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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 intuitional 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 intuitional reading of the formulas.  Just my initial guess.
 
My guess as to what's going on here &mdash; why the classical and intuitional 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 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:
+
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?
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