We derive the implication rule using the rules introduced last week.

We introduce sequents, where we have finite sets of predicates on both sides of the turnstile.

Venn diagrams on a sphere.

We show the intuition of contraposition using Venn diagrams.

We use the rules to reduce a sequent to a conjunction of simpler sequents. In this example we find that the expression asserted by the sequent is a tautology — it is equivalent to the empty…

We use the rules to reduce a sequent to a conjunction of simple sequents, sequents that only mentions propositional letters, with no connectives, and no repetitions — in this example, we find…

We can now give Gentzen's rules for ¬ ⋀ ⋁.

Additional predicates after the turnstile behave similarly.

We interpret additional predicates before the turnstile. These simply express validity in a sub-universe. This means that for any sound rule the corresponding rule with additional predicates is…

In this video, we try to arrive at the disjunction rule.

In this video, we label each region in the Venn diagram with a number from 0 to 7. We can then present our justifications and counter-examples by referring to those 8 regions.

This is an old recording of Lecture 2, from 2019.

This is the third video on Syllogisms. We use Venn diagrams to show that barbara is sound.

This is the first video on Syllogisms. We start by introducing barbara, the simplest classical syllogism, and the proposition, "all a are b", known as universal affirmation. We briefly …

Phil Methods 1: Week 1, part 4

This is an old recording of Lecture 1, from 2019.