# 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.**

| Term | Arabic | Meaning |
|------|--------|---------|
| ḍarūrī | ضروري | Necessary/always |
| mumkin | ممكن | Possible |
| wujūdī | وجودي | Existential |
| dā'im | دائم | Perpetual |
| waṣfī | وصفي | Descriptional |

**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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