Card 4.4.2 · Root IV — Logic
Paraconsistent Logic
If you believe one contradiction, must you believe everything?
Paraconsistent logics allow a system to contain a contradiction without everything becoming provable.
Where it sits
Under 4.4 Non-classical logics. Borders 2.5 Truth, 6.9 Philosophy of mathematics.
New to logic? Read the guide
The positions
| Position | Claim |
|---|---|
| Classical | Contradictions entail everything; any inconsistent theory is worthless |
| Paraconsistent | Block explosion; contradictions can be contained and reasoned around |
| Dialetheism | Some contradictions are actually true |
| Relevance logic | Implication requires relevance, which blocks explosion as a side effect |
Where do you stand?
If you believe one contradiction, must you believe everything?
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Key figures
| Figure | Dates | Tradition | Contribution |
|---|---|---|---|
| Newton da Costa | 1929–2024 | Brazilian | First systematic paraconsistent systems |
| Graham Priest | b. 1948 | Analytic | Dialetheism |
| Nagarjuna | c. 150–250 CE | Indian Buddhist | The catuskoti: four-cornered negation |
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
→ 4.4 · ↔ 2.5, 6.9, 4.1.1, 4.5 · ◇ dialetheism, relevance logic, paraconsistency · ○ Classical; 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 212.