In this paper (a sequel to [4]) I put forward a "local" interpretation of mathematical concepts based on notions derived from category theory. The fundamental idea is to abandon the unique absolute universe of sets central to the orthodox set-theoretic account of the foundations of mathematics, replacing it by a plurality of local mathematical frameworks - elementary toposes - defined in category-theoretic terms.

Genealogía y lógica de la ratio imperial romana -- Racionalización ética judía y religión de salvación cristiana -- La revolución teológica de Pablo y sus consecuencias -- Teología política imperial y militancia cristiana -- La teología trinitaria y el destino de la teología imperial -- Hilario, Ambrosio y el camino del catolicismo en Occidente -- Mal y salvación: Augstín de Hipona.

A key idea in both Frege's development of arithmetic in theGrundlagen[7] and Zermelo's 1904 proof [10] of the well-ordering theorem is that of a “type reducing” correspondence between second-level and first-level entities. In Frege's construction, the correspondence obtains betweenconceptandnumber, in Zermelo's (through the axiom of choice), betweensetandmember. In this paper, a formulation is given and a detailed investigation undertaken of a system ℱ of many-sorted first-order logic (first outlined in the Appendix to [6]) in which this notion of type reducing (...) correspondence is accorded a central role and which enables Frege's and Zermelo's constructions to be presented in such a way as to reveal their essential similarity. By adapting Bourbaki's version of Zermelo's proof of the well-ordering theorem, we show that, within ℱ, any correspondencecbetween second-level entities (here calledconcepts) and first-level ones (here calledobjects) induces a well-ordering relationW(c) in a canonical manner. We shall see that, whencis the “Fregean” correspondence between concepts and cardinal numbers,W(c) is (the well-ordering of) the ordinalω+ 1, and whencis a “Zermelian” choice function on concepts,W(c) is a well-ordering of the universal concept embracing all objects.In ℱ an important role is played by the notion ofextensionof a concept. To each conceptXwe assume there is assigned an objecte(X) in such a way that, for any conceptsX, Ysatisfying a certain predicateE, we havee(X) =e(Y) iff the same objects fall underXandY. (shrink)

The infinitesimal methods commonly used in the 17th and 18th centuries to solve analytical problems had a great deal of elegance and intuitive appeal. But the notion of infinitesimal itself was flawed by contradictions. These arose as a result of attempting to representchange in terms ofstatic conceptions. Now, one may regard infinitesimals as the residual traces of change after the process of change has been terminated. The difficulty was that these residual traces could not logically coexist with the static quantities (...) traditionally employed by mathematics. The solution to this difficulty, as it turns out, is to regard these quantities asalso being subject to (a form of) change, for then they will have the same nature as the infinitesimals representing the residual traces of change, and will become,ipso facto, compatible with these latter.In fact, the category-theoretic models which realize the Principle of Infinitesimal Linearity may themselves be regarded as representations of a general concept of variation (cf. Bell (1986)). While the static set-theoretical models represent change or motion by making a detour through the actual (but static) infinite, the varying category-theoretic models enable such change to be representeddirectly, thus permitting the introduction of geometric infinitesimals and, as we have attempted to demonstrate in this paper, the virtually complete incorporation of the methods of the early calculus.It is surely a remarkable — even an ironic — fact that the contradiction between the flux of the objective world and the stasis of mathematical entities has found its resolution in category theory, a branch of mathematics commonly, and, as one now sees, mistakenly, regarded as the summit of gratuitous abstraction. (shrink)

It will be noticed that, in the stemma above, no line of descent is marked from the first generation registered therein to the following generations. The genealogy of the Emperor Nerva is customarily traced back to the consul of 36 b.c., M. Cocceius Nerva. This short note will underline the ancient testimony found amongst the Pseudacroniana tracing his descent from the latter's brother, the consummate diplomat. There are ramifications. Amongst the items of interest will be the light shone upon what (...) Dio and Eutropius understood to be Nerva's standing at the time of his accession. Before passing on to Pseudacron's datum, it might be worthwhile pausing on that point, as well as briefly contemplating the factors that actually bore upon the emperor's ancestral training. (shrink)

In this chapter, Mackie presents a defence of Locke against Berkeley's attack on abstraction. It is argued that Locke's theory of ideas primarily concerns our ability to employ words and statements. Locke's theory concerning ideas of numbers is criticized. Three theories of universals are considered: realism, nominalism, and conceptualism; it is concluded, however, that the notion of there being distinct things with which we connect general words with particular things is mistaken. Mackie instead proposes a theory of general words being (...) ‘annexed’ to features of things. (shrink)

Mackie examines the distinction between primary and secondary qualities. It is argued that Locke's distinction supports the claim that he held a representative theory of perception. Mackie discussed Locke's arguments for the distinction. The relation of Locke's account to Molyneaux's problem is considered. Mackie critically compares his reformulation of the primary/secondary distinction with that of Jonathan Bennett.

These rhetorical texts by Apuleius, second-century Latin writer and author of the famous novel Metamorphoses or Golden Ass, have not been translated into English since 1909. They are some of the very few Latin speeches surviving from their century, and constitute important evidence for Latin and Roman North African social and intellectual culture in the second century AD, a period where there is increasing interest amongst classicists and ancient historians. They are the work of a talented writer who is being (...) increasingly viewed as the major literary artist of his time in Latin. (shrink)

What are the responsibilities of a business towards the city in which it operates? The Professor of Business Ethics at Nijenrode University, the Netherlands Business School suggests three practical ways of identifying them. This article is the substance of a paper which he delivered as Chairman of the European Business Ethics Network at its 1992 Conference in Paris.

The authors argue that while meaning holism makes massive error possible, it does not, as Donald Davidson fears, threaten interpretability. Thus they hold, in opposition to Davidson, that meaning holism need not be constrained by an account of meaning according to which in the methodologically most basic cases the content of a belief is given by the cause of that belief. What ensures interpretability, they maintain, is not that speakers' beliefs are in the main true, but rather that beliefs have (...) the contents they do because of events others can in principle identify and describe. (shrink)