ludlow (1999), Semantics, Tense, and Time: An Essay in
the Metaphysics of Natural Language. [A Bradford Book] Cambridge,
Massachusetts: The MIT Press. xxi + 252 pp. $45.00/�29.95

Reviewed by:
Gorel Sandstrom and Rognvaldur Ingthorsson, Department of Philosophy
and Linguistics, Umea university

The book under review argues for a version of the so-called "A-series"
conception of the nature of time, and against the opposing "B-series"
conception. The two series are defined as follows (cf. the
Introduction, p. 2)
- The B-series is reducible to the A-series.
- Temporal becoming is intrinsic to all events.
- There are important ontological differences between past and
- Change is analyzable solely in terms of A-series relations (past,
present, future)
- The A-series is reducible to the B-series
- Temporal becoming is psychological.
- The B-series is objective. All events are equally real.
- Change is analyzable solely in terms of B-series relations
(earlier-than, later-than).
According to the preface, however, the particular argument outlined is
not the main concern of the author, which is rather to "illustrate an
approach to metaphysics in which semantical theory and the philosophy
of language are central" (p. xvii). Thus, a large part of the text is
concerned with examining the extent and kind of "metaphysical
commitment" of different semantic theories of tense.

The book is divided into ten chapters of varying length, preceded by
an Introduction and followed by two "philosophical" and five
"technical" Appendices, notes and references. The philosophical
appendices contain discussions of I-language as the language of
thought (touched on in Chapter 1) and of language-world isomorphism (a
possibility hinted at in Chapter 4); the technical appendices present
T-theories for fragments of English using different semantic theories.

After the Introduction, which presents the argument in outline and
gives an overview of the remainder of the book, Chapters 1-3 lay the
groundwork for what is to follow by presenting some basic assumptions
and theoretical choices. Chapter 1, "The nature of language", argues
for language as I-language in the sense of Chomsky (1986), and against
the idea that I-language is "for" communication ("for" is taken here
in the rather strict sense of "evolved for the purpose of".) Ludlow
also argues against a "third medium" between I-language and the world,
on the grounds that such a medium would be redundant, an argument
which is expounded on in Appendix P1. A central assumption is that all
thoughts we have about the world ("genuine representational thoughts")
are propositional ? which here means that they are stored in the form
of interpreted logical forms (ILFs), i.e. phrase markers whose nodes
are paired with semantic values.
In Chapter 2, "The form of the semantic theory", Ludlow argues for
a particular form of semantic theory to characterize the first-order
semantic knowledge that an agent has, namely, an absolute
truth-conditional semantics. To exemplify the "T-theory" approach, he
gives a simple fragment from Larson & Segal (1995); more complex
fragments are in Appendices T1 and T2. Besides a context-free syntax,
the theory contains two kinds of axioms, one assigning semantic values
to lexical items, the other stating how the semantic value of a mother
node can be calculated from those of the daughter nodes. The question
of whether T-theory axioms can display senses receives some
discussion, in the course of which Ludlow draws a distinction between
first-order semantic knowledge (i.e., knowledge that 'snow' refers to
snow) and second-order semantic knowledge, i.e. knowledge of the
representation of the knowledge. A correct T-theory must correctly
characterize also the latter (which amounts to "displaying senses").
Chapter 3, "Attitudes and Indexicals", starts addressing issues
pertaining to the semantics of tense. In order to ground the idea that
tense morphemes are indexical predicates wich take interpreted logical
forms (ILFs), as arguments, Ludlow discusses first ILFs as used in
another context, that of propositional attitude verbs, and then
indexicals in general. Propositional-attitude verbs are analyzed as
expressing relations between agents and ILFs; Ludlow also proposes to
handle other intentional contexts, like intensional transitive
constructions ('John wants a donkey'), in the same way: these
sentences contain a hidden clause in their LF representation
(something like 'John wants [PRO (to have) a donkey]') and are thus
amenable to ILF analysis. As for indexicals, Ludlow argues that the
"role" or "character" of the indexical need not be kept out of the
semantics of the indexical expression, in effect, that indexical
expressions like "I" can be disquotationally entered into the
right-hand side of a T-theory axiom.
In chapter 4, "Drawing Metaphysical Consequences from a T-theory",
Ludlow sets out to show where metaphysical commitment arises in an
"absolute" theory such as he has adopted. The basically Quinian
position he takes is that we are committed to the existence of
whatever semantic values we metalinguistically quantify over. An axiom
like (i) above, which is shorthand for (i'), thus commits us to the
existence of snow.
(i) Val(x, _snow_) iff x = snow
(i') For all x, Val(x, _snow_) iff x = snow
>From this point of departure, he contrasts the different metaphysical
commitments which arises depending on what semantic theory we adopt.
The cases he explores concern properties, names, and events. Ludlow
contends that no T-theory can avoid metaphysical commitment
It is in Chapters 5 through 8 that the central argument of the
book is developed, concerning the relationship between tense semantics
and metaphysics of time. In Chapter 5 he expounds "what is essentially
the received view: the Reichenbachian theory of tense" (p. 77), which
he calls the B-theory semantics. The Reichenbachian semantics is a
B-theory semantics in that it involves tenseless truth conditions,
with temporal relations between events stated in terms of the
earlier-than/later-than relations, and where future and past events
are equally "real" as present ones. Axioms for tense have the basic
form of (ii).
(ii) Val(e, PAST, t) iff e is temporally before t
He gives axioms for seven tense morphemes, using the triple index
S,R,E; and for temporal adverbs like 'yesterday, 'today', and
'tomorrow' as well as temporal connectives like 'when', 'before', and
'after', all exploiting the temporal relations "earlier-than" and
In Chapter 6, "Problems with the B-Theory Semantics", Ludlow
argues (like many others have) that the B-theory semantics is
inadequate in that it cannot solve the problem of indexicality. The
most promising attempt thus far, the token-reflexive account, is
itself dependent on using an indexical to fix the reference to the
token referred to. That is, according to the token-reflexive
analhysis, the sentence 'my fifth anniversary is _today_' is true iff
my anniversary is the day of S -- the day of _this_ very utterance.
Instead of picking out the day of the utterance by the indexical
expression 'today, the utterance is picked out by the indexical
expression 'this'. Even if this problem could be solved, Ludlow
continues, the token-reflexive analysis will have as a consequence
that sentences like 'there are no linguistic tokens' are not just
simply false when tokened or uttered, but necessarily false. Ludlow
argues that it must of course be true that there are no linguistic
tokens when in fact there are no linguistic tokens, and that an
adequate semantic
theory should be able to give the conditions under which this would be
Chapter 7 develops the A-theory semantics, a basically Priorean
semantics in which tense is preserved in the metalanguage, so that the
indexical sense is "displayed" in the axiom, as in (iii):
(iii) Val(x, PAST) iff x was true
Ludlow notes the "modest" character of such axioms, defending his
approach by arguing that when we evaluate propositions in the past or
future tenses we do not imagine some past or future time and determine
whether the corresponding present-tensed proposition is true or not.
Rather, we examine the evidence available to us right now. This, he
claims, is an epistemological advantage to the A-theory. In general,
the axioms proposed for the A-theory semantics retain all indexical
and temporal relational morphemes of the object language in the
metalanguage. Tense morphemes are given axioms like
(iii) above, with complex tenses resulting from nesting of simple
tenses. Temporal connectives and temporal adverbs also receive a
disquotational treatment, as in (iv) and (v).
(iv) Val(T, [S1 _when_ S2]) iff Val(T, S1) when Val(T, S2)
(v) Val(x, _yesterday_) iff x was true yesterday
Also in this chapter, Ludlow notes some linguistic objections that
have been raised against an A-theory semantics, notably its inability
to account for temporal reference (to be dealt with in Chapter 8), and
the major philosophical objections, chiefly the so-called McTaggart
paradox. He recapitulates Prior's defense of the A-theory, leading to
the version of the A-theory known as presentism.
Chapter 8 is perhaps the chapter of most interest to the linguist
reader of STT. Here, Ludlow proposes that an A-theory can solve the
problem of temporal anaphora by treating them as E-type anaphors in
the sense of Evans (1977), or rather, of Cooper (1979) -- expressions
that stand proxy for Russellian definite descriptions. According to
this approach, in a discourse like (vi), the anaphoric pronoun stands
proxy for a definite description, made explicit in (vii).
(vi) A man came in. He tripped over a chair.
(vii) A man came in. The man who came in tripped over a chair.
This, on the theory, frees us from the assumption that there is some
object that is the referent of the pronoun; the second sentence makes
a general claim about the world, namely that "the world contains
exactly one man who came into the room, and he tripped over the chair"
(from the Introduction, p. 10). The proposal is, then, that the
anaphoric element so frequently observed in temporal discourse is an
E-type anaphor, often implicit, sometimes surfacing as "then". In
either case, it stands proxy for a when-clause (or other temporal
clause). Thus, a sentence like the second one in (viii) could be
spelled out along the lines of (ix) (p 11).
(viii) Sam adressed Bill. Bill didn't respond (then).
(ix) Sam adressed Bill. Bill didn't respond when Sam adressed him.
In a case such as this, the previous discourse provides the
spelling-out of the anaphoric element, just as with "ordinary" E-type
anaphors. In the proposal as developed in chapter 8 and appendix T5,
however, there is no context provided and hence no spelling out of the
implicit temporal clause. The work which the implicit temporal clause
does for Ludlow is similar to that of the R point in Reichenbach's
analysis. Each tense morpheme is the manifestation simultaneuously of
Absolute Tense and Relative Tense. The former takes the form of a
Priorean tense operator, the latter is a temporal connective (possibly
implicit, but present in the LF representation). T-axioms are of the
form in (x)-(xi).
(x) Val(x, PAST) iff x was true (Absolute Past)
(xi) Val(T, [IP1 _when_ IP2]) iff Val(T, IP1) when Val(T,
IP2) (Relative Present)
For a simple past sentence like "Smith swam", applying the axioms to
the proposed LF will give us truth conditions like (xii) (ILFs appear
within closed square brackets):
(xii) "Smith swam" is true iff [] there is an e, e is a swimming,
Smith is the agent of e and e culminates [] was true when [] [...] []
was true
He notes that "when" can no longer , as in the B-theory, mean "at the
same time as" -- instead, it must be "a kind of primitive". Ludlow
assumes that implicit when-clauses have the same structure as explicit
when-clauses, specifically (1) they are tensed, never infinitival and
(2) they are "coordinated with the tense of the matrix clause". This
"coordination" means that the when-clause has the same (absolute)
tense operator as the matrix, whether PRES, PAST, or FUT. Finally in
this chapter, he gives a novel solution to the McTaggart paradox, by
invoking the implicit when-clauses which on his theory are present in
every tensed sentence. A proposition that was future and is now past
will be coupled with different when-clauses for the different cases.
Ludlow's example is the proposition [] there is a dying of Queen Anne
[], which was future "when Queen Anne was born" and is past "as I
write these words". There can be no contradiction, since the content
of the when-clauses is different.
Chapter 9, "Broadening the investigation", brings in
psycholinguistic data from langauge acquisition and language disorders
to bear upon the A- versus B-theory controversy. Ludlow argues that
studies of the order of acquisition render support to the A-theory
semantics as the real one. Ludlow also claims support from acquisition
for "when" as a "primitive" notion, distinct from the notion "at the
same time". He calls in Merleau-Ponty to support the idea that
presentism is also in accord with our temporal intuitions, fairly
suggesting that intuitions of time passing are induced by philosophy
classes. "If we concentrate on _our_ experience of the world, we have
to reject the idea that time is a process or that it involves
reference to independent future and past events. Rather, we have to
think of the future and past being, as it were, in the present." (p.
At this point, Ludlow's position starts having very far-reaching
consequences, which he draws up in a rather speculative manner in the
final chapter. For philosophy, there is the apparent loss of
truth-value links, and consequences for the nature of memory. For
linguistics, the consequence is that the grammatical category of tense
must be eliminated, along with any talk of specifically temporal
anaphora, adverbs, etc. What we are accustomed to calling tense is
really " a mixture of modality and evidentiality" (p. 163) The
indexical character lies not in the time dimension but in
evidentiality, with aspect a "more abstract" form of evidentiality.
Languages that have been analyzed as having tense morphemes, aspect
morphemes and evidential morphemes "simply have three kinds of
evidentials" (p 161 ff)

A book that tries to balance, on less than 300 pages, the interests of
the linguist working in tense semantics with that of the philosopher
working in the metaphysics of time stands a fair chance of satisfying
neither. Both kinds of intended reader will feel that important issues
in his or her field have been passed over, with little hint as to how
they should be addressed in the proposed framework. The author signals
his awareness of this risk on p xvi ff, but he also seems to fear that
his linguistic readership will bored by too much philosophy, and vice
versa. This fear is certainly unfounded. The linguist or philosopher
who opens a book such as this one is in all probability quite willing
to listen to "the other side". But the brevity, even sketchiness, of
much of the argument is likely to leave the linguist without a true
appreciation of the philosophical import of the discussion, and the
philosopher without means of evaluating the linguistic side of the
argument. Even quite brief reviews of the issues raised, aimed at
readers from the other discipline, would have been most helpful. Not
all of us are lucky enough to be placed in joint philosophy and
linguistics departments, where there are suitably qualified colleagues
to pester.
In general, if the book places quite high demands on the patience
of the reader, it is because so many possible lines of argument are
picked up, shown to have far-reaching consequences for all kinds of
issues, and then dropped again, often with a comment to the effect
that "a lot of interesting work remains to be done".

[A comment from the linguist reviewer, largely on the analysis of
temporal anaphora:]
Those of his readers who come from philosophy will have to judge
whether Ludlow has succeeded in showing the relevance of linguistic
analysis to the metaphysical pursuit (see below for one such
assessment). As to the relevance for linguistics of the metaphysical
argument remains unclear, it is not even obvious that Ludlow meant it
to have such relevance. The A-theory "needs to avoid temporal
reference" (p. 130), and this concern guides the analysis, rather than
linguistic facts and intuitions. Let me expound this a bit.
Ludlow rightly points out what are the big hurdles for the
respective theories from a linguistic point of view, namely indexical
expressions for the B-theory, and temporal anaphora for the A-theory.
Most linguists would probably assume that both exist in language, and
that consequently, both theories are wrong and right to about the same
extent. Neither can be reduced to the other; we need resources from
both series to account for the full range of temporal phenomena in
language. The pure A- or B-theorist cannot take this way out, but must
in some way "explain away" the offending phenomenon from language, at
least if he takes the position that language in some sense mirrors
reality (a fortiori if he endorses language-world isomorphism). The
success of Ludlow's proposal then hinges on whether his explaining
away of temporal anaphora is better than the B-theorist's explaining
away of indexicality. Ludlow claims the latter fails because it cannot
at the same time account for the different meanings of "today"
(uttered on March 12) and "March 12" (uttered on March 12) AND for
the, according to Ludlow, contingent falsity of propositions like
"There is no language". The intuitions that have to be appealed to to
substantiate this claim appear less than clear (especially if we
restrict ourselves to philosophically "untutored" intuitions, as
Ludlow proposes on p. 142).
Let's see how Ludlow's own proposal for explaining away temporal
anaphora fares in this respect. As we saw, the proposal is basically
that a sentence which seems to be "about" some past time, like "Smith
swam", contains an implicit when-clause, which could be made explicit,
say "when I threw him in the water" (assuming I did so only once;
recall that the when-clause is a Russellian description). We should
get truth conditions as in (xiii).
(xiii) "Smith swam when I threw him in the water" is true iff []
there is a swimming by Smith [] was true when [] there is a
throwing-in-the-water of Smith by me [] was true.
But how are we to interpret these truth conditions? The sort of
situation we seem to interpret the natural language sentence as
describing is one of an episode of two consequentially connected
events: I threw Smith in the water, and (his way of dealing with this
was that) he swam. In temporal terms, his swimming follows "just
after" my throwing him (cf Partee 1986), but as Moens (1987) and
others have shown, felicitous linking of two events by "when" requires
that there be a more-than-temporal relation of consequentiality
between them (for a critique of Moens and a more detailed proposal,
see Sandstrom 1993). Ludlow is certainly correct when he says that
"when" cannot mean "at the same time as" (nor can it mean "just
after", as Partee suggested). When-linking of two events always
envokes an episodic interpretation.
With states, however, it is different. Sentences of the form
STATE1 when STATE2 mean that STATE1 holds throughout the time picked
out by STATE2. Thus given the fact that the Social Democrats held
office in Sweden for an unbroken period of more than 40 years, which
included my childhood, (xiv) is fine (while the inverse version in
(xv) is not).
(xiv) The Social Democrats held office when I was a child.
(xv) I was a child when the Social Democrats held office.
Also note that with states there is no longer any consequentiality
requirement; the situations have nothing to do with each other save
that the one serves to "date" the other.
Now return to the truth conditions in (xiii) above. Here, what
appears on either side of the (metalinguistic) "when" are two states,
"[] ... [] was true". Interpreting this using our ordinary language
intuitions will land us somewhere very different from where we
started, with the sentence "Smith swam when I threw him in the water".
(And use our natural language intuitions we apparently must, else the
T-theory will be no better than "Semantic Markerese", which Ludlow
rejects in Chapter 2.) We are now dating the hold-time of a particular
state (the being true of "there is a swimming by Smith") by means of
the hold-time of another state (the being true of "there is a
throwing-in-the-water of Smith by me"). These are simply the wrong
Thus, it is not clear that Ludlow's attempt at explaining away
temporal anaphora is successful. (In fact there are more problems with
it, which it would take us too far afield to discuss here.) Linguists
will probably not be induced by it to change their predilection for an
"impure" approach that utilizes both A-theory and B-theory resources.

[A comment from the philosopher reviewer on Ludlow's approach to
metaphysics and his claim that his thesis solves McTaggart's paradox:]

It has been argued, e.g. by Craig (1998), that a presentist
ontology "adroitly avoids McTaggart's Paradox because the only
intrinsic properties there are are present tensed and therefore
compatible". It would appear to follow that a presentist semantics,
like Ludlow's, would also avoid the contradiction, i.e. if it shows
that sentences that _appear_ to refer to entities that exist in the
future and past, really do not, and therefore do not involve
metaphysical commitment to the existence of such entities. It would
not be enough, though, to avoid commitment to the existence of future
and past entities. A presentist semantics must be able to tell us what
the difference is between future and past tensed sentences, and
account for temporal anaphora. Treating temporal anaphora as E-type
does the trick, according to Ludlow. Well, it seems to me that
Ludlow's approach to metaphysics makes it difficult to decide whether
or not he succeeds in solving McTaggart's paradox, or rather, in
arguing successfully that McTaggart was wrong about reality. It is
often overlooked that McTaggart's argument is not about language, and
its conten, but about the reality it describes (see e.g. Ingthorsson
1998). Ludlow's thesis is that one can study metaphysical questions by
studying the semantics of natural languages, because "there is a close
connection between language and reality" (p. xiv). To oversimplify:
doing metaphysics is just doing empirical linguistics; find out how
the world is by finding out how language mirrors the world. Ludlow's
own criteria for success seem then to be that in order to show that
the world is presentistic, one must show that, as a matter of
empirical fact, natural language does not contain any such thing as
tense, or "at least not the sort of tense system that is compatible
with currently favored philosophical theories of time" (p. xiv). As
pointed out above, there is reason to doubt that he is entirely
successful on this point, although he has certainly made a serious
attempt to challenge the thesis that tense is anything like currently
favoured theories of time claim it is. The truth of the matter may of
course be that natural languages contain traces of 'philosophical'
tense, traces of E-type temporal anaphora, as well as traces of all
the other conflicting and more or less confused conceptions of time
that are around. If this is the case then Ludlow does not have a good
case against McTaggart. McTaggart interpreted tensed language
according to his fully developed metaphysical system, and found it to
contain a contradiction (Ingthorsson 1998). A presentist metaphysics,
as Craig (1998) points out, gives an interpretation of tensed language
that does not contain a contradiction. Both McTaggart's view and the
presentist view are not dependent on how natural language actually is,
they can just claim that natural language just describes how the world
appears to us, not how it really is. Ludlow makes his argument
dependent on how natural language actually is, because he claims to be
discovering how reality is by a study of language. That makes his
argument weaker, from a metaphysician's point of view. I think however
that Ludlow presents enough persuading arguments to support the thesis
that natural language does not just contain the 'philosophical' tense,
but also a more presentistic tense, and that therefore presentism is
not just a philosophical view but one of our untutored intuitions
about how the world is. This is important in motivating the shift of
focus from a more traditional A-theory of time to a presentist
A-theory of time.

For the reader who sticks it out until the end, there is a lot of good
to be found in this book, not least in the form of almost
parenthetical suggestions made along the way. Also, Ludlow's
conclusions are radical enough to force anyone not willing to follow
him into that particular wilderness to carefully think through
precisely where the argument "went wrong". This in turn leads one to
explore a lot of little paths of enquiry that one had hitherto
neglected. Given the sort of intellectual temperament Ludlow seems to
be gifted with, this would probably be just what he wanted for his
readers. A rough and often quite unhelpful guide will in all
likelyhood make you better acquainted with a place than one who leads
you by the hand.

There seem to be few mistakes for a book with a reasonable amount of
formal notation. We noted the following:
p. 71, l. 5 from bottom: reference to a section 3.5 that does not
p. 100, example (6): the FUT rule is repeated and there is no PRES
p. 119, LF for Future in Past should have "after" instead of "when"
p. 134, ll. 15 and 18: reference to example (63) seems mistaken
p. 222, fn. 6, example (7'.a), second conjunct of the right-hand side
should have CONJ' instead of CONJP.

Chomsky, N. 1986. Knowledge of Language. New York: Praeger.
Cooper, R. 1979. The interpretation of pronouns. In Syntax and
Semantics 10, ed. E. Heny and H. Schnelle. New York: Academic Press.
Craig, W.L. 1998. McTaggart's Paradox and the problem of temporary
intrinsics. Analysis 58: 122-127
Evans, G. 1977. Pronouns, quantifiers, and relative clauses. Canadian
Journal of Philosophy 7:467-536.
Ingthorsson, R. 1998. McTaggart and the unreality of time. Axiomathes
9: 287-306.
Larson, R & G. Segal. 1995. Knowledge of Meaning. Cambridge: MIT
Moens, M. 1987. Tense, aspect and temporal reference. Ph.D. thesis,
Centre for Cognitive Science, University of Edinburgh.
Partee, B. 1984. Nominal and temporal anaphora. Linguistics and
Philosophy 7:243-286.
Sandstrom, G. 1993. When-clauses and the temporal interpretation of
narrative discourse. Ph.D. thesis, Department of Linguistics, Umea

Gorel Sandstrom is Lecturer in General Linguistics at the Department
of Philosophy and Linguistics, Umea university. Her research areas
include the syntax of nominals and the semantics of tense and aspect.

Rognvaldur Ingthorsson, also of the Department of Philosophy and
Linguistics, Umea university, is working on a Ph.D. thesis in the
philosophy of time, notably on the debate between the A- and B-views.


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