Philosophy
Inferentialism and the Meaning of Logical Constants
Quick fact
Inferentialism turns the usual order on its head: instead of defining 'and' by a truth table, it defines 'and' by the simple rules that let you infer 'A and B' from A and B, and infer A from 'A and B'.
Why this is interesting
You’ve used words like 'and' and 'or' thousands of times—but have you ever wondered what makes them mean what they do? Is it the truth tables, or could it be something else?
Read the full explanation
Understanding Inferentialism and the Meaning of Logical Constants
When you hear the word 'and', you probably don’t think about logic—you just use it. But philosophers and logicians have long debated where the meaning of such words comes from. The standard answer is 'truth conditions': 'and' means what it means because of the truth table that says 'A and B' is true exactly when both A and B are true. Inferentialism offers a refreshingly different answer: the meaning of 'and' is given entirely by the rules that tell you how to use it in arguments. For example, from two statements 'It’s sunny' and 'It’s warm', you can infer 'It’s sunny and warm'. And from that conjunction, you can infer each part. These introduction and elimination rules are like the 'definition' of 'and'. In the same way, 'or' is defined by the fact that from 'A' you can infer 'A or B', and from 'A or B' plus 'If A then C' and 'If B then C' you can infer 'C'. So, under inferentialism, the meaning of a logical constant is not something 'out there'—it’s the role it plays in our reasoning.
A deeper explanation
The mechanism behind inferentialism is that logical constants are implicitly defined by inference rules. For each connective, we have introduction rules (how to bring it into a proof) and elimination rules (how to use it once it’s there). These rules are meant to be 'harmonious': the introduction rules should not be too strong or too weak relative to the elimination rules. When they are harmonious, the connective is well-behaved and the system avoids paradoxes (like tonk, a connective whose rules allow you to prove anything). Inferentialism provides a foundation for proof-theoretic semantics, where the meaning of a logical expression is its derivation conditions. This approach naturally accommodates intuitionistic logic, which rejects the law of excluded middle because it lacks an introduction rule for it. The significance of inferentialism goes beyond logic: it bolsters a broader 'meaning as use' view in philosophy of language, and it challenges the idea that meaning must be about correspondence to an external truth.