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Booodaness committed May 22, 2024
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Expand Up @@ -41,7 +41,7 @@ We see that Plato's argument rests on the dialectics of ideas such as the acquir

Plato rules out the first two possibilities by arguing that Meno's slave cannot have possessed or acquired knowledge of geometry in this life. The third possibility suggests possession of knowledge from an indefinitely distant point in the past, and before this life, which he rules out in premise (6). Therefore, we are only left with the last possibility.

This is where a logician would say, "Hold up Plato! You've just used an extended form of the principle of excluded middle!". In its simple form, the principle constrains how we think of possibilities and actualization: if we have potentially A or B and A cannot be actualized, then B must be actualized (as long as one of them must be). This is to avoid contradiction, as per the principle of contradiction, which together with the principle of identity (to the effect that every object is identical with itself). A fun fact is that at least the first two principles can be traced back to Plato himself, and were extended into the framework of Aristotelian logic.
This is where a logician would say, "Hold up Plato! You've just used an extended form of the *principle of excluded middle*!". In its simple form, the principle constrains how we think of possibilities and actualization: if we have potentially A or B and A cannot be actualized, then B must be actualized (as long as one of them must be). This is to avoid contradiction, as per the *principle of contradiction*, which together with the *principle of identity* (to the effect that every object is identical with itself) forms the three *principles of thought*. A fun fact is that principles for rational discourse itself can be traced back to Plato, and were extended into the framework of Aristotelian logic.

# The Question of Transitory Worlds

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