if it ain’t moving it shall not be moved

If It Ain’t Moving It Shall Not be Moved

Emiliano Boccardi

© Springer Science+Business Media Dordrecht 2013

Abstract There are two no-change objections that can be

raised against the B-theory of time. One (McTaggart’s

objection) stems from the observation that in a B-theoretic

scenario changes of determinations can only be represented

by propositions which have eternal truth values. The other

(James’ objection) derives from the principle that nothing

can vary over a period of time if it doesn’t instantiate a state

of change at all the instants of time which compose it. Here I

argue that both objections apply to all comparative concep-

tions of change, regardless of whether they take tense

seriously or not. It follows that, contrary to what is widely

believed, A-theoretic accounts of time are not immune to no-

change objections, just in virtue of being realist about tense.

A-theorists must either (1) accept the conclusion that time,

according to their account, does not flow, or (2) put forward

an account of flow that is not comparative. A number of

difficulties with both of these options are discussed.

Keywords Time · Change · Passage · Becoming ·

Tense · A- and B-theories of time · Dynamic

conception of change

1 Introduction

Here are three related distinctions in the philosophy of

time. First, there is the distinction between (1) those who

believe that things change only if reality itself changes, i.e.

only if the totality of monadic states of affairs that exists or

obtains at a time is different from that which exists or

obtains at other times (also known as Dynamicists); and (2)

those who think that what states of affairs constitute reality

is not something that depends on what time it is, or on any

other temporal perspective (the Staticists). Sure things can

have different properties at different times, even under a

Static conception of the world; but whether a thing in-

stantiates a property (at a given time) or not, under a Static

account, is not itself a matter that “changes” over time in

any sense.

Another major divide is that between those who believe

that tense predicates, e.g. Present, Past or Future, refer to

mind independent properties or aspects of reality, and those

who don’t. The former thesis is often referred to as the

A-theory of time, or Tense Realism, and the now venerable

debate over its virtues and shortcomings constitutes one of

the major sub-industries in the philosophy of time. Tense

Realists disagree about the nature of tense determinations,

and even about whether tense predicates should be taken to

refer to dedicated tense properties at all. What all Realist

conceptions of tense have in common, however, is the

contention that tensed propositions (or utterances) do not

have tenseless truth-conditions. Anti-realists, on the con-

trary, think that tense determinations merely reflect

anthropocentric, mind-dependent or perspectival features

of reality (Smart 1949; Grunbaum 1963; Williams 1951).

They think that the facts that make tensed statements true

are reducible to tenseless facts (Russell 1938; Goodman

1966; Quine 1941), or at least that they have tenseless

truth-conditions (Mellor 1981; Oaklander 1991).

The third divide that I wish to discuss pertains to the

ontology that underlies tense discourse. According to some

authors (the Eternalists), past, present and future things and

states of affairs, while possibly located at different tem-

poral “positions”, all (tenselessly) exist on an equal

E. Boccardi (&)

Department of Philosophy, University of Venice (Ca’Foscari),

Palazzo Malcanton Marcora Dorsoduro 3484/D,

30123 Venice, Italy

e-mail: [email protected]

123

Topoi

DOI 10.1007/s11245-013-9230-7

footing. According to their foes (the non-Eternalists), on

the contrary, the differences between past, present and

future experiences reflect ontological distinctions. At thefar end of the spectrum of non-Eternalists views is the

doctrine of Presentism: the view that, necessarily, it is

always true that only present objects and states of affairs

exist.

Prima facie, one is tempted to think that there should be

a neat correspondence between Staticism, Anti-realism and

Eternalism (the B-package), on the one side, and Dynam-

icism, Realism and non-Eternalism (the A-package) on the

other. The intuition underlying these expected inferential

relations is the following. Dynamicists, Realists and non-

Eternalists, contrary to their respective opponents, are

typically committed to the view that temporal passage is an

objective feature of reality which plays an essential

explanatory role in accounting for change.

One would expect, for example, that Anti-realists about

tense should be committed to a Static conception of time,

and to an Eternalist ontology. It seems absurd, in fact, to

contend that things change because reality itself (the

totality of the facts) changes, as Dynamicists do, but to

deny that a state of affair’s going out of existence, or

ceasing to obtain, is tantamount to its becoming absolutelypast, as Anti-realists must think. Moreover, it seems absurd

to claim that reality does never contain the totality of things

that existed in the past, that exist in the present and that

will exist in the future, as non-Eternalists do, but to deny

that there are features of reality that make present truths

absolutely present, like Anti-realists must do. For similar

reasons, one would think, non-Eternalists, like Presentists

and Growing Block theorists, should be committed to a

Realist conception of tense, and to a Dynamic account of

change. They must believe, in fact, that the distinction

between present and non-present experiences reflects

objective distinctions in reality (as Realists think); further,

they must believe that those parts or features of reality that

make present truths true, whatever they are, keep changingin a sense that cuts some ice, as time goes by (like

Dynamicists do): it seems absurd, in fact, to claim that

there are states of affairs that are objectively present while

denying that which facts are present is a matter that keeps

changing..

In short, Eternalist and Anti-realist ontologies are

inhospitable to a Dynamical conception of change, while

non-Eternalist and Realist ones are more congenial to it,

essentially because Dynamicists tend to affirm, and Stati-

cists to deny, the reality of temporal passage. Indeed, it is

safe to claim that the chief allure of Realist conceptions of

tense is that they appear to be uniquely capable of

accounting for the passage of time.

Here I argue that, contrary to what is often assumed,

being Realist about tense and endorsing a non-Eternalist

ontology does not suffice to provide a dynamic account of

change. Further, I shall argue that Realist ontologies that

are purely Comparative do not have the conceptual

resources to express the fact of temporal passage. Com-

parative A-theoretic accounts of change and passage are

thereby argued to fail to deliver what they promise, i.e. to

provide us with a dynamic conception of reality.

The structure of the paper is as follows. In Sect. 2 I

discuss a familiar no-change objection raised against the B-

package (I call it McTaggart’s no-change objection). In

Sect. 3 I argue that McTaggart’s no-change objection to the

Static account of time can be generalized to become an

objection to the comparative nature of the account per se,

rather than (merely) an objection to the tenseless ontology

that it presupposes. This objection, therefore, has teeth (if it

has teeth), regardless of whether the relevant comparative

facts are expressed in tensed or tenseless terms. I conclude

that being Realist about tense, or endorsing a non-Eternalist

ontology is not enough, per se, to express the fact that we

live in a dynamic world. In Sect. 4 I introduce a largely

neglected, independent no-change objection. It can be

traced back to James’ criticism of Russell’s account of

motion, and it derives from the intuition that nothing can

change if it is never found in an instantaneous state of

changing. In Sect. 5 I argue that the same intuition can be

used to mount a no-change objection against comparative

theories of change and passage in general (regardless of the

ontological status of tense properties). If James’ objection

is a valid argument against Russell’s account of motion, I

argue, then it must also be a valid argument against com-

parativist accounts of passage in general. I conclude (Sect.

6) that A-theorists must either (1) accept the conclusion

that time, according to their account, does not flow, or (2)

put forward an account of flow that is not comparative.

2 Comparative Accounts of Change and the No-ChangeObjection

Imagine two friends sitting on a beach, looking at a ship far

away. Because of the distance, they cannot just tell by

looking at it whether the ship is moving or not. “I bet it’s

moving” says one. “No it’s not!”, says the other. Do they

disagree about something? And if yes, what is the dis-

agreement exactly about? After some time the two friends

look again and the ship has obviously moved, although it

looks to them just as still as it looked before: its position

(relative to them) has changed. “Aha!”, says the first, “I

told you it was moving!” “You were right, it was moving. I

lost the bet!”, says the other.

It is tempting to think that the initial disagreement

between the two friends is about a property instantiated by

the ship at (and only at) the time of the bet (t1). What they

E. Boccardi

123

observe at the time of the assessment of the bet (t2),

according to this intuitive view, is the comparative fact that

the ship’s location at t1 is different from its location at t2.

They agree that this provides indirect evidence for the

further (non-comparative) fact that the ship was moving at

t1. If the ship is found at different positions at times right

after t1, this must be because at t1 it possessed an intrinsic

kinematic quantity in addition to its position.

If this explanatory pattern is sound, then the compara-

tive fact that (a) the location of the ship at t1 is different

from its location at t2, must be ontologically distinct from

the (non-comparative) fact that (b) the object has been in

motion for enough times between t1 and t2.1 In short,

according to this view, the displacement of the ship is a

posthumous consequence of its state of motion throughout

the time interval considered, hence fact b (the explanans)cannot be identical to fact a (the explanandum). For thisreason, I shall call this view a dual-fact account of motion

(and change).2

The dual-fact account of change had its enemies since

memorable times. William of Ockham and his followers

advocated a view according to which change is nothing

over and above a sequence of different properties had at

different times. It was known as the doctrine of changing

form (forma fluens), and it opposed the dual-fact account

known as the doctrine of change of form (fluxa formae).According to the latter, when a leaf (for example) changes

its color from green to yellow, not only does it have a

determinate shade of (say) green at any given time, but,

over and above, it also has a changing shade of green (the

dual fact). According to the former, on the contrary, there

is no further fact over and above the leaf having different

shades of green at different times.

In our times the locus classicus of the Ockhamist (sin-

gle-fact) account of change is Bertrand Russell’s so called

at–at theory of motion. “We must entirely reject the notion

of a state of motion”, he wrote (Russell 1938): “motion

consists merely in the occupation of different places at

different times. There is no transition from place to place,

no consecutive moment, or consecutive position, no such

thing as velocity except in the sense of a real number which

is the limit of a certain set of quotients” (my emphasis, p.

473).

This deflationist understanding of change was heavily

inspired by Weierstrass’ and Cantor’s understanding of

limit and infinity. According to Weierstrass’ conception of

limits and infinitesimals (now the received view), variables

are just denotational schemas: they contribute to the sole

purpose of denoting large numbers of (unchanging) facts

about their values. The values of the variables do not

themselves vary: they do not “approach”, let alone “reach”their limits, or change in any sense, contrary to what they

were ambiguously alleged to be doing in prior formulations

(since Newton’s and Leibniz’s). Of course, according to

this conception, neither do variables themselves vary or

change, in spite of their evocative name.

It was this reconceptualization of the notion of limit that

inspired Russell’s treatment of the antinomies involved in

the notion of indefinitely growing series of things (such as

those involved in Zeno’s paradoxes): “Weierstrass”, he

says, “by strictly banishing all infinitesimals has at last

shown that we live in an unchanging world, and that

[Zeno’s] arrow, at every moment of its flight, is truly at

rest” (ibid., p. 347).Instead of treating these antinomies as reductiones ad

absurdum of the notion of actual infinity itself, Cantor

famously turned them into its very definition. A class was

decreed to be infinite if and only if it was found to be

similar (isomorphic) to its parts. Russell thought that this

conception of the infinite, together with Weierstrass’

account of limits, could be exploited to finally free phi-

losophy of the millennial nuisance of Zeno’s paradoxes.

Once freed from the burden of the (dual-fact) notion of a

state of change, he thought, we no longer have to explain

how Achilles can reach the Tortoise, starting from his

disadvantaged position: we only need to make sure that the

two respective paths are related by a suitable bijection. By

the same token, we should no longer worry about how

Zeno’s arrow, while not being in a state of motion at any

instant during its journey, can reach its target: there is no

such thing as a state of motion to start with.

The foes of this deflationist construal of change, the

Dynamicists, complain that the Ockhamist conception

“spatializes” time, thereby failing to acknowledge its

essentially dynamical nature. This objection is often

referred to as the no-change objection to the static view of

time. The complaint is not, of course, that Staticists (single-

fact theorists in our terminology) would view time as a

fourth spatial dimension: no one ever thought that. The

complaint is rather that if the world were as Staticists claim

it is, then what we call ‘temporal relations’ would not be

really temporal after all. Not because they would be spatial

1 We may add that, at least, the object must have been moving at a

number of time instants that constitute a set whose (Lebesgue)

measure is not zero. This clarification, however, is not going to have

any consequence for our discussion. In what follows, the expressions

“at least for some time” and “for enough time” will mean the same as:

“at a number of time instants that constitute a set whose Lebesgue

measure is not zero”.2 Notice that at each time during the motion of the ship its current,

past and future positions can be used to form a mathematical

(abstract) vector that consists of the time-derivative of the trajectory

at that time. However, if dual-fact accounts of motion are correct such

vectors should be taken to further represent real intrinsic properties

possessed by the ship at the respective times, rather than merely

reflecting global properties of the trajectory itself.


123

relations instead (they would not be): they would be non-

temporal for the same kind of reasons for which spatial

relations aren’t (cf. McTaggart 1908).

But what are these reasons? What makes spatial relation

“static” and temporal relations “dynamic”? Suppose that I

was standing before but I’m sitting now. I have changed

from standing to sitting. The account of change offered by

those who accept the B-package is that I am standing at t1and I am sitting at t2, and t1 is earlier than t2. I call this a

(B-theoretic) comparative account of change. Look at what

is true at t1, look at what is true at t2, and compare them: if

they differ, then there is change; if not, not.

Dynamicists typically argue that this comparative

account is not an account of genuine change at all. Change,

it is argued, must be more than just having different

properties at different times. Notice that no one denies that

a thing that has different properties at different times has

changed. Of course it has! What is at stake, rather, is

whether having different properties at different times could

be all there is to genuine change. To clarify this point, I

shall call the fact of having different determinations at

different times a “variation” of those determinations; while

I’ll simply call “change” only what turns out to deserve the

qualification of “genuine” change, or “real” change.

According to this use of the terms, there is variationwhenever there is a difference between what is the case at atime and what is the case at another time. The friends of theB-package will claim that changes of determinations are

just variations of those determinations (the Ockhamist

conception of change). Their foes will deny that.3

The no-change objection is typically thought to run as

follows. In a B-theoretic scenario we are allowed only

tenseless verbs, at least in as far as we are concerned with

describing the fundamental constitution of reality. If things

are so, then in accounting for the pattern of variations thatour world instantiates, we need to either (1) add an argu-

ment place for time to every predicate, or (2) talk about

time-slices of objects instead of enduring objects, or (3)

talk about temporally indexed properties (like sitting-at-

18:30-on-28/06/2014) instead of properties simpliciter. Thetrouble with all these ways of accounting for variation is

that the propositions that they can afford to express (let us

generically refer to them as temporally indexed proposi-tions) are all eternally true or eternally false. If this is the

case, then genuine changes must be more than mere vari-

ations. The thought behind this conclusion, I take it, is that

real change occurs only if reality itself changes. But

changes in reality must correspond to changes in the truth

values of the propositions that describe it. So, if according

to an account reality can be fully described by a collection

of propositions whose truth values do not vary, then

according to that account reality itself is static (cf. Zim-

merman 2005).

As I shall argue, this common way of expressing the no-

change objection is subtly misleading, as it wrongly blames

the tenseless ontology of the B-package for the fact that

genuine change has been left out of the picture.

3 A-Theoretic Comparative Accounts of Change andthe Enhanced No-Change Objection

The structure of the no-change objection, as it was pre-

sented above, is the following:

1. Changes in things are variations in the pattern of

instantiation of properties (the Ockhamist conception

of change).

2. If reality consists (solely) of tenseless facts, variations

can only be expressed by conjunctions of temporally

indexed propositions.

3. Temporally indexed propositions have changeless

truth values.

4. If reality can be wholly described by the conjunction

of propositions whose truth values do not change, then

realty does not itself change. It follows that

5. If reality consists solely of tenseless facts, then it does

not change. But

6. Reality consists solely of tenseless facts (the B-

package). Hence

7. Reality (according to the B-theorist) does not change.

Now, under this construal of the argument, the culprit

for the charge of changelessness appears to be the tenseless

ontology of the B-package. The friends of the A-package,

being Realist about tense, are happy to deny assumption 6,

and have therefore traditionally felt safe from the charge of

Staticism. The intuition underlying this response is quite

clear: A-properties (past, present and future), if they are

real at all, must be constantly changing. Nothing can be

past, present or future throughout all times. What is now

past must have once been present, what is future will one

day be present, and what is present shall not be so for long.

So, if reality comprises genuinely tensed facts, then it must

be genuinely changing all the time, in accordance with the

ever changing truth values of tensed propositions.

As I shall I argue, however, once one tries to spell out in

more detail what the alleged “change” of A-determinations

exactly amounts to, the Tense Realist response to the no-

change objection is easily seen to be at best a restatement

of the problem. The argument stems from the observation

3 Note that what the foes of the B-package deny is not that changes ofdeterminations are necessarily followed by variations of these

determinations. What they deny is the identity thesis: that changesin things are (identical to) variations in these things.

E. Boccardi

123

that standard tensed statements express essentially

changeless propositions.

Let us start with statements expressing the proposition

that a given time, fact, or state of affairs is present. The

statement that there is a time that is objectively present

does not (by itself) express the truth that time passes. The

passage of time, in fact, requires that different moments of

time be successively present, and this surely requires more

than the presentness of a single moment of time. In short,

the claim that reality (objectively) occupies a given posi-

tion in the A-series does not, of itself, introduce any

dynamic element into a picture of time. The A-theoretic

fact that the year 2014 is present, for example, or the fact

that the year 44 BC was present, are just as changeless (perse) as the B-theoretic fact that Caesar was assassinated in

44 BC.

This is particularly clear in those accounts of A-deter-

minations that offer a conceptual reduction of tense

properties to non-essentially temporal ones. Some authors

think that tense concepts are semantically reducible to

tenseless ones, while still thinking that what tenseless facts

there are changes depending on what time it is, i.e. while

endorsing a Dynamic conception of time. According to

these accounts, the present is picked out purely by the

relations it bears to preceding and succeeding times. “[A]

dynamic world”, observes Tooley (1997), for example,

“need not involve any special, irreducible tensed properties

—such as those of presentness, pastness and futurity—in

order for tensed sentences to be true: it may simply be a

world where what tenseless states of affairs are actual is

different at different times” (p. 20).

Indeed, although this goes often unnoticed, many

Dynamicists do in fact propose a conceptual reduction of

A-determinations. Many Presentists, for example, think

that presentness can be reduced to non-temporal concepts

such as truth (Crisp 2007), actuality (Bigelow 1991),

reality (Prior 1970) or existence (Christensen 1993). “The

property being present […]”, says Crisp, “is just the

property being true—the property a proposition has iff it is

true”.4 Thus Prior: “I want to suggest that the reality of the

present consists in what the reality of anything else consists

in”.5 “To be present”, says Christensen, “is simply to be, to

exist, and to be present at a given time is just to exist at that

time, no less and no more”.6 According to Growing Block

theorists (e.g. Broad 1923; Tooley 1997; Forrest 2004), the

passage of time consists in the fact that more of the world

comes to be as time goes by. Presentness, according to this

view, is thus reduced to the notion of reality at the edge of

existence: again, there is nothing intrinsically special about

present reality.7

Now, it is clear that the bases for the reduction of pres-

entness that these accounts offer do not comprise essentiallydynamic elements. Being true, or real, or actual, or being

located at the last frontier of existence, etc., in fact, are not

essentially dynamic qualities (i.e. qualities that change by

their own nature, in and of themselves): something can well

be true, or real, or actual, etc., without changing. It follows

that these theories, unadorned, are not sufficient to provide

us with an account of the passage of time.

It may be objected that the mere fact of defining pres-

entness or other A-determinations in terms of features of

reality that are not essentially changing does not force the

A-theorist to give up the irreducibility of tense. One, for

example, could define as present all those facts which standat the last frontier of existence, while continuing to inter-

pret the verb “stand” as irreducibly tensed.8 Notice,

however, that the contention that A-determinations don’t

vary essentially, i.e. by virtue of the mere fact of being

instantiated, is not confined to purely reductionist under-

standings. Even if A-determinations are construed as

irreducible, primitive properties, in fact, they can be argued

to be essentially changeless. This is why.

The concept of presentness, however it is construed, is

different from the concept of future pastness or from that of

past futurity; and from the fact that a time is present one

cannot infer that it will be past, or that any other time will

be (or was) present.9 It follows that the presentness of a

time does not suffice, by itself, to convey the information

that something (including presentness itself) is changing.

It will be immediately objected that, since the passage of

time, as we noted above, consists of different times being

successively present, from the premise that (1) the pres-

entness of a single time doesn’t suffice to make it true that

time passes, one cannot safely conclude that (2) tensed

statements can only express changeless propositions. It

may be granted, for example, that the singular proposition

that today is present does not suffice to express the fact thattime passes; but surely, it will be argued, today’s present-

ness together with the (distinct) proposition that yesterday

has been present too should be more than enough to

express the fact of passage. What more can one reasonably

ask for?

4 Cf. Crisp (2005).5 Prior (1970, pp. 246–247).6 Christensen (1993, p. 168); cf. p. 226.

7 “My present”, says Broad (1923), “is just the last thin slice that has

joined up to my life-history. When it ceases to be present and

becomes past this does not mean that it has changed its relations to

anything to which it was related when it was present. It will simply

mean that other slices have been tacked on to my life history” (p. 84).8 Thanks to an anonymous referee for pointing this out to me.9 As noted by Sanson (2011) (p. 6): “taken by itself, Presentism is

consistent with the view that reality is static: it does not entail that

reality is temporary or that there is any real change”.


123

Notice, however, that the information that a given event

(say yesterday’s presentness) is past does not contain the

information that something is or was changing (although a

proposition to this effect can be arguably inferred from it).

One can realize that things are so by noting that the

proposition that yesterday is past is logically equivalent to

the conjunction of: (1) the A-theoretic proposition that

today is present with (2) the B-theoretic proposition that

yesterday comes before today (in the B-series). Now, if, as

I have argued, proposition (1) can be made true by a

changeless fact, then surely its conjunction with the

obtaining of the B-theoretic (hence changeless) relation

expressed by proposition (2) can be made true by a

changeless fact too.

Another way to expose the essential changelessness of

A-theoretic facts is by noting that past tense propositions

express truths which obtain in the present. The pastness of

yesterday’s presentness, for example, is simultaneous with

today’s presentness: they are both present facts. Of course

this is not to say that yesterday is simultaneous with today,

which would be absurd: what is simultaneous is the currentfact that yesterday’s presentness is past and the current factthat today is present. Now, how can the obtaining of two

simultaneous changeless (albeit A-theoretic) facts make it

true that time passes? Put more metaphorically, both

today’s current presentness and yesterday’s (current)

pastness can be viewed as A-theoretic “snapshots”, since

they presuppose that a particular position within the A-

series has been reached, and provide us with an instanta-

neous “picture” of reality as seen from that position. How

could such any instantaneous snapshot of reality, or any

static sequence of similar snapshots, for that matter, make

it true that time passes?

We are tricked into thinking that irreducible tense

properties are immune from the charge of changelessness

because we tend to read more into the Realist contention

that there are past states of affairs than it actually conveys.

We assume that if something is (already) past it must have

become past first. While this assumption may be correct,

however, the proposition that an event is past does still notconvey the same thought as the proposition that that event

was becoming past, when (or before) it became past.

Tense Realists of all brands, therefore, must add an extra

element to their picture of the world, over and above their

account of A-determinations, if they want to guarantee that

their ontology is indeed a dynamic one. God, after

instantiating presentness, so to speak, must have made an

extra effort: he must have added an extra humph to reality

to turn it into the evolving universe that dynamical theorists

think we inhabit. What can this extra humph be? What kind

of extra fact can make it true that the world is dynamic?

A-theorists often express their commitment to the

dynamic nature of time by supplementing their realist

accounts of presentness with the comparative truth that

what is real (or true, or actual, or irreducibly present, etc.)

as of the present time is different from what was or will bereal as of other times. Thus, for example, Tooley (1997) (p.

16, my emphasis):

According to a dynamic conception of the world […],

what states of affairs exist does depend upon what

time it is. As a consequence, the totality of monadic

states of affairs which exist as of one time, and which

involve a given object, may differ from the totality

that exists as of some other time, and it is precisely

such a difference that constitutes change in an object,

rather than merely the possession by an object of

different properties at different times.

These differences between totalities of monadic states of

affairs that exist as of different times are supposed to

“constitute” change, explaining in virtue of what objects

have different properties at different times. The (compar-

ative) fact that the totality of states of affairs that constitute

reality as of one time (t1) is different from the same totality

as of another time (t2), i.e. the fact that there has been

variation (as opposed to change) in the constitution of

reality, ought to make it true that the world has changedbetween t1 and t2. But what constitutes reality as of one

particular time is not itself something that changes in any

sense. If so, then the conjunction of any number of these

changeless (albeit A-theoretic) truths cannot express the

fact that reality is Dynamic any more than the conjunction

of equally changeless (albeit for different reasons) B-the-

oretic truths does. Thus, the variations in the constitution of

reality mentioned in Tooley’s account can at best describe

the posthumous (unchanging) consequences of an under-

lying, unexpressed genuine change in A-determinations. If

this is the case, then such variations cannot possibly con-stitute, by themselves, the reality of passage itself.

Consider, as another example, the case of Crisp’s

Presentism. Crisp proposes to reduce the notion of pres-

entness to the truth of one (unique) element of a series of

abstract ersatz times, construed as maximally consistent

sets of propositions (abstract representations of an instan-

taneous state of the world).10 As we said, this account of

presentness, unadorned, is compatible with a static world, a

world where time doesn’t pass. The Presentist’s commit-

ment to a dynamical conception of the world must

therefore be added on an independent basis. The elusive,

impermanent aspect of time, according to this view, is

nothing over and above the conjunction of a thing’s former

existence with its current non-existence. Caesar did exist,

10 Cf. Crisp (2007, p. 99).

E. Boccardi

123

for example, and he doesn’t any more.11 According to

Crisp’s account, the presentness of Caesar’s existence,

during his life, was nothing over and above the truth of the

proposition that he (tenselessly) exists. Likewise, the

presentness of his current non-existence is nothing more

than the truth of the proposition that he doesn’t exist.

Temporal passage is supposed to supervene solely on

similar comparative truths about differences between what

exists, or is actual now and what will exist or will be actualin the future, or what did exist or was actual in the past.

These differences are usually thought to be made true by

brute contingent facts. Crisp (2007), for example, claims

that “it’s a brute, contingent fact that the abstract times

come temporally ordered as they do” (p. 132). If so, the

passage of time would consist in nothing but a brute con-

tingent fact as to the differing extensions of presentness at

different times.

A time, 44 BC for example, is past if and only if it

stands in the (primitive) earlier-than relation to the present

time, 2014. Notice that on this account of what it takes to

be past, the fact that 44 BC is past does not suffice to infer

that 44 BC was once itself present. Crisp must add his

commitment to temporal passage in terms of a commitment

to the idea that tenseless truths, such as that which makes

2014 present (i.e. true), change. It is this further commit-

ment that ought to explain why if 44 BC is now past it must

have been once present. Let us check how this is supposed

to work. The reality of passage, according to Crisp,

amounts to the truth of the following statement (cf. Crisp

2005):

(*) The B-series is such that (i) one and only one of

its members tα has the property being present, (ii) for

every time t1 in the series such that t1 is earlier than

tα, WAS[t1 has being present], and (iii) for every time

t2 in the series such that t2 is later than tα, WILL[t2has being present].

As of today, then, the passage of time would consist in

the truth of the following conjunctive statement:

(**) The B-series is such that (i) 2014 and only 2014

has the property being present; and (ii) WAS[44 BC

has the property being present] & WAS[43 BC has

the property being present] &… & WAS[2013 AD

has the property being present]; and WILL[2015 has

the property being present] &… etc.

This comparative understanding of passage is an

example of what I call an A-theoretic at–at picture of

change. It is ‘comparative’ in that it construes passage as

supervenient solely on the conjunction of different (indi-

vidually changeless) states of affairs. It is ‘A-theoretic’ in

that the truths that are so conjoined to form the grounding

comparative fact are A-theoretic: they pertain to facts that

obtain in the present, will obtain in the future or have

obtained in the past. According to this conceptualization of

passage, the presentness of 2014 and the former present-

ness of 44 BC must be added as independent axioms to the

theory of time. What needs to be checked, however, is

whether such axiomatization yields the desired results: in

particular, we need to check whether the theory is such that

the fact that 44 BC is past (in the specified sense) entails, asa matter of conceptual necessity, that it has become past.

Analogously, if the account entails that 44 BC was once

present, we further need to make sure that it entails also

that it ceased to instantiate presentness. I argue that, like all

other comparative accounts of passage, Crisp’s theory fails

to comply with this desideratum.

As noted by Oaklander (2010), given Crisp’s analysis of

tense operators, WAS[44 BC has being present] must be

understood as equivalent to:

F ¼ 44BC has the property beingtrue½ �is earlier than2014 has the property being true½ �

F and similar statements are (jointly) supposed to make

it true that time passes. It is important to notice that the

emphasized verbs that occur in F must be taken to express

tenseless truths. If they were interpreted as tensed, in fact,

then the proposed reduction would turn out to be circular,

for the reality of passage would be grounded on irreducible

tensed facts. As a consequence, F tells us nothing about

which time, 44 BC or 2014 AD, instantiates presentness

now. As Oaklander points out, “since on Crisp’s view all

times are present at the time they are regardless of what

time it is, there is no basis or ground in the ersatz B-series

for picking out one and only one time that has the property

of being present to the exclusion of all earlier and later

times that are (tenselessly) also present at their own

respective time […].”12

Now, if reality evolves in a dynamic way, I have argued,

the year 44 BC can be past only if it ceased to be present.

But, as we have seen, the claim that a time ceased being

present, according to Crisp, amounts to the claim that the

proposition that the ersatz time 44 BC is (tenselessly) truestands in the earlier/than relation to the proposition that2014 AD is (tenselessly) true. Such comparative claim, and

the proposition that it expresses, however, is true (or false)

regardless of what time it is now. Thus we conclude that, if

we unpack Crisp’s notion of passage, it turns out that

according to it the present is flowing through the year 201411 Here I disregard all the complexities related to the fact that Caesar

was not a well-defined simple entity. All the arguments put forward in

this paper should be understood as applying to simple entities and

states of affairs. 12 Ibid., p. 236. Underlined verbs must be understood as tenseless.


123

only if it is also flowing, in the same tenseless sense,

through 44 BC. The flow of time, in other words, would be

a tenseless feature of reality, not one that pertains to one

time rather than another.13 This clearly violates our con-

straint, for if time is flowing through 44 BC in the same

sense in which it is flowing through 2014, then there is a

clear sense in which 44 BC has not really become past.14

This, in turn, raises concerns about whether Crisp’s notion

of being past is compatible with a dynamical conception of

time, or, equivalently, about whether his earlier/later rela-

tions really deserve their name.

This and similar comparative conceptions of passage, I

argue, are not compatible with the (metaphysical) explan-

atory role that passage is typically supposed to play in

dynamic accounts of change. Standard no-change objec-

tions to static conceptions of change, in fact, can be

generalized to become objections to the comparative natureof the theory per se, rather than (merely) objections to the

tenseless ontology that they presuppose. These objections,

therefore, have teeth (if they have teeth), regardless of

whether the relevant comparative facts are expressed in

tensed or tenseless terms. What is objectionable about

Comparative accounts is not that they entail such com-

parative truths (few dare to deny these truths, modulo some

suitable paraphrasis); nor that such truths are made true by

tenseless facts (this, as I shall argue, is only a fatal con-

sequence of Comparative accounts). What is objectionable

is rather that these changeless comparative truths are pre-

cisely what stands in need of a dynamical explanation,

which entails that they cannot constitute such dynamical

explanation itself (on pain of circularity).

Let me summarize what was said by going back to the

overall structure of the no-change objection. The culprit for

the charge of changelessness raised against the B-package,

in that case, was seen to be the tenseless (hence changeless)

ontology to which Staticists confine themselves. At a closer

scrutiny, however, one realizes that the assumption that

reality is tenseless (assumption 5) is quite immaterial to the

conclusion that variation can only be expressed by

changeless propositions. If I wish to compare what is the

case at a time with what is the case at another time, i.e. if I

wish to express that there has been some variation, then I

am bound to do so by pointing at some B-theoretic relation,

quite regardless of whether the states of affairs that I wish

to so compare are tensed or tenseless.

Consider again the proposition that I was standing and

that I am now sitting. It consists of the conjunction of two

propositions: (1) I was standing and (2) I am now sitting.Now, as we have seen, neither of these propositions, taken

by itself, expresses the fact that genuine change is (or was)

taking place; and this regardless of whether we take a

realist stance about tense or not, and regardless of whether

we further take a reductionist stance about it or not. The A-

theoretic fact that I am sitting NOW, or that I WAS

standing (even where NOW and WAS are taken to be

primitive tense operators), by themselves, are just as

changeless as the B-theoretic fact that I am (tenselessly)

standing at 17:00 p.m. on 26/06/2014 is. To claim that I

WAS standing, in fact, is not the same as claiming that my

standing WAS becoming past (which would indeed express

the fact that non-comparative change was taking place); the

fact that I WAS standing simply conveys the thought that

my standing IS past, which is a state of affairs that can

obtain only after the relevant change (viz. becoming past)

has already happened.

As Aristotle observed in his analysis of the concept of

motion: “if a man is walking to Thebes, he cannot be

walking to Thebes and at the same time have completed his

walk to Thebes”.15 Analogously, I submit, if a time is (or

was) becoming past, it could not at the same time have

completed its “motion”, i.e. it could not at the same time be(or have been) past. Thus, it appears, it cannot be a vari-

ation of A-determinations, evaluated from a particular,

posthumous position in the A-series, which constitutes

genuine change. The relevant change, the A-theorist must

think, should consist of the transient feature of time which

made my standing and then my sitting present.

Now, in a comparative account of passage such transient

feature of time is nothing over and above the variation of A-determinations itself. But how are we to express such vari-

ation, if not by comparing the presentness of my standing

with the presentness of my sitting, i.e. by saying that the

presentness of my standing precedes—or, minimally, that it

differs from—the presentness of my sitting? And doesn’t

this express the obtaining of a B-theoretic relation after all,

albeit one which relates two A-theoretic facts?16

The A-theorist who advocates an Ockhamist account of

passage appears to be facing a dilemma. In expressing the

fact(s) of passage, she can either (1) take a perspective subspecie temporis, availing herself solely of tensed verbs,

13 Maudlin, a self-professed defender of the block universe, con-

ceives of temporal passage as an intrinsic tenseless feature of the four-

dimensional manifold (Maudlin 2007, 109); confront this feature of

Crisp’s Presentism also with Fine’s contention that “the fact that time

flows is a tenseless fact about time; it is not one that holds at one time

rather than another” (Fine 2005, 287).14 Not, at least, in any sense that is compatible with the explanatory

role of the notion of “becoming past” with respect to the notion of

“being past”.

15 Physics: 231b28–232a1.16 Kit Fine (2005) seems to have noticed this when he asked: “how

can the passage of time be seen to rest on the fact that a given time is

present and that various other times are either earlier or later than that

time?” (p. 287).

E. Boccardi

123

thus “freezing” reality at a particular position in the A-

series; or (2) she can take a perspective sub specie aeter-nitatis, in the attempt to capture the transitions of A-

determinations which constitute the dynamic aspect of

passage. The former move, we have seen, involves putting

oneself at a particular position in the A-series, taking an A-

theoretic snapshot of the flow, as it were (I was standing &I am sitting). From that position alone, unsurprisingly, no

dynamic change can be expressed. But the latter move (2)

involves committing to the view that passage is made true

by the fact that the presentness of my standing precedes the

presentness of my sitting. Such B-theoretic relation, how-

ever, can only be instantiated by changeless facts. Either

way it seems that, under an Ockhamist conception,

“changes” of A-determinations are made true by conjunc-

tions of changeless facts.

In its full generality, the no-change objection, I argue,

should be expressed thus:

1. Changes in things are variations in the pattern of

instantiation of properties (Ockhamist conception of

change).

2. Variations can only be expressed by conjunctions of

changeless propositions.

3. If at all times reality can be wholly described by the

conjunction of propositions whose truth values do not

change, then realty does not itself change. It follows that

4. Reality does not change.

If we express the no-change objection thus, it is clear

that the real culprit is the Ockhamist, or comparativist

conception of change per se, since comparative facts are

tenseless, hence changeless, whether the states of affairs

that they compare are themselves tenseless or not.

4 Plato’s Principle and James’ No-Change Objection

If variations of properties and A-determinations are only

posthumous changeless effects of genuine change and

passage, as the observations above seem to suggest, what

characterizes the elusive mechanisms of genuine change

and passage themselves? Here I shall only attempt to set

some constraints on the possible answers to this venerable

questions. In the previous sections I have argued that the

standard no-change objection raised against the B-package

can be enhanced to become an objection against compar-

ative accounts of change and passage in general (of either

the B-theoretic or A-theoretic variety). I shall introduce

another no-change objection against the B-package, which,

I shall argue, can also be generalized to become an

objection to comparative accounts of passage.

Let us consider again the story of the ship. In that case, we

said, it is intuitive to assume that the fact that the ship was in

motion at time t1 must be distinct from the comparative fact

that the ship has moved (some time after t1). In other words,

changes of location are intuitively distinct from the ensuing

displacements (variations) that they produce. One way to

unpack this intuition is by observing that, if the instantaneous

velocity of the ship at t1 were ontologically parasitic on some

property that the ship instantiated before or after that time

(such as the trajectory of the ship until t1), then it couldn’t

possibly fulfil its explanatory role. How could the ship

“know”, at time t1, where and when it had been before, if a

“logical snapshot” of themoving ship at t1 is indistinguishable

from an analogous snapshot of a resting ship located in the

same position? Why did it continue changing its position?Consider for example the following argument proposed

by Bigelow and Pargetter and purported to show that the

single-fact view of motion deprives velocity of its essential

explanatory role.17

Consider, for instance, a meteor striking Mars, and

consider the problem of explaining why it creates a

crater of precisely the size that it does. At the moment

of impact, the meteor exerts a specific force on the

surface of Mars. Why does it exert precisely that

force? Because it is moving at a particular velocity

relative to Mars. On the Ockhamist view, it exerts the

force it does because it has occupied such-and-such

positions at such-and-such times. In other words, the

Ockhamist appeals to the positions the meteor has

occupied in the past. But why should a body’s pastpositions determine any force now? This requires the

meteor to have a kind of “memory”—what it does to

Mars depends not only on its current properties but

also on where it has been. (my emphasis, 1990, 72).

The general principle at work in the pattern of meta-

physical explanation that underlies these dual-fact accounts

of change can be summarized as follows: nothing can

undergo a (comparative) change if it is never found in a

state of changing before the change has been produced. We

shall call this: Plato’s Principle.18 If one believes (like

17 An increasing number of philosophers (e.g. Lange 2005; Arntze-

nius 2000; Tooley 1988; Bigelow and Pargetter 1990; Carroll 2002)

are putting forward arguments to the same effect.18 “That a thing which is previously at rest should be afterwards in

motion”, observes Parmenides in Plato’s famous dialogue, “or

previously in motion and afterwards at rest, without experiencing

change, is impossible […]. [A thing] cannot change without

changing”. Parmenides (in the dialogue) uses Plato‘s Principle to

argue that change is impossible. “Surely”, he says, “there cannot be a

time in which a thing can be at once neither in motion nor at rest […]

But neither can it change without changing […] When then does it

change? For it cannot change either when at rest, or when in motion

[…]”. Here, however, we shall not be concerned with the alleged

contradictions involved in the endorsement of Plato‘s Principle, but

only with the reasons one may have to endorse it in the first place.


123

Staticists do) that there could be change without a state of

changing, i.e. if one believes Plato’s Principle to be false,

I argue, then one loses one of the best reasons for

endorsing a Dynamic account of change in the first place.

Conversely, if one endorses the principle and uses it to

mount an attack on B-theoretic at-at pictures of change,

like Dynamicists (should) do, then, coherently, she cannot

ask for a waiver when it comes to give an account of

temporal passage itself. If things are so, than the general

validity of Plato’s Principle constitutes the necessary

foundation for all dynamical theories of change. Dynam-

ical theorists who propose an A-theoretic comparativist

picture of passage, I argue, implicitly so withdraw their

commitment to Plato’s Principle, thus betraying their most

fundamental tenet.

William James observed that classes of things come in

two varieties: things conceived as standing, like space, pasttimes [sic!] and existing beings; and things conceived as

growing, like motion, change, activity (cf. James 1912/

1987, p. 1067). The trouble with Russell’s use of Cantor’s

theory of infinity to dissolve Zeno’s paradox of the race, he

thought, is that while Cantor and Weierstrass were in the

business of providing a theory of the standing (mathe-

matical) variety of infinity, Russell was trying, or should

have been trying to give an account of the growing variety,

which is necessarily involved in the notions of change and

motion. “Mr. Russell’s statements”, he wrote, “dodge the

real difficulty, which concerns the ‘growing’ variety of

infinity exclusively, and not the ‘standing’ variety, which is

all that he envisages when he assumes the race already tohave been run and thinks that the only problem that

remains is that of numerically equating the paths. The real

difficulty may almost be called physical, for it attends the

process of formation of the paths.” (ibid., p. 1074, my

emphasis).

Once the race has been run, i.e. once the running is past,

all that remains of change is a posthumous, changeless

bijective correspondence between the mathematical repre-

sentations of the respective trajectories of Achilles and of

the tortoise (in our terminology: the variations of the

respective locations), which can be perfectly accommo-

dated by Weierstrass’ account of limits. But the challenge

posed by Zeno’s paradox was precisely to explain how

such trajectories could be formed, one time at a time, and

not how their parts relate to each other after having been

already produced (hence assuming that they can be

produced).

If James’ objection is sound, then Dynamicists should

not be (merely) in the business of grounding the compar-

ative truths themselves (e.g. the former existence of Caesar

and his present non-existence); they should be further

asking for the metaphysically independent grounds of

Caesar’s disappearance, i.e. for the grounds of his ceasing

to be. If we consider things from a perspective where

Caesar is still alive, it is such disappearance, whatever it

amounts to, that should explain why, post factum, he

doesn’t exist any more. So, at any rate, should the enemies

of the Static conception of reality think.

Now, if Caesar’s disappearance is to explain the com-

parative truth that he did exist while he doesn’t now, then

that disappearance, I argue, cannot be grounded on the

same facts that ground the comparative truth itself. The

comparative theories examined here violate this constraint,

as they propose to explain the relevant comparative truths

by pointing at brute comparative facts as to the compo-

sition of reality at different times. The (comparative) fact

that reality did contain Caesar but doesn’t any more cer-

tainly explains the truth of the statement that Caesar did

exist but doesn’t any more, in the sense in which truth-

makers ‘explain’ their respective truths. But this sense of

‘explanation’, I argue, is not what dynamical theorists

(should) have in mind here. If Dynamicists are impressed

by standard no-change objections to the static account of

change, they should coherently want to know how the

relevant comparative facts came to be produced, while

they were being produced.19 In short, they should not only

want to know what makes it true (now) that reality has

changed, from a perspective whence the change has

already occurred: they should also want to know what

made it true that reality was changing while it was

changing.

Thus James’ no-change objection runs through (if it

does at all) regardless of whether one describes the relevant

comparative facts in tensed or tenseless terms. The (B-

theoretic) truth that Caesar did exist in 44 BC and that he

doesn’t exist in 2014, stands in need of a dynamical

explanation—if it does at all—just as much as the (A-

theoretic) truth that Caesar existed 2058 years ago and that

he doesn’t exist now. Analogously, if an object cannot be

moving solely in virtue of the (B-theoretic) fact that it

occupies different positions at different times, as the

Dynamicist foes of Russell’s at-at picture of motion argue,

how could it be moving solely in virtue of the (A-theoretic)

fact that the positions it has occupied in the past are dif-ferent from those that it occupies now and will occupy in

the future? Regardless of what she thinks are the grounds

for these changeless comparative truths, the Dynamicist

should seek an explanation as to how they came to be

19 Notice that the relevant notion of explanation here is not causalexplanation: we are not in the business of revealing the causes of

Caesar’s death. We are in the business of explicating the metaphysical

grounds of Caesar’s disappearance from reality, grounds which, in

turn, ought to provide us with a sufficient reason for the current

non-existence of Caesar (given his former existence).

E. Boccardi

123

produced as they were being produced.20 Those who do not

provide such further explanation are proposing what I

have called an A-theoretic at-at picture of change. Theircomparative account of passage, I argue, is subject to the

no-change objection just as much as that of their Staticist

foes.

5 James’ No-Change Objection as an ArgumentAgainst Comparativist Accounts of Passage

I see no reason why James’ no-change objection should not

apply to the case of varying A-determinations, just as well

as it does (if it does) against Russell’s account of varying

locations. That a time that is previously not present should

be afterwards present, or previously present and afterwards

past, without experiencing change, is impossible; thus, at

least, should Dynamical theorists think, for the A-series

constitutes a class of the growing variety, if anything does.

Moreover, notice that such transition cannot occur while it

is still a future transition, for then the relevant change

would not have become actual yet; nor while it is past, for

then it would be too late, as the relevant change would have

already happened. I conclude that if time flows at all, and if

it is to fulfill its explanatory role, it must be flowing now,solely by virtue of what is the case now.

To further illustrate this difficulty, consider again the

famous paradox of the arrow. In a standard Aristotelian

reconstruction21 the paradox (roughly) runs as follows. If

the arrow moved throughout a period of time T, then it

must have been moving at each instant t of T (ἐν τὸ νῦν).But at each instant t of T the arrow must have occupied a

space equal to itself, and while something occupies a space

equal to itself it cannot be moving. It follows that the arrow

was at rest throughout T, contrary to the hypothesis. The

standard Staticist response to the paradox (e.g. Russell’s)

consists in affirming that objects are in motion at an instant

of time t only in a derivative sense, i.e. by occupying dif-

ferent positions at times immediately preceding and

immediately succeeding t.

Now, as noted by Lear (1981) and Le Poidevin (2002), if

instead of interpreting the phrase ἐν τὸ νῦν as meaning “at a

(generic) instant of time”, like Aristotle and most com-

mentators do, we interpret it as meaning “in the present”,

the standard Staticist manoeuvre is blocked. Zeno’s argu-

ment, under this interpretation, in fact, takes the following

form. While the arrow is moving, it is moving in the

present. But in the present the arrow occupies a space equal

to itself, so in the present the arrow must be at rest.

Therefore, while the arrow is moving it is at rest

Contradiction.

The chief difference between the paradox as formulated

in Aristotle’s and in Lear’s interpretation of the phrase ἐντὸ νῦν, for our concerns, is that under the latter interpre-

tation the notion of being in motion, or moving, cannot be

construed as being (even partially) derivative on truths that

obtain at times other than the present: “what is true in the

present should not be derivative, but fundamental. It is theprivileged status of the present that insulates present fact

from past and future fact” (Le Poidevin 2002, p. 64). Thus,

at least, should those who take tense seriously think. “To

Zeno’s incredulous question, ‘So you think that an object

can be moving solely in virtue of positions it has occupied

in the past and will occupy in the future?’, one would

simply answer ‘yes.’”, says Lear: “this would be the

response of someone who did not wish to incorporate the

notion of a present duration into his scientific theory of

time” (Lear 1981, p. 90).

But, I argue, Tense Realists must so incorporate the

notion of present duration in their picture of time! So they

have to interpret the expression ἐν τὸ νῦν as meaning “in

the present”, as Lear suggests. It follows that those who

take tense seriously cannot dispense with Plato’s Principle

that easily. Lear’s interpretation of Zeno’s paradox of the

arrow, remember, bars the way to the standard at-at

manoeuvre. By the same token, I argue, it bars the way to

A-theoretic at-at manoeuvres.

According to comparativist accounts, we have seen, the

flow of time consists (solely) of the conjunction of the facts

that jointly make it true that (1) 2014 is present, and (2)

2013 and all previous years are past, and (3) 2015 and all

subsequent years future. But if time flows at all, it must be

flowing only in the present, hence it must do so in virtue of

something that happens only in the present. As I have

argued, in fact, the facts that pertain to the futurity or to the

pastness of 2014 (for example) are all ontologically inde-

pendent from those that pertain to the presentness of 2014.

It follows that, in the large conjunction of facts that

allegedly (jointly) ground passage according to compara-

tive accounts, the only one that could have any bearing as

to the reality of flow is the one that pertains to the pres-

entness of 2014. As we have seen, however, such fact,

unadorned, does not suffice to make it true that time passes.

20 Nedd Hall (2004) made a powerful case for distinguishing two

concepts of causation: dependence (mere counterfactual dependence)

and production, a stronger notion of cause that accounts for the

production of later states from previous ones. I think that this

distinction can (and should) be generalized to include all metaphys-

ical explanations. We can rephrase the complaint raised here by

saying that the facts which make comparative truths true fail to

provide us with a productive (metaphysical) explanation of these

truths. The facts which make it true that time passes, by contrast,

should provide such a productive explanation. This suggests that the

fact(s) of passage cannot be the same which make it true that A-

determinations vary.21 See for example Owen (1957), Vlastos (1966) and Barnes (1982).


123

To put it differently, if at all times presentness advances

not at all, isn’t it miraculous that in a series of such static

moments it manages to advance? If there is no sense in

which we are “going forward” in time, over and above the

fact that 2014 is present, then how are we possibly going to

“get out” of 2014 itself? Or, equivalently, how is 2015

possibly going to become present if now, as you are readingthese words, or at any other subsequent time, presentness is

not “approaching” it in any sense?22 It’s no good to be told

that 2014 is present and 2015 future, when what we are

asking is precisely in virtue of what the only time that is

now present will have ceased being 2014. To the friend of

the A-package, the mere mentioning of any time that is not

present, and of what is the case at that time (such as the fact

that 44 BC was once present), presupposes that time has

been passing; hence any account that makes irreducible

reference to such non-present times and facts cannot pos-

sibly provide us with the grounds of passage itself, on pain

of circularity.

Consider, as an example, a purely structuralist version of

the Growing Block theory of time (GBT), one according to

which the present is picked out solely by being the only

time that is preceded but not succeeded by other times. As

new slices are added, the fourdimensional manifold of

reality grows, and it is in such growth that the passage of

time is supposed to consist of (remember that the account is

supposed to be purely comparative). Now, the year 2000

was once present. In a purely structuralist GBT world, this

means (no more, no less) that back then the times that

would later accumulate after it, failed to exist: the (now

past) presentness of the year 2000 would amount to the fact

that 2000 has once been at the “edge of existence”. But the

true proposition that the year 2000 was once at the edge of

existence must express a (now past) contingent truth. Giventhe states of affairs that obtain at all later times, in fact,

including those that obtain now, one cannot even infer that

the year 2000 exists at all (the universe could have begun

existing only in 2001, for example), let alone that it was

once facing the abyss! If things are so, then the truth of that

proposition requires a truthmaker, like any other (past)

contingent truth. Now, where (and when) is such truth-

maker to be found? What makes it now true to say that the

year 2000 was once the edge of existence?

According to GBT the truthmakers for all past (contin-gent) truths are to be found “frozen” somewhere in the

growing block. But the relentless accretion of being that

characterizes the passage of time (according to the account)

has now densely “fused” the year 2000 with all the fol-

lowing times, up to the present. So in the comparativist

account under consideration no vestige is now to be found

of the departed fact that the year 2000 has once been the

last frontier of existence, facing the abyss of nothingness,

so to speak. Put differently, what distinguishes, today, past

states of affairs as viewed from a GBT perspective from the

same states of affairs as viewed from an Eternalist one? For

example, what distinguishes (today) the portion of a

growing world up to the year 2000 from the correspondent

portion of reality as described by an Eternalist ontology?

Nothing, it appears. As things stand now, the growing

block up to the year 2000 is utterly indistinguishable from

the portion of a static (Eternalist) block up to the same

year.23

To better appreciate this, consider the following hybrid

scenario. Let M*2000 denote the fourdimensional manifold

representing our growing universe up to the year 2000.

Imagine a fourdimensional manifold (call it M2000) iden-

tical to M*2000 under all respects, except that unlike

M*2000, M2000 was created by fiat, all at once, so to speak,

in the year 2000. Both manifolds are purported to represent

the universe as it was 13 years ago. Imagine further that,

starting from the year 2000, the manifold M2000 began to

evolve too, as prescribed by the GBT, through successive

accretions of being, up to the present. Suppose, finally, that

starting from the year 2000 nothing happened according to

M2014 that didn’t also happen according to M*2014 (and

viceversa). Today, after 14 years of growth, both M*2000and M2000 would have evolved into two larger manifolds,

M*2014 and M2014. Notice that these two manifolds must be

identical, now as they were 14 years ago. It follows that no

state of affairs contained in M2014 represents the fact that

time began to flow only starting from the year 2000. If

there were such a discriminating state of affairs within

M2014, it would have had to come into existence after theyear 2000, contrary to the hypothesis that, starting from

that year, nothing happened in M2014 that didn’t also

happen in M*2014. From the perspective of the present

time, then, there appears to be no qualitative difference

between the “Eternalist portion” and the “GBT portion” of

our imaginary hybrid world, which could help us recon-

struct the different ways in which they came to exist.

This difficulty can perhaps be best appreciated by

imagining time to come to an end. Suppose that the

growing block has grown till the very end of time, so that

we are now living at the (enduringly) last frontier of

22 Commenting the use of the “new infinite” in solving Zeno’s

paradoxes, James expressed an analogous worry: “that being should

be identified with the consummation of an endless chain of units (such

as ’points’), no one of which contains any amount whatever of the

being (such as ’space’) expected to result, this is something which our

intellect not only fails to understand, but which it finds absurd”. The

arguments presented here can be thought of as an application of this

line of argument to the case of temporal durations.

23 Braddon-Mitchell (2004) used this fact to argue that, in a Growing

Block world, it would be impossible to know if the current time is

really the present or not.

E. Boccardi

123

existence, at time n. From the perspective of time n, thewhole of reality (past and present) can be represented by

the manifold M*n. What can now distinguish this manifold

from an equivalent Eternalist one, Mn? What makes it true

that reality as described by M*n has evolved (in a dynamic

sense of the term), unlike what is the case in that described

by Mn? Nothing, it appears. The disagreement between the

Static ontology of the Eternalist and the Dynamic one of

the Growing Blocker appears to have vanished. According

to both accounts, in fact, n is the sole time that is not

succeeded by any other time. Moreover, there is now no

state of affairs (present, past or future) that feature in the

Dynamic description which does not also feature in the

Static one, and viceversa.This and similar unwanted results, I submit, follow from

the structuralist contention that nothing happens to a time

when it ceases being present, i.e. it follows from a denial of

Plato’s Principle (no-change without changing) as it appliesto the variations of A-determinations. As James acutely

observed, past times form a series of the standing variety

(cf. Ibid. 1067), while the growing block should be con-

strued as forming a series of the growing variety.

Comparative accounts of change of either the A-theoretic

or the B-theoretic brand, may be said to presuppose a view

from the end of time, so to speak, in that they treat reality as

if the passage of time had already spanned the whole of it,

producing its posthumous changeless ontological effects;

which are the comparative truths themselves (the varia-

tions), and the very existence of the different times at

which the size of the manifold, or the composition of

reality, can be assessed for comparison.

The view from the end of time is unsuitable for a

dynamical grounding of passage, as it presupposes what it

ought to explain, i.e. precisely that past states of affairs

became past, that later stages of reality were reachedstarting from earlier ones; and that the comparative truths

that one will later contemplate retrospectively (from the

point of view of the end of time), were being produced one

by one, in due turn, as newer facts (or events) becamepresent. In short, the perspective from the end of time fails

to provide us with a truthmaker for the passage of time,

hence it fails to provide us with a sufficient reason for the

ensuing fact that later and later times are continuously

reached.

6 Conclusions

There are two no-change objections that can be raised

against the B-Package. One (McTaggart’s objection, dis-

cussed in Sect. 2), stems from the observation that tenseless

propositions have eternal truth values. The other (James’

objection, discussed in Sect. 4), derives from the principle

that nothing can vary over a period of time T, if it doesn’t

instantiate a state of changing at all the instants of time

which compose T (Plato’s Principle). I have argued that

both objections can be generalized to become objections to

any comparative conception of change, regardless of

whether it takes tense seriously or not (Sects. 3, 5). The

arguments put forward in this paper, in fact, suggest that

variations of determinations are made true by conjunctions

of changeless facts, quite regardless of whether the deter-

minations that are thus compared are A- or B-theoretic.

When the no-change objection is formulated in its full

generality the culprit for the charge of staticity turns out to

be the Ockhamist conceptions of change and passage,

rather than the tenseless ontology of the B-theory of time

per se. It follows that, contrary to what is widely believed,

A-theoretic accounts of time cannot be considered immune

to the no-change objection, just in virtue of being realist

about tense. They must further ensure that their account

meets the following constraints. If reality is dynamic, then:

1. The fact(s) which make it true that a time (T) becamepast, or that it ceased being present (fact a), must be

distinct from the conjunction of the facts which make

it true that T was present and is now past (fact b). And2. Fact(s) a must fully explain fact(s) b.24

A-theorists who find these arguments compelling appear

to have two broad families of options. Either (1) they

accept the conclusion that time, according to their account,

does not flow, or (2) they put forward an account of flow

that is categorical (non-comparative). As I have already

said, I think that the A-package loses much of its allure, if

deprived of a realist conception of passage. Therefore I find

the first option by far the less palatable for the friends of

the A-theory of time.25

As for non-comparativist conceptions of passage, a few

considerations are in order. First, notice that Tense Realist

accounts which are susceptible of a structuralist interpre-

tation, i.e. those accounts according to which A-

determinations are picked out by comparing states of

affairs which obtain at more than a single moment of time,

are inherently incapable of contributing to a non-compar-

ative account of change and passage. According to

structuralist variants of Presentism, for example, the unique

time that is present is picked out by virtue of being the onlytime that exists. According to structuralist variants of the

24 While this paper is mainly concerned with explicating the

ontological grounds for truths of kind a, hence with explanations of

the kind offered by truthmakers, it is worth noting again that the

relevant kind of explanation which features in desideratum (2) is the

one that is captured by the notion of sufficient reason.25 See for example Tallant (2010, p. 18): As a presentist, I don’t

believe in the existence of a thing called “time”, or “temporal

passage”.


123

Growing Block theory, we have seen, the present is picked

out (solely) by being the only time that is not succeeded by

other ones. But being the only time that exists, or being the

only time that is not succeeded by other ones, are not truths

which supervene on what is the case solely at the present

time. Thus, any account of passage based on these struc-

turalist accounts of tense will be bound to be itself

comparative: if the instantiation of a (tense) property is a

comparative state of affairs to start with, then surely any

account of the variations of such property will have to be

comparative (hence tenseless) too. Thus, I argue, the

arguments put forward in this paper make a case in favour

of Primitivist conceptions of A-determinations, for only

these treat A-properties as being instantiated solely in vir-

tue of what is the case at an instant of time.

Being Primitivists about tense, however, as I have argued,

is not enough to account for the passage of time. The fact that

reality is located at a certain position in the A-series, or the

fact that different A-theoretic positions are occupied at dif-ferent times, we have seen, is not by itself sufficient to make

the world dynamic, regardless of how we construe of A-

properties.26 Thus the A-theorist must add an extra dynamic

ingredient to her Primitivist account of A-determinations.

Unfortunately, it is very hard to say what this Dynamic

ingredient should be. One may speculate that it be con-

strued of as an intrinsic property of A-determinations (a

second order property), to the effect that whenever pres-

entness is instantiated, it has the disposition to be

instantiated by another time, or to cease being instantiated.

A part from the numerous difficulties which dispositionalist

accounts face in general,27 I see further worries for dis-

positionalist accounts of passage.

Firstly, in order to comply with conditions i and ii, such

disposition must be capable of (1) obtaining solely in virtue

of what is the case at an instant of time (the present); and

nevertheless (2) be such as to constitute a necessary and

sufficient reason for the variations that it is thought to

produce.28 In short, a disposition grounded solely on

present states of affairs must necessitate the obtaining of

contingent states of affairs at later moments of time. This is

in sharp contrast with standard dispositional properties: a

glass can well be fragile throughout a period of time

without breaking, for example; but how could something

change throughout a period of time without bringing about

some variation of reality? Given the fundamental onto-

logical independence of the present time from any other

past or future time, it is not clear to me that there is any

way of constructing a coherent account of passage along

these lines.

Secondly, if times are thought to constitute a Cantorian

continuum (as most authors assume), there is a further

difficulty related to the lack of a particular A-theoretic fact(or facts) which such disposition is supposed to bring

about. The instantiation of presentness by a given time, we

have seen, ought to bring about the imminent fact that that

time has ceased being present. But for any present time T*

at which it is true to say that an earlier time T has (already)

ceased being present, there are infinitely many times pre-

ceding T* during which it was already true to claim that T

has ceased being present (these are all the times that

intervene between T and T*). If so, then, which particularA-theoretic fact would the putative disposition instantiated

by the presentness of T be disposed to bring about? It

appears there can be none.29

These considerations militate against the idea that the

passage of time supervenes on the instantiation of some

dispositional property. Unfortunately, however, it is hard to

free the notion of an intrinsic, instantaneous state of changingfrom its air of contradiction, when it is construed in non-

dispositional, categorical terms. Indeed, it is not surprising

that in accounting for change and passage some (e.g. Berg-

son) suggested that the transient aspect of time falls squarely

outside of the expressive capacities of our concepts and

perceptions; nor is it surprising that others (Hegel, Priest)

have been tempted by the controversial view that contra-

dictory states of affairs can obtain in reality (under specific

circumstances).30 Still less surprising, finally, is that some

(e.g. Bradley, McTaggart and many contemporary B-theo-

rists) came to the conclusion that time and passage should be

confined to the realm of appearances.

Acknowledgements Predecessors of parts of this paper were pre-

sented at a conference at the Universities of Geneva and Barcelona.

I’m grateful to the respective audiences for their useful comments. I

would also like to thank the anonymous reviewers of this essay.

Finally, I would like to acknowledge a special debt to Dr. Federico

Perelda for helpful discussions.

26 As Fine (2005, p. 287) aptly put it, “even if presentness is allowed

to shed its light upon the world, there is nothing in [a Tense Realist’s]

metaphysics to prevent that light being ‘frozen’ on a particular

moment of time”.27 Many authors, for example, argue that dispositions must be based

on categorical properties (cf. Armstrong 1997, p. 97).28 Analogously, we have seen, the ship must possess a dispositional

kinematic property that (1) is not dependent on its future and past

positions, but that nevertheless (2) is capable of fully explaining the

subsequent displacements of the ship.

29 A related difficulty stems from the observation that an instant of

time can become present only after each previous instant ceased being

present in its due turn. It follows that, if times form a class of the

growing variety, like Dynamicists should think, then the passage of

time involves the performance of a hypertask (an uncountably infinite

number of operations that occur sequentially within a finite interval of

time); something which many find impossible (cf. Clark and Read

1984).30 Passage, under these dialetheist accounts, would consist in a single

time being both present and not present (see for example Priest 1987).

E. Boccardi

123

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