' Here is Tolstoy's religion; and non-violence is at its heart. Simon Parke, author of The Beautiful Life.

In the present article two possible meanings of the term mathematical structure are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of view, a (...) superfluous undertaking. This is done by analyzing the role played by the concept, in the first place, within Bourbaki's own mathematical output. Likewise, the interaction between Bourbaki's work and the first stages of category theory is analyzed, on the basis of both published texts and personal documents. (shrink)

In this epistolary exploration, scholars delve into Spinozas profound observations, offering urgent insights for our contemporary crossroads. Illuminates Spinoza s relevance, emphasizing the need to prioritize love, generosity, and solidarity as the bedrock of an ethical responsibility. These letters, a beacon of wisdom nowadays, implore us to recognize our shared dependence and embrace a new ethical framework. Amidst societal disintegration, Spinoza s teachings serve as a guiding light, ushering us toward a profound transformation, where compassion and understanding shape a future (...) beyond our current precipice. (shrink)

Helvetius -- Die Sozietätsphilosophie Franz von Baaders -- Gewalt und Recht in der Staats- und Rechtsphilosophie Rousseaus und der deutschen idealistischen Philosophie -- Das Dämonische.

Though the common sense defense of affirmative action (or employment equity) appeals to principles of restitution, philosophers have tried to defend it in other ways. In contrast, I defend it by appealing to the notion of restitution, arguing (1) that alternative attempts to justify affirmative action fail; and (2) that ordinary affirmative action programs need to be supplemented and amended in keeping with the principles this suggests.

The Securities and Exchange Commission (SEC) sanctioned investor-paid rating agency Egan-Jones for falsely stating that it did not know its clients’ investment positions. The SEC’s action against Egan-Jones raises the broad question whether knowledge of clients’ investment positions creates a conflict of interest for investor-paid ratings. In an experimental setting, we find that investor-paid rating agencies are likely to assign credit ratings that are biased in favor of their clients’ positions, and that this effect is attenuated when the rated company (...) has a sophisticated investor base that is expected to scrutinize ratings. The effect is not conditional on the risk profile of the rated companies. Taken together, our findings suggest that a conflict of interest stemming from investors’ preferences is likely to bias ratings under investor-pays business models, but scrutiny by the company’s investor base can counteract this bias. (shrink)

The ArgumentThe belief in the existence of eternal mathematical truth has been part of this science throughout history. Bourbaki, however, introduced an interesting, and rather innovative twist to it, beginning in the mid-1930s. This group of mathematicians advanced the view that mathematics is a science dealing with structures, and that it attains its results through a systematic application of the modern axiomatic method. Like many other mathematicians, past and contemporary, Bourbaki understood the historical development of mathematics as a series of (...) necessary stages inexorably leading to its current state — meaning by this, the specific perspective that Bourbaki had adopted and were promoting. But unlike anyone else, Bourbaki actively put forward the view that their conception of mathematics was not only illuminating and useful for dealing with the current concerns of mathematics, but that this was in fact the ultimate stage in the evolution of mathematics, bound to remain unchanged by any future development of this science. In this way, they were extending in an unprecedented way the domain of validity of the belief in the eternal character of mathematical truths, from the body to the images of mathematical knowledge.Bourbaki were fond of presenting their insistence on the centrality of the modern axiomatic method as a way to ensure the eternal character of mathematical truth as an offshoot of Hilbert's mathematical heritage. A detailed examination of Hilbert's actual conception of the axiomatic method, however, brings to the fore interesting differences between it and Bourbaki's conception, thus underscoring the historically conditioned character of certain, fundamental mathematical beliefs. (shrink)

A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has (...) a certain "slowness" property whereby the elements must enter X slowly (under a certain precise complexity measure of speed of computation) even though X may have high information content. Second we prove that every X with this slowness property is computable in some member of any nontrivial orbit, namely for any noncomputable A ∈ ε there exists B in the orbit of A such that X ≤ T B under relative Turing computability (≤ T ). We produce B using the Δ 0 3 -automorphism method we introduced earlier. (shrink)

In this essay I examine and discuss the concept “system of philosophy” as a methodological tool in the history of philosophy; I do so in two moves. First I analyze the historical origin of the concept in the seventeenth and eighteenth centuries. Thereafter I undertake a discussion of its methodological weaknesses—a discussion that is not only relevant to the writing of history of philosophy in the seventeenth and eighteenth centuries, but also to the writing of history of philosophy in our (...) times, where the concept remains an important methodological tool. My first move is to analyze Jacob Brucker’s employment of the concept in his influential history of philosophy, Historia critica philosophiae, dating from 1742–1744. To Brucker, a “system of philosophy” is characterized by the following four features: it is autonomous in regard to other, non-philosophical disciplines; all doctrines stated within the various branches of philosophy can be deduced from one principle; as an autonomous system it comprises all branches of philosophy; the doctrines stated within these various branches of philosophy are internally coherent. Brucker employed the concept on the entire history of philosophy, and he gave it a defining role in regard to two other methodological concepts, namely “eclecticism” and “syncretism,” which he regarded as more or less successful forms of systematic philosophy. My second move is to point out the weakness of the concept of “system of philosophy” as a methodological tool in the history of philosophy. I argue that the interdisciplinary nature of much premodern philosophy makes Brucker’s methodological concept “system of philosophy” inadequate, and that we may be better off leaving it behind in our future exploration of premodern philosophy. (shrink)

Metaphysics, formerly the queen of science, fell into oblivion under the onslaught of empiricism and positivism and its very possibllity came to be denied. Professor Elders traces the history of this process and shows how St. Thomas innovated in determining both the subject of metaphysics and the manner in which one enters this science, particularly in the framework of his Aristotle commentaries. The work then considers being and its properties, its divisions into being in act and being in potency, into (...) the act of being essence, and into substance and the accidents. Finally the causes of being are considered. The work also introduces and surveys the extensive literature of Thomas interpretation of the past 50 years. (shrink)

British Journal for the History of Philosophy, Volume 20, Issue 3, Page 619-625, May 2012.