### Single Idea 8709

#### [catalogued under 5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle]

Full Idea

The law of excluded middle is purely syntactic: it says for any well-formed formula A, either A or not-A. It is not a semantic law; it does not say that either A is true or A is false. The semantic version (true or false) is the law of bivalence.

Gist of Idea

The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2)

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.108

A Reaction

No wonder these two are confusing, sufficiently so for a lot of professional philosophers to blur the distinction. Presumably the 'or' is exclusive. So A-and-not-A is a contradiction; but how do you explain a contradiction without mentioning truth?

Related Ideas

Idea 9024
Excluded middle has three different definitions **[Quine]**

Idea 17924
Excluded middle says P or not-P; bivalence says P is either true or false **[Colyvan]**