Paradox 3.2

Meta-time 3.2

Paradox is due to the mixing of para-level (meta-level) and original level. For example, consider this sentence:

“This sentence is false. “

There are two problems for this sentence.

First, is this sentence true or false? 

If it is true, according to itself, it is false.

But if it is false, then the assertion that “this sentence is false” is false, so it is true.

Second, what is the level of this sentence?

We don’t know, because it is referring to nothing, except itself. Let us just assume that it is an order-n sentence.

But since it describes itself, it describes an order-n sentence. So it is an order-(n+1) sentence.

But since it describes itself, it describes an order-(n+1) sentence. So it is an order-(n+2) sentence.

Contradiction!

How can the same sentence have more than one order?

That is exactly the problem of mixing levels. The meaning of the sentence and the meaning of the meta-sentence may contradict.

“This sentence is false.” is with level n, (n+1), (n+2), … at the same time.

But if it is true at level n, it is false at level (n+1), and true at level (n+2), etc.

So it is true and false and true …

Paradox is due to the mixing of para-level (meta-level) and original level. As long as we do not allow mixing levels, there are no paradoxes. Every sentence should only be allowed to describe sentences which have lower levels. For example, a sentence, S, is with level n.

Then S is not allowed to describe any other level n (or higher than level n) sentences.

— Me@2012-10-05 02:00:04 PM

2012.10.05 Friday (c) All rights reserved by ACHK

Paradox 3.1

Meta-time 3.1

Objects and events are of level zero.

Sentences about objects and events are of level one. They are called order-one sentences, e.g.

“Here is an apple.”

Sentences about sentences are of level two. They are called order-two sentences or meta-sentences, e.g.

“”Here is an apple.” has 4 words.”

Sentences about order-two sentences are of level three. They are called order-three sentences or meta-meta-sentences, e.g.

“”Here is an apple.” has 5 words.” is false.”

— Me@2012-10-05 12:00:04 PM

2012.10.05 Friday (c) All rights reserved by ACHK

Memory

.

I have collected in this book memories extending over fifty years.

I am well aware that memory is unreliable.

It not only selects and rearranges that facts of our lives, but also embroiders and invents.

I have checked my version of facts wherever possible against other people’s memories and against written documents.

.

– Freeman Dyson’s Disturbing the Universe

.

.

.

2009.09.05 Saturday ACHK