The Megaric Possibility Paradox

2.1 The Temporal Defense

One reading takes (M) as expressing a temporal conditional. On this reading, x can φ only when x is φ-ing. Owen and the seminar participants in (Burnyeat et al. 1984, 61–63) assume a temporal reading of the Megaric conditional. But Makin is the most prominent defender of the temporal reading. Makin philosophically defends the Megaric position, arguing that it is neither trivially true nor obviously false, but declines to offer historical evidence to attribute his temporal reading to the Megarics.^[6] Makin thinks that the Megaric view is false, but validly follows from some plausible premises about capacities. He only formulates his position with respect to capacities, but does suggest that his view has implications for possibility in general (Makin 1996, 253).^[7]

Is Makin correct? If Makin can show that the Megarics have a non-trivial, non-absurd view of capacities, there is some reason to attribute the temporal capacities view to the Megarics: a reconstruction of their view as non-trivial and non-absurd would, after all, be charitable. But, we will argue, Makin’s reading ends up attributing absurdly strong claims to the Megarics. Makin takes (M) to be the following biconditional:

Something has a capacity at t iff it is exercising that capacity at t

He argues that this follows from two claims: the present is necessary (NP) and all capacities are synchronic (S) (Makin 1996, 254; Makin 2006, 61).

(NP): If x does not φ at t, x does not have at t the capacity to φ at t

(S): For any two times t _n and t _m, a has at t _n the capacity to φ at t _m only if t _n = t _m

Roughly, (NP) says that the present is fixed. Presently, there are no unactualized possibilities. It is now too late to be doing something other than what you in fact are doing. If I’m sitting now, then it is no longer possible that I stand right now. (S) is less intuitive, but partly captures the idea that capacities cannot be exercised when not possessed. (S) makes two claims: (1) Capacities are indexed to times, and (2) capacities are possessed only at the times specified in that indexing. Given (1) there is no capacity to sit simpliciter. The capacity to sit must be indexed to a time. The capacity to sit is really a capacity to sit at some time, say noon. Given (2), not only must the capacity be indexed, but an agent can possess that capacity only at the time to which the capacity is indexed. Thus, I can only possess the capacity to stand at noon at that very time.

Makin offers a philosophical defense of (M), on the basis of an intuition which (NP) and (S) capture. That intuition is (INT): capacities can be exercised only when possessed (Makin 1996, 254; 2006, 63). If a capacity cannot be (rather than merely is not) exercised at a time, then it seems absurd to claim that the capacity is possessed at that time. For example, I cannot exercise the capacity to eat lunch at dinner time (since any meal I eat at dinner time is necessarily dinner).^[8] So it seems absurd to claim that (contrary to possibility) I do have the capacity to eat lunch at dinner time, but simply cannot exercise it. It is clear how (S) follows from (INT), but, Makin claims, (NP) does not and since both (NP) and (S) are needed to derive (M), the Megarics are mistaken that the intuition (INT) motivates (M). Makin thinks the mistake is to hold that (INT) entails (NP).

Makin (1996, 257) then sketches the reasoning that (NP) and (S) entail (M). Suppose that Socrates stands at noon. It follows that Socrates has the capacity, at noon, to stand at noon. By (S), Socrates lacks the capacity to stand at noon at any other time. So, if Socrates stands at noon, then Socrates has the capacity to stand at noon, only at noon. At dawn Socrates is not standing. Does Socrates have the capacity, at dawn, to stand? Not according to (NP), for, since Socrates is not standing at dawn, Socrates cannot stand at dawn. But what’s more, since Socrates is not, at dawn, standing at noon, (whatever that might mean) Socrates lacks, at dawn, the capacity to stand at noon. So, Socrates can stand at noon only when he is in fact standing, namely at noon.

Makin holds that the resulting Megaric view is neither trivial nor absurd and so could have seemed plausible. However, we think that Makin’s view lacks the hermeneutic virtues he claims for it. First, (NP) is stronger than Makin advertises. Second, we think that (S) is obviously false. Both points push Makin’s Megarics towards absurdity.

(NP) is stronger than Makin thinks. Makin supposes that (NP) says the present is necessary. No present possibilities are open. But as Makin formulates (NP), it quantifies not only over the present time, but over all times. (NP) claims that for every time, if something acts thus at that time, it must so act at that time. That entails that there are no open possibilities at any time, past, present, and future. So it is easy for Makin to show that something has a capacity only when that capacity is exercised. Given (NP), nothing can ever do anything other than what it is doing. So nothing ever has the capacity to do anything other than what it is doing. So, if Makin uses (NP) to derive (M), the position does not steer a course between triviality and absurdity, but rather ends up stranded on the rocks of the latter.^[9]

Second, (S) seems both false and implausible. We formulated (S) with a particularly amiable example: I lack the capacity to eat lunch at dinner time, because it is not possible to eat lunch at dinner time. But why should we think that all capacities are like the capacity to eat lunch, i.e. that all capacities are indexed to certain times? Many capacities are not indexed to times. I have the capacity to eat at any time: I exercise that same capacity at lunchtime or at dinner time. Makin replies that what appear to be non-time indexed capacities are actually determinables, which are determined into time-indexed capacities. Thus, Makin argues that my capacity to eat simpliciter is my capacity to eat at breakfast-time and my capacity to eat at lunchtime and my capacity to eat at dinner time.

This seems ad hoc. It is plausible to say that the basic capacities are the simpliciter capacities while time-indexed capacities are simpliciter capacities at certain times. My capacity to eat lunch is not indexed to lunch time, but rather just is my capacity to eat when lunchtime comes around. Makin could appeal to the conditions that obtain at certain times: I don’t have the capacity to eat at nighttime, because I’m asleep. Makin (1996, 267) considers this move. However, this surrenders the temporal reading of (M), relying on the conditional interpretation, which we discuss further below. So, lacking a decisive case that capacities are time-indexed, Makin’s Megarics risk basing their argument for the implausible (M), on an equally implausible premise, i.e. (S).^[10]

It might be possible to modify the account and make capacities double time-indexed, an option previously entertained by some scholars (Kirwin 1986; Liske 1996; Jansen 2016). So capacity attributions would be of the form: ‘x has at t ₁ the ability to φ at t ₂. For example, Socrates has, at midnight, the capacity to eat lunch at noon. This looks like a plausible account of capacities that, even if NP holds, does not entail (M), since, if it is now 9am, what happens at 9am is fixed, but not what happens at midnight or noon. However, this suggestion does not really help. For now consider what happens if Socrates does turn out to eat lunch at noon. This entails that at noon he actualised his capacity to eat lunch at noon. So, at midnight Socrates was actually eating lunch at noon. Either this makes no sense or it means that what Socrates does at noon is already fixed by midnight, leading to a stronger form of necessitarianism.

To claim that the Megarics hold such a counterintuitive view as (M) as a positive doctrine in modal metaphysics, we would need to attribute to them a strong philosophical case. Makin claims the Megaric position is neither trivial nor absurd, but rather plausible although false. But since Makin’s Megarics rely on the false (NP), and the implausible (S), their position is not strong, and hence Makin cannot cash in the hermeneutic advantages he claims for his interpretation.

2.2 The Conditional Defense

The conditional defense is more common.^[11] Nicolai Hartmann first developed this reading in his 1938 Möglichkeit und Wirklichkeit.^[12] He saw the Megarics as forerunners of his ideas of partial and total possibility. A partial possibility, according to Hartmann, describes a situation in which some but not all necessary conditions for a given event are satisfied. A total possibility describes a situation in which all necessary conditions are satisfied (49–50); this, for Hartmann, entails that a sufficient condition for the event is satisfied. Turning to the Megarics, Hartmann agrees that the builder can build only if actually building. According to Hartmann, the builder does not lose his ability to build when not building, but ability is not the only factor that decides whether a builder can build: it is a partial possibility for building; if other necessary conditions are unsatisfied (such as the building site, the materials, the workers, the contract, as well as the decision to take certain risks), the builder cannot build. Hartmann concludes ‘Thus, speaking from the perspective of real-ontology, he ‘can’ only build, when he is actually building, notwithstanding his enduring possession of the art of building’ (Hartmann 1938, our translation). Hartmann does not, however, offer a historical engagement with the Megarics – like Makin, Hartmann’s defense of (M) remains philosophical.

Beere (2009) follows the same line as Hartmann, but provides a more involved historical defense. According to Beere (2009, 94–95), the Megarics might have defended their thesis with examples like this: can a piece of wood at the bottom of the ocean burn? Answer: no, because in such conditions wood cannot burn; now imagine the stick is brought on land; can it burn? No, because there is no fire to light it; now imagine fire is brought; can it burn? No, as it is not close enough to ignite the stick. The Megaric can reiterate this move, identifying conditions which prevent the stick from burning, up to the point when the stick is actually burning. According to Beere, the core idea is this: if a sufficient condition for an event is not satisfied, the event will not occur. If we consider a case with only one set of jointly sufficient conditions, all of which are thus necessary conditions, we can see, Beere says (2009, 97), why the event cannot occur. It cannot occur because at least one necessary condition for its occurrence is unsatisfied. Thus, only what is actual can occur; and what is not actual cannot occur. Beere (2009) thinks that (M) concerns powers, but (Bailey 2012, 311–12) convincingly shows that the conditional defense generalizes to possibilities.

Beere bases his interpretation on ancient sources, but the historical adequacy of the sources he relies on is questionable. Beere borrows his example from Philo the Dialectician, who himself wasn’t a Megaric and whose ideas regarding possibility were quite different (see below); in fact, the ancient sources oppose Philo’s view to those of Diodorus Cronus, who stands in the Megaric tradition.^[13] Beere admits this, but if we reject such evidence as historically inadequate, Beere does not bring us closer to the Megarics’ own argument for (M). Beere tries to fortify his interpretation by referring to Plato’s Phaedo and Theaetetus, but these references remain too unspecific to provide independent evidence for the conditional defense; the outcome of Beere’s discussion is that these dialogues contain philosophical ideas that are compatible with and reminiscent of the Megaric modal claim.^[14] The references to Plato, therefore, support the claim that the Megarics put forward (M); the dialogues do not, however, support the view that they defended their thesis with the conditional defense.

Bailey (2012) also subscribes to the conditional defense. Bailey argues that (M) stands in relation to another Megaric thesis (D), which Bailey sees primarily defended by Stilpo. (D) says that each and every logos has its own object, and each and every object has its own logos. As each logos is entirely unique, a given object has nothing to do with an object to which a different logos applies. The lack of communality is in fact so extreme that Bailey calls these Megaric objects ‘monads’ (310). Bailey shows that (D) and (M) co-entail each other, which not only could be taken as support for (M) and the conditional defense, but also to show that the Megarics held a more encompassing metaphysical system. However, there are various problems with Bailey’s argument, regarding chronology, attribution of the theses, the detailed interpretation of the various texts Bailey relies on, and finally, whether the co-entailment really holds (Bailey himself admits that his interpretation is controversial and has, in part at least, to rely on guesswork; cf. 308, n. 10).

We cannot discuss these problems in detail, but we make two observations. First, Bailey does not offer support for the conditional defense, but only for (M); there is room to argue for (M) differently and still subscribe to Bailey’s co-entailment. Secondly, there is a problem for the conditional defense if the co-entailment argument goes through. Take an event (say a carpenter splitting wood) with necessary conditions N ₁, N ₂, …, N _n , (say wood, strong arms, etc.) which are, however, jointly not sufficient for the event to occur. The event has two further conditions F ₁ (axe) and F ₂ (saw) such that if either is satisfied along with the necessary conditions, the event will occur. Now, in analogy to Beere’s explanation, we are forced to include the disjunction F ₁ ∨ F ₂ in the set whose items are all necessary and jointly sufficient for the event. While this line of reasoning seems unproblematic on its own, it runs into difficulties in conjunction with the monad thesis, according to which no two things ever have anything in common. In forming the disjunction and putting it into the list of necessary conditions we have gone against this claim, for we have done so on the grounds that the axe and the saw have something in common, namely the ability to split wood. This does not mean that a conjunction of (M) and (D) is self-contradictory, but only that the conditional defense is in contradiction with Megaricism as Bailey understands it. Someone who sees merit in Bailey’s co-entailment argument, therefore, cannot subscribe to the conditional defense.

The conditional defense does better in rationalizing (M) than Makin’s defense. Makin tried to defend the highly unintuitive (M) by an equally unintuitive thesis about time-indexed potentialities; but the conditional defense appeals to an intuitive understanding of possibility: something can happen if nothing prevents it. But if some necessary condition is not satisfied then something prevents it. We believe, nevertheless, that the conditional defense is not the best way to understand the Megarics. Before we lay out our own interpretation of (M), we need to get one more approach on the table.

2.3 The Eleatic Defense

A third approach differs from Makin and Beere, and is more similar to our own approach. Unlike Makin and Beere, (Calvert 1976) does not take the Megarics as offering a positive metaphysical view, but considers (M) to be part of a paradox. This paradox calls into doubt the possibility of change. Calvert points out that Diogenes Laertius credits the Megaric group, in particular, Eubulides, with various paradoxes. So one might suppose Eubulides to be Aristotle’s source for (M).

According to Calvert, the paradox works by moving from the trivially true “that which sits necessarily, sits necessarily” to the problematic “necessarily a thing sits or necessarily a thing does not sit” (in symbols, from the unproblematic (☐S ⊃ ☐S), equivalent to (☐S ∨ ¬☐S), to the problematic (☐S ∨ ☐¬S)). Since, according to the latter statement, everything that sits, sits necessarily, everything that in fact sits, can never not sit, or, in other words, nothing sits contingently. This entails that everything can only do what it is actually doing, be it sitting or standing, but cannot do what it is not doing. That is, (M).

Calvert defends his reconstruction in two ways. First, he argues that Aristotle reports the premise of the modal argument at 1047a15-20 (Calvert 1976, 35). Aristotle says

for what stands will always stand and what sits will always sit; for it will not get up if it sits; for what is not able to stand up is incapable of standing up. Therefore, if it is impossible to say these things, it is clear that possibility and actuality are different; but these arguments make possibility and actuality the same, and so it is not a small thing they seek to abolish (our translation).

However, Aristotle does not attribute the premise to the Megarics here, but rather points to consequences of (M), which he thinks are undesirable.^[15]

Second, in fragments 2 and 8 of Parmenides’ Way of Truth, Calvert detects a similar slide from the necessity of a disjunction to the necessity of each disjunct. Parmenides slides from the necessity of ‘it is or it is not’ (in symbols (☐(E ∨ ¬E))) to ‘it is necessarily or it is necessarily not’ (☐E ∨ ☐¬E). Calvert argues that the Megarics may have found this slide convincing due to their Eleatic heritage. We think that there is a more charitable reconstruction of the Megaric paradox available, which does not rely on attributing this mistake to them, all else being equal. Furthermore, Calvert’s historical argument is based on a contentious reading of Parmenides’ argument.^[16] It is unclear whether Parmenides himself makes this slide in the Way of Truth. If Parmenides does not, then there is little reason to attribute the slide to the Megarics.

But we do agree with Calvert that the Megarics of Theta 3 are offering a paradox. We will next consider the historical evidence regarding the Megarics, which give no reason to construe (M) as a piece of metaphysical doctrine. This will clear the way for our own reconstruction of (M) as part of a paradox.

4.1 Presentation

So is there a way to motivate (M) without assuming that the Megarics are offering a positive doctrine? Recall that according to (M) only what is actual is possible. In order to challenge this, one has to claim the existence of unactualized possibilities. The Megarics can reject this claim by a very simple maneuver. They first ask whether it is possible for x to φ although x is not actually φ-ing. If x were to actually φ, x would actually both φ and not-φ. But this would be a contradictory state-of-affairs. So, the Megarics conclude, it is not possible for x to actually φ. Since the same result holds for all values of φ, it will be possible for x to φ if and only if x is actually φ-ing; but if x does not φ, it is not possible for x to φ, which is what (M) says. To illustrate this argument for (M), we can imagine the Megaric in action:

Megaric: Can you move your hand now,^[25] Socrates?

Socrates: Of course.

Megaric: But now you are not moving your hand, so if you were to move it now, you would move it and you would not move it. Surely that’s impossible.

Socrates: That’s true.

Megaric: But the same will happen to every single example we choose, except for those things that are actually happening. So only those things are possible that are actual.

We will call this argument the ‘contradiction argument’.^[26]

This argument consists of three elements: (1) the possibility under consideration, (2) the actual state-of-affairs, and (3) the principle of non-contradiction (PNC). The Megaric extracts the first element from the interlocutor by asking for some non-actual possibility. The Megaric and the interlocutor agree to the second element which is either established by the term ‘now’ or by stipulation; the relevant context here simply takes account of the non-actual possibility under consideration. Finally, the Megaric combines the first two elements. In virtue of the PNC, the interlocutor’s non-actual ‘possibility’ turns out to be impossible. An opponent of the Megarics’ thesis might object that the Megaric’s argument employs a scope ambiguity. The sentence ‘It is possible for something that is not φ-ing to φ’ can be understood to mean either: (i) x is not φ-ing and it is possible: x is φ-ing. (ii) It is possible: x is not φ-ing and x is φ-ing. While (ii) is a contradiction, (i) is not, and so the Megaric’s argument can be defused. However, (i) is the starting-point assumption of the Megaric’s interlocutor; the Megaric then moves from this point to (ii) and the contradictory conclusion. On the basis of which background assumptions he is or is not entitled to make this move is at issue between the Megarics and their opponents and so a simple reference to scope ambiguities will not do. We will say more about those assumptions later.

This argument lends itself to be used as a paradox: the Megaric asks a simple question, and the answer seems obvious. The relevant state-of-affairs (i.e. the non-actuality of what has been declared possible) is noted by the Megaric but can hardly be disputed; finally, the PNC is as sure as any principle. So it seems that we have moved from apparently true premises by apparently valid inferences to an – to say the least – highly counterintuitive conclusion, which is exactly what a paradox does.^[27] Moreover, the argument has the prima facie simplicity of ancient paradoxes. Ancient paradoxes, whether Eubulides’ or Zeno’s, tend to be straightforward.^[28] In a dialogical context, the perplexity motivates a search for a fallacy. Thus, a paradox like the contradiction argument for (M) fits the historical evidence of the Megarics as philosophers working in the negative mode.

The closest relative to the contradiction argument appears in a list of possible interpretations in (Burnyeat 1984, 61–62): “X doesn’t have the ability to (φ while not φ-ing). (The Law of Contradiction)”.^[29] But there are important differences between our readings. Burnyeat et al. hold that the Megaric modal thesis is an instance of the PNC, but the contradiction argument does not. Rather, the PNC is one part of the contradiction argument as we said above when we listed its elements. This response may not satisfy Burnyeat et al. because although they do agree that an interpretation along these general lines might be feasible (Burnyeat 1984, 63), they reject it because of its seeming triviality. What rendered this reading unattractive to Burnyeat et al., and the reason why they did not pursue it further, is that the thesis, as they have it, is a “truism” (Burnyeat 1984, 62), and “so obvious that there seems little interest in stating” it. While our own interpretation is more complex – the PNC is just one of three elements in the contradiction argument – we agree that the contradiction argument still could be considered trivial. But triviality is only grounds for dismissal if combined with further assumptions, pertaining to the significance of truisms, or a background philosophical project that would make truisms unwelcome. Assuming that the Megarics were engaged in a positive metaphysical project might indeed make truisms unwelcome. However, we have seen above that there is little evidence for the view that the Megarics were engaged in a positive metaphysical project. If, as we suggest, we understand the Megarics as negative philosophers, there is no need to worry, as Burnyeat et al. did, about invoking truisms in the way the contradiction argument does.

Why does our proposal rely on the Megarics not making genuine metaphysical claims, but only being committed to their view dialectically? Could it not be the case that the Megarics were holding (M) as a genuine metaphysical claim and that they tried to defend it with the contradiction argument? The answer is that if the Megarics were committed to (M) as a genuine metaphysical claim, it would be entirely puzzling why they would try to defend something trivial at all, let alone with the contradiction argument. But could the Megarics have been committed to (M) only dialectically, while being committed to the consequences of (M), such as the rejection of change, as positive metaphysical theses? Holding a thesis dialectically in this context entails that the holder believes the thesis to have unwelcome consequences which he plans to marshall against his opponent. So holding (M) dialectically, as we think the Megarics did, is incompatible with thinking that they held the consequences of (M) as genuine metaphysical claims.

One objection to the contradiction argument, which also applies to the conditional defense, is that it rules out present non-actual possibilities but not future non-actual possibilities.^[30] Thus, while x cannot φ now because x is not actually φ-ing, nothing has ruled out x being able to φ in the future. Since future possibilities are non-actual, the contradiction argument hasn’t ruled out all counterexamples to (M). The Megarics, however, can extend their response to block this move. Let the question be whether x can φ in the future (tn + 1) although x is not φ-ing now (tn). At tn + 1, therefore, x is either φ-ing or x is not φ-ing. If x does not φ at tn + 1, it is not possible for x to φ at tn + 1 (this is just an application of the simple contradiction argument that substitutes reference to the present with reference to any given point in time); but if x does φ at tn + 1, then x must have changed from not φ-ing at tn to φ-ing at tn + 1. It might be tempting, at this point, to refer to Aristotle’s no-change argument to close off this path.^[31] However, since Aristotle’s no-change argument is based on (M) as a premise, one cannot, on pain of circularity, use it to argue for (M). What the Megarics can do, however, is to ask when x changed from not φ-ing to φ-ing. Call that moment t c. It is a general condition of change that, if a changes to F, a is not F at the onset of the process of change. Hence, if x is supposed to change to φ-ing, we have to assume that x is not φ-ing at t c. But if it is not φ-ing at t c it cannot φ, as the Megarics can show by the simple contradiction argument above. Now both paths of the argument are closed off, and the Megarics can reject the objection of future non-actual possibilities. Future possibilities cannot, therefore, harm the Megarics’ contradiction argument for (M).^[32]

As soon as we give up the idea that the Megarics defended (M) as a metaphysical doctrine the contradiction argument becomes a viable candidate, as it makes an argument for (M) by way of a paradox. However, this does not give the contradiction argument a decisive edge against the conditional defense, which could also be construed as a paradox. So, we will consider one more piece of evidence: Aristotle’s modal test, which he formulates in various texts. The test is strikingly similar to the contradiction argument and contains an indeterminacy which could have been the target of the Megaric paradox. Thus, the paradox could be understood as putting pressure on such tests.

4.2 The Test for Possibility

Various conceptions of possibility, including an everyday notion of possibility, share the idea that in order to determine whether something is possible one must check for compatibility with the obtaining actuality. Most people would say that it is not possible for someone to be on time for an appointment if they are 100 miles from the location of the appointment and there are only a few minutes left. The obtaining actuality lacks what is needed to make the appointment on time, so the proposed possibility is rejected.^[33]

This idea, that the obtaining actuality is what decides whether something is possible, also figures in Aristotle’s official conception of possibility. Three passages contain a “test” for non-actual modalities, including possibility.^[34] They agree on the fundamental idea which is at work in the everyday notion of possibility: p is possible just in case, if p is actual, then nothing impossible follows. Before showing how the test relates to the contradiction argument, there are two issues to discuss.

It’s unclear what status the ‘test’ should have. Aristotle calls it a definition (horismos, Prior Analytics 33a25). If it is a definition, it is a circular definition, as possibility would be defined in terms of impossibility. Some commentators think that Aristotle would not have been concerned about this circularity; others propose that we should read the term adunaton as “contradiction”, to avoid circularity.^[35] Since our interpretation does not hang on the question whether or not Aristotle is giving a proper definition here, we do not want to engage in this debate. Regarding how adunaton should be read, we hesitate to translate with “contradiction”, but a contradiction would of course be an exemplary impossibility. Thus, applications of the test which result in contradictions unambiguously decide whether the candidate of the test is possible or not. Since our own interpretation can confine itself to contradictions, as we will show below, we can steer clear of this second issue, too.

Second, how should we apply the test? The basic idea is to assume that p is actual and then see if any impossibility comes about. But against which scenario do we check p? How far may this scenario deviate from what is actual – how accommodating should we be of p – and what criteria can we use to determine the degree of accommodation?^[36]

Commentators so far have suggested a scale of deviation. At one end of the scale, we might be minimally accommodating, when we suppose p is actual, but hold fixed the truth-values of all other propositions of the obtaining actuality. For example, suppose a situation in which the following two propositions are true: ‘Socrates is not sitting’; ‘no one is sitting’. To test whether it is possible that Socrates sits we assume ‘Socrates is sitting’ is true. But ‘Socrates is sitting’, entails ‘someone is sitting’, which contradicts ‘no one is sitting’ (‘no one is sitting’ is held true in the background against which we test the possibility of ‘Socrates is sitting’). But contradictions are impossibilities. So allowing only minimal accommodation entails that it is not possible that Socrates sits. That is, if we allow no further accommodations but assume that p is true while it is not, the test will yield a notion of possibility where p is possible only if p is actual, i.e. (M).

At the other end of the scale, we might apply the test in a maximally accommodating way. In this case, when we suppose that Socrates sits we will also change the truth-value of any attendant propositions, such as that ‘no one is sitting’. Since in this way contradictions can be avoided, allowing for maximal accommodation in the scenario against which we test, it is possible that Socrates sits. So all and only self-consistent propositions will be possible. That is, if we allow any accommodations whatsoever in addition to assuming p to be true, the test will test for broad logical possibility.

But commentators have overlooked an even stricter application of the test, namely, applying the test to a scenario that does not allow any deviations from the obtaining actuality, i.e. it allows no accommodations whatsoever. In this case, supposing that Socrates sits will immediately result in a contradiction because the scenario against which we test still contains the proposition ‘Socrates is not sitting’. With such a strict application of the test, ‘Socrates sits’ is possible if and only if it is true that Socrates sits. And ‘Socrates sits’ is impossible if and only if it is false that Socrates sits. So, the strict application of the test also leads to (M). More importantly for our purposes, however, is that this version of the test is close to the contradiction argument. For the contradiction argument does exactly this: ask someone to assume something to be true which is in fact false and test this truth against the obtaining actuality without any deviation.^[37]

The strong similarity between the strict application of the possibility test and the contradiction argument allows us to make the following observation.^[38] There is a conception of possibility that relies on a possibility test such as the one Aristotle reports in the Physics, the Metaphysics and the Prior Analytics. Such tests make intuitive sense because when we apply them we implicitly deviate from the obtaining actuality although we think that what we test against is the obtaining actuality.^[39] The Megarics, however, can insist on taking the test literally: assume to be true that of which you want to test the possibility and see if that assumption, in the context of the obtaining actuality, leads to an impossibility. If ‘obtaining actuality’ is taken strictly, i.e. without any deviations, this immediately leads to the paradoxical (M). Are the Megarics entitled to apply the strict version? Proponents of the test don’t intend it to be applied in that way. However, the three descriptions of the test that Aristotle offers do not contain any specifications regarding accommodation, and so the accommodation requirement, although crucial, is merely implicit. The Megarics, through the contradiction argument, force this requirement out into the open and thereby put pressure on the test and the conception of possibility relying on the test: how is the requirement to be specified and what criteria can be used to defend a given specification?

Can one avoid the paradoxical (M) but keep the test? The maximal accommodation option gives up on testing against the obtaining actuality and the possibility that results is broad logical possibility. Anything between this option and the unaccommodating application has to name a criterion that non-arbitrarily sets the level of deviation. The fact that Aristotle mentions the test in Metaphysics Theta after he has discussed the Megarics indicates that he is not willing to give up the test altogether (we’ll say more about this feature of the structure of Theta 3 below). It is not obvious how the Theta description of the test offers a solution to the Megaric challenge, and we cannot discuss this issue in detail, but we believe that the passage offers starting-points for an interpretation that takes account of the Megaric challenge.^[40]

So Aristotle’s test for possibility supports the contradiction argument for (M), especially if the Megarics were engaged in challenging contemporary philosophical presuppositions. But how does the test for possibility relate to the conditional defense? Can the latter be modified one more time to make yet another comeback?

The conditional defense, as presented by Beere, seems quite different from the possibility test, as it relies on a sorites-style cascade of necessary conditions narrowing in on a sufficient condition. But a conditional defense could result from multiple applications of the test for possibility. We could say that the Megaric begins by asking his interlocutor to suppose that a stick of oak lies at the bottom of the ocean. He then asks whether this stick can burn and that the answer should depend on the test for possibility: assume that the stick is burning and see if any impossibility follows. In the supposed scenario, if the stick would burn, there would be fire underwater, which the interlocutor will declare to be impossible. Now suppose the stick is taken out of the water and re-apply the test, and so on.

In effect, this presentation of the conditional defense moves through the scale of accommodation. The initial degree of accommodation will not be on the pole of the scale; at most it will be as the minimal version prescribes, for otherwise the defense is the contradiction argument and we won’t see a cascade, but sometimes the Megaric will have to allow for even more accommodation in order to elicit a first affirmative reply regarding the question whether something is possible, which is then the starting-point of the cascade. The terminal degree of accommodation likewise does not coincide with the other pole of the scale, i.e. maximal accommodation, but will retain all those supposed facts which, according to the questioning Megaric, do not bear on the possibility under investigation (for instance, the supposition that the stick is oak).

This conditional defense might be at least compatible with the test for possibility. But does it fit the dialectic as well as the contradiction argument, i.e. does it put pressure on the test for possibility? The Megarics force into the open the indeterminacy hidden in Aristotle’s formulation of the test by showing that (M) is a consequence of the test. But to achieve this, they need to agree with their interlocutor that certain situations are impossible, i.e. that certain proposed possibilities fail the test. No doubt the contradiction argument can bring about these agreements, for it works on clear-cut contradictions, which are agreed to be impossible. Whether the conditional defense can come to an agreement, and in particular with Aristotle, is unclear. For it seems that Aristotle does not think an impossibility results when applying the test for a proposed possibility against a context which does not assume the actuality of the event the possibility of which we test. It is unclear, therefore, where the Megarics’ confidence would come from that they would reach an agreement with Aristotle regarding the outcome of a series of tests that would ultimately lead to (M), while it is very easy to see where this confidence would come from in the case of the contradiction argument, namely from the PNC.

Finally, it could seem as if the very structure of Theta 3 speaks against our interpretation and in favor of the conditional defense, because, so the objection says, the fact that Aristotle brings up the test after discussing and, in this view, refuting (M), shows that (M) cannot have been designed as an attack on the test. We have already said above that we believe that an interpretation of the chapter can be developed that contains a defense of the test in face of the difficulties (M) brings up. Here we want to emphasize that if the chapter structure is a problem for our interpretation, it is likewise so for the conditional defense. For it is not the type of argument for (M) but rather (M) itself that has a direct bearing on the test. (M) says that only what is actual is possible. The test says that only that is possible which, if assumed to obtain, does not bring about impossibilities. But, according to (M), that is only the case if what is assumed to obtain does actually obtain. So, (M) is one way to give the test the criterion it needs to be applicable, no matter how (M) itself is justified. By refuting (M), Aristotle at best has indicated that he doesn’t wish (M) to be the test’s correct criterion of application, but that is not enough, as we have argued above. The crucial point here is that no matter how we justify (M), the fact that Aristotle brings in the test after discussing (M) is strange as long as we think that there isn’t an argument for a criterion of application different from (M). But if we think there is such an argument, or at least an indication of one (as in Witt’s interpretation), then our interpretation of (M)’s justification is superior to the conditional defense, because it links in directly with the test.