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Philosophy · 13

Every formula in this course and the easiest ways to remember them, on one page.

1. Thinking philosophically2. The history of philosophy3. Ethics, mind and society

1Thinking philosophicallyAdvanced

What is philosophy? Its branches and questions

Open lesson

Logic and critical thinking

Open lesson
(P → Q) ≡ (¬Q → ¬P)
where:
  • P → Q“if P, then Q” (implication)
  • ¬Q → ¬Pthe contrapositive: “if not Q, then not P”
  • ≡equivalence: both statements always have the same truth value

Modus tollens rests on exactly this. Careful: Q → P (the converse) and ¬P → ¬Q (the inverse) are different statements.

2The history of philosophyAdvanced

Ancient philosophy: Socrates, Plato, Aristotle

Open lesson

Philosophy in the Islamic world and the East

Open lesson

Modern philosophy: Descartes, Locke, Hume, Kant

Open lesson

3Ethics, mind and societyUniversity

Ethics: virtue, duty and consequences

Open lesson
U(A) = u₁ + u₂ + … + uₙ = Σ uᵢ ; EU(A) = Σ pⱼ · Uⱼ
where:
  • U(A)total utility of action A (in notional wellbeing units)
  • uᵢchange in the wellbeing of person i (+ or −)
  • pⱼprobability of outcome j (Σ pⱼ = 1)
  • Uⱼtotal utility if outcome j happens

Where it comes from: the principle “everyone counts as one” means adding up each person's wellbeing with equal weight. When the outcome is uncertain, each scenario's utility is multiplied by its probability and the results are added — expected utility.

Philosophy of mind and science: mind and body, Popper, Kuhn

Open lesson
(T → O) ∧ ¬O ⊢ ¬T
where:
  • Tthe theory being tested (together with auxiliary assumptions)
  • Othe prediction (observation) derived from the theory
  • ⊢“it follows logically”

Popper's asymmetry uses the forms from the logic lesson: if the prediction comes true, T is not proven (that would be affirming the consequent); if it fails, T is refuted by modus tollens.

Political philosophy: the social contract and justice

Open lesson
maximin: max_A ( min_i xᵢ(A) ) ⟷ average utility: max_A ( (1/n) · Σ xᵢ(A) )maximin: max_A ( min_i xᵢ(A) ) ⟷ average utility: max_A ( (1/n) · Σ xᵢ(A) )
where:
  • Athe society (distribution option) being compared
  • xᵢ(A)the wellbeing index of group i in society A (for example, an income index)
  • nnumber of equal-sized groups

Where it comes from: behind the veil you could end up in any position. When life's basic prospects are at stake, it is reasonable to choose the option that makes the worst position as good as possible (maximin). A utilitarian instead maximises average (or total) wellbeing.