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CL - Implication

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

From  Haoran Peng on October 20th, 2020 0 likes 0 plays 0  

CL - Sequents

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

From  Haoran Peng on October 20th, 2020 0 likes 0 plays 0  

CL - Review 2 - Venn Apples

Venn diagrams on a sphere.

From  Haoran Peng on October 20th, 2020 0 likes 0 plays 0  

CL - Review 1 - Contraposition

We show the intuition of contraposition using Venn diagrams.

From  Haoran Peng on October 20th, 2020 0 likes 0 plays 0  

CL - Lecture 4.i - Reduction 1

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…

From  Claudia-Elena Chirita on October 15th, 2020 0 likes 295 plays 0  

CL - Lecture 4.j - Reduction 2

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…

From  Claudia-Elena Chirita on October 15th, 2020 0 likes 256 plays 0  

CL - Lecture 4.h - Sequents 3

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

From  Claudia-Elena Chirita on October 15th, 2020 0 likes 276 plays 0  

CL - Lecture 4.g - Sequents 2

Additional predicates after the turnstile behave similarly.

From  Claudia-Elena Chirita on October 15th, 2020 0 likes 281 plays 0  

CL - Lecture 4.f - Sequents 1

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…

From  Claudia-Elena Chirita on October 15th, 2020 0 likes 331 plays 0  

CL - Lecture 4d - Disjunction

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

From  Haoran Peng on October 11th, 2020 0 likes 397 plays 0  

CL - Lecture 3f - Presenting your justifications and counterexamples

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.

From  Haoran Peng on October 3rd, 2020 0 likes 447 plays 0  

CL - 2019 Lecture 2

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

From  Claudia-Elena Chirita on September 26th, 2020 0 likes 177 plays 0  

CL - Lecture 2.b - Aristotelian Syllogisms. First Example

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

From  Claudia-Elena Chirita on September 26th, 2020 0 likes 455 plays 0  

CL - Lecture 2.a - Aristotelian Syllogisms. Euler diagrams

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 …

From  Claudia-Elena Chirita on September 26th, 2020 0 likes 522 plays 0  

Hornsby’s Objection

Phil Methods 1: Week 1, part 4

From  Dave Ward on September 18th, 2020 0 likes 39 plays 0  

CL - 2019 Lecture 1

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

From  Claudia-Elena Chirita on September 12th, 2020 0 likes 124 plays 0