Smullyan's Drinking Principle/Paradoxical Aspects

Paradoxical Aspects to Smullyan's Drinking Principle

Smullyan's Drinking Principle is often considered to be a counter-intuitive result.

Hence it is often classified as a veridical paradox.

However, it can be resolved by analyzing the possible scenarios.

The semi-formal proof attempts to do just that.

Thus, a careful analysis of the possible scenarios, as well as certain Paradoxes of Material Implication, show this to be a veridical paradox.

Note that this is a theorem for arbitrary non-empty universes of discourse and arbitrary propositional functions $\map D x$.

So this theorem is valid for all interpretations of $\map D x$.

For example:

let the universe of discourse be the objects in Philadelphia

let $\map D x$ mean:

$x$ is a dog

Then there exists something in Philadelphia such that, if it is a dog, then everything in Philadelphia is a dog.

Source of Name

This entry was named for Raymond Merrill Smullyan.