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

We show the intuition of contraposition using Venn diagrams.

In week 4 we introduced Gentzen's sequents.You should make sure you understand when a sequent is valid, and what it means to provide a counter-example to a sequent -- a universe in which the…

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 ¬ ⋀ ⋁.

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

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

We describe the traditional presentation of the syllogisms, and introduce Aristotle's existential assumption, on the basis of which he derives nine more syllogisms. These are not sound in our…

Using meta-/object-level contrapositions, we can derive all 15 sound syllogisms from Barbara.

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.

In this video on syllogisms, we introduce the logic of negation.

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

Part 2 Fine Tuning Lecture: The Fine Tuning Argument

The Kolmogorov axioms are the foundations of probability theory introduced by Andrey Kolmogorov in 1933. Using these axioms, this video shows how many other familiar results can be derived from these…