BlizzArt

Seriously, ask yourself that question, "what are you not thinking of at this moment?"

If you know the answer, you don't have to read on. Actually you'll never need to read anything anymore. You are all done. But for the fast majority of us, the question shows the limitations of out accustomed 'dual thinking & experiencing'. That takes us quite a stretch, but we are not prepared for questions like this one. The dual creates the 'is' and the 'is not', the negation. But we cannot handle it well, we cannot NOT make a picture of something, or NOT think about something specific. The moment we're being asked what we're not thinking of, we are forded to think of it. A nice paradox, it seems.

Paradoxes as keys

But paradoxes can help us, help us to pry open hidden heights. Paradoxes can reveal a cranny through which we might hope to escape our dual thinking. I am fascinated by paradoxes and some are not to hard to conquer within our referential framework, but always on a higher logical level than the paradox itself.

Arguably the most famous paradox, the 'Liars Paradox' of Epimenides, a wise man of Crete from bygone times. He said "All men from Crete are liars." He was saying that all people of Crete were lying all the time. He himself included. This sentence of Epimenides can be transformed, without loosing any of its meaning or paradoxicality into "This sentence is false."

Play with it for a minute. You got stuck, like everyone? The sentence is true if it is false and false if it is true. This goes on forever. At least on this level.

The mother of your mother is not your mother

If you take the sentence "This sentence is false" as true, then the sentence says it's false. If you take it to be false, then it says it's true. We can continue until politicians do what they promise. Any idea what is happening and where the crux of the matter lies ?

This sentence talks about itself. You'll need to step up a level to get untangled. You cannot solve it on the same level as the paradox itself. Ask yourself what exactly is happening. Here a statement (the sentence itself) is being compared with a statement about a statement. The sentence (statement) compares itself to a statement about this same sentence about itself (statement about the statement).  That's right, the mother of your mother still is not your mother. This is an error in the use of logical levels. It is a construction that is faulty in its construction, but it is not obvious to the eye.

Why would this have any relevance in the world, you could ask. For me, it sharpens my understanding, forces me to different thinking and challenges me in a number of other ways as well. There are many interesting paradoxes, based on different errors. The famous Russell paradox, which caused set theory to be revised, is of the same logical order as the Liars Paradox. A maybe easier example of the same order as the Russell paradox, is the Russell Barber paradox :

Every man in town is clean-shaven. Each man does this one and only one way — either by shaving himself, or by going to the barber. Who shaves the barber?