Universal generalization is a rule of inference for predicate logic. It states that if we can derive a formula with free variables then me may infer a formula in which those variables are bound with a universal quantifier, or symbolically:

\frac{\phi (x)}{\therefore \forall x \phi }

where \phi is a metavariable representing a wff and x is a term representing all occurances of x in \phi.


The term that is going to be universally quantified must be a variable, not a constant. In other words, it must not evaulate to some object in the Universe of discourse. The reason this necessary is because if this restriction does not exist, then saying that all objects in the universe have a certian property because at least one object in the universe has a certian propery would be valid, or symbolically:

Line: Formula: Reason:
1 P(a) Hypothesis
2 \forall x P(x) Faulty Universal Generalization

Clearly this is absurd.

See alsoEdit

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