Logic & Critical Thinking

Core Philosophical Problems

Course 3 · Chapter 2 · Logic & Critical Thinking

Chapter 1 named the argument as philosophy's own core tool. This chapter opens it up properly — what makes an argument actually good, and what makes a bad one merely look convincing.

Deductive vs. Inductive Reasoning

A deductive argument aims for certainty: if the premises are true, the conclusion must be true — there's no logical room for the premises to hold while the conclusion fails. An inductive argument aims lower but covers more ground: the premises make the conclusion probable or likely, without guaranteeing it. "Every swan I've ever seen is white, so the next one probably will be too" is inductive; it can be strong evidence without being airtight.

Validity and Soundness

These two words get used loosely in everyday speech but mean something precise in logic. An argument is valid if its conclusion would have to be true whenever its premises are true — purely a matter of logical structure, regardless of whether the premises are actually true in reality. An argument is sound only if it's valid and its premises are actually true. A perfectly valid argument can still be worthless if it starts from a false premise; soundness is the stronger, real-world-anchored standard.

The Categorical Syllogism

Aristotle's own real contribution to formal logic, laid out in the Prior Analytics (circa 350 BCE), was the categorical syllogism — a structured argument with two premises and a conclusion, each a general statement about categories of things. Aristotle's own real definition: "a discourse in which certain things having been supposed, something different from the things supposed results of necessity because these things are so." When it was rediscovered and studied by later logicians, it was regarded as such a complete, closed system that it stood essentially unchallenged for roughly two thousand years.

A Genuine Correction — the syllogism everyone learns first, "All men are mortal; Socrates is a man; therefore Socrates is mortal," is not actually confirmed to be an example Aristotle himself ever used. It functions as the standard modern teaching illustration, but the real record traces it more directly to John Stuart Mill's own 1843 A System of Logic — the same Mill covered in Course 2, Chapter 6, for utilitarianism — rather than to Aristotle's own original text.
A Direct Echo of Both Earlier Courses This chapter closes a loop Course 2, Chapter 7 already opened: Frege's Begriffsschrift (1879) finally superseded Aristotle's own syllogistic system after roughly two millennia of dominance, since predicate logic could express relationships syllogistic logic structurally couldn't. The two-thousand-year reign this section just described is exactly what Course 2 covered ending.

Formal vs. Informal Fallacies

A formal fallacy is a flaw in an argument's own logical structure — it's invalid no matter what the premises actually say. An informal fallacy can have a perfectly valid structure, but goes wrong somewhere else — a false premise, an irrelevant point, a manipulative framing.

Affirming the Consequent (Formal)

"If P then Q; Q is true; therefore P is true." Invalid — Q could easily be true for some other reason entirely.

Denying the Antecedent (Formal)

"If P then Q; P is false; therefore Q is false." Invalid — Q might still hold true through a completely different path.

Ad Hominem (Informal)

Attacking the arguer's character instead of the actual argument they made.

Straw Man (Informal)

Misrepresenting an opponent's position as a weaker version, then refuting that weaker version instead of the real one.

False Dilemma (Informal)

Presenting only two options as though they were the only possibilities, when genuine alternatives exist.

Appeal to Authority (Informal)

Treating a claim as true simply because an authority figure said it, without regard to whether that figure is actually a relevant expert.

A Worked Example

"If the theory were correct, we'd expect to see X. We do see X. So the theory is correct." This is a textbook case of affirming the consequent — X being observed doesn't rule out every other possible explanation for X. A genuinely valid version would need to establish that X could only be explained by the theory being true, a much harder thing to actually show.

Where This Goes Next — this toolkit isn't academic for its own sake; every later chapter of this course leans on it directly. Chapter 3 turns it toward epistemology's own central question: what can we actually know, and how do we know it?

Questions to Sit With

Reflection 1

An argument can be perfectly valid while still being unsound, if a premise is false. Can you think of a real, everyday argument that's logically valid but relies on a premise you'd actually reject?

Reflection 2

The famous "All men are mortal" syllogism isn't confirmed as Aristotle's own example. Does that change how you think about how ideas get attached to famous names over time, even when the underlying concept genuinely is theirs?

Reflection 3

Informal fallacies like the straw man or false dilemma can be persuasive precisely because they don't look obviously wrong. Can you spot one you've encountered recently — in an ad, a debate, or your own reasoning?

Quick Reference — Chapter 2

  • Deductive — premises guarantee the conclusion; inductive — premises make the conclusion probable, not certain
  • Valid — the conclusion follows from the premises structurally; sound — valid, and the premises are actually true
  • The categorical syllogism — Aristotle's Prior Analytics (c. 350 BCE); the famous "All men are mortal" example isn't confirmed as his own, tracing more to J.S. Mill's System of Logic (1843)
  • Formal fallacies — affirming the consequent, denying the antecedent; informal fallacies — ad hominem, straw man, false dilemma, appeal to authority