MyWikiBiz, Author Your Legacy — Tuesday November 26, 2024
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, 16:04, 7 December 2008
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| 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. |
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| + | 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? |