Gödel's Incompleteness Theorems: An Informal Introduction to Formal Logic

My entry into SoME2. Also, my first ever video. I hope you enjoy.

The Book List:

Logic by Paul Tomassi
A very good first textbook. Quite slow at first and its treatment of first-order logic leaves a little to be desired in my opinion, but very good on context, i.e. why formal logic is important/how it benefits us to learn it.

Deduction: Introductory Symbolic Logic by Daniel Bonevac
Oops - I slipped up and allowed a book of philosophical logic to sneak into my recommendations. Regardless, this is a good treatment of different deductive systems, something which I could certainly have explored further in the video.

The Logic Manual by Volker Halbach
Despite being many students' least favorite textbook, this was my gateway drug into the world of formal logic; I remember reading it in the back of my parents' car and literally laughing out loud with joy. But perhaps I'm just a freak of nature. At any rate, the fact that this is the recommended introductory logic textbook for first-year students at the University of Oxford should be a testament to its quality.

Intermediate Logic by David Bostock
For those who welcome The Logic Manual, but call on it to go further. This book makes the curious decision of tackling semantics first, before switching gears halfway through and devoting the rest of its pages to proof theory. Not a first textbook for the subject, but an excellent second or third.

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(JJJreact)

0:00 - The Knight and the Blacksmith
3:34 - Part 0: Introduction
6:22 - Part 0.5: What is Pure Maths Good For?
9:58 - Part 1: Axiomatic Systems
14:42 - Part 2: Formal Logic
17:08 - Part 2.1: Propositional Logic
29:24 - Part 2.2: Predicate Logic
37:40 - Part 3: Syntax and Semantics
46:02 - Part 4: Soundness and Completeness
49:03 - Part 4+i: Paradoxes
54:43 - Part 5: What Happens When You Give Numbers Numbers?
58:23 - Ranking the Peano Axioms
1:08:06 - Gödel Numberings
1:11:12 - Part 5.1: Gödel's First Insight
1:16:18 - Part 5.2: Gödel's Second Insight
1:20:00 - Part 5.3: Breaking the 5.3th Wall
1:21:34 - Part 6: The Theorems
1:22:53 - Part 6.1: The First Incompleteness Theorem
1:27:24 - Part 6.2: The Second Incompleteness Theorem
1:29:51 - Part 7: Living in a Post-Gödel World (Conclusion)