Aim: The plan is to introduce you to classical logic. Our approach will be somewhat more mathematical than that of usual undergrad intro to logic courses. The reason for doing so is that we can then also prove stuff about systems of logic. You will then have suitable background to explore a whole range of areas in logic, and in philosophy generally.
Meeting information: Saturday, 1:30pm–3pm on Zoom
Basic Material: Course Notes and Open Logic Project's Complete PDF
I am thankful to Dr. Norbert Gratzl and Bendix Kemman for allowing me to use these course notes.
13.06.20 - Introduction and foundations
We talked about what logic is and defined some basic notions such as validity. We then introduced the connectives for propositional logic, as well as their truth tables. Lastly, we looked at translation of English sentences into formulas of propositional logic.
Reading: Teller (p.1-7)
Class 1 Notes (JPG) (Apple Notes)
Additional material:
Hurley 6.1 (More on connectives. Note that for some connectives they use symbols different from ours.) Shorter handout on this: 6.1 Handout
Truth tables (we use different symbols for negation and conjunction)
Exercises on translation are given on the second page of the above handout (Solutions)
As an exercise, you can make truth tables for the formulas you obtained from the above translations. You can use the following link to make the truth tables, and it will check each of your steps: https://www.cs.utexas.edu/~learnlogic/truthtables/
20.06.20 - Basic notions in Propositional Logic
After a quick recap, we used truth tables in order to determine whether a particular formula is contingent, tautologous, or self-contradictory. Similarly for multiple statements, we defined what it means for a group of statements to be consistent/satisfiable or inconsistent. We then saw how truth tables can be used to determine validity. At the end of the meeting we started to formally define the language of propositional logic.
Reading: pages 3-12 of course notes.
Class 2 Notes (JPG) (Apple Notes)
Handout on counterexamples (JPG) (Apple Notes)
27.06.20 - Semantics of Propositional Logic
We formally defined the language of propositional logic, and thereby formalised the ideas captured by truth tables. This allowed us to prove things that hold for all formulas in the language. Lastly, we introduced the notion of semantic consequence.
Reading: pages 10-22 of course notes, chapter 7 of Complete PDF (OLP).
Class 3 Notes (JPG) (Apple Notes)
Exercises are given on page 23 of course notes.
04.07.20 - Review session / Introducing Natural Deduction
This was primarily a review session, and we went over all the previous course notes (except for the proofs done at the end of the previous session; we will return to those later). At the end, the difference between syntactic and semantic approaches to logic was briefly considered, and the rules for natural deduction were introduced.
Class 4 Notes (JPG) (Apple Notes)
Example done during class (JPG) (Apple Notes)
18.07.20 - Natural Deduction
We talked about what a proof system is intended to do, and then saw a number of natural deduction derivations.
Reading: Ch8 (sections 8.1 and 8.3) and Ch10 (sections 10.1-10.4) of Complete PDF (OLP)
Class 5 Notes (JPG) (Apple Notes)