We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first ‘local-to-global’ principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms are (...) necessary to prove Pincherle's theorem, does not have an unique or unambiguous answer, in contrast to compactness. We establish similar differences for the computational properties of compactness and Pincherle's theorem. We establish the same differences for other local-to-global principles, even going back to Weierstrass. We also greatly sharpen the known computational power of compactness, for the most shared with Pincherle's theorem however. Finally, countable choice plays an important role in the previous, we therefore study this axiom together with the intimately related Lindelöf lemma. (shrink)

This paper, which is mainly based on unpublished material, focuses on the scientific influence that Felice Casorati exerted on Salvatore Pincherle. This influence can be traced, in particular, in Casorati’s work on the finite-difference calculus as conceived and published between 1879 and 1880 when Pincherle was living in Pavia. Casorati’s work has an interesting back story related to his entry to the 1880 Grand Prix of the French Académie des Sciences that helps us in understanding Casorati’s personality. Moreover, (...) the correspondence that Casorati exchanged with other mathematicians on his work reveals that some of the results contained in Casorati :10–45, 1880b) had been obtained—though in a narrower context—in an early paper by Christoffel. Finally, the letters between Casorati and Pincherle contain a short unpublished note by Pincherle on a paper by Jules Tannery :113–182, 1875). This note offers the first evidence of the influence of Casorati :10–45, 1880b) on Pincherle’s work on the finite-difference calculus. (shrink)

Монография предназначена студентам старших курсов высших учебных заведений факультета иностранных языков, аспирантам и преподавателям.

On the life and works of Maṇḍanamiśra, philosopher of Saṅkarācārya tradition.

In lieu of an abstract, here is a brief excerpt of the content:James's Faith-Ladder JAMES C. S. WERNHAM JAMES WROTE OFTEN of a "faith-ladder."' What he said about it has drawn some side-glances from critics, but not yet any sustained and careful look.' That is surprising, for what he says is puzzling enough to invite inquiry. It is also important enough to deserve it. His presentations of the ladder show significant variation, so it is useful to look at a generous (...) sample. In the interest of brevity the following six passages have been extracted from contexts which sometimes have an important bearing on them. The unquoted contexts will get attention as needed. 1. "The inner process is a succession of 'synthetic judgments'. What is so good, may be, ought to be, must be, shall be,--so far as I am concerned, I won't admit the opposite. ''s 2. "[W]e have a conception which being opposed by another is only probab /e. But we feel, it is so good that it isfit to be true, it ought to be true, it must be true etc. And then we say it shall be true for me, it/s true. ''4 3- "Its [faith's] natural logic is the Sorites: fit to be, ought to be, may be, must be, shall be, is etc.''5 4. "The following steps may be called the 'faith-ladder': ~. There is nothing absurd in a certain view of the world being true, nothing self-contradictory; ' To the best of my knowledge, the name "faith-ladder'"does not occur before 19o6. It occurs in "Faith and Reason" and in "Faith and the Right to Believe," both written in that year. But expositions of the thing predate the name. They are found as early as 1899, and in close connection with the will-to-believe doctrine. 9 Levinson's discussion is a partial exception. His treatment is more extended than most. See H. S. Levinson, $c/ence, Metaphysicsand the Chan~e of Salvation (Missoula, MT: Scholars Press, 1978), 161--67; also his The Religious Investigations of Wdliam James (Chapel Hill: University of North Carolina Press, 198 0, 231-34. s Letter to Baldwin, quoted in'R. B. Perry, The Thoughtand Characterof WilliamJames, 2 vols. (Boston: Little, Brown and Co., 1935), 2: 243. 4 Letter to Marshall, Feb. 9, 1899, quoted in Perry, Thought and Character,2: 24~. 5 William James, A Pluralistic Universe (Cambridge, MA and London: Harvard Universit~t Press, 1977), 199. [1o5] lO6 JOURNAL OF THE HISTORY OF PHILOSOPHY 28" 1 JANUARY I990 2. If might have been true under certain conditions; 3- It may be true even now; 4. It isfit to be true; 5- It ought to be true; 6. It must be true; 7- It s/m//be true, at any rate true for me. ''6 5. "Faith's form of argument is something like this: Considering a view of the world: 'It isfit to be true', she feels; 'it would be well if it were true; it might be true; it may be true; it ought to be true', she says; 'it must be true', she continues; 'it shall be true', she concludes, 'for me; that is, I will treat it as if it were true so far as my advocacy and actions are concerned'. ''7 6. "A conception of the world arises in you somehow, no matter how. Is it true or not? you ask. It might be true somewhere, you say, for it is not self-contradictory. It may be true, you continue, even here and now. It is fit to be true, it would be well if it were true, it ought to be true, you presently feel. It must be true, something persuasive in you whispers next; and then--as a final result--it shall be held for true, you decide; it shall be as if true, for you. ''s 9. Between these statements there are clear similarities and clear differences too. Some of them deserve to be noted, some to be noted and explored. a. In these accounts of it the ladder varies in the number of its rungs. By James's own count in one place, it has as many as seven. In... (shrink)

The present study investigates whether people can infer the preferences of others from spontaneous facial expressions alone. We utilize a paradigm that unobtrusively records people's natural facial reactions to relatively mundane stimuli while they simultaneously report which ones they find more appealing. Videos were then presented to perceivers who attempted to infer the choices of the target individuals—thereby linking perceiver inferences to objective outcomes. Perceivers demonstrated above-chance ability to infer target preferences across four different stimulus categories: people (attractiveness), cartoons (humor), (...) paintings (decorative appeal), and animals (cuteness). While perceivers' subjective ratings of expressivity varied somewhat between targets, these ratings did not predict the relative “readability” of the targets. The findings suggest that noncommunicative, natural facial behavior by itself suffices for certain types interpersonal prediction, even in low-emotional contexts. (shrink)

On history of Buddhist philosophy; contributed articles.

John Stuart Mill's Utilitarianism continues to serve as a rich source of moral and theoretical insight. This collection of articles by top scholars offers fresh interpretations of Mill's ideas about happiness, moral obligation, justice, and rights. Applying contemporary philosophical insights, the articles challenge the conventional readings of Mill, and, in the process, contribute to a deeper understanding of utilitarian theory as well as the complexity of moral life.