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MyWikiBiz, Author Your Legacy — Friday April 04, 2025
Jump to navigationJump to search→The allegedly counterintuitive dichotomy law: add explanation
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It is usually written in this form:+Written as an order law, its sense is more sensible:+
+
: <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>
