j*****x
发帖数: 33 | 1 Look at following parts:
logic is often divided into two parts, inductive reasoning and deductive
reasoning. The first is drawing general conclusions from specific examples,
the second drawing logical conclusions from definitions and axioms. A
similar dichotomy, used by Aristotle, is analysis and synthesis. Here the
first takes an object of study and examines its component parts. The second
considers how parts can be combined to form a whole.
Even for the second, the definitions is generated... 阅读全帖 |
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g****t
发帖数: 31659 | 2 战争有战争的逻辑,历史有历史的逻辑,这个大家都能听懂吧?
logic跟小学数学关系其实并不大.
Look at following parts:
logic is often divided into two parts, inductive reasoning and deductive
reasoning. The first is drawing general conclusions from specific examples,
the second drawing logical conclusions from definitions and axioms. A
similar dichotomy, used by Aristotle, is analysis and synthesis. Here the
first takes an object of study and examines its component parts. The second
considers how parts can be combined to form a whole.
... 阅读全帖 |
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t**k
发帖数: 260 | 3 If r u saying that induction is from experience, I suppose u r trying to say
the application of induction is on empirical knowledge. However, for the
induction reasoning itself (aka, the rules), it's probably not from
experience.
The same for deduction, i.e., the logic rules and logic axioms are probably
not from experience.
You said for deduction, "the definitions is generated from what I describe
before, by experience of detection and recoginization".
Definitions of what?
second |
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j*****x
发帖数: 33 | 4 I think you are talking about reasoning, not logic. My understanding is
logic is consequence of reasoning, a well organized reasoning lead to a
logic output．That logic isn't equal to reasoning. My understanding logic is
more like judgement of a specific topic.
Even when we talk about our reasoning, there is an axiom, which means the
deduction can't contradict with itself. Which I would like to call as a "
close operation". But indeed, this kind of close operation is from
experience, based on wha... 阅读全帖 |
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s**********n
发帖数: 3199 | 5 闲了 @ __ @ 娱乐一下娱乐一下
造成
说明
最后举正弦特例的时候我有考虑到这个问题，我很清楚P(a) for some a \in A
implies (forall b \in A. P(b))的错误， (1)
我的point这里不是证明P，特据正弦a \in A更多是想说明，古人尚且能体会到数学的
重要，看到数学教育的重要，何以现代人竟然割裂所谓文科与数学？
你会贴那么多无法是说上面那个推导（1）的错误，
但我吃饱了post那个帖子不是用错误的inference rule （1）+ 郑玄这个 ground
statement来证明我的（所谓）结论：数学对所有人如何如何。。。
我没想要逻辑上题出什么，上文不是讲了么，只能模糊的，，，我连在逻辑系统里
fromalize还做不到呢，何来证明、证伪？
那个claim本来也是我的倾向而已。
大部分人一生也没什么重要贡献，巨大损失我也没定义，，，所以我上文有说讲的很含
混。
要拿来作逻辑上的proof read，那首先大家要有一个common ground吧。
什么... 阅读全帖 |
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g****y
发帖数: 323 | 6 Suppose we have finite number of symbols.
Words are made of these symbols.
Sound means that only true statements can be proved.
complete means all true statements can be proved.
Godel proved that
in any logical system there exist TRUE theorems which CANNOT BE PROVEN
on the basis of the axioms and operations of that system.
Which means
There are TRUTHS that are not scientifically verifiable.
or you can say:
There are TRUTHS that are in the realm of the subjective. They can never
be proven true.
G |
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b*****y
发帖数: 163 | 7
come on. trying to refresh my middle school education? :-)
i don't know which one you are mentioning. but if you
mean the changing government thing, i think that is a fundamental
point. Naive assumption is different and should not
be treated as self-explanatory axiom. Is this a common ground for us? :-)
anyway, think about those questions. they may give you a better view
for your observations. In fact, I want to say it is one thing
to just talk the talk, but backing your talk is another. |
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r****y
发帖数: 26819 | 8 从自私说起
任何辩论都必然有一个起点，科学当然不会例外。假若我们在起点上就有争议，那么
科学就难以成事了。所以在任何科学发展中，参与的人都遵守一个大家不言自明的规则
：凡指明是基础假设（postulate），或是公理（axiom），大家都不在这基础上争论。
这不是说每个人都衷心同意这些假设或公理；是否认同不重要，重要的是同意不在起点
上有所争议。科学辩证的规则是：「且不要反对我在理论上必须有的起点，让我从这起
点以逻辑推出一套理论，有了可以用事实验证的含意（testable or refutable
implications），有了内容，到那时，你要反对才有所依凭的。事实上，假若可以验证
的含意被事实无情地推翻了，那我就不能不考虑我的基础假设是错了的。」
说起来，那些所谓不容许有争议的基础假设或公理，可能近于无稽，令人难以置信
的。例如，在数学上一个重要假设是这样说的：「假若一加一等于一个数字，这数字叫
作二；又假若二加一等于另一个数字，这数字叫作三.. 」听起来，这真的有点傻气。
但假若没有这个基础的假设，我们是无从知道一至二之间不可能有另一个数字。要是我
们在这基础上有纷争 |
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c****n
发帖数: 21367 | 9 it is a critical question that
can we human differentiate good and bad without God?
the answer in traditional Chinese culture is: yes
like building the modern scientific system, everything comes from
the axiom of "the human race should survive and thrive"
古人认为，小孩子子生下来就可以享受祖先多少辈人辛苦建设的成果：比如开辟的田地
，住的房子，走的路，生活里应
用的各种技术，都是前人积累而来。生下来就有这些，是得了前人的好处的。享受这些
的前提，是承诺尊重前人，而且
自己贡献添加一些，留给后人。（类似于GPL？:)）所以一个人不是为了它自己活着，
也不仅仅是为了它爹妈活着，而是
对整个社会，对前人和后人都有义务有责任的。这个责任就是继承和发展社会，把物质
和精神财富传递下去。
这里讲的是教育，实际上灌输了儒家身家国天下的思想。身，来自 |
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D*****r
发帖数: 6791 | 10 The Relativity of Biblical Ethics
by Joe Edward Barnhart (1988)
It is an axiom among fundamentalists and evangelicals that theology is the
foundation of ethics and morality in North America culture. Without this
foundation, they fear, ethics would fragment into total relativism of
dissolve into whim, arbitrariness, and chaos. I would like to contest that
view by showing how some organized religions are parasitical to the body of
ethics and how the Bible itself exemplifies moral relativism.
Vario... 阅读全帖 |
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l**********t
发帖数: 5754 | 11
It is not a proof but an axiom. All things in the Universe (including math/
logic & all natrual laws) are created by the Creator, so He is beyond proof.
As to your belief in the "evolution theory" -- if you can prove that the
causes are truly "random", it would be a respectable "theory" instead of a
blind faith. |
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E*****m
发帖数: 25615 | 12 既然你要講 Godel, 那麼問你點正經的
1. Godel Incompleteness Theorem 是對countable infinite 的 axiom
systems 就有效，還是對不可數的公理系統才有效？
2. 請問什麼叫做"描述一个可数无穷的理论集合，根本无法描述不可数
无穷的理论集合", 可否具體說明？ "理论集合" 英文是什麼？你這是在講
自然科學還是數學？
先兩個問題吧
描述 |
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l**********t
发帖数: 5754 | 13
Hi, brother wildcat2002. I enjoyed reading your testimony and thanks for
your sharing. IMHO, don't get stuck with the logic proof of God -- it is a
paradox. If you could logically prove the existence of God, God would be a
subset of human knowledge, and then there won't be any need for God.
The faith in God is the axiom.
箴 言 1:7 敬 畏 耶 和 华 是 知 识 的 开 端
have a nice weekend. |
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c******r
发帖数: 889 | 14 The faith in God is the axiom
对啊，在此基础上创造一个有一定内洽的假说理论体系。是啊，体系内make sense.
但是，这样内洽的假说可以有无穷多。
最后还是要落到凭什么来抉择上。
凭是否听之有理可以么？
这就是科学的区别。
科学寻找客观依据来判断，所以是确实的，可重现的。
信来的，终究还归到信上，就是自己选择性的固执。 |
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j*****6
发帖数: 1059 | 15 亨利马太的圣经注释，仅供参考
Jhn 14:15-17
Christ not only proposes such things to them as were the matter of their com
fort, but here promises to send the Spirit, whose office it should be to be
their Comforter, to impress these things upon them.
I. He premises to this a memento of duty (v. 15): If you love me, keep my co
mmandments. Keeping the commandments of Christ is here put for the practice
of godliness in general, and for the faithful and diligent discharge of thei
r office as apostles in particular. N... 阅读全帖 |
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l**********t
发帖数: 5754 | 16 "推翻" is only applicable to theroms proved beyond reasonable doubts, not to
assumptions or axioms. |
|
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l**********t
发帖数: 5754 | 18
"但是谁能证明这个呢？" - -this is a typical misunderstanding about belief vs
. science. Science needs assumptions & proof, Belief needs faith (not proof). They are in two different realms and address different issues.
You can think "圣经是对的" as an axiom. |
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r********t
发帖数: 66 | 19 那我能不能认为"圣经是错的" as an axiom。我能不能质疑这个"圣经是对的".
你什么时候认为"圣经是对的"，从你生下来就是这样的吗， 还是后来又了转变？ 为什
么会转变？是有人向你传道，还是你看圣经领悟了？ 如果是前者，请替我向你传道的
人问同一个问题，如果是你自己看圣经领悟的，这个逻辑就成了"圣经是对的"导出"圣
经是对的"。
vs
proof). They are in two different realms and address different issues. |
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l**********t
发帖数: 5754 | 20
4. God forbid: yea, let God be true, but every man a liar; as it is written,
That thou mightest be justified in thy sayings, and mightest overcome when
thou art judged.
"
4. But let God be true, etc. Whatever may be the opinion of others, I regard
this as an argument taken from the necessary consequence of what is opposed
to it, by which Paul invalidates the preceding objection. For since these
two things stand together, yea, necessarily accord, that God is true and
that man is false, it follow... 阅读全帖 |
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l**********t
发帖数: 5754 | 21 good points.
but it is even more true with math (抽象科学) -- all mathametic systems are
built from a set of axioms that are assumed to be true and can not be proven. |
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l**********t
发帖数: 5754 | 22
faith doesn't need evidence, otherwise faith won't be faith. it is similiar
to the axiom of reasoning system. |
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l**********t
发帖数: 5754 | 23
do you understand what axiom means? |
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l**********t
发帖数: 5754 | 24
because God is the creator of the Universe, and that is the axiom of the "
logic" system in Christian belief (Gensis 1:1 起 初 神 创 造 天 地 。)-- it is self-evident
and doesn't need proof for Christians.
Also
Romans
9:20 你 这 个 人 哪 ， 你 是 谁 ， 竟 敢 向 神 强 嘴 呢 ？ 受 造 之 物 岂 能 对 造 他 的 说 ， 你 为 什 么 这 样 造 我 呢 ？ |
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l**********t
发帖数: 5754 | 25
科学不需要宗教, 科学需要公理(axioms)-- which is just another name for
beliefs. |
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l**********t
发帖数: 5754 | 26
no, I simply said there is no logic to start reasoning if both sides can't
agree on the common axioms as a starting point. |
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v****e
发帖数: 360 | 27 axiom也是可以被修正的。例如“平行线不相交”在非欧几何中就不成立。 |
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v****e
发帖数: 360 | 28 对，说“替代”比修正更准确些。表达的意思有一点是共同的，就是这个axiom本身并
不是事实，而是assumption。这么说来，基督信仰是assumption，你同意吗？ |
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j*******7
发帖数: 6300 | 29 更正一下，那个术语是“同义反复（Tautology）“，这个网页说的是：
http://richardhartersworld.com/cri/2004/tautology.html
Mathematics and Tautologies
"What we are left with is the rather vague notion that the theorems of a
system are tautologies because they are "true by definition" by virtue of
being deducible from the axioms."
你的例子是一个丢失信息的证明，不是同义反复,但这类证明一般也没有大的意义。
人们期望数学/逻辑系统能证明所有真理，甚至发现未知的真理。所以我认为高等数学/
逻辑学更关心不丢失信息的证明（可能就是要基于同义反复的路径），但数学家却早已
经给出了悲观的结论。
my 2 cents. |
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E*****m
发帖数: 25615 | 30 哇哈？ 你數學分析是在玩 Tautology?
你自己引得那個網站都說了，
To begin with, suppose we have an axiom system, call it A, and a theorem,
call it B. The condensed proof of B is A=>B, i.e., there is a sequence of
steps that are equivalent to "A implies B". Now what is it that is supposed
to be a tautology? Is it B? Not so, because the truth of B is contingent on
A. Is it A=>B? Not so, because the inference A=>B isn't true for all values
of A and B. The (logical) tautology is (A & A=>B) => B.
要證明的 B 不是Tautology 的。
ps. Tau... 阅读全帖 |
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A*******1
发帖数: 985 | 31 转天是安妮的追思礼拜和葬礼。一种负疚感让多数中国学生学者都来参加。大家相对无
语，神色黯然。没想到我平生第一次参加葬礼，竟是美国人的，还在教堂里。更想不到
的是，葬礼上没有黑幔，没有白纱。十字架庄重地悬在高处。讲台前鲜花似锦，簇拥着
安妮的遗像。管风琴托起的歌声在空中悠悠回荡：Amazing Grace, How Sweet the
Sound（奇异恩典，何等甘甜）……人们向我伸手祝福：“愿上帝的平安与你同在。”
牧师说：“如果我们让仇恨笼罩这个会场，安妮的在天之灵是不会原谅我们的。”安妮
的邻居、同事和亲友们一个个走上台来，讲述安妮爱神爱人的往事。无尽的思念却又伴
着无尽的欣慰与盼望：说安妮息了地上的劳苦，安稳在天父的怀抱，我们为她感恩为她
高兴！
礼拜后的招待会上，三兄弟穿梭在中国学生中间。他们明白中国人心中的重担，便努力
与每个中国学生握手交谈。如沐春风的笑容，流露出心中真诚的爱。许多女生哭了。我
的“黑手党”朋友，高大的男子汉也在流泪。爱的涓流从手上到心里，泪水的脸上绽出
微笑。哦，这样的生，这样的死，这样的喜乐，这样的盼望，怎不让我心里向往！大哥
弗兰克握着我的手说，“你知道... 阅读全帖 |
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l**********t
发帖数: 5754 | 32
have you ever heard of "assumptions"? It is the base of each and every
scientific theory -- it is something that you can't prove and have to accept
by faith.
if you have never heard of it, I guess you are not academically trained in
natural science or math -- in which every system is built on a set of axioms
, which you can't prove but have to accept by faith. |
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O**********0
发帖数: 61 | 33 ☆─────────────────────────────────────☆
BHistory (往者的影子) 于 (Fri Sep 9 00:20:11 2011, 美东) 提到:
俺曾认为生命是进化起源的，后来越找越发现进化论像是信仰而非科学结论。可是每有
飞机网友觉着俺如此看待进化论是反科学了。
所以俺本着科学的精神，问个问题，求各位飞机进化论牛人给个科学的答案。
大家知道达尔文进化论是以遗传机制为基础的，第一个有遗传机制的生命怎么来的，当
时根本没有提及。
后人发现这一问题后，就又提出了化学进化论，就是无机分子在某种机制下，自动组合
出了第一个有遗传的生命。此后达尔文进化论似乎可以take care（其实未必，今后再
讨论）。
今天我们先看比第一个有遗传生命的出现简单万亿倍的问题，第一个蛋白质如何化学进化出
现？
先亮亮俺一个愚昧基督徒的愚见：
已知最简单的具有遗传机制的单细胞生命的复杂度已经远远超出人们最初的想象，大概
有400种蛋白质几十万个组成。其中较小的蛋白质大概100个氨基酸，如果在随机热运动
中组成，因为自然界对称的氨基酸不少于40种（20多种氨基酸及... 阅读全帖 |
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G*******h
发帖数: 185 | 34 如果你读一下非欧几何的历史，非欧几何的发现源于最初人们试图用欧几的前四条公理
来证明第五条未果，从而发现彻底否定第五条(有不同的否定方式），也会构成（各自
，根据否定方式）完备的公理（Axiom）系统。也就是说它的所有的定理（Theorem），
都可以有这4条公理和这第五条新公理推出来。它作为公理系统的完备性不依赖于后来
人们发现它在很多方面（曲面，球面以及相对论上）的应用。也就是说即使到现在为止
，没有任何应用，它依然是一个完备的公理系统。
现在讨论你的那个例子：
欧几：三角形内和180度
非欧：根据第五条公理的不同的否定方式，有的公理系统三角形内和小于180度，有的
公理系统三角形内和大于180度。
以上结果都可以有各自的5条公理来证明，你举得例子只是帮助理解解释结果，证明不
需要曲面，球面。
下面附上第五条公理,有一点明确，所谓的非欧的施用范围（曲面，球面等）在此没有
体现而且根本不需要（如果你能否定这一点，我愿赌服输），而是公理系统创立后，发
现非欧可以用来解释理解曲面球面上的现象，也许以后还会有其他方面的应用也未可知。
欧几：
Given a line l and a poi... 阅读全帖 |
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l****e
发帖数: 476 | 35 lazy guy's axiom. 请走开, 别挡住偶的阳光... :)) |
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o*****s
发帖数: 1445 | 36 啧啧，就你这出身，华东理工煤化工，就你这眼界，gatech去鸟不生蛋的炼油厂。。。
还在思考到底是上财还是华师大金融？我跟你说，连中南财经政法大学都不靠谱啊。看
一个学校好坏，就看在湾区和新泽西+boston+dc的买房率。其他全假的。你现在的想法
，就跟只有在sugarland tx买3000sqft的实力，还要思考我到底是该买los altos hill
的山景房，还是住在palo alto做jobs的邻居。
我先问你这样一个问题：你有过去的同学在cupertino买房子的吗？你有同学在美国做
associate的律师吗？你见过湾区available的漂亮女生吗？我都有。
湾区available的漂亮女生，你找个出来吃饭，如果你能找到的话哈。开的是MBA or
equivalent的入门款。拎的是lv,chanel之类的包。穿的都是上千的品牌外衣。工资都
是12万以上。化妆都好的跟专业出身的一样，头发都是做过的。你现在拿个镜子照一下
自己，你头发最近一个月里面理过吗？发胶每天打吗？看见lv speedy认的出来吗？开
过keyless entry的车吗？报的出几个名牌包的牌子？说的... 阅读全帖 |
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o*****s
发帖数: 1445 | 37 啧啧，就你这出身，华东理工煤化工，就你这眼界，gatech去鸟不生蛋的炼油厂。。。
还在思考到底是上财还是华师大金融？我跟你说，连中南财经政法大学都不靠谱啊。看
一个学校好坏，就看在湾区和新泽西+boston+dc的买房率。其他全假的。你现在的想法
，就跟只有在sugarland tx买3000sqft的实力，还要思考我到底是该买los altos hill
的山景房，还是住在palo alto做jobs的邻居。
我先问你这样一个问题：你有过去的同学在cupertino买房子的吗？你有同学在美国做
associate的律师吗？你见过湾区available的漂亮女生吗？我都有。
湾区available的漂亮女生，你找个出来吃饭，如果你能找到的话哈。开的是MBA or
equivalent的入门款。拎的是lv,chanel之类的包。穿的都是上千的品牌外衣。工资都
是12万以上。化妆都好的跟专业出身的一样，头发都是做过的。你现在拿个镜子照一下
自己，你头发最近一个月里面理过吗？发胶每天打吗？看见lv speedy认的出来吗？开
过keyless entry的车吗？报的出几个名牌包的牌子？说的... 阅读全帖 |
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a****s
发帖数: 8624 | 38 虽然不是完全明白，但是很喜欢。
http://www.youtube.com/watch?v=BipvGD-LCjU
The path of love is never smooth
But mine’s continuous for you
You’re the upper bound in the chains of my heart
You’re my Axiom of Choice, you know it’s true
But lately our relation’s not so well-defined
And I just can’t function without you
I’ll prove my proposition and I’m sure you’ll find
We’re a finite simple group of order two
I’m losing my identity
I’m getting tensor every day
And without |
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j******w
发帖数: 690 | 40 这个要看你相对于哪个公理系统。
如果是相对于PA(Peano axioms)证明PvsNP的独立性还有可能。但是这个基本也是毫无
进展。很多
搞证明论的试图在PA的极弱的子公理下证明PvsNP的独立性都没有成功。
如果是相对于ZFC就麻烦了。ZFC对于表述简单的命题有个绝对性原理。这本来对于证明
是件好事
情。但是如果这类简单的命题是独立于ZFC的，那么它的独立性都不可证。也就意味着
不能像
Cohen那样用个forcing 就造出来了。也许Pvs NP就是个大基数公理也说不定。 |
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f*********g
发帖数: 632 | 41 Princeton, 20 March 1956
Dear Mr. von Neumann:
GÄodel Book|Wigderson - rev. 2010-0708 5
With the greatest sorrow I have learned of your illness.
The news came to me as quite unexpected. Morgenstern
already last summer told me of a bout of weakness you once
had, but at that time he thought that this was not of any
greater significance. As I hear, in the last months you
have undergone a radical treatment and I am happy that this
treatment was successful as desired, and that you are now
doing ... 阅读全帖 |
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M********t
发帖数: 5032 | 42 是1600的。不过ebay买东西靠运气，原价350，我给了个220的offer，结果卖家接受了
。是IBM的axiom内存。 |
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M********t
发帖数: 5032 | 43 我买的是IBM的axiom server ram |
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f**c
发帖数: 629 | 44 I will create google checkout for online store. I need to create web service
to accept message from google. What kind of knowledge will I need, Axiom,
adp, soap, wsdl...? there are lots of information online. I dont know where
to start? |
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g****t
发帖数: 31659 | 45 你需要看清楚我写的东西。我讲了，Chruch发表在先，但是有一个gap,什么鸟step
wise axiom 过不去。这里不存在抄袭的问题。本身是不同的计算模型。怎么抄袭。
: Turing machine和lambda calculus都是30年代产物，没有谁抄谁之说。
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g****t
发帖数: 31659 | 46 你需要看清楚我写的东西。我讲了，Chruch发表在先，但是有一个gap,什么鸟step
wise axiom 过不去。这里不存在抄袭的问题。本身是不同的计算模型。怎么抄袭。
: Turing machine和lambda calculus都是30年代产物，没有谁抄谁之说。
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t****t
发帖数: 6806 | 47 You have to define \begin{theorem} with
\newtheorem{theorem}{Theorem}
(Because latex can't have one environment for each structures, such as
Lemma, Theorem, Proposition, Axiom, Conjecture, etc.) |
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l**********t
发帖数: 5754 | 48 All theories are based assumptions just as all math systems are based on
axioms that can't be proven. So is "evolution theory"-- assuming mutations
are random/spontaneous which can't never be proven rigorously.
You simply choose to believe whatever you prefer to believe. |
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c**r
发帖数: 51 | 49 如果您指的是Bader的Atoms in Molecules, 大致看过一次，没注意到对这个题目的反复讨论，可能是我看得不细。用transferability作为关键词在index里面没找到相关页码。只发现在P133，5.2 Need for a quantum definition of atom里画了LiF,LiO,LiH的电子密度图，和一些文字说明，似乎Bader很注意对一个理论的构成元素的观察，他通过电子密度发现大概Li原子在这三个分子中有一些类似的分布，作为发展所谓 quantum definition of atom的一个动机。您能提供一下其他讨论的内容或者页码吗，谢谢
不过从P. Ayers的Atoms in molecules, an axiomatic approach. I. Maximum
transferability,JCP, 113,10886上发现了一些更加明确的观点。Ayers以公理的方式提出
Axiom T (maximal transferability): An atom in a molecule
is defined so that the p |
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i*******e
发帖数: 349 | 50 “公平与效率是相冲突的”还没有达到公理的级别吧，起码我是这么觉得。不知道有没
有论文把这个列为axiom？ |
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