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So in classical logic either p is T or p is F. But is it same in doxastic logic, ie, is B(p) V B(~p) an instance of LEM?

And the second issue, is it equivalent to B(p) V ~B(p)?

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  • In general, not-something(p) is not the same as something(not-p). Apr 12 at 17:22
  • think of the empty acessibility relation
    – ac15
    Apr 12 at 17:57
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    B(p) v ¬B(p) is an ordinary example of LEM. B(p) v B(¬p) means something different and is implausible, since it rules out being indifferent to some proposition p and neither believing it nor disbelieving it.
    – Bumble
    Apr 12 at 20:45
  • <<So in classical logic either p is T or p is F.>> No, in classical logic either P is given or ~P is given. Every proposition is true or false by definition, just classically we postulate that we unconditionally have access to which it is. Apr 12 at 21:40
  • @JulioDiEgidio I don’t understand what you mean. What is wrong with the OP’s statement? Apr 13 at 4:50

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