Logic
Logic
Logic is the study of valid reasoning — the principles that distinguish good arguments from bad ones. It is the shared backbone of mathematics, science, Epistemology, and all rigorous philosophical inquiry.
What Is an Argument?
An argument consists of premises (statements taken as given) and a conclusion (the statement claimed to follow from them).
- Valid — if the premises are true, the conclusion must be true
- Sound — valid and all premises are actually true
- Strong (inductive) — premises make the conclusion probable
Types of Reasoning
| Type | Description | Example |
|---|---|---|
| Deductive | Conclusion necessarily follows | All humans die; Socrates is human; ∴ Socrates dies |
| Inductive | Conclusion is probable | Every swan I've seen is white; ∴ all swans are white |
| Abductive | Inference to the best explanation | The grass is wet; best explanation is rain |
Aristotle's Syllogistic Logic
Aristotle in the Organon developed the first formal logic — syllogistic — based on subject-predicate propositions:
All mammals are animals. All dogs are mammals. Therefore, all dogs are animals.
This remained the dominant system for over 2,000 years, until Frege's predicate logic in the 19th century.
Propositional Logic
Studies logical relations between whole propositions using connectives:
| Symbol | Meaning | Read as |
|---|---|---|
| ¬P | Negation | "not P" |
| P ∧ Q | Conjunction | "P and Q" |
| P ∨ Q | Disjunction | "P or Q" |
| P → Q | Conditional | "if P then Q" |
| P ↔ Q | Biconditional | "P if and only if Q" |
Predicate (First-Order) Logic
Extends propositional logic with quantifiers and predicates:
- Universal quantifier ∀x: "for all x, …"
- Existential quantifier ∃x: "there exists an x such that …"
Example: ∀x(Human(x) → Mortal(x)) — all humans are mortal.
The Liar's Paradox and Self-Reference
"This statement is false." If true, it's false; if false, it's true. Self-referential paradoxes drove developments in formal logic and influenced Wittgenstein's view that some propositions are nonsensical rather than false.
Logical Fallacies
Common errors in reasoning philosophers must recognize:
- Ad hominem — attacking the person, not the argument
- Straw man — misrepresenting an opponent's position
- False dilemma — presenting only two options when more exist
- Post hoc ergo propter hoc — assuming causation from temporal succession
- Circular reasoning / begging the question — assuming what you're trying to prove
- Slippery slope — asserting one step inevitably leads to an extreme
- Appeal to authority — using an authority as decisive evidence
Logic and Language
Wittgenstein's early work (Tractatus Logico-Philosophicus) held that logical form mirrors the structure of reality: a proposition is a logical picture of a fact. His later work (Philosophical Investigations) abandoned this "picture theory" in favor of meaning as use in social practice.
Dialectics as Alternative Logic
Hegel proposed Dialectics as a dynamic logic of contradiction and synthesis — rejecting the law of non-contradiction as the highest principle. Marx adapted this as materialist dialectics. See Dialectics.
Related Topics
- Aristotle — inventor of formal logic
- Wittgenstein — logic, language, and the limits of what can be said
- Epistemology — logic as a tool for evaluating knowledge claims
- Dialectics — Hegel's alternative to classical formal logic
- Metaphysics — logical analysis as a method for metaphysical clarification
