This is an earlier version of a chapter from my book "Plato's Republic as a Philosophical Drama on Doing Well" (2014). The book analyses Plato’s Politeia (= Republic) as a philosophical drama in which the participants turn out to be models of various types of psychic constitution, and nothing is said by them which may be considered to be an opinion of Plato himself (with all that that entails for Platonism). The debate in Book I between Socrates and Thrasymachus serves (...) as a test case for the assumptions that the Socratic method involves searching for truth or examining the opinions of interlocutors and that Socrates is the mouthpiece of Plato. Socrates and Thrasymachus are usually assumed to be arguing about justice. In fact, they are going through the motions of an eristic debate, where the aim is not to discover the truth about the matter under discussion but to defeat the opponent by fair means or foul, but especially foul. The outrageous wordplay used by both men is not so obvious in translation, and in any case tends to be ignored or explained away by scholars who assume that Plato the philosopher was writing a philosophical treatise (an exposition of philosophical ideas) and not a philosophical drama (a presentation of philosophically interesting models, to be compared and contrasted by the reader). (shrink)

C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed (...) with many fortunate circumstances, not least of which was entering the field when mathematical logic, after only six decades of toil, had just reaped one of its most important harvests with publication of the monumental Principia Mathematica. It was a time of joyful optimism which demanded an historical account and a sober philosophical critique. Lewis was one of the first to apply to mathematical logic the Aristotelian dictum that we do not understand a living institution until we see it growing from its birth. (shrink)

Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth) Also see https://www.academia.edu/s/a6bf02aaab This article uses ‘equals’ [‘is equal to’] and ‘is’ [‘is identical to’, ‘is one and the same as’] as they are used in ordinary exact English. In a logically perfect language the oxymoron ‘the numbers 3 and 2+1 are the same number’ could not be said. Likewise, ‘the number 3 and the number 2+1 are one number’ is just as bad from a logical point (...) of view. In normal English these two sentences are idiomatically taken to express the true proposition that ‘the number 3 is the number 2+1’. Another idiomatic convention that interferes with clarity about equality and identity occurs in discussion of numbers: it is usual to write ‘3 equals 2+1’ when “3 is 2+1” is meant. When ‘3 equals 2+1’ is written there is a suggestion that 3 is not exactly the same number as 2+1 but that they merely have the same value. This becomes clear when we say that two of the sides of a triangle are equal if the two angles they subtend are equal or have the same measure. -/- Acknowledgements: Robert Barnes, Mark Brown, Jack Foran, Ivor Grattan-Guinness, Forest Hansen, David Hitchcock, Spaulding Hoffman, Calvin Jongsma, Justin Legault, Joaquin Miller, Tania Miller, and Wyman Park. -/- ► JOHN CORCORAN AND ANTHONY RAMNAUTH, Equality and identity. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] The two halves of one line are equal but not identical [one and the same]. Otherwise the line would have only one half! Every line equals infinitely many other lines, but no line is [identical to] any other line—taking ‘identical’ strictly here and below. Knowing that two lines equaling a third are equal is useful; the condition “two lines equaling a third” often holds. In fact any two sides of an equilateral triangle is equal to the remaining side! But could knowing that two lines being [identical to] a third are identical be useful? The antecedent condition “two things identical to a third” never holds, nor does the consequent condition “two things being identical”. If two things were identical to a third, they would be the third and thus not be two things but only one. The plural predicate ‘are equal’ as in ‘All diameters of a given circle are equal’ is useful and natural. ‘Are identical’ as in ‘All centers of a given circle are identical’ is awkward or worse; it suggests that a circle has multiple centers. Substituting equals for equals [replacing one of two equals by the other] makes sense. Substituting identicals for identicals is empty—a thing is identical only to itself; substituting one thing for itself leaves that thing alone, does nothing. There are as many types of equality as magnitudes: angles, lines, planes, solids, times, etc. Each admits unit magnitudes. And each such equality analyzes as identity of magnitude: two lines are equal [in length] if the one’s length is identical to the other’s. Tarski [1] hardly mentioned equality-identity distinctions (pp. 54-63). His discussion begins: -/- Among the logical concepts […], the concept of IDENTITY or EQUALITY […] has the greatest importance. -/- Not until page 62 is there an equality-identity distinction. His only “notion of equality”, if such it is, is geometrical congruence—having the same size and shape—an equivalence relation not admitting any unit. Does anyone but Tarski ever say ‘this triangle is equal to that’ to mean that the first is congruent to that? What would motivate him to say such a thing? This lecture treats the history and philosophy of equality-identity distinctions. [1] ALFRED TARSKI, Introduction to Logic, Dover, New York, 1995. [This is expanded from the printed abstract.] . (shrink)

ONE of the most celebrated mathematical physicists, Pierre-Simon Laplace is often remembered as the mathematician who showed that despite appearances, the Solar System does conform to Newton’s theories. Together with distinguished scholars Robert Fox and Ivor Grattan-Guinness, Charles Gillispie gives us a new perspective, showing that Laplace did not merely vindicate Newton’s system, but had a uniquely creative and independent mind.

Prior to the nineteenth century, those who are now regarded as scientists were referred to as natural philosophers. With empiricism, science was claimed to be a superior form of knowledge to philosophy, and natural philosophy was marginalized. This claim for science was challenged by defenders of natural philosophy, and this debate has continued up to the present. The vast majority of mainstream scientists are comfortable in the belief that through applying the scientific method, knowledge will continue to accumulate, and that (...) claims to knowledge outside science apart from practical affairs should not be taken seriously. This is referred to as scientism. It is incumbent on those who defend natural philosophy against scientism not only to expose the illusions and incoherence of scientism, but to show that natural philosophers can make justifiable claims to advancing knowledge. By focusing on a recent characterization and defense of natural philosophy along with a reconstruction of the history of natural philosophy, showing the nature and role of Schelling’s conception of dialectical thinking, I will attempt to identify natural philosophy as a coherent tradition of thought and defend it as something different from science and as essential to it, and essential to the broader culture and to civilization. (shrink)