Curry’s paradox 1.1

Paradox 4.1

When you equal the meta sentence level and the sentence level, it is nothing special about the paradox, for it is just a contradiction between the sentence and the meta-sentence.

In Curry’s paradox, “X -> Y” is what you want to prove. So you try “if X”, to see if you can get Y.

But by letting “X = X -> Y” and if X, and X = X -> Y, then Y. You are actually doing circular proof. 

Effectively you use X to prove X, which is a useless proof.

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.

— Me@2012.04.01

— Me@2012.10.05

— Me@2012.10.13

2012.10.13 Saturday (c) All rights reserved by ACHK


next ~ scalable

— Me@2011.12.02

Anything not scalable cannot make sure its own long-term survival.

— Me@2012-10-13 11:26:12 AM

Information survives by people copying it.

– John Baez, mathematical physicist

2012.10.13 Saturday (c) All rights reserved by ACHK

Independent vs Mutually Exclusive

這段改編自 2010 年 6 月 8 日的對話。

大部分 probability(機會率)的初學者,都會混淆「independent events」(獨立事件)和「mutually exclusive events」(互斥事件)。只要記住以下兩個重點,就不會再混淆兩者。

第一個重點是,「兩件事」和「一件事」之別。「Independent」通常是指,兩件事件互不相干。「Mutually exclusive」通常是指,同一件事件的兩個可能結果,不會同時發生。例如,骰子甲和骰子乙是 independent 的話,即是甲乙的結果不會影響對方。而骰子甲不會在同一次,同時「擲到 2」和「擲到 3」。所以,「甲 2」和「甲 3」是 mutually exclusive 事件。

第二個重點是,「沒有關係」和「有關係」之別。「Independent」是指,兩個結果互不相干。「Mutually exclusive」是指,兩個結果十分相干;它們是敵人關係。

— Me@2012.10.13

2012.10.13 Saturday (c) All rights reserved by ACHK