「The notion of a function is fundamental in mathematics, and the λ-calculus is an attempt to make this notion precise.」- 阿隆佐·邱奇经典语录

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The notion of a function is fundamental in mathematics, and the λ-calculus is an attempt to make this notion precise.

阿隆佐·邱奇 阿隆佐·邱奇
💡 解读： 函数的概念在数学中是基础的，而λ演算试图使这一概念精确化。
👤 更多 阿隆佐·邱奇 经典语录 10句
The fact that a certain proposition can be deduced from a certain set of axioms by means of a certain system of rules does not in itself make it true.
阿隆佐·邱奇 阿隆佐·邱奇
The λ-calculus is, in essence, a purely abstract theory of functions.
阿隆佐·邱奇 阿隆佐·邱奇
The paradoxes of set theory are not to be regarded as indicating any inconsistency in the theory itself, but rather as showing that certain methods of reasoning which had been thought to be valid are in fact not so.
阿隆佐·邱奇 阿隆佐·邱奇
The λ-calculus is not merely a formalism but a language in which computations can be expressed.
阿隆佐·邱奇 阿隆佐·邱奇
The notion of a function is fundamental in mathematics, and the λ-calculus provides a way to formalize this notion.
阿隆佐·邱奇 阿隆佐·邱奇
The fundamental concept of the λ-calculus is that of a function, regarded as a rule of correspondence.
阿隆佐·邱奇 阿隆佐·邱奇
The problem of deciding whether two λ-expressions are equivalent is unsolvable.
阿隆佐·邱奇 阿隆佐·邱奇
The discovery of the antinomy of the liar and of related antinomies has led to the realization that the intuitive notion of truth is not as simple as it appears at first sight.
阿隆佐·邱奇 阿隆佐·邱奇
A function is a rule of correspondence by which when anything is given (as argument) another thing (the value of the function for that argument) may be obtained.
阿隆佐·邱奇 阿隆佐·邱奇
The λ-calculus is, in essence, a theory of functions and their application.
阿隆佐·邱奇 阿隆佐·邱奇
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但是在这里，真正属于我的世界只有脚下的小路那么宽。我一步也不会离开这条路。我从不曾需要多么宽阔的通道，能侧身而过就足够了。像鸟在天空侧身飞翔，鱼在大海里侧身遨游，我从来不曾渴望过全部的世界。我只是经过这个世界，去向的一个小小的所在。我只依赖熟知的事物而生活，我心有牵挂，不想迷路，不想回不了家。我在山野里，游荡在节制之中。但已经感到足够的自由。
李娟 李娟
但愿同入梦。
琼瑶 琼瑶
悲伤就是知识
拜伦 拜伦
表面看起来糟糕的事，本质上却往往并非如此。
塞涅卡 塞涅卡
我绝不坚信这个时代没有放之四海而皆准的正义和良善的价值观，它们不仅仅有，而且不是朝令夕改流动无常的，它们是稳定而永恒的。
亚历山大·索尔仁尼琴 亚历山大·索尔仁尼琴
我们根本没想到要怀疑或轻视“历史的启示”；历史就是我们的一切。
恩格斯 恩格斯
奇花与丽日争妍，翠竹共青天斗碧。
吴承恩 吴承恩
大家礼义教子弟，小家凶恶训儿郎。
周希陶 周希陶
真理就是自由人的祖国。真理不存在于丑化了的现实里。生命的第一个行动就是创造的行动。在争论中是不分高贵卑鄙，也不管称号姓氏的，重要的只是真理，在它面前人人平等。
罗曼·罗兰 罗曼·罗兰
人人为我，我为人人。
列宁 列宁
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The distinction between the a priori and the a posteriori is epistemic, not metaphysical.
索尔·克里普克 索尔·克里普克
现代模态逻辑创始人之一
Logic is the foundation of philosophy, and philosophy is the foundation of science.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
The principle of contradiction is not a law of thought but a law of being.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
In logic, as in life, it is essential to distinguish between what is possible and what is necessary.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
The history of logic is the history of the liberation of thought from the constraints of language.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
A true proposition is one that corresponds to reality, not merely to our beliefs about reality.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
Logic is the foundation of all sciences, and the art of reasoning is the most valuable of all arts.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
In logic, as in life, we must distinguish between what is possible and what is necessary.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
The history of logic is the history of the liberation of the human mind.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
A true proposition is one that corresponds to reality, not merely to our thoughts.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
Logic is the foundation of philosophy, but philosophy is not logic.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
In logic, as in life, it is not enough to be right; one must also be understood.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
The truth of a proposition does not depend on our knowledge of it.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
Modal logic is not just about necessity and possibility, but about the structure of reasoning itself.
扬·武卡谢维奇 扬·武卡谢维奇
创立波兰逻辑学派，贡献命题逻辑与模态逻辑
The fact that a certain proposition can be deduced from a certain set of axioms by means of a certain system of rules does not in itself make it true.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
A function is a rule of correspondence by which when anything is given (as argument) another thing (the value of the function for that argument) may be obtained.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The λ-calculus is, in essence, a purely abstract theory of functions.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The fundamental concept of the λ-calculus is that of a function, regarded as a rule of correspondence.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The λ-calculus is a formalism for representing functions and their application.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The λ-calculus is, in essence, a theory of functions and their application.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The problem of deciding whether two λ-expressions are equivalent is unsolvable.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The λ-calculus is not merely a formalism but a language in which computations can be expressed.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The discovery of the antinomy of the liar and of related antinomies has led to the realization that the intuitive notion of truth is not as simple as it appears at first sight.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The paradoxes of set theory are not to be regarded as indicating any inconsistency in the theory itself, but rather as showing that certain methods of reasoning which had been thought to be valid are in fact not so.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The notion of a function is fundamental in mathematics, and the λ-calculus provides a way to formalize this notion.
阿隆佐·邱奇 阿隆佐·邱奇
提出λ演算，影响计算理论
The theory of moral sentiments is the foundation of the theory of political economy.
亚当·斯密 亚当·斯密
经济学的主要创立者
Man naturally desires, not only to be loved, but to be lovely.
亚当·斯密 亚当·斯密
经济学的主要创立者
The natural price of labour is that price which is necessary to enable the labourers, one with another, to subsist and to perpetuate their race, without either increase or diminution.
大卫·李嘉图 大卫·李嘉图
英国古典政治经济学的主要代表之一
Gold and silver, like other commodities, have an intrinsic value, which is not arbitrary, but is dependent on their scarcity, the quantity of labour bestowed in procuring them, and the value of the capital employed in the mines which produce them.
大卫·李嘉图 大卫·李嘉图
英国古典政治经济学的主要代表之一
The exchangeable value of all commodities rises as the difficulties of their production increase.
大卫·李嘉图 大卫·李嘉图
英国古典政治经济学的主要代表之一
There is no way of keeping profits up but by keeping wages down.
大卫·李嘉图 大卫·李嘉图
英国古典政治经济学的主要代表之一
The interest of the landlord is always opposed to the interest of every other class in the community.
大卫·李嘉图 大卫·李嘉图
英国古典政治经济学的主要代表之一
Gold and silver, like other commodities, have an intrinsic value, which is not arbitrary, but is dependent on their scarcity, the quantity of labour bestowed in procuring them, and the value of the capital employed in the mines.
大卫·李嘉图 大卫·李嘉图
英国古典政治经济学的主要代表之一
The only way that has ever been discovered to have a lot of people cooperate together voluntarily is through the free market.
米尔顿·弗里德曼 米尔顿·弗里德曼
诺贝尔经济学奖获得者
The social responsibility of business is to increase its profits.
米尔顿·弗里德曼 米尔顿·弗里德曼
诺贝尔经济学奖获得者
Nothing is so permanent as a temporary government program.
米尔顿·弗里德曼 米尔顿·弗里德曼
诺贝尔经济学奖获得者
In the long run, the economic prognosis is favorable.
保罗·萨缪尔森 保罗·萨缪尔森
第一个获得诺贝尔经济学奖的美国人
Theories are not so much wrong as they are incomplete.
保罗·萨缪尔森 保罗·萨缪尔森
第一个获得诺贝尔经济学奖的美国人
In the long run, the economic prognosis is favorable for those who are flexible and well-informed.
保罗·萨缪尔森 保罗·萨缪尔森
第一个获得诺贝尔经济学奖的美国人
It is not enough to know how to use tools; one must also understand when they are applicable.
保罗·萨缪尔森 保罗·萨缪尔森
第一个获得诺贝尔经济学奖的美国人
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