The famous liar's paradox hinges on the word "false."

This sentence is false.

Now consider the famous example of a glass that can be perceived as either half full or half empty. Does that qualify as a paradox, or is it just a simple play on words?

  • Why is it a paradox? An object can be half green, half red, for example. Both. Same with glass: it can be half empty and half full at the same time and actually not only can, one implies another, thus being yet different from colored object. But you may consider that a glass is not really empty.
    – rus9384
    Aug 27 '18 at 1:11
  • Good point. I'm anxious to learn if there are other interpretations, or if that's the correct answer right there. Aug 27 '18 at 1:13
  • I guess that also boils down to the language. Human language is a thing where there is no truth: you cannot say the word actually has any meaning in itself, therefore there are no real truths related to symbols and words themselves. Only interactions between words really matter.
    – rus9384
    Aug 27 '18 at 1:15
  • I wonder if the following wording has some bearing on the answer: half empty OR half full vs half empty AND half full. Aug 27 '18 at 1:27
  • Given that a glass which is both half empty and half full still may be perceived only as half empty or half full, I think it's correct.
    – rus9384
    Aug 27 '18 at 1:35

A paradox is self-contradictory. It proves that itself cannot be true. The glass half full/glass half empty arguments are merely contradictory viewpoints. Each viewpoint is trivially self-consistent.

One could try to argue that there's a paradox in claiming the glass is simultaneously half empty and half full, and trying to argue that that is a self-contradiction there. However, it is mathematically completely sound, so there's no mathematical way to argue that a paradox can form.

So if we have to contort the original meaning of the phrase and leave behind the well accepted rules of mathematics, at some point we're really inventing a new phrase all together. We'd probably want to start from the question of "what should the paradox teach," and come up with a new phrasing.

A joke I remember from my Boy Scout days:

An optimist says the glass is half full.

A pessimist says the glass is half empty

A realist knows that if they sit around arguing long enough, eventually they're going to have to wash the glass.

Obligatory XKCD.

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