Philosophy as it is understood today simply means “thinking about…” or “reasoning about…” For example “philosophy of mathematics”=“reasoning about mathematic”. “Philosophy of religion”=“Reasoning about religion”. Isn’t that what we are all doing in this forum? It is such reasoning that GIVES us spiritual clarity.
I have always found it almost unbelievable that so many people can hold to a self-contradictory concept and justify it in their own minds by relegating it to the realm of the “mysterious” or “paradoxical”.
The basic meaning of paradox is “a self-contractory statement”. When one fully understands the situation the paradoxical statement must be denied. That which is truly self-contradictory can never be explained. For example “This book cover is both black and not black” is self-contractory and therefore false. However, “I am both hungry and not hungry” may appear self-contradictory but may really mean, “I want to eat some things but not others.”
-
A simple example of a paradox is the Sentence paradox: “This sentence is false.” For if the sentence is true, then it is false. If it is false, then it is true. If “logical statement” refers to a sentence which is either true or false, the sentence is not a logical statement at all. For it is neither true nor false. When one understands that, the sentence loses its “mystery” as a supposed statement.
-
Let’s consider the Barber’s Paradox. In a particular town a barber shaves all men and only those men who do not shave themselves. Does the barber shave himself? If the answer is “yes” then he must not shave himself. For he shaves ONLY those men who do not shave themselves. So the answer must be “no”. But in that case, he must shave himself. For he shaves ALL men who do not shave themselves. So what do we do with this paradox? Do we have to say we “cannot understand it with the rational mind”? Do we classify this paradox a deep mystery along with the mystery of the Trinity? No. We need to realize that such a barber cannot exist.
-
It was once thought that any set at all could be represented mathematically. For example, the set of positive intergers is represented as {1,2,3,…}. Even the set of pink elephants now in this room can be represented as { }. In other words the empty set. But then Bertrand Russell came up with a description of a set which could not be represented: “The set of all sets and only those sets which are not members of themselves.” Let’s assign S as the name of that set.Then we ask “Is S a member of itself?” If the answer is “yes”, then S is NOT a member of itself. For S is the set of only those sets which are NOT members of themselves. If the answer is “no” then S is a member of itself. For S is the set of all sets which are NOT members of themselves. How could such a set be represented mathematically? The answer is that such a set cannot exist, and for that reason cannot be represented mathematically.
So we found:
- In the Sentence Paradox, no such logical statement exists.
- In the Barber Paradox, no such barber exists.
- In Russel’s Paradox, no such set exists.
And in my opinion:
4. In the Trinitarian paradox, no such entity exists.
Now of course, one can be in such a psychological condition that he wants to affirm these paradoxes.
- In the Sentence Paradox, the sentence actually IS a logical statement. It is true and yet it is false. A great mystery!
- In the Barber Paradox, there CAN be such a barber. Somehow it is true that he both shaves himself and does not shave himself. A great mystery!
- In Russel’s Paradox, there IS such a set. It is a member of itself and yet it isn’t a member of itself. A great mystery!
- In the Trinitarian paradox, there IS such an entity as the Trinity. He is one, and yet He is three. A great mystery!