MyWikiBiz, Author Your Legacy — Tuesday November 26, 2024
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, 16:12, 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: | + | 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: |
| | | |
| <blockquote> | | <blockquote> |
− | <math>(\forall x \in X)(p \Rightarrow q) \lor (q \Rightarrow p)</math> | + | <math>(\forall x \in X)(Px \Rightarrow Qx) \lor (Qx \Rightarrow Px)</math> |
| </blockquote> | | </blockquote> |
| | | |
| <blockquote> | | <blockquote> |
− | <math>(\forall x \in X)(p \Rightarrow q) \lor (\forall x \in X)(q \Rightarrow p)</math> | + | <math>(\forall x \in X)(Px \Rightarrow Qx) \lor (\forall x \in X)(Qx \Rightarrow Px)</math> |
| </blockquote> | | </blockquote> |
| | | |
| Or maybe these are really the same guess? | | Or maybe these are really the same guess? |