Avicenna's Temporal-Modal Logic

Origin. Ibn Sīnā/Avicenna (980-1037). Al-Shifā, Al-Ishārāt. Temporal reading of modality. Absolute vs conditional necessity. Extended Aristotelian syllogistic. Foundation of Arabic modal logic.

Models. Necessity as "always." Possibility as "sometime." Propositions with temporal conditions. Descriptional vs substantial reading. Refined modal syllogistic.

Formalism.

Basic proposition types: ḍarūrī (necessary): always true of subject wujūdī (existential): sometime true while subject exists mumkin (possible): not necessarily true or false

Absolute vs conditional: Absolute necessity (ḍarūrī muṭlaq): always, unconditionally Conditional necessity (ḍarūrī bi-sharṭ): while condition holds "Human is necessarily breathing" — while alive

Substantial vs descriptional: dhātī (substantial): by essence of subject waṣfī (descriptional): while subject has description "Writer is moving" — while writing

Temporal reading of modality: □p ≈ "always p" (ḍarūrī) ◇p ≈ "sometime p" (mumkin) Necessity temporalized.

Proposition classification: Fifteen types in later tradition. Combinations of: necessity, perpetuity, actuality. Time specifications: always, mostly, sometime.

Two-dimensional: lā-dā'im (not-always): sometime not lā-ḍarūrī (not-necessary): possibly not Negations of temporal modes.

Syllogistic: Modal syllogisms with temporal conditions. Mixing modal types. More restrictive than Aristotle.

Conditional propositions: ittifāqī (coincidental): connection in fact luzūmī (implicative): necessary connection

Symbols.

Metatheory. Richer than Aristotelian modal syllogistic. Temporal semantics for modality. Later systematization by al-Kātibī, al-Taftāzānī.

Applies to. Modal logic history. Temporal logic. Arabic philosophical tradition. Syllogistic extensions.

Limitations. Historical context. Translation difficulties. Not fully formal. Limited modern engagement.

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