1
Evaluate a modal claim
Compute □p and ◇p at a world from the worlds it can see, and say which frame property each of the axioms T, D, B, 4 and 5 corresponds to.
Course · Philosophy
Identity, Modality and Freedom
Treat the oldest questions in metaphysics as questions about structure. Evaluate a claim of necessity at a world, find out which axioms a frame forces, decide where a modal argument goes wrong, and see what each position on identity, freedom and evil has to give up.
□p at w ⟺ p at every world w can see
T: reflexive 4: transitive
□p ∧ □(p → q) → □q on every frame
□(p ∨ ¬p) does not give □p ∨ □¬p
inconsistent: drop one, a model appears
What this course is about
- Subject
- Philosophy
- Lessons
- 12
- Format
- Interactive
Overview
What you will be able to do
By the end you can say what a claim of necessity, identity or freedom commits you to, and name the premise to doubt when an argument for it fails.
2
Locate a modal fallacy
Find the scope shift in the fatalist's argument, the premise the ontological argument needs from the frame, and the substitution that fails inside a box.
3
Run an identity puzzle as a chain
State the ship of Theseus as a tolerance chain, and read off what each treatment says; separate connectedness from continuity as a relation from its transitive closure.
4
Write a puzzle as an inconsistent set
Formalise fission, the free-will triad and the problem of evil, find the smallest subset that cannot hold together, and name the position each deletion yields.
5
Evaluate an argument about freedom
Show the transfer step of the consequence argument is valid on every frame, and test a Frankfurt case in a structural model.
Lessons
12 lessons
Modality comes first, because three of the later arguments use it; then identity over time, then freedom, and the last lesson applies the inconsistent-set method to evil.
Necessity, Possibility and Possible WorldsA claim of necessity is a claim about every world a given world can see, and what it can see is part of the model.Not marked
Frames, Axioms and What Necessity ObeysEach of the modal axioms T, D, B, 4 and 5 is the fingerprint of one property of the arcs.Not marked
Modal Fallacies and the Sea BattleFrom a necessary disjunction it does not follow that one disjunct is necessary, and the fatalist's argument needs that step.Not marked
The Ontological Argument in S5The modal ontological argument is valid when the frame is euclidean, so the dispute is over its first premise and over the choice of frame.Not marked
Leibniz's Law and the Masked ManTwo sentences that are true together can still not be swapped inside a box, which is why the masked man does not refute Leibniz's law.Not marked
The Ship of TheseusReplacing one plank at a time is a chain of tolerance conditionals, and each way of treating the chain says something different about the all-new ship.Not marked
Personal Identity and Psychological ContinuityA direct tie between stages of a life, such as a memory, is not transitive, and the chain of such ties is what identity can follow.Not marked
Fission and What MattersIf one person divides into two who are each continuous with the original, four plausible claims cannot all be true, and each way of giving one up is a position.Not marked
Free Will, Determinism and CompatibilityDeterminism, free will and the claim that they exclude each other cannot all be true, and each of the three standard positions deletes a different one.Not marked
The Consequence ArgumentThe consequence argument for incompatibilism is valid because its transfer step is the K axiom, so the dispute is over its two premises and over the reading of its box.Not marked
Frankfurt Cases and the Ability to Do OtherwiseA counterfactual intervener removes the agent's ability to do otherwise and leaves the agent's decision as the cause of the act, which tells against the claim that responsibility needs that ability.Not marked
The Problem of Evil as an Inconsistent SetThe logical problem of evil is a set of five sentences with no model, and each response to it is a deletion or a weakening of one.Not marked
Recommended background
Arguments and Validity, for validity, consistency and the counterexample, and Science, Induction and Causation, for the causal models used in one lesson.
Practice suggestions
Work forward through the first five lessons. “Frames, Axioms and What Necessity Obeys” needs the evaluation rule from “Necessity, Possibility and Possible Worlds”, and “The Ontological Argument in S5” and “The Consequence Argument” both use the frame properties the second lesson establishes.
Build the model before you read the verdict. Every modal lab lets you retype the arcs and the valuation. Predict the tile, then press on the model until the prediction fails; the arcs are the whole content of the theory, and a change of one arc often changes the axiom list.
Keep the logic apart from the metaphysics. The labs decide whether an argument is valid on a frame, whether a set can all be true, whether a variable is a cause. They never decide whether the frame is the right one for God, for time, or for what is in anyone's power. That question is left open on purpose in every lesson.
Take each puzzle to the end. The identity and freedom lessons each name an exit for every position, and a position whose exit you cannot state is a position you have only heard of.
What it does not cover
Quantified modal logic and counterpart theory. Every model here has worlds, an accessibility relation and sentence letters, and no domain of individuals that varies from world to world, so questions such as whether I could have been a different person are left to the prose.
Temporal logic. The sea battle is treated as a scope error with the box, not with a logic of past and future, so what the lab shows is the fallacy and not a theory of time.
Bodily and narrative criteria of personal identity. They appear as prose beside the psychological criterion, and nothing computes whether a body or a story is the same one.
Philosophy of religion beyond the two arguments taught. The ontological argument and the problem of evil are tested for validity and consistency; the cosmological argument, religious experience and the rest are not here.
Neuroscience and the experimental literature on free will. The lessons test whether positions are consistent and whether arguments are valid. Whether determinism is true is an empirical question and is not decided here.