Diodorus cronus and the logic of time.
Massie, Pascal
Diodorus cronus and the logic of time.
THIS PAPER ADRESSES A debate sometimes referred to as logical
fatalism. It brings together three majors ancient texts: the
"fatalist argument" discussed by Aristotle in De
interpretatione 9, the claims attributed to the Megarians in Metaphysics
9, and, my main concern, Diodorus Cronus's master argument reported
by Epictetus in Discourses 2.19. (1) By "logical fatalism" I
mean the claim according to which it can be shown, on the grounds of
logic alone, that the course of events in the world is governed by
necessity. Most contemporary efforts have focused on reconstructing the
unstated reasoning that led Diodorus to his conclusion, even though such
an argument--as Epictetus himself suggests--probably never existed. (2)
In this paper I argue that the efforts to formalize the argument
forget its ontological nature. Diodorus was engaged neither with a
problem of formal logic nor, it should be added, with a critique of
freedom. Rather, the master argument must be recast, along with other
extant fragments, as part of Diodorus's critical engagement with
Aristotle's ontology. More specifically, Diodorus does away with
Aristotle's [TEXT NOT REPRODUCIBLE IN ASCII] understood as a power
oriented toward being which nevertheless retains the possibility of not
being. It proclaims that possibilities that fail to actualize are simply
nothing. The debate opens fundamental ontological questions: Can there
be a coherent concept of being without the assumption of immutability?
In what sense of being can we say that there are unactualized
possibilities? Aren't determinacy and the corresponding exclusion
of alternative possibilities necessary conditions for being and being
true?
Even though, according to Diodorus, nonactualized possibilities are
devoid of any ontological weight, his so-called fatalism doesn't
assume that the future course of events is already established. The
world of temporal becoming may stand in opposition to eternity, but it
is not incompatible with necessity. I argue that Diodorus's main
contribution resides in the invention of an ontologico-temporal concept
of possibility. While Aristotle finds in present activities and actual
performances the utmost manifestation of being, Diodorus's ontology
privileges the past, for only what has been is fully complete and
achieved; it is the finished statue, rather than the actual process of
chiseling, that truly is. As for the future, since all that what will be
is destined to become past, it can never harbor possibilities that will
not obtain. Thus, any futurai possibility that does not actualize is
neither futurai nor even possible.
To support this interpretation, I will first discuss some
difficulties associated with the concept of buvapic. I will then examine
the master argument itself in order to show that it is not reducible to
Diodorus's teaching on hypothetical implication and modalities but
depends on his conception of time and being. Finally, in section III, I
explore Diodorus's ontology in light of a conception of time that
envisions the future sub specie praeteriti and makes of the past the
time of truth. This, however, contains an aporia which, I submit,
prevents Diodorus from offering a viable alternative to Aristotle's
[TEXT NOT REPRODUCIBLE IN ASCII].
I
The Ontological Ambivalence of [TEXT NOT REPRODUCIBLE IN ASCII]. It
is said that Diodorus Cronus's master argument ([TEXT NOT
REPRODUCIBLE IN ASCII]) was a famed topic of discussion among ancient
philosophers. Yet what it is supposed to establish remains disputed.
Even the meaning of its enduring name is uncertain. (3) It is often
read, along with De interpretatione 9, as an argument about fatalism and
free will, and there is no doubt that it raises far-reaching moral
questions. Yet the practical import is mostly stressed by its opponents
who didn't fail to protest its "absurd consequences."
Thus, as Cicero argues, should the Megarians be correct our existence
would be ruled by an inflexible fate:
while the statement: "This man will die of this disease" is true in
the case of a man who is suffering from a deadly disease, if this
same statement is made truly in the case of a man in whom so
violent an attack of the disease is not manifest, nonetheless it
will happen. It follows that no change from true to false can occur
even in the case of the future. For "Scipio will die" has such
strength that although it is a statement about the future it cannot
be converted into a falsehood, for it is a statement about a human
being who must inevitably die. If the form of the statement had
been "Scipio will die by violence in his bedroom at night," the
statement in that form would have been a true one, for it would
have been a statement that a thing was going to happen that was
going to happen, and that it was going to happen is a necessary
inference from the fact that it did happen. (4)
Thus, a future statement about Scipio that (a) stipulates the
particular condition of his death and (b) is not grounded on the present
observation of his condition (as in seeing now that Scipio is afflicted
with a deadly disease) would be no less necessary than a universal truth
about the common lot of human beings. This explicitly contradicts De
interpretatione 18a28-33 where Aristotle maintained, on the contrary, a
distinction between "particulars that are going to be" (for
instance, a prediction concerning Scipio's particular condition of
death) and the case of a universal taken universally (for instance,
"man is a mortal animal").
Yet nothing suggests that the purpose of the master argument was to
demonstrate fatalism. In fact, what we usually understand by
"fatalism" doesn't seem to be implied. It is significant
that Cicero doesn't call it the "master argument" but
mentions that it was known by the name: "Peri Dunaton, in which the
meaning of the term 'possible' is investigated." (5) Even
though the expression "master argument" remains in use,
"On the Possible" could be a more accurate title. A proponent
of Diodorus's argument need not interpret events as signs, as many
a fatalist does; one need not assume that a plan is secretly woven in
the fabric of reality or that there is a reason for everything that
happens. Furthermore, the argument doesn't depend on a commitment
to any particular conception of causality. Diodorus doesn't
stipulate how, why, or through which causes the future will occur; he is
neutral as to whether we should admit final or efficient causes or some
combination of both; he advocates neither divine predestination nor
physical determinism. The necessity Diodorus proclaims is not a decree
that welds events to an implacable verdict. Rather, its primary concern
is to refute a conception of potency understood as a power oriented
toward the future that nevertheless retains the possibility of not
actualizing, that is, the very ambivalence that Aristotle placed at the
heart of ouvapiC when he declared that "a thing may be capable of
being something and yet not be it, or it may be capable of not being
something [else] and yet be it." (6) In that respect,
Diodorus's thesis would perhaps be more accurately described as
actualism rather than fatalism.
Today, we often assume that actuality and possibility are
modalities of judgments, taking for granted the shift that occurred with
modernity when, as Heidegger observed in Nietzsche 1:
the determination of being, potentia and actus, slip into the
vicinity of the basic forms of thought and judgment. Possibility,
actuality, and necessity along with them become modalities of being
and of thinking. Since then the doctrine of modalities [became] a
component part of every doctrine of the categories. (7)
Thus, a statement expresses actuality when it reports some fact,
whereas possibility connotes what is counterfactual (or even fictional).
The first difficulty is of a linguistic nature. It is well known
that the terms [TEXT NOT REPRODUCIBLE IN ASCII] are not univocal.
Depending on the context they may designate a disposition, a capacity, a
power, a tendency, a license, or a skill. To this Aristotle adds two
further distinctions, between (a) a rational and an irrational potency
and (b) an active and a passive one. Despite the equivocation, however,
Aristotle identifies the "chief sense" of [TEXT NOT
REPRODUCIBLE IN ASCII] as the "principle of change in something
else or in itself qua something else." (8) The link with motion is
further confirmed by the fact that motion is defined as "the
actuality of that which is in potency, as such." (9) Thus, motion
is potency at work; it is the fulfillment of a "not yet" since
it actualizes not the form that motion strives to accomplish but potency
as such. Motion is a doubling of potency: it is achieved when it remains
in potency, not when it results in a final form.
The issue is not to demonstrate the existence of motion (which is
phenomenologically indisputable) but to do so without violating the
Parmenidean principle (which is conceptually indisputable). This leads
Aristotle to extend ontology beyond the consideration of actual entities
and activities. When he claims that motion "is," Aristotle
doesn't declare that it is simply observable but that is has a
nature. As Remi Brague has argued, Aristotle's definition of motion
is not construed for the sake of "demonstrating" that it
exists (this would be better done by induction) but to show that
"the manifest reality of motion possesses a consistency of its
own.... [I]f Aristotle has to display this consistency, this is so owing
to its having been denied--above all by Parmenides." (10) But how
can what constantly ceases to be what it was to become but is not yet
harbor permanence, consistency, and identity? So long as they are
moving, bodies in motion do not coincide with themselves. Even mobiles
that change only their location but (seemingly) retain their substantial
identity are not, on closer examination, immune to the paradox; as
Massumi puts it: "[a body in motion] coincides with its own
transition: its own variation. The range of variations it can be
implicated in is not present in any given moment, much less in any
position it passes through. In motion, a body is in an immediate
unfolding relation to its own nonpresent potential to vary." (11)
To be in motion is to belong simultaneously to what is no more and what
is not yet; it is to occupy a space between potency and actuality.
Doesn't motion then violate the Parmenidean principle--being is,
nonbeing is not?
Aristotle's solution proposes that being is not reducible to
actuality but encompasses potentiality. It is difficult to see how an
account of motion wouldn't presuppose [TEXT NOT REPRODUCIBLE IN
ASCII] in some form, since to deny it would entail that everything is
either actual or unable to be actual, thus, that nothing can be in the
process of actualizing.
If, therefore, it is impossible to possess technical skills without
having at some time learned and mastered them and subsequently
not to possess them without having lost them at some time either
through forgetting or misfortune or through time (for certainly the
objects cannot be destroyed since they always exist), whenever
someone stops building, he will no longer know how to build; but
then, when he starts building again, how will he have mastered that
knowledge? (12)
Experience shows the opposite: change is real; activities do not
suddenly burst out of nothing; skills must be learned first, and when
they are not exercised, they are not ipso facto lost. If it weren't
the case, the ability to resume an interrupted action would be
miraculous.
While the connection with motion indicates the chief sense of the
term, Aristotle declares it "not useful" for the present
inquiry. (13) This doesn't mean that what Aristotle is seeking will
be found outside motion, but rather that it requires a deepening of the
"chief' sense. Yet it proves elusive, and Aristotle, instead
of providing a definition, invites us to grasp it by analogy. (14)
What builds is to what can build, as someone waking is to someone
sleeping, as someone seeing is to a sighted person with his eyes closed,
as that which has been shaped out of some matter is to the matter from
which it has been shaped, and as what has been finished off to what
hasn't been formed. Of these let actuality be defined by one part
and what is potential by the other. (15)
If being is not limited to the actually present entities and their
properties, nonbeing must likewise not be limited to unqualified
nothingness. (16) As Stanley Rosen observed: "Nonbeing must be a
form of being. Nonbeing cannot be found in energeia; complete presence
cannot be marked by partial absence. It appears, therefore, that
nonbeing must be in dunamis." (17) Borrowing from Duns
Scotus's terminology, we can distinguish nihil absolutum--the
absolute nothingness prohibited by Parmenides--from nihil relativum--the
nonbeing of absence, negation, and privation without which there
couldn't be change, difference, or plurality. (18) While the former
is an ontological and conceptual impossibility, nihil relativum can be
compatible with being.
Yet, the concept of [TEXT NOT REPRODUCIBLE IN ASCII] raises many
conceptual difficulties. First, consider Aristotle's own example in
Metaphysics 9.3:
There are some, such as the Megarians, who say that a thing only
has potency when it is active ([TEXT NOT REPRODUCIBLE IN ASCII])
and that when it is not active it has no potency. They say, for
instance, that a man who is not building cannot build but only the
man who is building and at the moment when he is building. (19)
Aristotle regards this view as absurd. Yet it seems to agree with
his own definition; if motion is "the actuality of that which
potentially is, as such," (20) then is most manifest when it is
fully active. Furthermore, Aristotle himself admits that unless an
appropriate patient is also present, the agent "will not be able to
act according to its capacity." (21) If so, as Nicholai Hartmann
objected, although the claim "Dio can build a house"
identifies Dio as one who has a potency, it still remains that without
land, capital, workers, building material, tools, and so forth, the
builder is de facto unable to build anything. These, of course, are
external conditions, but they are necessary nonetheless. In that case
[TEXT NOT REPRODUCIBLE IN ASCII] would rather express a "partial
possibility" (Teilmoglichkeit)--an incomplete and therefore
powerless ability, not a total one (Totalmoglichkeit)--that is, a
possibility that is such that all the conditions for its actualization
are fulfilled.
Ontologically speaking, the possibility to build consists precisely
in an interrelation of external and internal conditions and in such
a way that, in truth, a possibility occurs only when both kinds of
conditions are simultaneously fulfilled. (22)
While not insurmountable, Hartmann's objection highlights the
difficulty of claiming that a being has a potency when it is actually
incapable of actualizing it on its own.
Second, [TEXT NOT REPRODUCIBLE IN ASCII] designates power and
capacity but also indeterminacy and indecision. The material component
of a hylomorphic substance, for instance, retains the possibility of
actualizing some other forms. The bronze of this dagger could be melted
to smith a bracelet. Potentiality introduces alterity; it shows that
actually present beings are constantly open to being otherwise than they
are. Yet, these apparently contrary characteristics (power and
indeterminacy, capacity and indecision) must be held together. The power
to accomplish something, insofar as it is a power, holds within itself
the possibility of not being deployed. (23)
Finally, what and where are these possibilities before they
actualize? Is, for instance, the potency to be a statue already
"in" the block of marble along with its other properties (its
size, color, weight)? This is ruled out. Aristotle's ontology
distinguishes being as articulated in the categories from being qua
potency and actuality, and doesn't reduce the second to the first
one. As Brague puts it:
the buildable will appear as such only in between the point of
departure (the material as stone or bronze) and the point of
arrival (the house or the statue), and it will be neither of these
two points. This in-between is motion. (24)
Does the world, in addition to the actual entities it contains,
also harbor a latent reserve of beings? If so, the same entity would
conceal infinitely many potential beings. To admit such an indefinite
plurality that can never actually be seen and may never be realized is
to open the door to an indeterminateness that threatens the identity of
substances. This populates ontology with an infinite number of invisible
and intangible potential beings and violates the principle of parsimony
according to which entities must not be multiplied beyond necessity
(entia non sunt multiplicanda praeter necessitatem).
No doubt, an a fortiori inference applies from actuality to
possibility (whatever is actual is a fortiori possible) and it seems to
even extend into the past (whatever is now actual was possible before it
happened). Yet, it is not obvious that the possibilities that are not
and never will be should still be granted being.
These are some of the reasons why Diodorus (and his Megarian
predecessors) concluded that possibilities that never occur or
capacities that never produce anything are simply nothing. What then is
a real possibility? What else but an actualized possibility? Thus,
Diodorus concludes that being is actuality or is not. To grant being to
unactualized potentialities would ultimately amount to granting being to
nonbeing. On a Megarian interpretation, Parmenides' injunction
"being is, nonbeing is not" entails the identification of
being with actuality and the rejection of any shadowy virtuality that
would posit indeterminacy at the heart of being. (25)
II
The Master Argument. The goal of this section is to examine the
master argument in order to establish (a) how it is related to the
Megarian teachings on hypothetical implication and modalities but cannot
be reduced to them, and (b) that it depends on a specific metaphysical
interpretation of time. The text is preserved in Epictetus's
Discourses 2.19, where it appears in the form of a trilemma, that is, a
dilemma composed of three claims, each one seemingly true (or at least
plausible), but such that their juxtaposition yields a contradiction:
The master argument appears to have been proposed on premises of
this sort: since there is a mutual contradiction among the three
following propositions: (a) all past truth is necessary, (b) the
impossible doesn't follow the possible ([TEXT NOT REPRODUCIBLE IN
ASCII]) and (c) the possible is what is neither true nor ever will
be, Diodorus, realizing the contradiction, appealed to the
credibility of the first two to establish that that which is
neither true nor ever will be is not possible ([TEXT NOT
REPRODUCIBLE IN ASCII]). (26)
It seems likely that in the Metaphysics Aristotle examined a claim
made by some unnamed Megarian and that Diodorus's trilemma is a
subsequent response to Aristotle's objections, for, as Schull
observed, (27) the trilemma is entirely composed of Aristotelian claims:
the necessity of the past is stated in Nicomachean Ethics 6.2.1139b7-9;
the principle according to which if something is possible then nothing
impossible should follow from it is stated in Metaphysics 9.41047b10-11;
so is the claim "nothing prevents a thing which is capable of being
or coming to be from neither being nor being likely ever to be."
(28)
Three things can be observed from the outset: First, the argument
posits a universal principle; it applies to entities, events, actions,
states of affairs, properties, and so forth. Second, (pace Gaskin)
"truth" and "being true" refer to statements as well
as to the very objects denoted by these statements. It is a consequence
of the correspondence theory that truth posits necessity (if it is true
that p, it cannot be that p; thus p [contains] [??]p). (29) Finally, the
conclusion affirms the principle of plenitude: the real contains all
that is possible and, conversely, all that is possible must, at some
point of time, be realized. (30) Thus, a future actuality, rather than
the continuity of a nonmanifest potency, is enough to warrant
possibility.
Usually, the solution of a trilemma consists in rejecting one of
the premises. In this case, Diodorus abandoned the third one, (c):
"the possible is what is neither true nor ever will be," and
replaced it with (c'): "that which is neither true nor ever
will be is not possible," which can be rephrased in the affirmative
as: "the possible is either what is or what will be." Thus,
instead of identifying possibility with actuality, as the fatalist
portrayed in Metaphysics 9 did, Diodorus posits that the possible
coincides either with a present or a future. This solution wouldn't
abolish [TEXT NOT REPRODUCIBLE IN ASCII] but would recast it as a
futural actuality. (31) As for what is neither true nor ever will be, it
is not possible at any time. Diodorus doesn't give any reason in
support of his solution beyond the fact that the first two premises seem
"credible" ([TEXT NOT REPRODUCIBLE IN ASCII]).
Future events appear to be possible in the sense that their
occurrence or nonoccurrence seem to be in a state of equilibrium; so
long as they are undecided, one doesn't cancel the other. But
Diodorus's argument is not concerned with the way things appear to
us; the future strictly designates what will be; it corresponds to the
segment of actuality which, relative to the present, hasn't yet
occurred. In that sense, undecidability is not a property of the future
itself but a mark of our ignorance. What will be is no less closed than
what has been; accordingly, the future doesn't have any special
ontological status.
Depending on when they are stated and on the temporal location of
their referent, the truth value of many statements (for example,
"Today is Monday" or "Lauryn visited Tokyo") will
change. (32) Many commentators (33) have proposed to relate the master
argument to Megarian propositional logic and Diodorus's account of
modalities. (34) As with Stoic logic, a Megarian conditional
doesn't require any connection between antecedent and consequent.
It simply designates any implication in the broadest sense that is open
to a truth-functional interpretation. Thanks to Sextus Empiricus we know
of a controversy between Diodorus and his student Philo:
Philo claimed that the hypothetical is true when it doesn't begin
with what is true to conclude to what is false; thus there is,
according to him, three ways for a hypothetical to be true [TT, FT,
FF] and one to be false [TF]. (35)
Philo's conditional (which is analogous to the modern material
implication) can be represented in the following manner:
p q p [contains] q
T T T
T F F
F T T
F F T
The consequence, however, is disconcerting. To take Sextus's
example: "if it is night, it is day," will be false if it is
night [TF] but it would have to be true if it is day [FT], In response
to this difficulty, Diodorus corrected Philo by rephrasing the rule of
implication in the following manner: "an implication is true which
neither admitted nor admits of beginning with what is true to conclude
to what is false." (36) Philo would consider that the implication
"if it is day, I speak" is true if it is actually day and I am
actually speaking. Diodorus, on the contrary, sees it as false because
it is possible that the antecedent be true but the consequent false,
"since before I began to speak the antecedent 'it is day'
was true, but the consequent 'I speak' was false." (37)
Thus, Diodorus's solution corrects Philo by taking into account the
consideration of modality and time. (38) That is, modalities can be
translated in the temporal equivalents of "never" (for the
impossible), "always" (for necessity), and
"sometime" (for possibilities). The concern that guides
Diodorus is whether the truth-value is mutable or immutable when the
proposition is specified by a date. As Bobzien observes, "for
Diodorus a conditional cannot change its truth value. If it is true
(false) at one time it is true (false) at all times." (39) The
hypothetical p [contains] q is valid if there is no time t in which p
could be true and q false. An inference which at times obtains and at
others doesn't is treated as a false inference.
This means that modalities can be expressed in terms of temporal
frequency. According to Boethius, "Diodorus defines the possible as
what is or what will be; the impossible as what is false and will not be
true; the necessary as what is true and will not be false; and the
non-necessary as what is already false or will be." (40) Necessity
expresses what is temporally always arid impossibility what is never at
any point of time. Truth and falsity are determined by temporal
occurrences and modalities by temporal frequency. This produces a modal
square that makes room for what is possible (redefined as what is true
or will be true) and for what is not necessary (redefined as what is
already false or will be false) and can be represented in the following
manner (using F to denote the future): (41)
Necessity: T [conjunction] FT Impossibility: F [conjunction] FF
Possibility: T [disjunction] FT Nonnecessary: F [disjunction] FF
Yet does Diodorus's doctrine on implication and modalities
truly preserve contingency and possibility? One could suspect that even
though possibility and nonecessity are now construed as intermittent
truths, the solution conceals what, in fact, turns out to be a bleak
alternative of necessity or impossibility. Three problems arise at this
juncture:
(1) How can Diodorus make room for a modal category of possibility
as something that would supposedly be distinct from necessity, when his
argument affirms that whatever will be must be? Although an event may
occur only once, it nevertheless cannot be otherwise. Thus, in a sense,
it is both possible (since it doesn't always happen) and necessary
(since it has to happen). Although it occurred only once, prior to 49
B.C. "Caesar will cross the Rubicon" was a future truth (which
is not the same as being a truth about the future), (42) and it will be
true forever afterward. Even propositions that are sometimes true but
not always (for instance, "it is day") must fall under this
rule. In other words, so long as they are specified, indexical
expressions can be translated into atemporal truths.
Bobzien has attempted to exonerate Diodorus from the accusation of
construing an empty concept of possibility by declaring that
it is not the case that for Diodorus every proposition is either
necessary (and possible) or impossible (and non-necessary). There
are propositions that are contingent in the sense of being both
possible and non-necessary, namely all those which will change
their truth values at some future time. The proposition "it is day"
is such a case. (43)
Yet this doesn't show that the so-called nonnecessary
assertions are truly contingent; it simply shows that they are
intermittent. Intermittence, however, even if it admits of chance and
randomness at the causal level, cannot save contingency since at each
instant nothing other than what must be can be. (44)
(2) Temporal frequency by itself is not enough to establish
necessity and impossibility. The fact that some things never happen
doesn't prove that they are impossible; just as always seeing
things happen in the same manner doesn't prove that they are
necessary. In order to establish necessity, what needs to be
demonstrated is that other possibilities (those that do not actualize)
are truly prevented from happening; but this is something the modal
table alone cannot do.
(3) Any attempt to treat the argument as an application of Megarian
propositional logic (45) assumes a modern representational
interpretation of possibility. In so doing, it ignores the metaphysical
question raised by the concept of [TEXT NOT REPRODUCIBLE IN ASCII], that
is, the existence of an ambivalent power to be that is simultaneously a
power not to be. Most of us believe that many things that did not occur
could nevertheless have occurred. We think so because we do not see any
contradiction in their occurrence; they are conceptually consistent,
even though they didn't happen. A Diodorean impossibility, however,
is not a matter of inconsistency. In most instances there is nothing
logically impossible in my doing something else (or nothing at all)
rather than what I am doing, and Diodorus doesn't deny our
imagination's ability to entertain all sorts of counterfactual
scenarios and alternative histories. The concept of [TEXT NOT
REPRODUCIBLE IN ASCII] we are dealing with, however, belongs to the
ontological-temporal plane, not the logico-semantic plane where
"possible" means conceivable and where the impossible is
determined by contradiction (square circles, married bachelors, or
time-travel paradoxes). The kind of impossibility that is defined by the
internal contradiction of incompatible features (incompossibility)
treats as possible whatever is conceivable so long as no contradiction
results from the combination of various components. The issue raised by
the master argument, however, concerns real futural possibilities. The
question is not whether we can conceive other universes but whether we
should grant being to possibilities that will not actualize. Alexander
of Aphrodisias's examples clearly demonstrate this point:
Diodorus claimed that that alone is possible which either is or at
all events will be. On his view, for me to be in Corinth was
possible if I was already in Corinth or if I were at all events
going to be there; if I were not to be there, then it was not
possible either. And it was possible for a child to become literate
if he was at all events going to become so. Diodorus puts forwards
the master argument in order to establish this principle. (46)
Diodorus's contribution resides in the creation of an
ontologico-temporal concept of possibility and impossibility.
Nonactualized possibilities are impossible because they are achronic;
there is no time in which it could occur. On an actualist view, no
alternative to what is can occur at the time it occurs. Temporal
necessity posits that at each instant, things are what they are and it
is too late for them to be otherwise. This thesis appeals to an
atomistic conception of time that Diodorus probably developed in the
context of a critical engagement with Aristotle's Physics. Diodorus
is credited for having coined the term "bodies without parts ([TEXT
NOT REPRODUCIBLE IN ASCII])" to describe the absolute simplicity of
elemental beings and avoid the infinite divisibility of matter, space,
and time. (47) Simplicius reports that for Diodorus not only bodies but
"instants too are without parts, and so are units, so that even if
some declare that there are bodies without parts (as Diodorus thought)
the same assertions would have to be made about instants." (48)
Thus, a body without parts occupies a space without parts in an
instant-without-parts.
In the Physics Aristotle confronted a famous aporia: if the past is
no more and the future not yet, the whole reality of time must depend on
the present instant. But how can we make sense of this? If it wholly
coincides with itself, the temporal flow is broken and instants become
fixed and immutable. If it doesn't, intermediate instants can
always occur between the prior and the posterior ad infinitum, and we
fall into Zeno's paradoxes. Aristotle concluded that a continuum
cannot be composed of actually indivisible units. Rather, instants must
be grasped both as repetition and difference ("the now is in a way
the same, in another sense not; insofar as it is always somewhere else,
it is different" (49)). As structural, the now is always the same;
as prior and posterior, it is always different. Diodorus, on the
contrary, pursued the first branch of the dilemma. As a consequence, he
accepted the discontinuity of time, the absolute coincidence of the
instant with itself, and of being with punctual actuality.
A body without parts [[TEXT NOT REPRODUCIBLE IN ASCII]] must be
contained in a place without parts, and for this reason it cannot
move, neither in it (for it fills it up totally and what moves
requires a space larger than itself), nor in the place where it
isn't, since it isn't yet there to move. Consequently, nothing is
in motion. (50)
In agreement with the Eleatic exclusion of becoming from being,
Diodorus appeals to the ultimate spatiotemporal indivisibility of the
[TEXT NOT REPRODUCIBLE IN ASCII] to reject motion. Unactualized
possibilities didn't occur in the past, cannot occur in the
present, and will not occur in the future.
Yet is this enough to rule out alternative courses of events?
Wiggins envisions the following counterscenario: suppose that the
kingdom is lost for want of a battle that is lost for want of a message
that is lost for want of a rider that is lost for want of a horse, and
so forth. One could still argue that although
whatever the defenders do or achieve or fail to achieve by way of
preparation at instant [t.sub.3], it is necessary at [t.sub.3] for
them to achieve or fail to achieve at [t.sub.3]. But this doesn't
count against the fact that they could have done differently and
better at [t.sub.3]. And there is nothing comical or irrelevant in
stressing this ability. (51)
Wiggins's objection is that even though at each instant what
is cannot be otherwise (thus, at [t.sub.3] an alternative wasn't
possible), the sequence as a whole could still have been different (it
would have been possible for the army to prepare for battle differently
such that another outcome would have resulted). However, I do not think
that this objection is adequate and sufficient. Wiggins's
distinction between "what was possible" and "what would
have been possible" doesn't eliminate the fact that if time
contains only actualized instants, the series of what would have been
possible is composed of what never was. In other words, the sequence in
which [t.sub.3] is otherwise is not the sequence that contains
[t.sub.3]. Its possibility simply expresses its hypothetical status: if
something else had happened at [t.sub.1] (when a nail could have been
found to shoe the horse), something else could have happened at (the
rider would have delivered the message), and so on until [t.sub.10] (the
kingdom would have been saved). But the alternative events belong to a
parallel narrative--a fully conceivable one, no doubt, but one that is
powerless ([TEXT NOT REPRODUCIBLE IN ASCII]) in the actual world.
We can now return to the master argument and consider its foremost
current interpretations. It is presumably because the incompatibility of
the three premises is not immediately evident (at least for modern
readers) that many reconstructions of the alleged Diodorean argument
have appealed to additional (although unstated) premises. Thus, Bobzien
(following Prior) adds, "if something is the case now, then it has
always been the case that it will be the case," and "if
something now neither is nor ever will be the case, then it has by now
been the case that it will never be the case"; (52) Vuillemin adds
the necessity of the present and the "principle of synchronic
contraction," which states that "if there is an instant
[t.sub.0] such that it is possible at [t.sub.0] that p at t, then there
is on the interval [t.sub.0]-t an instant t, where [t.sub.0][less than
or equal to] [t.sub.1] [less than or equal to] t, such that it is
possible at [t.sub.1] that p at t." (53) In so doing, they forget
that Epictetus tells us where we should be looking: Diodorus realized
(a) that the claims of the trilemma form a contradiction, and (b) that
accepting the first two (on the ground that they seem plausible) leads
to the negation of the third one. Furthermore, (c) as with all trilemma,
other solutions are open (thus Cleanthes rejected the first claim while
others rejected the second one). The task is therefore to elucidate the
premises themselves in order to exhibit the contradiction. (54)
The first premise is ambivalent. The claim "all past truth is
necessary" could designate an objective necessity (in which case
"past truth" refers to past events of which it is said that
they had to be); or it could mean that, insofar as all that is past is
achieved and complete, what is true about it is necessarily so (in which
case "past truth" refers to a now irrevocable fact which,
nevertheless, prior to its occurrence, didn't have to be). In
agreement with Cicero I believe we must retain the second reading:
"all things true in the past are necessary ... because they are
immutable (immutabilia) and because what is past cannot turn from true
to false." (55) Although no alternative could have happened at the
time it happened, the argument need not assume the fatalist undertones
of the first version. Truth requires that the corresponding state of
affairs be determinate; it excludes alternative possibilities, but it
need not do so in advance. By virtue of being bygone, whatever happened,
even if causally random or statistically unlikely, has become
unassailable.
Of course, what is necessary is a fortiori possible; and we could
say that, in a sense, the past contains former possibilities. This
point, however, is not in dispute. Rather, the first premise excludes
contingency from the past. In De caelo Aristotle claims that: "no
potentiality is of the past, but only of the present and the
future." (56) The purpose of the first premise is to exclude
possibilities of being that are equally possibilities of nonbeing. As
Gaskin observed "[TEXT NOT REPRODUCIBLE IN ASCII] in premise 1 of
the Master Argument is functioning not so much in its role as the dual
of possibility, but rather as the negation of contingency." (57)
Necessity extends to the whole of the past because the passing of time
creates an inalterability that excludes the possibility of not having
been (or of having been otherwise).
The second premise ("the impossible doesn't follow the
possible") explains why unactualized possibilities are ruled out.
Impossibility is the strict complement of necessity since what is
necessary excludes otherness and difference. This premise, once again,
appeals to a rule introduced by Aristotle himself:
The possible is such that if that of which it is said to have the
potency becomes actual, nothing impossible will result. I mean, for
instance, if it is in something's power to sit ([TEXT NOT
REPRODUCIBLE IN ASCII]) and it is permissible ([TEXT NOT REPRODUCIBLE IN
ASCII]), then should it sit, there will be nothing impossible. (58)
The second premise posits a formal condition for [TEXT NOT
REPRODUCIBLE IN ASCII]: if something is possible, its actualization
cannot yield impossibility. Thus, not everything is possible. Among the
innumerable things that are not actually the case, those are possible
for which no impossible outcome would follow should they be actualized.
By contrast, an impossible outcome shows that it wasn't a real
possibility in the first place, as we can see with the example of the
incommensurability of the diagonal of a square to its side.
I mean, for example, someone who doesn't take into account the
impossible could assert that it is possible for the diagonal [and
the side of a square] to be measured by the same unit (although it
will not be measured) on the ground that nothing prevents what is
possible from being out of nonbeing or from becoming out of
non-becoming. But from what has been laid down, it is necessary
that if we were to assume that something which is not [actual] but
possible, is or has become, nothing will be impossible. Yet, in
this instance there will be something impossible, namely, for a
common unit to measure both the diagonal and the side. (59)
Following Aristotle, Diodorus appeals to the fact that if the
consequent of an inference is impossible, the antecedent is also
impossible. (60) Thus, the maximum extension of all that is possible is
ultimately governed by the principle of noncontradiction. (61) This
provides us with "a method for deciding whether something which is
not actually the case could possibly be the case or not." (62) It
is unwarranted, however, to turn this principle into a definition of
[TEXT NOT REPRODUCIBLE IN ASCII] (as Weidemann suggests). The principle
of noncontradiction provides a criterion of consistency that delimits
the largest extension for the exercise of [TEXT NOT REPRODUCIBLE IN
ASCII], but contradiction doesn't define it. Furthermore, as the
previous example of someone sitting demonstrates, the inconsistency
exemplified by the geometric example doesn't cover the full extent
of Diodorus's second premise. It is not enough that the possible
contains no intrinsic contradiction, it must also agree with the
circumstances. Thus, "Socrates can sit" means not only that
there is no contradiction between the subject "Socrates" and
the predicate "is sitting" (Socrates belongs to the class of
things that can sit), but that in his present circumstances nothing
forbids him to sit (Socrates is not forced to stand, he is not tied down
to a tree, and so forth). In other words, the second premise stipulates
as conditions of possibility for the exercise of [TEXT NOT REPRODUCIBLE
IN ASCII] that neither contradiction nor constraint be present. But the
Megarian opponent of Aristotle in Metaphysics 9 (and presumably
Diodorus) extend the condition one step further, positing what Makin
dubs an "extremely isolationist" requirement according to
which "the truth of p should be assumed in complete isolation from
anything else." (63) Thus (on the Megarian view) if I am sitting,
my actual position contradicts a putative possibility to be actually
standing, thereby making it impossible.
It is tempting to appeal to the principle of the extension of truth
to the totality of time and declare that if something is the case now,
it has always been true that it would be and, similarly, that if
something neither is nor will be, it has always been true that it will
never be. This would make the master argument depend on an inference
from truth to necessity. Diodorus would probably not have ignored this
option, which is at the core of the fatalist's argument in De
interpretatione; but it is nevertheless not a premise of the master
argument (contra Bobzien). By contrast with the fatalism discussed in De
interpretatione 9, the master argument doesn't depend on any prior
truth to establish the necessity of the future. (64)
The difficulty arises because of an ambiguity in Diodorus's
solution according to which something is possible if it becomes actual
in the future (x is potentially y if y becomes actual). One could in
effect understand the claim as stating that:
(a) Prior to its actualization, y is already a possibility for x in
the sense that it is a real attribute. Thus, if "Lauryn will travel
to Tokyo" is true, Lauryn already possesses the potentiality to
travel to Tokyo.
(b) Or we could think that Diodorus's solution doesn't
grant any potency to the subject because only an actual predicate can be
had by an actual subject. Thus, x will be y when y is actualized in the
future.
The first case (a) assumes that the possibility of a future
actuality already exists, that in some sense it already belongs to the
present. But the idea that the possible could have some ontological
standing independently from actuality is the very thing that
Diodorus's argument denies. Thus, when claiming that possibilities
are what will become actual, Diodorus doesn't mean that they are
already here. Rather, just as there is in the present instant only one
state of affairs in which the possible coalesces with the actual, there
will be only one state of affairs in the future.
Thus, on the ground of the first two premises, we obtain the
following:
(a) Whatever doesn't become actual neither is not ever will
be.
(b) All past truths are necessary.
(c) All that is or will be must eventually become necessary (by
virtue of the necessity of the past alone, not on the assumption of an
antecedent truth about the future).
(d) Necessity entails the impossibility of the contrary.
Since the future will become past and since "all past truth is
necessary," all future events will become necessary in a more
distant future. In other words, it is not just that a possibility that
doesn't actualize doesn't belong to any temporal point (by
itself, this wouldn't generate necessity), but (a) what will be
will, at some ulterior point, be past (thus, it will be immutably and
irreversibly true), and (b) the necessity of a proposition entails the
impossibility of its contradictory. If we assume two mutually exclusive
possibilities, whichever occurs becomes necessary; consequently, the
alternative becomes impossible. If so, however, this alternative
wasn't truly possible, since otherwise an impossible would follow
from a possible.
III
Motionless Time and Ontological Modalities. There remains in this
last section to explore the metaphysical assumptions that sustain the
master argument. Although the remarks that follow are admittedly
speculative, I believe they offer a plausible account. Superficially,
Diodorus's construal of necessity as what is always true and of
nonnecessity as what is intermittent seems to overlap with the
distinction between a temporal realm that contains all that is transient
and mutable and an everlasting realm that contains all that cannot fail
to be. In this view, time denotes deficiency and negation; it is the
reason why beings do not remain, why all is impermanent. Yet this seems
to apply more fittingly to earlier Megarian thinkers (Euclid in
particular) than to Diodorus. For what is carried by temporal flux and
irrevocably passes away is also transfigured into an immutable truth.
What was, even if it was only once, will forever have been. Even death
and its nevermore cancels the possibility of never having been. The past
may be ignored, denied, or distorted, but its occurrence cannot be
undone. The passage of time entails simultaneously the loss of presence
and the gain of immutable determinacy. Truth depends on this
transmutation whereby necessity arises out of temporality.
The so-called necessity-of-the-present thesis claims that whatever
holds at instant t cannot but hold at t since whatever actualizes at a
given instant cancels any alternative. In that sense, what is has
already fallen into the past. As Cicero observed, the argument shows
that "no change from true to false can occur even in the case of
the future." (65) Since the future will, at some point, become
past, the truth about the future must be as immutable as the truth about
the past; or, as Cicero puts it, it was going to happen is "a
necessary inference from the fact that it did happen." (66)
If, in agreement with common practice, we represent time as a
linear vector, the future appears as the mirror image of the past on the
other side of the point that stands for the present and divides the line
into two segments (past/present on the left and present/future on the
right). In this guise, the future is a one-dimensional series of not-yet
actual instants that prolongs the linear series of the no-longer actual
instants of the past. Symmetry demands that just as there is no room in
the past for any alternative course of events, the future cannot admit
of any alternative to what will be. It is strictly identical with what
will have been. The function of the master argument is to warrant this
symmetry. Since what is true about the past is necessary and since there
cannot be a future which at some subsequent time will not have been, all
that is future is destined to become an immutable past truth. Thus the
future is what, at some ulterior point, will have been. The necessity of
the past is not just a feature of bygone history; it is the fate of all
that is still to come. Diodorus invites us to conceive of the future as
a past that is still to come, that is, to envision the future sub specie
praeteriti. This complicates the common linear representation of time,
which understands the past as something that is "behind" us.
Conceived sub specie praeteriti there can be only one future.
Alternative possibilities, insofar as they do not actualize, will never
have been true.
The grammar of tenses provides a clue. The preterit denotes the
past and stresses that an action or state of affairs is no more. We can,
however, give to the future a similar expression. In that case, the
future is not simply what will be but what will have been; thus, what
will be past. The future perfect expresses this grammatical aspect. When
we say, "Tomorrow I will have completed this task," we
describe a future event ([F.sub.1]) in the language of the perfect; we
envision this future from the standpoint of some even more remote future
[F.sub.2] ([F.sub.2] > [F.sub.1]) in relation to which F, will be
over; we envision tomorrow from the standpoint of the day after
tomorrow. Thus, the master argument requires that we translate all
imperfective verbs (verbs that express a progressive, habitual, or
iterative aspects) into perfective descriptions (as a series of bounded
and unitary events).
We often think of causality as having a past-to-future orientation,
since the causes of actual events are mostly behind us, while their
effects are still to come. The master argument invites us to reverse
this order. The "being past" of a future event follows its
actual occurrence. The past is the future of the future. This demands
that we envision the three dimensions of time in reverse order: just as
the past was--at some still anterior point--future, the future will--at
some further point--be past. In a sense, it is our usual chronology with
its flow from past to present and future that distorts the
future-to-past direction of time. But doesn't this conflict with
our experience? In response to Diodorus, Wiggins suggests,
We must take continuous and imperfective verbs for what they are;
as irreducible to punctual or perfective vocabulary; and we must
describe within our empirical experience not only events but also
continuous and irreducible states and processes, not only instants
but also intervals--or (as I find it so natural to say) times. (67)
This clearly states a fundamental problem; it does little, however,
to resolve it, since the fact remains that all that is and will be is
translatable into perfective language. It is true that, for what is
still to come, this translation hasn't occurred yet, but (as argued
earlier) the master argument need not assume the anteriority of truth.
All that matters is that this translatability is inscribed in the nature
of time. Truth requires accomplishment, and only what is accomplished
can be said to be. If eternity contains time in its entirety, the
accomplished is the translation of any temporal event into the language
of eternal truth.
What happens when the imperfective is eliminated or, to restate the
question in ontological rather than grammatical terms, what is excluded
from being? The argument doesn't deny time (if by this we mean the
order of juxtaposition in which beings present themselves); rather, what
it eliminates is mobility and transition, the very passing of time, the
fluidity of a multiplicity without juxtaposition (in short, what Bergson
calls "duration"). In the fragments that deal with motion
Diodorus seems to assume its existence and, simultaneously, to exclude
it from being. "One can say that something has moved, but not that
it is moving." (68) Motion can be acknowledged in retrospect: we
are forced to admit that things are not identical to what they were; but
motion itself can never be caught in the act. This is why Sextus lists
Diodorus (along with Parmenides and Melissus) among those who deny
movement, but distinguishes him as one who acknowledged that motion has
occurred:
He shows that nothing at all is moving, and yet, that there has
been motion.... [I]t follows from reason ([TEXT NOT REPRODUCIBLE IN
ASCII]) that there has been motion for what was then observed in
this place is now observed in that place; which couldn't have
occurred if it hadn't moved.... However, to demonstrate that
nothing moves, he submits the following argument: 'if something
moves, it does so either in the
place where it is or in the place where it is not; but it moves
neither in the place where it is (since it remains there), nor in
the place where it is not (since it is not there); therefore
nothing moves. (69)
The paradox rests on a conflict of reason with itself rather than
with sensory appearance. Reason, not perception, bears testimony to the
fact that motion must have occurred; motion is deduced, it is not
experienced. Yet, the same reason that concludes that there has been
motion demonstrates the impossibility of its actuality.
Isn't Diodorus led to admit that something impossible (since
there is no instant in which it could have taken place) nevertheless
just happened? One could object that if something is true once it has
been accomplished, it cannot be false when it was in the process of
being accomplished. Sextus, who reports these arguments, vents his
frustration: "in trying to support his own dogma this man has
professed an absurdity; for how is it not absurd that while nothing
moves something has moved?" (70) Yet the metaphysical question is
whether motion possesses the subsistence and reality that is required to
deserve of being called "being." Diodorus can claim that there
has been motion without thereby granting it any ontological status. When
reason concludes that there has been motion, it acknowledges a
difference, it doesn't posit a being. Thus, it is misleading to say
that Diodorus acknowledges past motion; it would be more accurate to say
that he acknowledges the prior existence of a different (but equally
determinate) order of things. Nor can we object that motion must have
happened between these determinate moments, since the question concerns
the reality of this mediation. The leaf that was green yesterday is now
yellow. To acknowledge this is to acknowledge two distinct and complete
states of affairs. The transition from the first to the second, however,
is not itself a third state. If we cut shorter and shorter intervals
until we reach the "instants-without-parts," we only find
further determinate states of affairs, each one equally achieved and
complete. (71)
As mentioned earlier, the necessity-of-the-present principle posits
that whatever holds at t must hold at t; but for this reason, change
itself cannot happen in the present. While this principle is, for
Aristotle, compatible with activity (the builder actually engaged in the
activity of building), Diodorus sees the necessity of the present as
incompatible with motion. For Aristotle [TEXT NOT REPRODUCIBLE IN ASCII]
expresses the coalescence of activity and outcome, production and
product; for Diodorus, however, [TEXT NOT REPRODUCIBLE IN ASCII] can
refer only to the accomplished result severed from any accomplishing.
The Diodorean account of the necessity-of-the-present principle excludes
process and equates being with what has ceased to become. Accordingly,
one cannot talk of the actuality of motion without expressing a
contradiction.
The privilege Diodorus grants to the past is a consequence of the
requirement of truth. Insofar as it is achieved, the past truly is; it
has escaped becoming and possesses the immutability that is the
condition of possibility of true statements. This is why the fatalism of
the master argument doesn't need the assumption that the future is
already set in stone before it occurs; all that matters is that the
future will possess the same determinateness as the past; as a
consequence, any possible that doesn't actualize is necessarily
excluded from the chain of being and is deemed impossible. Logos is
recollection; as soon as we acknowledge what is, it is no longer
occurring but has occurred. (72) The so-called metaphysics of presence
is thus a metaphysics of the past for what truly is is what is wholly
accomplished.
Diodorus's privilege of the past is further supported by the
observation that a past statement can be true even if there is no
corresponding true proposition in the present tense.
It is possible then for the present to be false when the preterit
is true. Of the same sort is the proposition: "Helen had three
husbands" for neither when she had Menelaus as a husband in Sparta,
nor when she had Paris in Ilium, nor finally when, after his death, she
married Deiphobus was the present "she has three husbands"
true; and yet, the preterit "she had three husbands" is true.
(72)
One could object, as Sextus does, that "Diodorus is using
sophistry and wishes to deceive us by ambiguity." (74) Indeed, the
claims: "Helen had three husbands" and "Helen has three
husbands" do not differ simply with respect to their tenses but in
their meaning, since in the present tense the proposition means that
Helen practiced polyandry, which is not what the preterit suggests. Yet,
Sextus's objection misses the point. The example shows that the
truth of an assertion doesn't depend on its coincidence with a
present state of affairs but on the completion of its subject matter.
This further illustrates the claim that an unachieved process, so long
as it is unachieved, cannot be the object of a true statement.
In conclusion, it appears that the debate between Aristotle and
Diodorus is concerned with two alternative attempts to resolve the same
issue. Aristotle and Diodorus aim at maintaining the fullness of being.
Diodorus's admission of temporal discontinuity, however, renders
his ontology quite paradoxical. Even though difference itself has no
substantial existence, to acknowledge that there has been motion is to
admit difference. There cannot be any gap between the
"instants-without-parts," and yet each one must be a discrete
reality. In order to avoid granting being to nonbeing Diodorus ends up
with a discontinuity for which there is no possible account. For
Aristotle, being is differentiated and multifarious, but it is
continuous. This is why negation exists only in logos; a negative
proposition doesn't translate into an affirmation of nonbeing
anymore than the absence of something designates an actual cut in the
fabric of reality. Predicative discourse is, of course, articulated and,
as such, it must dissociate; but it doesn't thereby tear apart the
continuum of reality. Aristotle's admission of [TEXT NOT
REPRODUCIBLE IN ASCII] is another way of maintaining that there cannot
be gaps of nonbeing within the fabric of reality ("nature abhors a
vacuum"). The unactualized, the latent, and the virtual guarantee
the continuity of being; thus, being and indeterminacy can belong
together. The builder who is not exercising his skills retains something
that is not actualized; he has his power in reserve, even if he will
never use it again. Likewise, matter guarantees that an underlying
substratum remains that guarantees continuity between the various forms
that nature and art are capable of bringing forth.
By contrast, Diodorus's ontology must assume gaps since time
is a juxtaposition of infinitesimal but determinate and immutable units
of being. Yet there is no possible account for these gaps since there is
no ontology of the between. The Diodorean concept of being cannot be
reconciled with what is unachieved or indeterminate any more than it
could grant being to nonbeing. Time is the ordering of what was, what
is, and what will be. These are determinate, complete, and achieved
units. Insofar as they are complete, they are finite and differentiated
states of affairs. Yet the very logic of discrete temporal grains of
reality demands a separation that guarantees the fullness of each
individual moment but for which there cannot be any account. Thus,
Diodorus cannot avoid the paradox of saying that between what was, what
is, and what will be there is nothing.
Miami University
Correspondence to: Department of Philosophy, Miami University, Hall
Auditorium, Room 212, 101 S. Campus Avenue, Oxford, OH 45056.
(1) Other important sources are found in Sextus Empiricus's
Adv. Math. X, Cicero's De fato, and Boethius's Commentary on
De Interpretatione.
(2) The main contributors are Arthur Prior, Time and Modality
(Oxford: Oxford University Press, 1957); Robert Blanche, "Sur
l'interpretation du [TEXT NOT REPRODUCIBLE IN ASCII]," Revue
Philosophique de la France et de l'Etranger 155 (1965): 133-49;
Frederick S. Michael, "What Is the Master Argument of Diodorus
Cronus?" American Philosophical Quarterly 13, no. 3 (July 1976):
229-35; R. McKirahan, "Diodorus and Prior and the Master
Argument," Synthese 42, no. 2 (October 1979): 223-53; Michael J.
White, "Facets of Megarian Fatalism: Aristotelian Criticisms and
the Stoic Doctrine of Eternal Recurrence," Canadian Journal of
Philosophy 10, no. 2 (June 1980): 189-206; Richard Gaskin, The Sea
Battle and the Master Argument: Aristotle and Diodorus Cronus on the
Metaphysics of the Future (Berlin: Walter de Gruyter, 1995); Susanne
Bobzien, Determinism and Freedom in Stoic Philosophy (Oxford: Oxford
University Press, 1998); Susanne Bobzien, "The Megarics," in
The Cambridge History of Hellenistic Philosophy, ed. Keimpe Algra,
Jonathan Barnes et al. (Cambridge: Cambridge University Press, 1999),
83-92; Hermann Weidemann, "Aristotle, the Megarics, and Diodorus
Cronus on the Notion of Possibility," American Philosophical
Quarterly 45, no. 2 (April 2008): 131-48.
(3) Was it called "master argument" because it was the
most impressive and hardest Megarian paradox? As with all trilemmas, it
is open to various resolutions. Diodorus's solution (for which he
gave no reason beyond its plausibility) is simply one among others.
Furthermore, in terms of difficulty and reputation, the liar paradox
seems at least as deserving of the title. The epithet "master"
has also been interpreted as suggesting that the argument denies freedom
and places human existence under the yoke of an unshakable necessity
which "masters" our fate. Pierre-Maxime Schuhl, Le Dominateur
et les possibles (Paris: Vrin, 1960), 8-10. Yet, at best, this account
is derived; grammatically [TEXT NOT REPRODUCIBLE IN ASCII] can only
qualify [TEXT NOT REPRODUCIBLE IN ASCII]. According to Robert Muller,
Les Megariques, Fragments et Temoignages (Paris: Vrin, 1985), 158, and
Gaskin, The Sea Battle, 222-24, the name derives from the particular
example of Cypselus's rule in Corinth (mentioned by Cicero in De
fato VII, 13). This too is unlikely. Besides the fact that the example
doesn't appear in any other fragment, Cicero places it in the mouth
of Diodorus's opponent who declares that the rule of the tyrant was
not necessary, even if it had been predicted by the oracle a thousand
years ago. Finally, it has been interpreted as suggesting that (in the
eyes of its proponents at least) it successfully defeated
Aristotle's conception of obvapiC. While I do not believe that the
argument defeats Aristotle, this seems to me the most plausible
interpretation of its name.
(4) Cicero, Defato, IX, 17-18. Translation from Cicero, vol. 4,
trans. Harris Rackham (Cambridge, Mass.: Harvard University Press,
1982), 211-13. Translation revised.
(5) Cicero, Defato, IX, 17.
(6) Metaphysics 9.3.1047a21-22.
(7) Martin Heidegger, Nietzsche, vol. 1, trans. David Farrell Krell
(New York: Harper & Row, 1979), 64.
(8) Metaphysics 9.1.1046al2.
(9) Physics 3.1.201all.
(10) Remi Brague, "Aristotle's Definition of Motion and
its Ontological Implications," Graduate Faculty Philosophy Journal
13, no. 2 (1990): 3.
(11) Brian Massumi, Parables for the Virtual, Movement, Affect,
Sensation (Durham, N.C.: Duke University Press, 2002), 4.
(12) Metaphysics 9.3.1046b36-1047a4.
(13) This is surprising since the purpose of this section is to
exhibit the fundamental sense of [TEXT NOT REPRODUCIBLE IN ASCII].
Heidegger attempts to resolve the difficulty by interpreting kuqlcuC as
"most common." This translation, however, is not justified. In
fact, as Boutot observed, in another lecture course in which he also
refers to book 9 (Vom Wesen der menschischen Freiheit, G.A. Bd. 31
[Frankfurt am Main: Klostermann, 1994], 84-85) Heidegger declares the
opposite: [TEXT NOT REPRODUCIBLE IN ASCII] does not refer to the
frequency of a term but to its "proper and authentic
signification." Alain Boutot, "Heidegger et les
Megariques," in Socrate et les Socratiques, ed. G. Romeyer-Dherbey
and J. B. Gourinat (Paris: Vrin, 2001), 438.
(14) In a similar fashion, Aristotle mentions in the Physics a
difficulty that hampers his project from the beginning: How does one
define ([TEXT NOT REPRODUCIBLE IN ASCII]) the indefinite ([TEXT NOT
REPRODUCIBLE IN ASCII])? Physics 4.4.2llb24-28.
(15) Metaphysics 9.6.1048b 1-3.
(16) What Plato in the Sophist 237b refers to as to [TEXT NOT
REPRODUCIBLE IN ASCII] (that which in no way is/what is not at all).
(17) Stanley Rosen, "La critique Aristotelicienne des
Megariques," Les Etudes Philosophiques 3 (1982): 310.
(18) In Lib. Sentent. I, d. 43.
(19) Metaphysics 9.2.1046b28-31.
(20) Physics 3.1.201all.
(21) Metaphysics 9.6.1048a16.
(22) Nicolai Hartmann, "Der Megarische und der Aristotelische
Moglichkeitsbegrieff. Ein Beitrag zur Geschichte der Ontologischen
Modalitats Problems," in Kleinere Schriften, Bd. 2 (Berlin: Walter
de Gruyter, 1957), 94.
(23) In a prephilosophical (and military) sense of the term,
Xenophon uses [TEXT NOT REPRODUCIBLE IN ASCII] to describe pedestrian,
equestrian, and naval forces (Anabasis 1.3.12). These "forces"
are fully themselves when they are held on reserve at the general's
disposal. To command these forces is to be capable of using them at any
point.
(24) Brague, Aristotle's Definition of Motion, 12. Emphasis
added.
(25) It is not obvious at all that Parmenides identified being with
actuality (he may very well not have had any concept of actuality). Yet,
frag. 6.1-3 of Parmenides' Poem have often been read as making an
inference from possibility to necessity (the possible must be) and from
nonexistence to impossibility (what is not cannot be). See Alexander
Mourelatos, The Route of Parmenides (Las Vegas: Parmenides Publishing,
2008); and Jonathan Barnes, The Presocratic Philosophers (New York:
Routledge ,1983).
(26) Epictetus, Discourses, trans. William Abbott Oldfather
(Cambridge, Mass.: Harvard University Press, 1925), 359. Translation
revised.
(27) Schull, Le Dominateur, 34.
(28) Metaphysics 9.4.1047b8-9.
(29) Gaskin assumes a mutually exclusive dichotomy of logos and
being and claims that "the modalities are attached to linguistic
items ... rather than states of affairs." Gaskin, The Sea Battle,
243 n. 3, emphasis added. This not only is not justified by the text,
but it conflicts with Gaskin's own understanding of
"necessity" in the first premise as meaning that "there
is nothing anyone can do about the way the past was" as well as his
interpretation of [TEXT NOT REPRODUCIBLE IN ASCII] as "contingent
rather than possible." Gaskin, The Sea Battle, 282, 286.
(30) As Bobzien puts it: "Diodorus's definition of that
which is possible can be split into two distinct claims: first that
everything that is or will be true is possible, and second, that
everything that is possible either is or will be true." Bobzien,
Determinism and Freedom, 88.
(31) Heidegger stresses an important problem to which we will
return in the last section. In Aristotle's formulation, actuality
is activity (one is fully a builder when one is actually engaged in the
activity of building); to be actual is to be at work. The Megarians,
however, wouldn't have accepted such a definition, which assumes
the coincidence of actuality and motion. Heidegger notes that the
Megarians did not understand actuality as accomplishment (thus as
movement or process) but as "being accomplished." Aristoteles:
Metaphysik IX, 1-3, G.A. Bd. 33 (Frankfurt am Main: Klostermann, 1992),
172.
(32) This introduces some ambiguity in several respects; as Gerhard
Seel observed: "1) it is ambiguous because of the relativity
regarding the time of the speech-act. Since in written formulations of
the sentences the speech-act is not identified, written sentences are in
principle ambiguous in this respect; 2) the past and future inflections
of verbs contain--because of the relativity regarding what is in each
case the present time of the speech-act--not one, but two indications of
time, the second of which concerns not a point of time but a period of
time; 3) because of the ambiguity of the copula, it is undecided whether
these time indications represent a temporal characterization of the
state of affairs itself or whether they delimit the time at which the
state of affairs is the case." Gerhard Seel, Ammonius and the
Seabattle, Texts, Commentary, and Essays (Berlin: Walter de Gruyter,
2001), 5-6.
(33) Blanche, Sur L'Interpretation, 138-41; Bobzien, The
Megarics, 102-08.
(34) The master argument must, of course, agree with
Diodorus's teaching on logic (although this raises some
difficulties). Whether it can be reduced to it, however, is another
issue. A hypothetical implication ([TEXT NOT REPRODUCIBLE IN ASCII])
links two unrelated propositions p and q (for example, "it is
day" and "I speak"). The master argument, however, does
not link dissimilar and simultaneous propositions but bears on the
connection between what was, what is, what will be, and (as we shall
see) what will be past (what will have been) in a temporal continuum.
Contra Michael, What is the Master Argument? 232; and Muller, Les
Megariques, 144.
(35) Sextus, Adv. Math. VIII, 113.
(36) Sextus, Adv. Math. VIII, 115. It is important to note that
Philo and Diodorus use [TEXT NOT REPRODUCIBLE IN ASCII] (to accept,
admit, grant) in their accounts of the rules of implication (hence my
translation by "admits" rather than "is possible").
The argument about conditional is concerned with what follows from
whatever is posited; it has no bearing on a metaphysical critique of
Aristotle's [TEXT NOT REPRODUCIBLE IN ASCII].
(37) Sextus, Adv. Math. VIII, 116. This solution arises from a
concern to avoid the paradoxes of material implication; in that respect
it is akin to the strict conditional in modern logic.
(38) Blanche, Sur l'Interpretation, 140; Bobzien, The
Megarics, 85.
(39) Bobzien The Megarics, 85.
(40) In Arist. De int. 3.9.234.22-25. Translation from Boethius, On
Aristotle on Interpretation 1-3, trans. Andrew Smith (London: Bloomsbury
Academy, 2010), 141. Translation modified.
(41) Joseph M. Bochenski, Ancient Formal Logic (Amsterdam: North
Holland Publishing, 1951), 86; Blanche, Sur L'Interpretation, 142.
(42) Should we align the master argument with the fatalist position
exposed in De interpretatione 9? Bobzien thinks so since in her
reconstruction she adds the premise "if something is the case now,
then it has always been the case that it will be the case," which
she borrows from De interpretatione 9. Bobzien, The Megarics, 91. If so,
we should say that truth was already determined before the occurrence of
the corresponding state of affairs. By talking of "future
truth," on the contrary, I am suggesting that the proposition
becomes true only with the occurrence of the event. I think this second
version is the correct one, and it avoids the connotation of a
foreordained history. There is, furthermore, another crucial issue that
I reserve for the next section: the time of truth is the past.
(43) Bobzien, The Megarics, 88.
(44) Bobzien maintains that Diodorus doesn't preclude
contingency even though "it doesn't follow that because of
this his modal theory is also indeterministic." Bobzien,
Determinism and Freedom, 105. She doesn't explain, however, how
determinism (which, by definition, excludes the possibility of being
otherwise) is compatible with contingency and seems to assume that
contingency is identical with (or at least sufficiently captured by)
temporal intermittence. Yet, this is the very issue at the center of the
debate; "contingency" translates Aristotle's [TEXT NOT
REPRODUCIBLE IN ASCII], which literally refers to what is
"in-either-of-two-ways, as-it-chances" (in Boethius's
Latin, utrumlibet). It designates an indeterminate openness to
alternative--which is exactly what Diodorus denies.
(45) Michael, What is the Master Argument?; McKirahan, Diodorus and
Prior, Bobzien, The Megarics; and Bobzien, Determinism and Freedom.
(46) In An. Pr. 183.36-184.6. Translation from Alexander of
Aphrodisias, On Aristotle's Prior Analytics, 1.14-22, trans. Ian
Muller and Joshua Gould (London: Duckworth, 1999).
(47) At De sensu 445b 13-20 Aristotle mentions (critically) the
idea that the ultimate components of matter would be imperceptible
corpuscles endowed only with the mathematical reality of a geometric
point. It may be surprising to find this doctrine here since the
negation of the sensible world was a Megarian hallmark (at least
according to Plato's portrayal of the--presumably
Megarian--"friends of the forms"). Muller has suggested two
hypotheses: (a) The bodies without parts could represent a theoretical
model rather than a material reality, or (b) Diodorus could have
maintained that these bodies have reality but that the physical world
they compose, because of its diversity and mutability, lacks substantial
reality. Muller, Les Megariques, 134. Muller embraces the second
interpretation. I am not convinced, however, that Diodorus is committed
to a form of materialist atomism. It seems likely that, in the spirit of
Megarian paradoxes, the "bodies without parts" designate a
branch of a dilemma: either we deny their existence, in which case we
encounter the paradox of infinite division, or we assume them, in which
case movement is impossible.
(48) In Phy. 926, 19-21. Translation from Simplicius, On Aristotle
Physics 6, trans. David Konstan (London: Bloomsbury, 1989), 18.
Translation modified.
(49) Physics 4.11.219bl0.
(50) Sextus Empiricus, Adv. Math. X, 86.
(51) David Wiggins, "Temporal Necessity, Time and Ability: A
Philosophical Commentary on Diodorus Cronus' Master Argument as
Given in the Interpretation of Jules Vuillemin," in Causality,
Method, and Modality, ed. G. G. Brittan Jr. (Dordrecht: Kluwer, 1991),
200.
(52) Prior, Time and Modality, 87; Bobzien, The Megarics, 91.
(53) Jules Vuillemin, Necessite ou Contingence, L'Aporie de
Diodore et les Systemes Philosophiques (Paris: Editions de Minuit,
1984), 32, 39. Vuillemin's premise is (rightly) rejected by
Wiggins, Temporal Necessity, 197-99.
(54) I agree with Gaskin's effort to reconstruct the master
argument on its own grounds without introducing unmentioned premises.
Gaskin, The Sea Battle, 292. The whole point of a trilemma is that the
three claims are sufficient to generate an incompatibility.
(55) Cicero, De fato, VII, 14.
(56) De caelo 283M3-14.
(57) Gaskin, The Sea Battle, 283.
(58) Metaphysics 9.3.1047a24-28. Aristotle uses two distinct
expressions: [TEXT NOT REPRODUCIBLE IN ASCII] (which I translated as
"it is in something's power to sit") and [TEXT NOT
REPRODUCIBLE IN ASCII] (which I translate as "it is permissible to
sit"). The first expression refers to the agent's own ability
and the second to the conditions which allow him to exercise his power;
see Gaskin, The Sea Battle, 286-88; and Weidemann, "Aristotle, the
Megarics, and Diodorus," 132.
(59) Metaphysics 9.4.1047b6-12.
(60) Whereas the converse, as Alexander of Aphrodisias mentions, is
not true: "If it is impossible that the consequent comes to be, it
is also impossible for the antecedent to do so.. .. For, as we have said
before, the implication is in the reverse direction. For the possible in
all its meanings has its implication from the antecedent, the impossible
from the consequent. For if the antecedent is impossible, the consequent
is not prevented from being possible, as in the case of 'if you are
a centaur you are an animal.' But if the consequent is impossible
it is necessary that the antecedent also be impossible, whatever meaning
of impossibility is taken." In An. Pr., 183, 8-17.
(61) Aristotle's distinction between [TEXT NOT REPRODUCIBLE IN
ASCII] suggests that, at least in the case of rational potency, [TEXT
NOT REPRODUCIBLE IN ASCII] is not exhausted by the presence of the
necessary conditions that are required for its exercise (as Hartmann
would have it).
(62) Weidemann, "Aristotle, the Megarics, and Diodorus,"
132.
(63) Stephen Makin, Aristotle, Metaphysics Book Theta (Oxford:
Clarendon Press, 2006), 75.
(64) Weidermann also appeals to anterior truth when he declares
that "if it is impossible that it is and always has been true that
the thing in question [that is, a possibility that doesn't and will
not actualize] happens and will happen what this impossibility follows
from, namely that it is the case that the thing in question happens, is
impossible too because what is impossible doesn't follow from
something possible. Hence, nothing that neither is not will ever be the
case is possible." Weidermann, "Aristotle, the Megarics, and
Diodorus," 139. My emphasis. The tacit assumption is that the
statement "it is the case that x happens" entails "it has
always has been true that x happens or will happen"; N (p [right
arrow] HFp).
(65) Cicero, Defato, IX, 17.
(66) Ibid.
(67) Wiggins, Temporal Necessity, Time and Ability, 202.
(68) Aetius, Placita, I, 23, 5; Muller, Les Megariques, frag. 121,
43.
(69) Sextus, Adv. Math. X, 85-87.
(70) Sextus, Adv. Math. X, 86.
(71) Wiggins, in a striking formulation, talks of "a world
shifting as if stromboscopically from a state of being frozen stiff in
one way to being frozen stiff in another way." Wiggins, Temporal
Necessity, Time and Ability, 196.
(72) Perhaps this is how we can understand Diodorus's example
of the ball: while "at the point of time that is mid-way the
proposition: 'the ball touches the roof is false; since it is still
to come, when it has touched the roof, the preterit 'the ball has
touched the roof becomes true; therefore, it is possible for the
preterit to be true when the present is false, and therefore possible
for a thing not to be moving in the present but to have moved in the
preterit." Sextus, Adv. Math. X, 101. Touching is not truly a
process; as soon as it occurs it is already past.
(73) Sextus, Adv. Math. X, 98.
(74) Ibid., 99.
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