Card 4.1 · Root IV — Logic
Formal Logic
What makes an argument work, regardless of its subject?
Formal logic studies which inferences are valid in virtue of their structure alone — independent of what the statements are about.
On this card
Where it sits
Root IV Logic. Parent of 4.1.1 Propositional Logic, 4.1.2 Predicate Logic, 4.1.3 Syllogistic Logic. Borders 4.3 Modal Logic, 6.9 Philosophy of Mathematics.
New to logic? Read the guide
Narrower questions under this one:
- 4.1.1 Propositional Logic What follows from "if this, then that"?
- 4.1.2 Predicate Logic Why could two thousand years of logic not handle "every boy loves some girl"?
- 4.1.3 Syllogistic Logic What follows from two statements about classes of things?
The core distinctions
This card carries distinctions rather than rival positions, because at this question there is very little to dispute.
| Distinction | What separates them |
|---|---|
| Valid vs sound | Valid: the conclusion follows. Sound: valid and the premises are true |
| Deductive vs inductive | Deductive: conclusion guaranteed. Inductive: conclusion supported |
| Syntax vs semantics | The rules for manipulating symbols, against what makes them true |
| Completeness vs soundness of a system | Everything true is provable; everything provable is true |
Where do you stand?
What makes an argument work, regardless of its subject?
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Key figures
| Figure | Dates | Tradition | Contribution |
|---|---|---|---|
| Aristotle | 384–322 BCE | Greek | The first formal system; the syllogistic |
| Chrysippus | c. 280–207 BCE | Greek Stoic | Propositional logic, largely lost and later rediscovered |
| Gautama and the Nyaya school | trad. c. 2nd c. CE | Indian | The five-membered inference |
| Gangesa | c. 14th c. | Indian | Navya-Nyaya; highly technical logic of relations |
| Gottlob Frege | 1848–1925 | Analytic | Predicate logic; quantifiers; the modern foundation |
| Kurt Gödel | 1906–1978 | Analytic | Completeness, then the incompleteness results |
Talk about it here
Conversations about this question in Logic & argument:
- Vitaṇḍā is not always illegitimate: a critic with no thesis can still be doing philosophy 7 replies
- Quine was right that even logic could be revised in the light of experience 6 replies
- Reading group: the first book of the Nyāya Sūtra with Vātsyāyana’s commentary 6 replies
- Keep the losing opinion on the page: what the Talmud could teach an online forum 6 replies
- Reading group: Toulmin’s The Uses of Argument, starting from the middle 6 replies
Join free to ask about it Everything in Logic & argument
Connections
→ 4.1.1, 4.1.2, 4.1.3 · ↔ 4.2, 4.3, 6.9, 2.8, 4.5 · ◇ classical logic, logicism, logical pluralism · ○ Axial Age; 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 180.