We describe in some detail how to build an infinite computing machine within a continuous Newtonian universe. The relevance of our construction to the Church-Turing thesis and the Platonist-Intuitionist debate about the nature of mathematics is also discussed.

The ideas and methods of cybernetics are increasingly penetrating the biological and medical sciences, and today we are justified in speaking of a new branch of science: biological and medical cybernetics. This branch already has a number of important and encouraging subfields.

We discuss the philosophical status of the statement that (9n – 1) is divisible by 8 for various sizes of the number n. We argue that even this simple problem reveals deep tensions between truth and verification. Using Gillies's empiricist classification of theories into levels, we propose that statements in arithmetic should be classified into three different levels depending on the sizes of the numbers involved. We conclude by discussing the relationship between the real number system and the physical continuum.

Although many physicists have little interest in philosophical arguments about their subject, an analysis of debates about the paradoxes of quantum mechanics shows that their disagreements often depend upon assumptions about the relationship between theories and the real world. Some consider that physics is about building mathematical models which necessarily have limited domains of applicability, while others are searching for a final theory of everything, to which their favourite theory is supposed to be an approximation. We discuss some particular recent (...) debates about quantum theory in which the underlying assumptions are not fully articulated. Introduction Setting the scene The Ghirardi, Rimini and Weber theory Quantum marbles Radioactive decay and isomerism The limits of quantum theory. (shrink)

This article examines the text of Principia Mathematica to discover the extent to which Newton's claims about his own contribution to it were justified. It is argued that for polemical reasons the General Scholium, written twenty-six years after the first edition, substantially misrepresented the methodology of the main body of the text. The article discusses papers of Wallis, Wren and Huygens that use the third law of motion as set out by Newton in Book 1. It also argues that Newton's (...) use of induction is quite different from and subtler than the ‘logical’ and ‘probabilistic’ notions of induction discussed and then rejected by a number of twentieth-century philosophers. (shrink)

I examine Popper’s claims about Newton’s use of induction in Principia with the actual contents of Principia and draw two conclusions. Firstly, in common with most other philosophers of his generation, it appears that Popper had very little acquaintance with the contents and methodological complexities of Principia beyond what was in the famous General Scholium. Secondly Popper’s ideas about induction were less sophisticated than those of Newton, who recognised that it did not provide logical proofs of the results obtained using (...) it, because of the possibilities of later, contrary evidence. I also trace the historical background to commonplace misconceptions about Newton’s method.Author Keywords: Newton; Popper; Induction; Principia; Kepler’s laws. (shrink)

A dialogue between a foreign philosopher and a powerful statesman outline Plato's reflections on the family, the status of women, property rights, and criminal law.

Russia of the 1990s, in spite of its thousand-year traditions, is in some respects a new country in an unfamiliar and strange world: a country confronting a complex of hitherto unencountered macro-economic, technological, and ecological circumstances; a country compelled, in fact, to renounce its past global imperial ambitions, which in previous periods were defended in terms of the exclusive truth of the "autocratic-Orthodox" or "Marxist-Leninist" doctrine.

The lecture of V. S. Solov'ev on "The Historical Tasks of Philosophy" [Istoricheskie dela filosofii] was given by the young privat-docent on November 20, 1880 at St. Petersburg University; the text of the lecture was published in the periodical Russkaia mysl' soon thereafter. The lecture prepared the way for two parallel courses: a course in metaphysics at the university and a course in the history of ancient philosophy in the Advanced Women's Courses of K. N. Bestuzhev-Riumin. It is clear from (...) the text of the lecture how important a role Solov'ev's simultaneous and mutually related pursuits in metaphysics, the history of philosophy, comparative mythology, and the history of religion played in his early works. (shrink)

The regular increase in the proportion of resolved feet in the iambic trimeters of Euripides' later plays was first commented upon in 1807 by J. Gottfried Hermann, who therefrom deduced the principle that the date of any play of Euripides could be directly determined from the frequency of its resolutions. This criterion he restated in several of his works in the following years, and when Elmsley objected that it was of uncertain value on account of the small number of plays (...) of certain date by which it might be verified, he replied with a strong defence of his case: he did not, however, develop his principle in detail or give figures in its support. The first scholar to publish the totals of trisyllabic feet in each play was Zirndorfer: relying largely on these, he produced a chronology of Euripides' dramatic composition in several respects superior to any predecessor's. His conclusions were questioned by C. F. W. Müller, who, while accepting Hermann's thesis as being in general correct, doubted its reliability for determining the exact period of a tragedy's composition. Consequently, although he gave the totals of trisyllabic feet en passant, Müller made no attempt to suggest dates. At almost the same time as Müller's treatise appeared, J. Rumpel published an article giving a full and detailed list of references to all trisyllabic feet in Euripides: from this evidence he divided the dramas into four age-groups, but did not go so far as to assign specific dates. (shrink)

We discuss the extent to which the visibility of the heavens was a necessary condition for the development of science, with particular reference to the measurement of time. Our conclusion is that while astronomy had significant importance, the growth of most areas of science was more heavily influenced by the accuracy of scientific instruments, and hence by current technology.