西瓜 10
As we already noted above, in a sense, logically valid formulas “do not contain information” (are “content-free”) − just because they are true in all interpretations, i.e. they are true independently of the “meaning” of language primitives.
— Introduction to Mathematical Logic
— Hyper-textbook for students
— Vilnis Detlovs and Karlis Podnieks
2013.10.06 Sunday ACHK
事件實在論 2
Although the Book of the Past cannot be changed, we can publish some errata.
— Me@2011.05.07
2013.10.06 Sunday (c) All rights reserved by ACHK
因果律 1.20 | 語意互相推卸責任論 1.20 | Verification principle, 5.20 | 西瓜 9.20 | Make a difference, 3
這段改編自 2010 年 4 月 3 日的對話。
「
那彷彿就好像，你中了彩票，獲得了一千億元的獎金，存入了你的銀行戶口。但是，銀行的職員跟你說，你每日最多只能從那個戶口中，提款一百元。你就立刻發覺，窮你一生，甚至是十世的時間，都不能用盡那一千億元。如果你的朋友問你：「你是否擁有一千億元？」
你就唯有無奈地答：「那要視乎你『擁有』的定義。擁有而不能用，還算不算是『擁有』呢？」
安：但是，你又真的可以，從那一千億元的戶口之中，每天提取一百元去用。因為那些一百元，始終是來自那一千億元的，你不能說，那一千億元完全沒有用，完全不屬於你。）
無錯。
」
在這個例子中，你既可以說
「
我有一千億元的金錢，不過每日只可以提取一百元來使用
」；
亦可以說
「
我根本沒有一千億元的金錢，不過之後的每一天，也可以得到一百元的獎金。
」
（安：兩個講法之中，哪一個講法才是正確的？）
兩個都正確。兩個都可以用，因為兩個講法，都準確而完整地，描述了事實。
（安：那樣，哪一個講法，會比較好一點？）
因為兩個都正確，所以客觀上，並沒有所謂，哪一個會比較好一點。主觀上，你可以用經濟原則 —— 哪一句精簡一點，你就用哪一句。但是，在這個例子中，兩句的字數差不多。所以，基本上，你喜歡用哪一句，就用哪一句。
根據「印證原則」(confirmation principle/weak verification principle)的延伸，或者根據萊布尼茲的「同一律」(identity of indiscernibles)，
無論句子甲乙的字眼有多大的不同，如果，即使只在原則上而言，你都講不出句子甲和句子乙的意思，在什麼情況之下，有怎麼樣的分別，句子甲乙就根本地，有著同一個意思。兩句只不過是，同一個意思的兩個表達方式而已。
正如「二加二」和「五減一」，雖然貌似不同，實質意思一樣。爭論「二加二」和「五減一」哪個才算正確，只是言辭之爭，浪費時間。
— Me@2013.10.03
2013.10.04 Friday (c) All rights reserved by ACHK
distance = length of the path travelled
displacement = change of position
Distance is about the input; displacement is about the output.
— Me@2013-10-03 11:03 AM
Price is what you pay; value is what you get.
— Ben Graham
2013.10.03 Thursday (c) All rights reserved by ACHK
The least of all evils 8 | 眾害取其輕 8 | Second best 7
Sometimes, you have to allow something bad to happen, in order to create something good.
Sometimes, you need to give up something in order to get something.
That’s why you need to set priorities, in case of conflicts of goals.
— Me@2013-10-01 10:01 AM
— Me@2013-10-01 1:41 PM
Price is what you pay; value is what you get.
— Ben Graham
2013.10.03 Thursday (c) All rights reserved by ACHK
這段改編自 2010 年 7 月 27 日的對話。
…
你為什麼要把這個要點，寫在草稿紙上，而不直接把它，記錄於那本「魔法筆記」之中？
（CYW：我回家才把它抄回筆記。）
那豈不是會浪費時間？
可以即刻完成的事情，就即刻完成。可以一步了結的事情，就不要花兩步。
你現在立即記在筆記的話，只需花十幾秒。但是，你回家才抄回的話，就要拿本「魔法筆記」回來，會引發多幾個工序，前後起碼花你十多分鐘。
— Me@2013.10.02
2013.10.02 Wednesday (c) All rights reserved by ACHK
All consistent axiomatic formulations of number theory include undecidable propositions …
Gödel showed that provability is a weaker notion than truth, no matter what axiom system is involved …
How can you figure out if you are sane? … Once you begin to question your own sanity, you get trapped in an ever-tighter vortex of self-fulfilling prophecies, though the process is by no means inevitable. Everyone knows that the insane interpret the world via their own peculiarly consistent logic; how can you tell if your own logic is “peculiar” or not, given that you have only your own logic to judge itself? I don’t see any answer. I am reminded of Godel’s second theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent.
— Godel, Escher, Bach: An Eternal Golden Braid
— Douglas Hofstadter
2013.10.02 Wednesday ACHK
Step-by-step approach
1. “He who would learn to fly one day must first learn to stand and walk and run and climb and dance; one cannot fly into flying.” — Friedrich Nietzsche
2. “For things we persist doing become easier, not because of the change of the nature of the thing, but because of the increase of our ability. ” — Emerson
3. “What does not destroy me, makes me stronger.” — Friedrich Nietzsche
.
.
.
2008.09.08 Monday (c) CHK2
Physics Town 