You can find slides and handouts below, together with an outline of each lecture.

Please note that these may be revised even after the lecture occurred.

Graphical depiction of learning objectives for this course.

definitions

Gives some examples of the formal language awFOL and explains their relation to ordinary English. Also explains terms like 'name' and 'predicate'.

Reading: §1.1, §1.2, §1.3

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 1.1--1.5, *1.6, 1.8--1.10

definitions

Explains the notion of logically valid argument. This is the central notion for this course.

Reading: §2.1

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 2.3, 2.4

definitions zoxiy ex-create

Explains the notion of a counterexample. Discusses a counterexample to a simple argument. Demonstrates using zoxiy to construct a counterexample involving shape and size properties.

Reading: §2.5

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 2.8, 2.10, 2.12, 2.21

Alternative textbook exercises (fast): 2.8, 2.10, 2.12, 2.21

definitions zoxiy ex-create

Introduces the notion of identity used in studying first-order logic. Includes example argument and the two principles. Also demonstrates how to assign names in zoxiy, and using zoxiy to make identity statements true and false.

Reading: §2.2

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 2.5, 2.6

definitions

Explains what sentence letters are and why we use them.

definitions

Introduces truth tables for conjunction, disjunction and negation. Truth tables give the meanings of connectives in our formal language awFOL.

Reading: §3.1, §3.2, §3.3

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 3.1, 3.2, 3.5, 3.7

Alternative textbook exercises (fast): 3.1, 3.3, 3.5, 3.7

truth-tables

Illustrates how to construct complex truth tables with an example, not(P and Q).

translation

Illustrates how for formalise simple arguments with the 'pigs' illustration.

Reading: §3.7

truth-tables

Illustrates the use of truth tables to determine logical validity.

Reading: §4.3

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 5.1-5.4

definitions

Provides two reasons for studing logic, one abstract the other practical.

truth-tables

Illustrates how to construct complex truth tables with an example, not(P and Q).

Exercises for this topic (regular)

Exercises for this topic (fast)

truth-tables

Illustrates how to construct complex truth-tables with an example, the truth-table for (P and Q) or R. Also describes how to order the reference columns.

Reading: §3.3, §3.5

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 3.12, 3.13, 4.4-4.7, 4.12-14

Alternative textbook exercises (fast): 3.14, 3.15

truth-tables

Illustrates and defines the terms 'tautology' and 'contradiction' with some quotes from George Bush.

Exercises for this topic (regular)

Exercises for this topic (fast)

truth-tables

Continues exploring the use of truth-tables to establish whether sentences are contradictions or logical truths, and to demonstrate logical validity. Notes that logical validity is not what you think it is.

Reading: §4.1, §4.2, §5.4

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 4.1, 4.2

Alternative textbook exercises (fast): 4.1, 4.2, 4.12--4.16

proof

Marks the transition from truth-tables, in which the notion of truth plays a central role, to fitch proofs which are purely formal entities.

proof

Marks the transition from truth-tables, in which the notion of truth plays a central role, to fitch proofs which are purely formal entities.

translation

Illustrates how to translate an argument from English into our formal language awFOL.

Reading: §3.2

proof zoxiy ex-proof

Introduces and illustrates the use of rules of proof for conjunction. Explains how to create proofs using logic-ex.

Reading: §5.1, §6.1

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 6.1

Alternative textbook exercises (fast): 5.3--5.6

proof

Contrasts two rules of proof and explores how their differences are related to truth-tables.

Reading: §6.1

Exercises for this topic (regular)

Exercises for this topic (fast)

definitions

Describes how to write proofs.

proof

Introduces and illustrates the rules of proof for identity, =Intro and =Elim.

Reading: §2.2

Exercises for this topic (regular)

Exercises for this topic (fast)

definition

Is the definition of logical validity flawed?

Reading: §2.1

Exercises for this topic (regular)

Exercises for this topic (fast)

proof

Quick introduction to two connectives, ¬ and ⊥, together with illustration of rules of proof for ⊥.

Reading: §6.3

Exercises for this topic (regular)

Exercises for this topic (fast)

proof syntax

Distinguishes lexical from structural ambiguity. Asks how we can know there is no structural ambiguity in our formal language awFOL.

Reading: §3.5

Alternative textbook exercises (regular): 3.20, 3.21, 3.22

truth-tables

Illustrates how to construct complex truth tables for (A ∧ B) ∨ C and A ∧ (B ∨ C).

truth-tables

Uses two arguments to show that (A ∧ B) ∨ C and A ∧ (B ∨ C) really are different.

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 3.14, 3.15

Alternative textbook exercises (fast): 3.14, 3.15, 7.2, 7.5, 7.6

proof

Explains that Fitch is a formal (non-sematic) system of proof by highlighting an incorrect use of =Elim.

quantification

Quantifiers are for talking about things without naming them.

Reading: §9.1, §9.2

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 9.1 odd numbers only, 9.2 even numbers only

Alternative textbook exercises (fast): 9.8–-9.10

quantification

We're going to be using quantifiers a lot. We understand them thanks to Frege and Taski. It's important to get a pair you like.

Reading: §9.1

semantics

Explains the meaning of ∃ with a simple example.

Reading: §9.4

Exercises for this topic (regular)

Exercises for this topic (fast)

proof

Explains that Fitch is a formal (non-sematic) system of proof by highlighting an incorrect use of =Elim.

Exercises for this topic (regular)

Exercises for this topic (fast)

proof

Returns to the discussion of what it is for a system of proof to be formal and explains how to do awkward proofs involving identity.

proof proof-example

Introduction to the rules of proof for →, →Intro and →Elim. This is the first time subproofs are used. Also illustrates a proof without any premises. The proof is from premises P→Q and Q→R to conclusion P→R.

Reading: §8.1, §8.2

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (fast): 8.20--8.25

proof proof-example zoxiy ex-proof

Introduction to the rules of proof for →, →Intro and →Elim. This is the first time subproofs are used. Also illustrates a proof without any premises. The proof is from premises P→Q and Q→R to conclusion P→R.

Reading: §8.1, §8.2

Exercises for this topic (regular)

Exercises for this topic (fast)

proof proof-example

Illustrates the use of ∨Elim, a rule of proof. Uses the inference from A∨B to B∨A as an example.

Reading: §5.2, §6.2

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 5.1--5.6, 6.2--6.6

proof

Introduces the rule of proof ∨Elim and links it to the truth table for ∨.

Reading: §5.2, §6.2

translation

Negating disjunctions is tricky. This contrasts ¬(A ∨ B) with ¬A ∨ ¬B.

Reading: §3.7

Exercises for this topic (regular)

Alternative textbook exercises (regular): 3.19, 5.18

semantics

Shows how to derive a truth table for → from the rules of proof for →, →Intro and →Elim.

Reading: §7.1

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 7.1--7.6, 8.1 (yes/no answers are ok)

Alternative textbook exercises (fast): 7.2, 7.5, 7.6

quantification

Explains how to express propositions like 'I met a philosopher' by using the existential quantifier together with conjunction.

Reading: §9.2, §9.3, §9.5

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 9.1 odd numbers only, 9.2 even numbers only, 9.4, 9.5, 9.8, 9.9, 9.10, 9.12

Alternative textbook exercises (fast): 9.8, 9.9, 9.10, 9.12, 9.13

quantification revision

Explains how to translate 'All squares and blue' and 'Some squares are blue' into awFOL using quantifiers.

Reading: §9.2, §9.3, §9.5

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 9.4--9.5, 9.8--9.10

semantics

Explains the meaning of ∀ with an example.

Reading: §9.4

Exercises for this topic (regular)

Exercises for this topic (fast)

quantification

Practices translating an English argument involving quantifers into awFOL.

Reading: §9.2, §9.3, §9.5

Exercises for this topic (regular)

Exercises for this topic (fast)

quantification

Illustrates giving a counterexample to an argument involving quantifiers.

Exercises for this topic (regular)

definition

Some arguments are logically valid even though the conclusion is unrelated to the premises.

Exercises for this topic (regular)

Exercises for this topic (fast)

translation

Negating sentences whose main connective is the arrow is tricky. This contrasts ¬(A → B) with A → ¬B.

Exercises for this topic (regular)

Exercises for this topic (fast)

translation

Mentions the truth-tables and rules of proof for the biconditional, ↔.

Exercises for this topic (regular)

Exercises for this topic (fast)

semantics quirk

Argues that ‘if’ must mean what ‘→’ means, and that it cannot.

Reading: §7.3

translation

Discusses how to translate 'Some persuasive arguments are not valid' and 'All quadrumanous discordians weep and wail except Gillian Deleude' into first-order logic.

Reading: §9.5, §9.6

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 9.4–-9.5, 9.8–-9.9

Alternative textbook exercises (fast): 9.12-–9.13

truth-tables

Introduces DeMorgan's Laws relating ¬, ∧ and ∨. The laws can be stated as A ∧ B ⫤⊨ ¬(¬A ∨ ¬B) and A ∨ B ⫤⊨ ¬(¬A ∧ ¬B). Also mentions that A → B ⫤⊨ ¬A ∨ B.

Reading: §3.6, §4.2

Exercises for this topic (regular)

Alternative textbook exercises (regular): 3.19, 4.15--18, 7.1--7.2, *7.3--7.6

Alternative textbook exercises (fast): 3.19, 4.31

truth-tables

Distinguishes if A, not B (A → ¬B) from the negation of if A,B (¬(A → B)).

Reading: §3.6

translation

Mentions the truth-tables and rules of proof for the biconditional, ↔.

Exercises for this topic (regular)

Exercises for this topic (fast)

translation

Covers translation of simple sentences like 'All cats are grey' using single quantifiers.

quantification revision

Reminder that the universal quanifier works with the arrow, whereas the existential quantifier works with conjunction.

translation

Stresses that ∀ works with → by examining sentences with ∀ and ∧, and ∃ with →.

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 9.10, 9.15--9.17, *9.18--9

Alternative textbook exercises (fast): 9.10

proof proof-example

Introduction to the rule of proof ¬Intro with an illustration. Discusses the proof from premise A∧B to conclusion ¬(¬A∨¬B).

Reading: §5.3, §6.3

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 6.7--6.10, *6.11--6.12

Alternative textbook exercises (fast): 6.7--6.12, 6.18--6.20, 6.24--6.27, *6.40--6.42

proof proof-example

Discusses an intermediate proof involving ¬Intro, from premises P→Q and ¬Q to conclusion ¬P.

Reading: §5.3, §6.3

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 6.24--6.26

proof

Offers what appears to be a proof of an argument that is not logically valid in order to illustrate a restriction on the use of subproofs.

Exercises for this topic (regular)

Exercises for this topic (fast)

quantification proof

Explains the rule of proof ∀Elim with an example.

Reading: §13.1

revision quantification semantics translation

Preliminary to discussion of multiple quantifiers.

Reading: §11.1

Exercises for this topic (regular)

quantification semantics

Introduces a simple sentence involving multiple quantifiers. Illustrates how to apply the procedure for determining the truth of sentences involving quantifiers to sentences containing multiple quantifiers.

Reading: §11.1

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (fast): 11.2, 11.4

quantification semantics translation

Introduces translation from English to awFOL using multiple existential quantifiers with an example.

Reading: §11.1

translation

Mentions several ways of expressing the idea that there is exactly one creator in our formal language, awFOL.

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 14.10--14.12, *14.13

Alternative textbook exercises (fast): 11.10, 11.13, 14.2

quantification proof

Explains the rule of proof ∃Intro.

Reading: §13.2

Exercises for this topic (regular)

Exercises for this topic (fast)

proof

Introduces the rule of proof ∃Elim with an example. The example proof is from premise ∃x( Blue(x) ∧ Square(x) ) to conclusion ∃x Blue(x).

Reading: §12.2, §13.2

Exercises for this topic (regular)

Exercises for this topic (fast)

translation

Discusses how to translate 'Some persuasive arguments are not valid' and 'All quadrumanous discordians weep and wail except Gillian Deleude' into first-order logic.

Reading: §9.5, §9.6

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 9.4–-9.5, 9.8–-9.9

Alternative textbook exercises (fast): 9.12-–9.13

semantics

Explores differences between ∃x(Square(x) ∧ Blue(x)), some squares are blue, and ∃x Square(x) ∧ ∃x Blue(x), something is square and something is blue.

Reading: §9.5, §9.6

Exercises for this topic (regular)

Exercises for this topic (fast)

proof proof-example

Introduces the rule of proof ∀Intro with an example. The example proof is from premise ∀x(Square(x) → Blue(x)) to conclusion ∀x Square(x) → ∀x Blue(x).

Reading: §12.1, §12.3, §13.1

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 12.4--12.5, *12.6--12.7, 12.9--12.10

proof

Quick recap of the four main quantifier rules.

Reading: §13.1, §13.2

Alternative textbook exercises (fast): 10.20, *10.24--10.7, 10.28--10.29, 13.2--13.3, 13.8--13.9, 13.11, 13.13, 13.15

quantification semantics

Explains how to translate sentences involving number into awFOL using quantifiers and identity.

Reading: §14.1

proof

Explains that in doing a proof, it is not allowed to cite lines from a closed subproof, thereby answering a question asked earlier.

proof proof-example

Introduces the rule of proof ∀Intro with an example. The example proof is from premise ∀x(Square(x) → Blue(x)) to conclusion ∀x Square(x) → ∀x Blue(x).

Reading: §12.1, §12.3, §13.1

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 12.4--12.5, *12.6--12.7, 12.9--12.10

quantification semantics translation

Explains how to translate English sentences involving a combination of universal and existential quantifiers into awFOL with an example.

Reading: §11.2, §11.3

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 11.3, 11.4, 11.8, 11.9, 11.11, 11.13, *11.10

Alternative textbook exercises (fast): 11.8, 11.9, *11.11

translation syntax

Explains the role of variables in the formal language awFOL. Stresses that translations into English should not mention variables (e.g. 'there is an x such that ...' does *not* count as English for the purposes of this course).

Exercises for this topic (regular)

Exercises for this topic (fast)

quantifiers translation

Discusses translating English sentences about loving and being loved in order to illuminate the difference between ∃y∀x Loves(x,y) and ∃y∀x Loves(y,x).

Reading: §11.2, §11.3

Exercises for this topic (regular)

Exercises for this topic (fast)

translation quantification

Continues discussion of how to translate sentences involving quantifiers and negation from English into our formal language awFOL? Discusses translating 'Some person is not dead' and 'No person is dead'; also 'Every person is not dead' and 'Not every person is dead'.

Exercises for this topic (regular)

translation quantifiers semantics

Introduces the logical equivalence that allows us to turn ∀ into ∃, and conversely. Explains how to prove informally that the equivalence holds using the truth-conditions for quantified statements.

Reading: §10.1, §10.3, §10.4

Exercises for this topic (regular)

Exercises for this topic (fast)

quantification translation

Extremely brief introduction to definite descriptions. Hints at how sentences such as 'The winner is hungry' might be translated into awFOL.

Reading: §14.3

Exercises for this topic (regular)

Exercises for this topic (fast)

Alternative textbook exercises (regular): 14.26, 14.28

Alternative textbook exercises (fast): 14.2, 14.4, 14.5, 14.10, 14.11, 14.26, 14.28