Logic
Logic is about validity, not truth. An argument can be perfectly valid and entirely false. The distinction matters.
Logic is about validity, not truth. This distinction is easy to miss and worth sitting with.
An argument is valid if the conclusion follows necessarily from the premises. It may still be false — if the premises are false. Logic tells you whether the structure of an argument is sound; it does not tell you whether the premises are correct. That is the job of empirical investigation. The two are complementary, not the same.
Consider the classic demonstration:
Premise 1: Socrates is a man.
Premise 2: All men are mortal.
Conclusion: Socrates is mortal.
The structure works regardless of the content. Swap in a catfish and the argument remains valid. Swap in nonsense syllables:
Premise 1: A flibber-jabber is a wigwom.
Premise 2: All wigwoms are burderkerder.
Conclusion: A flibber-jabber is burderkerder.
Still valid. The conclusion follows from the premises. Logic cannot tell you whether any of these claims are true — only whether, if they were, the conclusion would hold.
Deductive and inductive reasoning
Deductive logic is the form used in mathematics. Its conclusions are guaranteed if the premises are true. Nothing about the world can invalidate a valid deductive argument; it can only challenge a premise.
Inductive logic extends beyond the data given. When we predict that the sun will rise tomorrow, or that sugar will continue to taste sweet, we are reasoning inductively — drawing a general conclusion from observed instances. Inductive conclusions are not guaranteed; they are supported, to varying degrees, by the evidence. This makes inductive reasoning the form most relevant to science and everyday life.
The laws of logic
The law of non-contradiction: two incompatible claims cannot both be true simultaneously. An unstoppable force and an immovable object cannot coexist. Either one can exist, or neither, but not both.
The law of the excluded middle: any claim is either true or false. There is no half-true, no sort-of-true. This makes for uncomfortable conversation in a culture that often prefers “you both raise good points.” But on any well-formed question, someone is wrong.
Applying this to the claim “vaccines cause autism”: the law of the excluded middle tells us this claim is either true or false. Before logic can adjudicate, though, precision is required. What does “cause” mean? If causing autism means occasionally being statistically associated with slightly elevated rates in some subgroup under some conditions — that is a different claim from “vaccines reliably produce autism in children who receive them.” The first might be defensible in some narrow form; the second is not.
This is one of logic’s more demanding requirements: terms must be defined precisely before logical analysis is applied. Imprecise language allows contradictions to hide in plain sight. It also allows people to slide between meanings mid-argument — asserting a strong claim when evidence is absent, retreating to a weak one when challenged, then treating confirmation of the weak version as vindication of the strong.
The basic connectives
The building blocks of logical expressions are three connectives: and (∧), or (∨), not (¬). These combine premises into compound statements whose truth can be evaluated systematically.
- P ∧ Q is true only if both P and Q are true.
- P ∨ Q is true if either P or Q (or both) are true.
- ¬P is true when P is false, and vice versa.
From these three, every other logical relationship can be constructed. The complexity of formal logic is built from these simple operations.
Logic cannot find truth on its own. But reasoning toward truth without it produces conclusions that are immune to challenge — which is worse than being wrong. A valid argument can be corrected by attacking the premises. An invalid argument can be asserted indefinitely because it has no real structure to examine.
That is why logic matters: not as an end, but as the discipline that keeps arguments honest.