12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Saturday May 04, 2024
Jump to navigationJump to search→Reports of my counter-intuitiveness are greatly exaggerated: another guess?
My guess as to what's going on here — why the classical and intuitional reasoners appear to be talking past each other on this score — is that they are really talking about two different domains of mathematical objects. That is, the variables <math>p, q\!</math> range over <math>\mathbb{B}</math> in the classical reading while they range over a space of propositions, say, <math>X \to \mathbb{B}</math> in the intuitional reading of the formulas. Just my initial guess.
My guess as to what's going on here — why the classical and intuitional reasoners appear to be talking past each other on this score — is that they are really talking about two different domains of mathematical objects. That is, the variables <math>p, q\!</math> range over <math>\mathbb{B}</math> in the classical reading while they range over a space of propositions, say, <math>X \to \mathbb{B}</math> in the intuitional reading of the formulas. Just my initial guess.
On the reading <math>p, q : X \to \mathbb{B},</math> another guess at what's going on here might be the difference between the following two statements:
<blockquote>
<math>(\forall x \in X)(p \Rightarrow q) \lor (q \Rightarrow p)</math>
</blockquote>
<blockquote>
<math>(\forall x \in X)(p \Rightarrow q) \lor (\forall x \in X)(q \Rightarrow p)</math>
</blockquote>
Or maybe these are really the same guess?
