Godel 11

1931: Publication of Gödel’s incompleteness theorems, showing that essential aspects of Hilbert’s program could not be attained.

It showed how to construct, for any sufficiently powerful and consistent recursively axiomatizable system – such as necessary to axiomatize the elementary theory of arithmetic on the (infinite) set of natural numbers – a statement that formally expresses its own unprovability, which he then proved equivalent to the claim of consistency of the theory; so that (assuming the consistency as true), the system is not powerful enough for proving its own consistency, let alone that a simpler system could do the job.

It thus became clear that the notion of mathematical truth [cannot] be completely determined and reduced to a purely formal system as envisaged in Hilbert’s program. This dealt a final blow to the heart of Hilbert’s program, the hope that consistency could be established by finitistic means (it was never made clear exactly what axioms were the “finitistic” ones, but whatever axiomatic system was being referred to, it was a ‘weaker’ system than the system whose consistency it was supposed to prove).

— Wikipedia on Foundations of mathematics

2013.07.21 Sunday ACHK

無限旅程 4

Meaningful 12

這段改編自 2010 年 4 月 3 日的對話。

(安:為什麼必須要有一個「無限旅程」,人才會感到「有意義」?

或者說,為什麼一件事有「下一步」還不夠,而一定要「不斷地」有下一步,人才會感到真正的快樂?)

「有限價值」會帶來短暫的開心;「永恆價值」則會引發長久的幸福。

一件事如果有無限個「下一步」,那就代表「那件事」本身,可以長存於時間之中,不會消失。

一件事如果沒有起碼一個「無限旅程」,你的「機會成本評價系統」,自然會令你沒有心機、提不起勁,因為「那件事」早晚會消失;而你付出的努力,亦注定要白費。

有意義

~ (不斷地)有下一步

~ 可保存

~ 可繼續存在

~ 可儲存於時間之中

— Me@2013.07.21

2013.07.21 Sunday (c) All rights reserved by ACHK