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1 hypothesis
1) гипотеза2) допущение; предположение3) постулат•hypothesis states that — гипотеза утверждает, что
- concurrent hypothesis - empirically testable hypothesis - incompletely confirmable hypothesis - indirectly testable hypothesis - multiple hypothesis - multivariate hypothesisto make a hypothesis — строить гипотезу; выдвигать гипотезу
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2 theorem
- analytical hierarchy theorem - arithmetical hierarchy theorem - closed range theorem - formally provable theorem - implicit function theorem - initial value theorem - integral representation theorem - local limit theorem - maximal ergodic theorem - mean value theorem - normal form theorem - ratio limit theorem - rational root theorem - second mean value theorem - theorem of consistency proofs - theorem of corresponding states - three line theorem - three series theorem - uniform convergence theorem - uniform ergodic theorem - uniform mean value theoremtheorem implies — из теоремы следует, что…
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3 Philosophy
And what I believe to be more important here is that I find in myself an infinity of ideas of certain things which cannot be assumed to be pure nothingness, even though they may have perhaps no existence outside of my thought. These things are not figments of my imagination, even though it is within my power to think of them or not to think of them; on the contrary, they have their own true and immutable natures. Thus, for example, when I imagine a triangle, even though there may perhaps be no such figure anywhere in the world outside of my thought, nor ever have been, nevertheless the figure cannot help having a certain determinate nature... or essence, which is immutable and eternal, which I have not invented and which does not in any way depend upon my mind. (Descartes, 1951, p. 61)Let us console ourselves for not knowing the possible connections between a spider and the rings of Saturn, and continue to examine what is within our reach. (Voltaire, 1961, p. 144)As modern physics started with the Newtonian revolution, so modern philosophy starts with what one might call the Cartesian Catastrophe. The catastrophe consisted in the splitting up of the world into the realms of matter and mind, and the identification of "mind" with conscious thinking. The result of this identification was the shallow rationalism of l'esprit Cartesien, and an impoverishment of psychology which it took three centuries to remedy even in part. (Koestler, 1964, p. 148)It has been made of late a reproach against natural philosophy that it has struck out on a path of its own, and has separated itself more and more widely from the other sciences which are united by common philological and historical studies. The opposition has, in fact, been long apparent, and seems to me to have grown up mainly under the influence of the Hegelian philosophy, or, at any rate, to have been brought out into more distinct relief by that philosophy.... The sole object of Kant's "Critical Philosophy" was to test the sources and the authority of our knowledge, and to fix a definite scope and standard for the researches of philosophy, as compared with other sciences.... [But Hegel's] "Philosophy of Identity" was bolder. It started with the hypothesis that not only spiritual phenomena, but even the actual world-nature, that is, and man-were the result of an act of thought on the part of a creative mind, similar, it was supposed, in kind to the human mind.... The philosophers accused the scientific men of narrowness; the scientific men retorted that the philosophers were crazy. And so it came about that men of science began to lay some stress on the banishment of all philosophic influences from their work; while some of them, including men of the greatest acuteness, went so far as to condemn philosophy altogether, not merely as useless, but as mischievous dreaming. Thus, it must be confessed, not only were the illegitimate pretensions of the Hegelian system to subordinate to itself all other studies rejected, but no regard was paid to the rightful claims of philosophy, that is, the criticism of the sources of cognition, and the definition of the functions of the intellect. (Helmholz, quoted in Dampier, 1966, pp. 291-292)Philosophy remains true to its classical tradition by renouncing it. (Habermas, 1972, p. 317)I have not attempted... to put forward any grand view of the nature of philosophy; nor do I have any such grand view to put forth if I would. It will be obvious that I do not agree with those who see philosophy as the history of "howlers" and progress in philosophy as the debunking of howlers. It will also be obvious that I do not agree with those who see philosophy as the enterprise of putting forward a priori truths about the world.... I see philosophy as a field which has certain central questions, for example, the relation between thought and reality.... It seems obvious that in dealing with these questions philosophers have formulated rival research programs, that they have put forward general hypotheses, and that philosophers within each major research program have modified their hypotheses by trial and error, even if they sometimes refuse to admit that that is what they are doing. To that extent philosophy is a "science." To argue about whether philosophy is a science in any more serious sense seems to me to be hardly a useful occupation.... It does not seem to me important to decide whether science is philosophy or philosophy is science as long as one has a conception of both that makes both essential to a responsible view of the world and of man's place in it. (Putnam, 1975, p. xvii)What can philosophy contribute to solving the problem of the relation [of] mind to body? Twenty years ago, many English-speaking philosophers would have answered: "Nothing beyond an analysis of the various mental concepts." If we seek knowledge of things, they thought, it is to science that we must turn. Philosophy can only cast light upon our concepts of those things.This retreat from things to concepts was not undertaken lightly. Ever since the seventeenth century, the great intellectual fact of our culture has been the incredible expansion of knowledge both in the natural and in the rational sciences (mathematics, logic).The success of science created a crisis in philosophy. What was there for philosophy to do? Hume had already perceived the problem in some degree, and so surely did Kant, but it was not until the twentieth century, with the Vienna Circle and with Wittgenstein, that the difficulty began to weigh heavily. Wittgenstein took the view that philosophy could do no more than strive to undo the intellectual knots it itself had tied, so achieving intellectual release, and even a certain illumination, but no knowledge. A little later, and more optimistically, Ryle saw a positive, if reduced role, for philosophy in mapping the "logical geography" of our concepts: how they stood to each other and how they were to be analyzed....Since that time, however, philosophers in the "analytic" tradition have swung back from Wittgensteinian and even Rylean pessimism to a more traditional conception of the proper role and tasks of philosophy. Many analytic philosophers now would accept the view that the central task of philosophy is to give an account, or at least play a part in giving an account, of the most general nature of things and of man. (Armstrong, 1990, pp. 37-38)8) Philosophy's Evolving Engagement with Artificial Intelligence and Cognitive ScienceIn the beginning, the nature of philosophy's engagement with artificial intelligence and cognitive science was clear enough. The new sciences of the mind were to provide the long-awaited vindication of the most potent dreams of naturalism and materialism. Mind would at last be located firmly within the natural order. We would see in detail how the most perplexing features of the mental realm could be supported by the operations of solely physical laws upon solely physical stuff. Mental causation (the power of, e.g., a belief to cause an action) would emerge as just another species of physical causation. Reasoning would be understood as a kind of automated theorem proving. And the key to both was to be the depiction of the brain as the implementation of multiple higher level programs whose task was to manipulate and transform symbols or representations: inner items with one foot in the physical (they were realized as brain states) and one in the mental (they were bearers of contents, and their physical gymnastics were cleverly designed to respect semantic relationships such as truth preservation). (A. Clark, 1996, p. 1)Socrates of Athens famously declared that "the unexamined life is not worth living," and his motto aptly explains the impulse to philosophize. Taking nothing for granted, philosophy probes and questions the fundamental presuppositions of every area of human inquiry.... [P]art of the job of the philosopher is to keep at a certain critical distance from current doctrines, whether in the sciences or the arts, and to examine instead how the various elements in our world-view clash, or fit together. Some philosophers have tried to incorporate the results of these inquiries into a grand synoptic view of the nature of reality and our human relationship to it. Others have mistrusted system-building, and seen their primary role as one of clarifications, or the removal of obstacles along the road to truth. But all have shared the Socratic vision of using the human intellect to challenge comfortable preconceptions, insisting that every aspect of human theory and practice be subjected to continuing critical scrutiny....Philosophy is, of course, part of a continuing tradition, and there is much to be gained from seeing how that tradition originated and developed. But the principal object of studying the materials in this book is not to pay homage to past genius, but to enrich one's understanding of central problems that are as pressing today as they have always been-problems about knowledge, truth and reality, the nature of the mind, the basis of right action, and the best way to live. These questions help to mark out the territory of philosophy as an academic discipline, but in a wider sense they define the human predicament itself; they will surely continue to be with us for as long as humanity endures. (Cottingham, 1996, pp. xxi-xxii)10) The Distinction between Dionysian Man and Apollonian Man, between Art and Creativity and Reason and Self- ControlIn his study of ancient Greek culture, The Birth of Tragedy, Nietzsche drew what would become a famous distinction, between the Dionysian spirit, the untamed spirit of art and creativity, and the Apollonian, that of reason and self-control. The story of Greek civilization, and all civilizations, Nietzsche implied, was the gradual victory of Apollonian man, with his desire for control over nature and himself, over Dionysian man, who survives only in myth, poetry, music, and drama. Socrates and Plato had attacked the illusions of art as unreal, and had overturned the delicate cultural balance by valuing only man's critical, rational, and controlling consciousness while denigrating his vital life instincts as irrational and base. The result of this division is "Alexandrian man," the civilized and accomplished Greek citizen of the later ancient world, who is "equipped with the greatest forces of knowledge" but in whom the wellsprings of creativity have dried up. (Herman, 1997, pp. 95-96)Historical dictionary of quotations in cognitive science > Philosophy
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