GoKawiilToday, I’d like to talk about logic — and before I do, I should probably explain why. But before we get to that, a definition may be in order: in a nutshell, logic is a system for drawing conclusions from premises (“facts”).
Formal logic usually isn’t taught in high school; as far as I know, a rigorous treatment of it isn’t even a requirement for most computer science degrees. The concept is familiar to most mathematicians and to a handful of software engineers who dabble in esoteric programming languages. As for everyone else, we might know about “digital logic”, a simple algebra of binary numbers that involves operators such as AND, NOT, and OR. What’s less clear is how we get from zeroes and ones to some semblance of human reasoning.
A mathematician’s lament
For mathematicians, the most common role of formal logic is to provide a more precise vocabulary for proofs. To illustrate some of the ambiguities of everyday speech, consider the following statement in the form of “if A then B”:
\(\text{“If }\underbrace{\text{you finish house chores}\vphantom{|}}_{A}\text{, }\underbrace{\text{you can play Minecraft}\vphantom{|}}_{B}\text{.”}\)
It’s something a parent could say to a child. In that use, the phrasing clearly implies its own inverse, “if not A then not B”:
\(\text{✅ "If you }\textbf{don't}\text{ finish chores, you }\textbf{can't}\text{ play Minecraft."}\)
The statement may imply its converse (“if B then A”) and the contraposition (“if not B then not A”), but only if we take substantial liberties with the phrasing. If we simply shuffle A and B around, we break the implied temporal relationship between the propositions and end up with mild gibberish:
\(\text{❓ "If you can play Minecraft, you finish chores."}\)
\(\text{❓ "If you }\textbf{can't}\text{ play Minecraft, you }\textbf{don't}\text{ finish chores."}\)
... continue reading