Mathematical Logic Explained
Logic is the study of what follows from what.
Given some premises, what can you legitimately conclude? Logic doesn't tell you whether your premises are true — that's the job of observation, experiment, or other domains. Logic tells you what's guaranteed to follow if your premises are true.
This is the machinery underneath all rigorous thought.
Every mathematical proof. Every legal argument. Every debugging session. Every time you say "if this, then that" — you're doing logic.
What You'll Learn
This series builds formal logic from the ground up:
Foundations:
- What logic is and why it matters
- Propositions and truth values
- Logical connectives (and, or, not, if-then)
Propositional Logic:
- Truth tables
- Logical equivalence
- Valid argument forms
- Proof techniques
Predicate Logic:
- Quantifiers (for all, there exists)
- Variables and predicates
- Translating English to symbols
Meta-Logic:
- Soundness and completeness
- The limits of formal systems
- How logic connects to mathematics
The Series
Why Logic Matters
Logic is the immune system of thought.
Bad arguments feel persuasive. Fallacies are common. Wishful thinking is natural. Logic provides tools to distinguish valid reasoning from sophisticated nonsense.
Logic makes invisible structure visible. When someone says "All politicians lie, and John is a politician, so John lies" — logic shows you the skeletal structure: All A are B, x is an A, therefore x is B. That structure is valid regardless of whether the premises are true.
Logic won't tell you what to believe. It tells you what you're committed to believing if you accept certain premises.
Prerequisites
This series assumes:
- Basic comfort with mathematical notation
- Willingness to think abstractly
No prior logic experience required. We'll build everything from scratch.
This is the hub page for the Logic series.
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