Card 4.3.3 · Root IV — Logic
Temporal Logic
Is it already true that it will rain tomorrow?
Temporal logic formalises reasoning about before and after — what holds now, what will hold, and what held.
Where it sits
Under 4.3 Modal logic. Borders 1.4 Philosophy of time, 1.7 Free will.
New to logic? Read the guide
The apparatus
On the symbols. F, G, P and H are Prior's tense operators. F and P here mean future and past, not forbidden and permitted as on card 4.3.1; the two cards use one alphabet for two jobs, as the literature does.
| Symbol | Reads |
|---|---|
| FP | It will at some point be the case that P |
| GP | It will always be the case that P |
| PP | It was at some point the case that P |
| HP | It has always been the case that P |
Where do you stand?
Is it already true that it will rain tomorrow?
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Key figures
| Figure | Dates | Tradition | Contribution |
|---|---|---|---|
| Aristotle | 384–322 BCE | Greek | The sea battle problem |
| Diodorus Cronus | c. 4th–3rd c. BCE | Greek | The Master Argument |
| Ibn Sina | 980–1037 | Islamic | Temporally qualified modal propositions |
| Arthur Prior | 1914–1969 | New Zealand | Founded modern tense logic |
Talk about it here
Conversations about this question in Modal & non-classical logic:
- If you had to give up one classical principle, which would you choose? 6 replies
- What do Prior’s four tense operators actually say, in plain words? 5 replies
- Newton da Costa and why paraconsistency has a Brazilian accent 5 replies
- Syādvāda is not a seven-valued logic, and treating it as one loses the point 5 replies
- Is Nyāya tarka a kind of counterfactual reasoning, and does it need possible worlds? 5 replies
Join free to ask about it Everything in Modal & non-classical logic
Connections
→ 4.3 · ↔ 1.4, 1.7, 1.6, 4.4 · ◇ presentism, eternalism, open future · ○ Axial Age; Modern; Table 3
→ depends on · ↔ borders: genuine overlap, neither prior · ◇ answered by: points from question to answers · ○ appears in: points to the timeline and the comparisons
The full card is in the book
In The Coordinates of Thought this card goes on to a worked example that sets the answers against one case, and to where the question touches daily life — page 205.