数学を初めとした理系の学問と哲学について　１５

1 ：考える名無しさん：2019/11/23(土) 22:30:06 ID:0.net

前スレ
https://lavender.5ch.net/test/read.cgi/philo/1536636403/

952 ：考える名無しさん：2021/08/05(木) 02:34:33.83 0.net

Deism is also defined as the belief in the existence of God solely based on rational thought,
without any reliance on revealed religions or religious authority.
Deism emphasizes the concept of natural theology, that is, God's existence is revealed through nature.

Since the 17th century and during the Age of Enlightenment, especially in 18th-century England
and France, various Western philosophers and theologians formulated a critical rejection of the
religious texts belonging to the many institutionalized religions and began to appeal only to truths
that they felt could be established by reason alone as the exclusive source of divine knowledge.

953 ：考える名無しさん：2021/08/05(木) 02:35:36.40 0.net

Such philosophers and theologians were called "Deists", and the philosophical/theological position
that they advocated is called "Deism"Deism as a distinct philosophical and intellectual movement
declined towards the end of the 18th century.

Some of its tenets continued to live on as part of other intellectual movements, like Unitarianism,
and it continues to have advocates today.

954 ：考える名無しさん：2021/08/07(土) 07:04:15.70 0.net

viz.

955 ：考える名無しさん：2021/08/08(日) 07:43:01.99 0.net

parallelepiped

956 ：考える名無しさん：2021/08/08(日) 20:36:04.21 0.net

Causality does not require determinism. Every event can have a cause without every event being determined,
without every event being (in principle) predictable. There is merit to this charge.

In claiming that causality is not necessary to the flow of information, I have assumed that:
If C is the cause of E, then C is an essential part of some nomically sufficient condition for E.

957 ：考える名無しさん：2021/08/08(日) 20:54:09.13 0.net

This principle gives expression to a traditional idea, the idea that C cannot be the cause of E
if (an event such as) C can occur, under relevantly similar circumstances,
without (an event such as) E occurring. In other words, causality is a manifestation of a regular,
lawlike, succession between events of type C and events of type E under relevantly similar conditions.

958 ：考える名無しさん：2021/08/08(日) 20:55:53.82 0.net

This is an orthodox empiricist view of causality. Its most illustrious ancestor is, of course,
David Hume, but one need not accept Hume's view that causation is only a matter of regular succession
to endorse the idea, expressed by the above principle, that causation at least involves regular succession.

959 ：考える名無しさん：2021/08/09(月) 04:35:01.14 0.net

"The smallest number of light quanta required for vision however is not large.
A few quanta acting upon the human retina are capable of giving a sensation of light
to a human observer. By activating one molecule of visual pigment, one single quantum
may cause the excitation of a dark-adapted rod cell in the retina.

And one quantum is of course the smallest quantity of light which may be emitted or
absorbed by matter."

M. H. Pirenne and F.H.C. Marriott, "The Quantum Theory of Light and the Psycho-Physiology
of Vision," in Psychology: The Study of a Science, Sigmund Koch (ed.), New York, 1959.

960 ：考える名無しさん：2021/08/10(火) 03:57:42.91 0.net

In this case the information contained in a signal exceeds (in a sense) the conventional meaning of the signal.
The same thing often happens with ordinary verbal communications. If I already know that someone lives in
Wisconsin, but you do not, hearing him say he lives in Madison tells me where he lives but not you.

A glance at the calendar tells you the date only if you already know the day of the week.
What one learns, or can learn, from a signal (event, condition, or state of affairs), and hence
the information carried by that signal, depends in part on what one already knows about the alternative possibilities.

961 ：考える名無しさん：2021/08/10(火) 04:23:31.29 0.net

There is, of course, a use of the term "meaning" that is close (if not equivalent) to the ordinary sense of
"information." When we say, for example, that a blown fuse means the circuit has been overloaded,
a sputtering engine means we are out of gas, and George's fingerprints on the glass mean that
he was at the scene, we are using "meaning" in what Paul Grice calls its natural sense.

962 ：考える名無しさん：2021/08/10(火) 04:27:22.45 0.net

When I say that information must be distinguished from meaning, I have in mind Grice's nonnatural meaning,
the sense of meaning that is relevant to language and semantic studies.

The way in which spots mean measles (natural meaning) is quite different from the way in which
"I have the measles" means he (the speaker) has the measles (nonnatural meaning), and
it is the latter sort of meaning that I intend to be distinguishing from information.

See Grice's "Meaning," Philosophical Review, vol. 66

963 ：考える名無しさん：2021/08/12(木) 12:18:53.02 0.net

[Definitions 1-5 define the ancillary arithmetical concepts
(being the n-th prime number, etc.) used in his method of arithmetization.]

As examples, definition 8 (p. 50) defines the arithmetical operation ✴ upon
two numbers x and y in such a way that the number x ✳ y which is the result of performing
this operation is the Gödel number of the string obtained by taking the string whose
Gödel number is x and placing the string whose Gödel number is y immediately after it.

964 ：考える名無しさん：2021/08/12(木) 12:20:00.98 0.net

And definition 45 (p. 55) defines the arithmetical relation B between x and y so that
the proposition x B y is the same as the conjunction of the proposition that x is
the Gödel number of a series of series of signs forming a ‘proof-schema’ with
the proposition that the series of signs whose Gödel number is y is the last series of signs
in this ‘proof-schema’,

i.e. this ‘proof-schema’ is a ‘proof’ of the last formula in it. For the sake of clarity
I shall not follow Gödel’s abbreviating practice of using italicized words and phrases
to refer to arithmetical concepts applicable to Gödel numbers, and shall use italics
only in the ordinary way for emphasis.

For example, while Gödel paraphrases the x B y of definition 45 (p. 55) as:
x is a proof of the formula y, I paraphrase it as: x is the Gödel number of
a ’proof’ of the formula whose Gödel number is y.

965 ：考える名無しさん：2021/08/14(土) 17:40:59.02 0.net

Proposition VI simplified in this way may be stated as follows: If the formal system P satisfies
a certain condition of ‘consistency’, then there is at least one recursive class-sign r in P such
that neither υ Gen r nor Neg (υ Gen r) is ‘provable’ within P, where υ Gen r is the generalization of r
with respect to its free variable υ.

The undecidability of υ Gen r within P depends upon P’s satisfying a certain ‘consistency’ condition.
Since this condition is only relevant to the last stage of the proof, and itself raises important questions,
consideration of ‘consistency’ will be deferred until the main part of the proof has been discussed.
This main part is given in pp. 58f. from (8.1) to (16).

966 ：考える名無しさん：2021/08/14(土) 17:42:21.29 0.net

Gödel states his argument in terms of Gödel numbers and of relations between Gödel numbers;
and when the expressions relation-sign, free variable, class-sign, provable are used
they are italicized to show that they refer to arithmetical concepts applicable to Gödel numbers.

Because of the correspondence between these concepts as applied to Gödel numbers and
metamathematical concepts as applied to the strings which have these Gödel numbers,
Gödel’s whole argument applies equally well if his symbols are interpreted as strings and
the terms relation-sign, free variable, etc. are taken in their usual sense.

967 ：考える名無しさん：2021/08/14(土) 17:43:14.17 0.net

Since Gödel’s argument, though couched in terms of numbers, is a metamathematical argument,
it may be convenient for philosophical logicians if I give it wholly in metamathematical terms.

This will have the additional advantage that interpretations of the formulae can be inserted
parenthetically at appropriate places, on the assumption that the calculus (Gödel’s formal system P)
is to be interpreted as representing a deductive system which includes propositional and first-order predicate logic―
though, strictly speaking, any actual interpretation is irrelevant to the argument.

968 ：考える名無しさん：2021/08/15(日) 09:38:08.05 0.net

The Mathematical Theory of Communication, p. 59.

When C is the channel capacity (in bits per second) and H is the amount of information being
generated at the source (in bits per second), this theorem says that by devising proper coding procedures
it is possible to transmit symbols over the channel at an average rate which is nearly C/H but which,
no matter how clever the coding, can never be made to exceed C/H.

To put the point even less technically, when the rate at which information is generated is less than
the channel capacity, it is possible to code it in such a way that it will reach the receiver with arbitrarily
high fidelity. For this "informal" expression of the theorem, see J. L. Massey, "Information, Machines and Men,"
p. 50 in Philosophy and Cybernetics.

969 ：考える名無しさん：2021/08/15(日) 09:40:27.14 0.net

Unless one keeps in mind the divergent interests of communication theorists, some of
their claims will appear extravagant or absurd. For instance, in many discussions of information theory
one finds calculations of how much information is contained in a sample text of the English language.

These calculations are carried out in terms of 27 possibilities (26 letters and the space).
Discounting for the different probabilities of each letter (i.e., i is more probable than x) and
a high degree of redundancy (a string of letters narrows the possibilities, and changes the probabilities,
for the next letter), it is estimated that each letter in written English text has an average informational
measure of approximately 1 bit. Hence, each 5-letter word has an average informational measure of 5 bits.

See Shannon's original estimate (2 bits per symbol) in The Mathematical Theory of Communication,
p. 56, and his lowered estimate (1 bit per symbol) in "Prediction and Entropy of Printed English,"
Bell System Technical Journal, vol. 30 (1951), pp. 50–64. For a nontechnical exposition, see J. R. Pierce,
Symbols, Signals and Noise, New York, 1961, chap. 5.

970 ：考える名無しさん：2021/08/16(月) 17:01:42.98 0.net

At least there is a reasonable approximation to the conditions governing the theory's application.
In telecommunications one is dealing (or, at least, assumes that one is dealing) with stochastic processes
in which events occur with certain determinate probabilities.

Assumptions are also (more or less reasonably) made about the character of these stochastic processes―
e.g., that they are ergodic or "statistically homogeneous." Events are deemed "possible" that occur
with some frequency (however small) in the process under consideration. For a discussion of the restrictions
on the theory's application see Shannon, The Mathematical Theory of Communication, pp. 45–56.

971 ：考える名無しさん：2021/08/16(月) 17:02:51.54 0.net

Despite these limitations, formulas (2.1) and (2.2) have an important use. They can be used to make comparisons,
in particular comparisons between the amount of information generated by the occurrence of an event and
the amount of information a signal carries about that event.

Such comparisons can be made without ever determining absolute values for either magnitude.
That is, one can use these formulas in the way one would use a piece of string that is not marked off in inches and feet.
One can use the string to determine whether A is longer than B without ever determining the length of either A or B.

972 ：考える名無しさん：2021/08/23(月) 05:21:30.40 0.net

コロナはキリストの最後の審判に近づいてきてます

973 ：考える名無しさん：2021/09/18(土) 21:17:40.71 0.net

tes

974 ：考える名無しさん：2021/09/18(土) 21:17:40.71 0.net

tes

975 ：考える名無しさん：2021/09/18(土) 21:17:40.89 0.net

tes

976 ：考える名無しさん：2021/09/18(土) 21:18:04.07 0.net

てす

977 ：考える名無しさん：2021/09/18(土) 21:18:04.45 0.net

てす

978 ：考える名無しさん：2021/10/15(金) 16:38:17.66 0.net

英数国理社あるにもかかわらず、
youtubeは数学系動画に占拠されてしまった。

979 ：考える名無しさん：2021/10/15(金) 17:28:35.32 0.net

数学が苦手な奴＝数弱という言葉がネットを席巻している。

980 ：考える名無しさん：2021/10/15(金) 18:32:14.31 0.net

どれくらい努力できるかは数学によって決まるという価値観が、
若年層の間で広がっている。
このスレパート１ができた頃はそれほどまでではなかった。

981 ：考える名無しさん：2021/10/27(水) 00:27:34.30 0.net

数学が一般的に嫌われてるのは
能力マウントの道具になってるから
本や漫画だったら早く読めたとか数多く読んでるなんて
ことは別に自慢や評価にはならないし
本や漫画が自分が書けるかということも問わない
他人ではなく自分がどう味わえたかというところに関心はおかれる
だから多くのひとが数学と違って好んで嗜好する

982 ：考える名無しさん：2021/10/27(水) 10:57:14.61 0.net

本の場合博学自慢に使われていたことが昔あったみたいだけど、
今はもう数学に取って代わられたな。

983 ：考える名無しさん：2021/10/27(水) 12:04:26.51 0.net

本を買う余裕のない学生がいっぱい現れるようになったのだから致し方のないことだ。

984 ：考える名無しさん：2021/10/27(水) 13:19:12.34 0.net

数学は教科書と参考書だけで勉強できる。
文学や哲学は教科書だけでは足りない。

985 ：考える名無しさん：2021/10/27(水) 15:00:56.45 0.net

まあ、青空文庫で学ぶという手もあるが、
著作権の関係で宙ぶらりんな位置にあるサイトである。

986 ：考える名無しさん：2021/10/27(水) 15:54:33.68 0.net

日本の場合、崩し字や旧仮名遣いを学ばなければ先人の知恵に触れられないのが、
勉強する上で厄介なものである。

987 ：考える名無しさん：2021/10/27(水) 17:45:21.24 0.net

江戸時代に高度な算術が発展していたとは言え、
よく日本人は西洋の数学を取り入れられたものだと思う。

988 ：考える名無しさん：2021/10/27(水) 19:08:39.16 0.net

とは言え、理数系が突出してできる人間が一部いるだけではダメで、
科学リテラシーを全人類が持っているようでないと、
これから先の世界は持たないだろう。

989 ：考える名無しさん：2021/10/27(水) 19:34:56.11 0.net

何も知らない人をだまくらかして原発を建設したりすればろくなことにはならない
というのは日本を見ればわかる。

990 ：考える名無しさん：2021/10/27(水) 20:04:33.22 0.net

一部の国立大学の医学部で物理化学生物を全部課したりするのは良くわかる。

991 ：考える名無しさん：2021/10/27(水) 20:21:43.76 0.net

数学だけ出来ても、
自然現象や生身の人間の複雑さを捨象した
安易な思考に陥る恐れがあるからな。

992 ：考える名無しさん：2021/10/27(水) 20:28:49.80 0.net

最近の一次試験では地学が難しくなっている。
一部の進学校では地学は暗記科目だから楽だと言って選択する輩がいたものだから、
思考力を問う難しい出題になったのだろう。

993 ：考える名無しさん：2021/10/27(水) 20:35:31.71 0.net

暗記数学が流行る昨今は、果たしてどれくらい若者の間で思考力が身に付いているのか。

994 ：考える名無しさん：2021/10/27(水) 20:49:44.02 0.net

国語の教科書に関して、
論理国語と文学国語を分けるとか話題になっているようだから、
論理的思考が身に付いていないのかもしれない。

995 ：考える名無しさん：2021/10/27(水) 21:01:32.50 0.net

まあ結局これからの世の中は理数系の全分野がごっちゃになった工学的発想が
あらゆる分野に浸透しつくすのだろうなと悲観的に思ったりもする。

996 ：考える名無しさん：2021/10/27(水) 21:12:59.05 0.net

人体も既に開発され尽くしているが、
サイボーグやロボコップみたいなのが当たり前の世の中が来るのかもしれない。

997 ：考える名無しさん：2021/10/27(水) 21:25:52.50 0.net

データサイエンスが浸透するとどうなるのだろう。
京大の情報系は人気が上がって偏差値も暴騰しているとか。

998 ：考える名無しさん：2021/10/27(水) 21:32:24.31 0.net

一橋大学はソーシャルデータサイエンス学部を近く設置するようだ。
元から数学の難易度の高い一橋に理系の学部が置かれることになるのは無理筋ではないのだろう。

999 ：考える名無しさん：2021/10/27(水) 21:39:21.31 0.net

日本が斜陽になってから高校数学で統計を必須にするようになるのは、
なんとも皮肉なことだと思う。

1000 ：考える名無しさん：2021/10/27(水) 21:53:23.26 0.net

まあ、数学を初めとした理系の学問と哲学が、
社会の再建に資すれば良いのだが。

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