A8. Hartmann and Hintikka: Two influential interpretations

We are now prepared to review two recent interpretations of Aristotle's teachings about dynamis, which were probably the most influential in the twentieth century: those by Nicolai Hartmann and Jaakko Hintikka.

In his ontology of modality, Hartmann distinguishes two kinds of possibility: total possibility and mere partial possibility.[1] In Hartmann's eyes, it is total possibility that is the only serious candidate for a rigorous treatment in an ontology of modality: A state of affairs s is called totally possible if and only if all necessary conditions for s are given. It is a consequence of Hartmann's own determinism that the necessary conditions are jointly sufficient. For this reason, in Hartmann's theory there is a collapse of modalities. Contrary to intuition, there is no longer an extensional difference between the possibility and necessity: All and only totally possible states of affairs are necessary.

Hartmann accepts this consequence while it is a very much unwanted result in my eyes. But more important for his interpretation of Aristotle is Hartmann's concept of partial possibility: A state of affairs s is partially possible if and only if at least one necessary condition for s is given. Hartmann now accuses Aristotle that he has only dealt with the inferior concept of partial possibility and rejected the Megarian concept of dynamis (to be discussed in the next section), which Hartmann sees as a precursor to his own views.[2] However, of course, there are many different kinds of necessary conditions for s, even if we take only those necessary conditions into account, for which it is a contingent matter whether they obtain or not.[3] Thus, it is clear that Hartmann's interpretation is far too unspecific as an interpretation of dynamis – while having a dynamis for F certainly is a necessary condition to do F, we do not do justice to Aristotle's account of dynamis if we treat it on a par with the obtaining of just any necessary condition.

While Hartmann interprets Aristotle in terms of his concept of partial possibility, Jaakko Hintikka's interpretation draws on the so called principle of plenitude. In Hintikka's wording, the principle of plenitude says that “[n]o unqualified possibility remains unrealised through an infinity of time”.[4] The principle of plenitude is closely related to a temporal interpretation of the alethic modalities, i.e. of possibility and necessity. According to such a temporal interpretation, a proposition p is necessary if and only if it is always the case that p, and it is possible if and only if it is at least at one time the case that p. Now, it is normally not disputed that it is always the case that p if p is necessary and that whatever is the case at some point in time must be possible.[5] It is, however, not that clear that all possibilities will or even could be realised at some point of time. It is both possible that I sit at noon and that I stand at that time, but, of course, I can realise only one of these possibilities at noon. Even if we forgot the reference to a certain time, there remain problems: It is possible that, in the future, my son will marry and found a family, but it is also possible that he will remain a bachelor all his life. However, of course, both possibilities cannot be realised. To discard such obvious counterexamples to the principle of plenitude, Hintikka talks about “unqualified possibilities”. Unqualified possibilities are such possibilities that can, in principle, be realised at any point of a maybe eternal history, like the possibility that something red is round or that there exists an animal that is able to fly.

It has been a matter of debate whether Aristotle does or does not accept the principle of plenitude. While Lovejoy, in his great study on the principle of plenitude,[6] claimed that Plato accepted the principle, but Aristotle did not, Hintikka takes the opposite stand and attributes the principle to Aristotle, but not Plato. I will not argue for any of these alternatives here, but rather draw attention to two important observations:

(a) If Aristotle subscribed to the principle, it was nothing he took for granted, for in his De Caelo I 12 he presents a rather lengthy (and maybe fallacious) proof of this principle for the very special case of eternal entities. The claim he argues for in De Caelo is if it is possible for something to exist eternally, it will exist eternally, which in turn implies that all eternal beings are necessary beings. If the principle of plenitude would be some tacit background assumption of the semantics of dynaton or dynamis, he would not have needed such an elaborated argument for this claim. Thus, for Aristotle, the principle of plenitude cannot be a trivial element of the semantics of dynaton.

(b) Even if it were such an element, the “unqualified possibilities“ that feature in the principle of plenitude are not the topic of Met. IX, but rather the dispositions of finite things and people. In Met. IX, Aristotle talks about architects and people of other arts and sciences, about blind and seeing animals, about sitting and standing men, about flute players, sperms and wooden boxes. These are all finite things having finite dispositions, i.e. dispositions that do not have all of eternity at their disposal for realising themselves. Thus, a principle about “unqualified possibilities” would be of no help at all in explaining the teaching of Met. IX. Therefore, the principle of plenitude is nei- ther a plausible nor helpful starting point when making sense of Aristotle's theory of dynamis.

As different as Hartmann's and Hintikka's interpretations are, they do have something in common. Both analyse Aristotle' dynaton solely in terms of modal operators, i.e. as being the Greek equivalent of something like “It is possible that ...” or, in logical notation, “◊p”. As I have argued in the last two sections, such a translation is both syntactically and ontologically misleading if we care about the dynaton that is related to a disposition. Who, like me in this paper, cares about Aristotle's theory of dispositions has to analyse dynaton as a predicate modifier, which is both truer to the Greek syntactical constructions that Aristotle uses to ascribe dispositions and more appropriate for representing the ontological structure underlying these ascriptions.

  • [1] Cf. Hartmann 1938. On Hartmann's modal ontology cf. Hüntelmann 2000, on his interpretation of Aristotle cf. Seel 1982 and Liske 1995
  • [2] Cf. Hartmann 1937. Hartmann's interpretation of Aristotle is influenced by the – different – position of Zeller 1882
  • [3] As any necessary proposition is implied by any statement, a necessary statement like “1 + 1 = 2” may be seen as expressing a condition that is necessary for any other statement. If seen thus, there are no states of affairs that are not partially possible; even impossible states of affairs are partially possible when we take “necessary condition” in the logical sense and allow necessary propositions to be included within the set of conditions
  • [4] Hintikka 1973, 96
  • [5] Of course, these two observations correspond to the rules of medieval logic that (a) it is valid to conclude actuality from necessity (ab necesse ad esse valet consequentia) and (b) to conclude possibility from actuality (ab esse ad posse valet consequentia). It is, however, disputable, what the range of the rules formulated in the main text is, for there are necessary propositions like “1 + 1 = 2” or “At twelve o'clock it is twelve o'clock” which may be said to be true at no point of time, but rather in some timeless manner
  • [6] Lovejoy 1936
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