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MyWikiBiz, Author Your Legacy — Thursday November 14, 2024
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My guess as to what's going on here &mdash; why the classical and intuitionistic reasoners appear to be talking past each other on this score &mdash; 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 intuitionistic reading of the formulas.  Just my initial guess.
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My guess as to what's going on here &mdash; why the classical and intuitionistic reasoners appear to be talking past each other on this score &mdash; 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>p, q : X \to \mathbb{B}</math> in the intuitionistic reading of the formulas.  Just my initial guess.
    
On the reading <math>P, Q : X \to \mathbb{B},</math> another guess at what's gone awry here might be the difference between the following two statements:
 
On the reading <math>P, Q : X \to \mathbb{B},</math> another guess at what's gone awry here might be the difference between the following two statements:
12,080

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