Symbolic Logic

Existential Instantiation and Existential Generalization are two rules of inference in predicate logic for converting between existential statements and universal statements.

Universal Generalization is a rule of predicate logic that lets you go from a statement about an individual to a generalization, but there are restrictions on how it can be used.

For the past 14 lessons, we have been focused on sentential logic. This is where we use single letters in place of whole sentences and focus on the logical relations made between whole claims. But an argument can be valid without there being logical relations between whole sentences.

In this last lesson on sentential logic, though not on symbolic logic, we go over solutions to proofs for De Morgan’s theorems.

Indirect proof, or reductio ad absurdum, is a method for proving something by showing that the assumption of its opposite would entail a contradiction.

This symbolic logic lesson goes over proofs of both forms of the rule of Distribution, which is one of the rules of replacement.

This lesson in symbolic logic focuses on how to use conditional proof to prove disjunctions.

Here we take a closer look at how to nest conditional proofs, illustrating it with a proof of the rule of exportation.

To keep the lines in our proofs shorter, this introduces rules of inference for introducing or eliminating biconditionals.

Conditional proof is a method for proving a conditional by assuming its antecedent and deriving its consequent. Read this post or watch the video to learn how it’s done.