Card 4.3.2 · Root IV — Logic
Epistemic Logic
If you know something, do you know that you know it?
Epistemic logic formalises knowing and believing — what follows from the fact that someone knows something, including what they know about what others know.
On this card
Where it sits
Under 4.3 Modal logic. Borders 2.1 Theories of knowledge, 2.3.2 Internalism vs externalism, 2.8 Formal epistemology.
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The apparatus and its disputed axioms
| Axiom | Says | Status |
|---|---|---|
| KᵢP → P | What is known is true | Near-universally accepted |
| KᵢP → KᵢKᵢP | Positive introspection | Contested; rejected by externalists |
| ¬KᵢP → Kᵢ¬KᵢP | Negative introspection | Widely rejected |
| Closure | Knowing P, and that P entails Q, yields knowing Q | Contested; denied by some anti-skeptics |
Where do you stand?
If you know something, do you know that you know it?
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Key figures
| Figure | Dates | Tradition | Contribution |
|---|---|---|---|
| Jaakko Hintikka | 1929–2015 | Finnish | Knowledge and Belief; the founding treatment |
| Robert Nozick | 1938–2002 | Analytic | Denied closure to block skepticism |
| Robert Aumann | b. 1930 | Economics | Common knowledge; agreeing to disagree |
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 · ↔ 2.1, 2.3.2, 2.7, 2.8 · ◇ internalism, externalism, reliabilism · ○ 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 203.