CSLI Publications logo
new books
knuth books
for authors
CSLI Publications
Necessity or Contingency cover

Necessity or Contingency

The Master Argument

Jules Vuillemin

From three premises having to do with necessity and contingency, the Master Argument derived a contradiction which imperiled freedom. A text of Aristotle helds to reconstruct the argument in historical terms, to show its soundness to understand its architectonic power for opening clear perspectives in ancient but also in modern philosophy.

The original meaning of these premises belong to a special branch of modal temoral logic (with temporal indexing of modalities and of sentences). In other words, the difficulties concerning the conditions that make freedom possible are dependent on physics rather than on logic. This is true for the Stoics and the Epicureans as well as for John Duns Scotus and Kant. An epilogue explores the consequences of this state of affairs by outlining the Master Argument in terms of present physics.

Jules Vuillemin is Professor Emeritus of Philosophy, Collège de France (Paris 1962-1990). He has published historical and systematic studies about the relationships between the theory of knowledge and the development of mathematics and physics. He has used this methodology to outline what he calls his “skepticism about the cathartic virtues of grammar–even in moral philosophy–or of often prejudiced ‘rational reconstructions’ in the matter of knowledge.”


  • Introduction
  • Acknowledgements
  • Part I The Master Argument

  • 1 The Master Argument. On the Shortcomings of Some Past Interpretations. Conditions to be Fulfilled by andy Acceptable Interpretation
    • 1.1 The text of Epictetus
    • 1.2 Zeller's interpretation. Confusion of the logical and chronological
    • 1.3 Ambiguity in the first premise: Necessity and irrevocability. Signification of the first premise.
    • 1.4 Prior's interpretation: It supposes two supplementary premises, one of which is explicity rejected by Aristotle; it supposes the first premise ambiguous

  • 2 Reconstruction of the Master Argument
    • 2.1 An Aristotelian paradigm: De Caelo, I 283b6–17; its context.
    • 2.2 The principle of the conservation of modal status.
    • 2.3 The principle of the possible realization of the possible interpreted as a principle of pure modal logic.
    • 2.4 The principle of possible realization of the possible and diachonic expansion of the necessary.
    • 2.5 The principle of conditional necessity.
    • 2.6 The irrevocability of the past or the principle of the impossibility of realizing the possible in the past.
    • 2.7 The principle of the subsistence of a possible that is not to be realized.
    • 2.8 Reconstruction of the De Caelo demonstration.
    • 2.9 Reconstruction of the Master Argument.
    • 2.10 Sketch of a formal reconstruction of the Aristotelian reasoning at De Caelo, I, 283b6-17.
    • 2.11 Sketch of a formal reconstruction of the Master argument.

    Part II Systems of Necessity: The Megarians and the Stoics

  • 3 A System of Logical Fatalism: Diodorus Cronus
    • 3.1 Diodorus' Solution.
    • 3.2 Two possible interpretations as regards the object of the Diodorean Modalities: nominalism and realism.
    • 3.3 The meaning of Diodorean implication.
    • 3.4 Diodorean nominalism.
    • 3.5 Diodorus' necessitarianism.

  • 4 Eternal Return and Cyclical Time: Cleanthes' Solution.
    • 4.1 First conjection. Necessity of the past secundum vocem and secundum rem: Okham's conception on Prior's hypothetical reconstruction. Modality de dicto and modality de re.
    • 4.2 Inadequacy of Okham's solutio. Indcrimination of the principle of conditional necessity: John Duns Scotus.
    • 4.3 Cleanthes again and the second conjecture: the conditional character of the necessity of the past according to Cleanthes; the interpretation of Leibniz.
    • 4.4 Third conjecture: cyclical time and the numerical conception of the identity of beings in eternal retun.

  • 5 Freedom as an element as an Element of Fate: Chrysippus
    • 5.1 Wer Chysippus' doubts about the thesis of pure modal logic according to which from the possible the impossible does not follow, they would be about its negative form, not about its positive form.
    • 5.2 Chrysippus' doubt about the interdefinability of the modalities. From the non-possibility of an event's occurence it cannot be concluded that its opposite is necessary.
    • 5.3 The non-standard modal system according to Chrysippus.
    • 5.4 A system related to Prior' system Q; the double logical square of Chrysippean modalities and the double temporal index in the Master Argument's second premise.
    • 5.5 A Philonian doubt about the second premise?

    Part III Systems of Contingency: The Lyceum, The Garden, The Academy

  • 6 Towards Rehabilitating Opinion as Probable Knowledge of Contingent Things. Aristotle.
    • 6.1 De Interpretatione, Chapter IX.
    • 6.2 Outline of the passage: Introduction (18a28-34): The problem raised.
    • 6.3 Validity of the principle of non-contradiction and the law of excluded (18a38 abd 18b-17-25).
    • 6.4 Critical examination of the Magarian theory (18a34-18b17 and 18b25-19a22).
    • 6.5 Aristotle's general solution (19a22-19b4); conditional necessity and exceptions to the principle of bivalence.
    • 6.6 Aristotle's general conception confirms the De Interpretatione solution; the difference between Aristotle and Diodorus.
    • 6.7 First interpretive hypothesis: propositions without a determinate truth-value.
    • 6.8 Second interpretative hypothesis: More than two truth-values.
    • 6.9 Third interpretative hypothesis: probability.

  • 7 Epicurus and Intuitionism
    • 7.1 First logical interpretation of the Epicurean denial of the excluded middle: the three-valued logic of Lukasiewicz; reasons for rejecting this solution.
    • 7.2 Second logical interpretation of the Epicurean negation of the excluded middle: The Intuitionist System.
    • 7.3 Are the Epicurean ‘criteria’ compatible with intuitionism?
    • 7.4 Consequences of the Epicurean criteria: Plurality of hypotheses and rejection of the excluded middle.
    • 7.5 Epicureanism and the Master Argument.
    • 7.6 Other intuitionist conceptions of reality: Descartes and Kant.

  • 8 Carneades and the Skeptical Nomminalism of the Modalities.
    • 8.1 What is the relation between the principle of the excluded middle and the principle of causality (De Fato, X-XII)?
    • 8.2 Aristotle's dogmatic definition of truth called into question (De Fato, XIV)
    • 8.3 Carneades abd the Master Arguments (De Fato, IX).
    • 8.4 From Carneades to the logics of “fictive” names: Buridan's amplation.
    • 8.5 Carneades does not abandon the principle of conditional necessity; he simply deprives it of the ontological involvement conferrered upon it by the dogmatic interpretation of truth.

  • 9 Platonism and Conditional Necesity
    • 9.1 Platonism and the principle of conditional necessity
    • 9.2 Consequences of the connection between conditional necessity and the substantiality of the sensible for modality, causality and freedom.
    • 9.3 The consequences of abandoning the principle of conditional necessity and the substantiality of the sensible world for the Platonic and Platonistic theories of modality, causality and freedom. The same abandoment entails similar consequences for Duns Scrotus.

  • 10 Epilogue
    • 10.1 The impasse of natural language
    • 10.2 The probabilistic reconstruction of Master Argument: Diodorus' solution.
    • 10.3 The special status of premise (C): Chrysippus' solution and the ‘Unique Law of Chance’.
    • 10.4 Contingency and ignorance: The statistical mix
    • 10.5 Contingency and nature: The state of superposition

  • Bibliography
  • Index of quotations of ancient and mediaeval texts
  • Index of Proper Names


ISBN (Paperback): 1881526852 (9781881526858)
ISBN (Cloth): 1881526860 (9781881526865)

Subject: Philosophy; Necessity; Contingency

Add to Cart
View Cart

Check Out

Distributed by the
University of
Chicago Press

pubs @ csli.stanford.edu