X -> [W, WxY]
Here the operation [W, Wx(-)) is the monad on the type system which is induced by the above adjunction; and this latter function is naturally regarded as a morphism in the Kleisli category of this monad.
Classification is a halfway house between the immediate concreteness of
the individual thing and the complete abstraction of mathematical
notions. The species take account of the specific character, and the
genera of the generic character. But in the procedure of relating
mathematical notions to the facts of nature, by counting, by
measurement, and by geometrical relations, and by types of order, the
rational contemplation is lifted from the incomplete abstractions
involved in definite species and genera, to the complete, abstractions
of mathematics. Classification is necessary. But unless you can progress
from classification to mathematics, your reasoning will not take you
very far.
The practical counsel to be derived from Pythagoras, is to measure, and thus
to express quality in terms of numerically determined quantity. But the
biological sciences, then and till our own time, have been
overwhelmingly classificatory. Accordingly, Aristotle by his Logic
throws the emphasis on classification. The popularity of Aristotelian
Logic retarded the advance of physical science throughout the Middle
Ages.
Whitehead. Science ..., 1925
It often happens, therefore, that in criticising a learned book of
applied mathematics, or a memoir, one’s whole trouble is with the first
chapter, or even with the first page. For it is there, at the very
outset, where the author will probably be found to slip in his
assumptions. Farther, the trouble is not with what the author does say,
but with what he does not say. Also it is not with what he knows he has
assumed, but with what he has unconsciously assumed. We do not doubt the
author’s honesty. It is his perspicacity which we are criticising. Each
generation criticises the unconscious assumptions made by its parents.
It may assent to them, but it brings them out in the open.
Whitehead. Science in the modern world, 1925.
...thought can penetrate into every occasion of fact, so that by comprehending its key conditions, the whole complex of its pattern of conditions lies open before it.
...
Pythagoras was the first man who had any grasp of the full sweep of this general principle.
...
He asked, ‘What is the status of mathematical entities, such as numbers for example, in the realm of things?’ The number ‘two,’ for example, is in some sense exempt from the flux of time and the necessity of position in space. Yet it is involved in the real world. The same considerations apply to geometrical notions—to circular shape, for example.
...
unless you can progress from classification to mathematics, your reasoning will not take you very far.
Whitehead. Science in the modern world. 1925. Chapter II.
https://www.gutenberg.org/cache/epub/68611/pg68611.txt
Accordingly the full universe, disclosed for every variety of experience, is a universe in which every detail enters into its proper relationship with the immediate occasion. The generality of mathematics is the most complete generality consistent with the community of occasions which constitutes our metaphysical situation.
Whitehead. Science in the modern world, 1925.
https://www.gutenberg.org/cache/epub/68611/pg68611.txt
«Мифы составляют, говоря буквально, наиболее драгоценное сокровище племени. Они относятся к самой сердцевине того, что племя почитает как святыню. Наиболее важные мифы известны лишь старикам, которые ретиво оберегают их тайну... Старые хранители этих тайных знаний сидят в селении, немы, как сфин- ксы, и решают, в какой мере они могут, не навлекая опасности, доверить знания предков молодому поколению и в какой именно момент эта передача тайн может оказаться наиболее плодотворной...» (Леви-Брюль 262). Мифы — не только составные части жизни, они — части каждого человека в отдельности. Отнять у него рассказ — эти значит отнять у него жизнь.
...
Лишившись мифов, племя было бы не в состоянии удержать свое существование.
...начало этого процесса, процесса перерождения мифа в сказку, сказывается в откреплении сюжета и акта рассказывания от ритуала. ^Момент этого открепления от обряда есть начало истории сказки, тогда как ее синкретизм с обрядом представляет собой ее доисторию.
...
Связь этих обрядов с мифами и связь их обоих со сказкой еще совершенно не исследована.
...
- Из всего сказанного видно, что уже очень рано начинается «профанация» священного сюжета (под «профанацией» понимаем превращение священного рассказа в профанный, т. е. не духовный, не эсотеричёский, а художественный). Это и есть момент рождения собственно сказки. Но отделить, где кончается священный рассказ и начинается сказка, — невозможно.
-- В. Пропп. Исторические корни волшебной сказки.
“Cultural representations such as Little Red Riding Hood, the Golden Rule, or multiplication tables are, most of the time, considered in the abstract, even though they must be instantiated in mental and public representations in order to play a role in human affairs.. Since representations are recognized in our commonsense ontology, the question arises: What cognitive mechanisms do we have, if any, for drawing inferences about them? ”
“There must be a mindreading module—actually a minds-reading module, with “minds” in the plural—that has the job of managing, in our mental files about other people, what these people have in their men “mental files. No such module, however, could do the job on its own. In order to perform mindreading inferences about the inferences that are performed in other people’s mind, the mindreading module must be linked to a great variety of other inferential modules and use them for updating the information represented in individual files.”
Dan Sperber. “The Enigma of Reason: A New Theory of Human Understanding.”
“IV. (9)
The understanding
forms positive ideas
before
forming negative ideas.
V. (108:10)
It perceives things not so much under the condition
of duration as under a certain form of eternity, and in an
infinite number; or rather in perceiving things it does not
consider either their number or duration, whereas, in imagining
them, it perceives them in a determinate number, duration, and quantity.”
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