Some Paradoxes
I read over some of my philosophy notes from last summer, and they seemed interesting again. I was especially focusing on paradoxes.
This statement is false.
Ok, if this statement is in fact false, then the statement that this statement is false must be true.
Fine then, let’s pretend that the statement is actually true. If we assume the statement to be true, then it must be true that it is false.
The problem with relativism
There are no real truths in life. Everything is simply relative.
My teacher hated relativism with a passion. The theory of relativism is self-contradictory. If there are no real consistencies, then why does relativism itself deserve to be consistent?
Grelling’s Paradox
A word is considered autological if it describes itself. For example, polysyllabic is a polysyllabic word and is therefore autological.
All other words (those that do not describe themselves) are considered heterological.
What about the word heterological itself?
If we treat heterological as an autological word, then it should describe itself. Thus, heterological is heterological if we try to treat it as autological.
If we treat it as a heterological word, then it must not describe itself. Thus, the word heterological can’t be heterological if we were to count it as heterological.
Russell’s paradox
M is defined as the set of all sets that do not contain themselves as members.
In other words, in order for A to be a member of M if and only if it is not a member of A
M cannot be a properly defined set. If M contains itself, then it cannot be a member of M. If it does not contain itself, then it has to be a member of M. M cannot both be and not be a member of M.
Strongest Shield and Sword Paradox
A seemingly omnipotent weapon and armour maker claims that he can make the best shields and swords possible.
His shield is the strongest on earth. Nothing can penetrate it
The sword is the strongest on earth. There is nothing that it cannot penetrate.
What would happen if we tried to stick his sword through his shield?
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