#logic #prooftheory #modeltheory #goedel Access exclusive content on Patreon: All the way at the foundations of mathematics, you will find the language of logic. We look at its syntax and semantics, uncovering two completely different approaches to proving things. One approach is called proof theory. The other approach uses mappings (models) and is called model theory. Then we ask: can we link these two approaches to each other? The soundness and completeness of our logic system provide the answer. 0:00 Introduction 0:47 The syntax of logic 1:34 Axioms and inference rules 3:41 Introduction and elimination 5:59 The semantics of logic 7:51 Semantic inference using truth tables 10:05 Soundness and completeness This video is published under a CC Attribution license ( )