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→The allegedly counterintuitive dichotomy law: add explanation
: <math>ab \lor a = a</math>
: <math>ab \lor a = a</math>
===The allegedly counterintuitive dichotomy law===
===Reports of my counter-intuitiveness are are greatly exaggerated===
We have the following theorem of classical propositional calculus:
: <math>(p \Rightarrow q) \lor (q \Rightarrow p)</math>
: <math>(p \Rightarrow q) \lor (q \Rightarrow p)</math>
The proposition may appear counter-intuitive on some ways of reading it, and it is usually excluded from intuitionist propositional calculi.
Read as a statement about the values of propositions — that is, values <math>p, q \in \mathbb{B} = \{0, 1 \}</math> — and written as an order law, its sense may become more sensible:
: <math>(p \le q) \lor (q \le p)</math>
: <math>(p \le q) \lor (q \le p)</math>