Card 4.3.1 · Root IV — Logic
Deontic Logic
What follows logically from "you must"?
Deontic logic applies modal machinery to obligation, permission and prohibition — formalising what follows from what is required or allowed.
Where it sits
Under 4.3 Modal logic. Borders 6.2 Philosophy of law, 3.2.2 Duty-based approaches.
The apparatus
| Symbol | Reads | Defined as |
|---|---|---|
| OP | P is obligatory | True in all ideal worlds |
| PP | P is permitted | ¬O¬P |
| FP | P is forbidden | O¬P |
Key figures
| Figure | Dates | Tradition | Contribution |
|---|---|---|---|
| Ibn Sina and Islamic jurists | 10th c. onward | Islamic | Five-fold classification of acts, worked formally |
| Gottfried Leibniz | 1646–1716 | European modern | Noted the parallel between modal and deontic terms |
| Ernst Mally | 1879–1944 | Austrian | First formal attempt |
| G. H. von Wright | 1916–2003 | Finnish | The standard system |
| Roderick Chisholm | 1916–1999 | Analytic | The contrary-to-duty paradox |
Connections
→ 4.3 · ↔ 6.2, 3.2.2, 3.2.6, 4.3.2 · ◇ standard deontic logic · ○ Islamic golden age; Modern; Table 3
→ narrower questions · ↔ questions it borders · ◇ the positions, mapped in Part III of the book · ○ the eras and comparison tables (Parts IV and V)
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 201.
On Coordinates of Thought
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