Necessity or Contingency

Part I The Master Argument

• 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

• 2.1 An Aristotelian paradigm: De Caelo, I 283^b6–17; 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, 283^b6-17.
• 2.11 Sketch of a formal reconstruction of the Master argument.

Part II Systems of Necessity: The Megarians and the Stoics

• 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.

• 4.1 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.

• 5.1 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

• 6.1 De Interpretatione, Chapter IX.
• 6.2 Outline of the passage: Introduction (18^a28-34): The problem raised.
• 6.3 Validity of the principle of non-contradiction and the law of excluded (18^a38 abd 18^b-17-25).
• 6.4 Critical examination of the Magarian theory (18^a34-18^b17 and 18^b25-19^a22).
• 6.5 Aristotle's general solution (19^a22-19^b4); 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.

• 7.1 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.

• 8.1 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.

• 9.1 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.

• 10.1 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