The decision of some provinces of the Anglican communion to extend to women the threefold ordained ministry has compromised the possibility of the recognition of Anglican orders by the Catholic church: they were declared invalid by pope Leo XIII in the bull Apostolicae Curae of 1896. The refusal to recognise as valid the sacrament of Order , administered in the Anglican church, does not signify, however, denial of efficacy on account of the grace present in the ordained minister of the (...) Anglicans. By taking up the formal distinction, introduced by Vatican II, between the church of Christ and the Catholic church , it is possible to reinterpret the question of the relationship between grace and order in the light of the ecclesiological implications of sacrum commercium - which occurs in baptism, ministry and eucharist - between the Catholic church and other ecclesial communities. (shrink)

Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collectionAis properly included in a collectionBthen the ‘size’ ofAshould be less than the (...) ‘size’ ofB(part–whole principle). This second intuition was not developed mathematically in a satisfactory way until quite recently. In this article I begin by reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers (Thabit ibn Qurra, Grosseteste, Maignan, Bolzano). Then, I review some recent mathematical developments that generalize the part–whole principle to infinite sets in a coherent fashion (Katz, Benci, Di Nasso, Forti). Finally, I show how these new developments are important for a proper evaluation of a number of positions in philosophy of mathematics which argue either for the inevitability of the Cantorian notion of infinite number (Gödel) or for the rational nature of the Cantorian generalization as opposed to that, based on the part–whole principle, envisaged by Bolzano (Kitcher). (shrink)

Some philosophers find the following thesis attractive: for every logical constant C there is a set of logical rules of inference R such that a subject knows the meaning of C if and only if she accepts the rules in R. I point out some obvious but, apparently, easily forgotten difficulties concerning this thesis.

Suppose you’re certain that a claim—say, ‘Frida is tall’—does not have a determinate truth value. What attitude should you take towards it? This is the question of the cognitive role of indeterminacy. This paper presents a puzzle for theories of cognitive role. Many of these theories vindicate a seemingly plausible principle: if you are fully certain that A, you are rationally required to be fully certain that A is determinate. Call this principle ‘Certainty’. We show that Certainty, in combination with (...) some minimal side premises, entails a very implausible claim: whenever you’re certain that it’s indeterminate whether A, it is rationally required that you reject A. This is a surprising result, which requires abandoning at least some intuitive views about indeterminacy and cognitive role. (shrink)

This article argues that Tolstoy’s What Is Art? had a direct influence on David Foster Wallace’s conception of literature, and most specifically that Wallace appropriated Tolstoy’s discourse (down to most of its most specific details) to found his literary project. The article seeks to prove this by exhibiting the striking extent of Wallace’s alignment with Tolstoy’s beliefs, by retracing the multiple direct references to Tolstoy in Wallace’s work, and by uncovering Wallace’s annotations on his own copy of What Is Art? (...) as further confirmation of what a careful comparative analysis of the works of the two authors makes manifest. (shrink)

In this paper I show that proofs by contradiction were a serious problem in seventeenth century mathematics and philosophy. Their status was put into question and positive mathematical developments emerged from such reflections. I analyse how mathematics, logic, and epistemology are intertwined in the issue at hand. The mathematical part describes Cavalieri's and Guldin's mathematical programmes of providing a development of parts of geometry free of proofs by contradiction. The logical part shows how the traditional Aristotelean doctrine that perfect demonstrations (...) are causal demonstrations influenced the reflection on proofs by contradiction. The main protagonist of this part is Wallis. Finally, I analyse some epistemological developments arising from the Cartesian tradition. In particular, I look at Arnauld's programme of providing an epistemologically motivated reformulation of Geometry free of proofs by contradiction. The conclusion explains in which sense these epistemological reflections can be compared with those informing contemporary intuitionism. (shrink)

This article argues that Sartre’s “What Is Literature?” had a profound and direct influence on David Foster Wallace’s conception of literature. At the very least, a number of factors oblige scholars to take this interpretation seriously. We know that Sartre’s existentialism pervades Wallace’s fiction, that Wallace repeatedly mentioned the Existentialists throughout his work, that he’d learned French to read them in the original, and that Sartre was one of his favorites, as testified by Zadie Smith. Most importantly, a comparative analysis (...) of Sartre’s text and Wallace’s nonfiction shows not only striking parallels but also almost exact repetitions in the writers’ fundamental ideals. In this sense, Sartre’s direct influence on Wallace appears so major as to invest multiple specific details of Wallace’s conception of literature both in its content and in the logical structuring of that content. In this article, we explore the extent of this influence through a structured investigation of its multiple features, showing that many of Wallace’s tenets – the rejection of Realism, the affirmation of meaning-as-use and of literature as a means to human communion and individual and social engagement, and many many more – follow from Sartre’s discourse. (shrink)

About a century ago, Ernst Mach argued that Archimedes’s deduction of the principle of the lever is invalid, since its premises contain the conclusion to be demonstrated. Subsequently, many scholars defended Archimedes, mostly on historical grounds, by raising objections to Mach’s reconstruction of Archimedes’s deduction. In the debate, the Italian philosopher and historian of science Giovanni Vailati stood out. Vailati responded to Mach with an analysis of Archimedes’s deduction which was later quoted and praised by Mach himself. In this paper, (...) my objective is to show that the debate can be further advanced, as Mach indicated, by reframing it in terms of the empirical vs. the logical dimensions of mechanics. In this way, I will suggest, the debate about Archimedes’s deduction can be resolved in Mach’s favour.Keywords: Equilibrium; Experience; Thought experiment; Archimedes; Ernst Mach; Giovanni Vailati. (shrink)

It is reported that in reply to John Wisdom’s request in 1944 to provide a dictionary entry describing his philosophy, Wittgenstein wrote only one sentence: “He has concerned himself principally with questions about the foundations of mathematics”. However, an understanding of his philosophy of mathematics has long been a desideratum. This was the case, in particular, for the period stretching from the Tractatus Logico-Philosophicus to the so-called transitional phase. Marion’s book represents a giant leap forward in this direction. In the (...) preface, Marion provides a diagnosis for why it has taken such a long time to obtain an accurate picture of Wittgenstein’s ideas in the foundations of mathematics. When the Remarks on the Foundations of Mathematics came out in 1956 the reception by specialists, such as Kreisel, was negative. This led many Wittgenstein scholars to set aside the issues in the foundations of mathematics and go on with the business of the day, focusing on Wittgenstein’s philosophy of language and psychology. However, these early negative appraisals were severely limited by two facts. First of all, the nature of the Remarks was a hindrance to an understanding of what Wittgenstein was up to. The book was edited by Wittgenstein’s literary executors by collating together passages from several manuscripts dating from 1937 to 1944, cutting, however, many passages in between remarks. Second, many of the original manuscripts and typescripts of the transitional phase were not available and thus it was virtually impossible to obtain a balanced picture of Wittgenstein’s development. Finally, a stark contraposition between the early and late Wittgenstein did not encourage people to work seriously on the development of Wittgenstein’s position from the Tractatus through the transitional period to the later writings. (shrink)

Part one: the act of speaking -- The speaker as performing artist -- The absolute performative -- The repetition of anthropogenesis -- Part two: toward a critic of interiority -- Second-degree sensualism: a physiognomic project -- In praise of reification -- Part three: from the beginning and right now -- Natural history -- The multitude and the principle of individuation -- Appendix: Wittgenstein and the question of atheism.

This paper extends the axiomatic treatment of intuitionistic mereology introduced in Maffezioli and Varzi (_Synthese, 198_(S18), 4277–4302 2021 ) by examining the behavior of constructive notions of overlap and disjointness. We consider both (i) various ways of defining such notions in terms of other intuitionistic mereological primitives, and (ii) the possibility of treating them as mereological primitives of their own.

The homeopathic principle of similitude is not based on the principle of vaccination but on the more general principle of inversion of effects, a widespread medical phenomenon. Based on the systemic networks which play an important role in response to stress, this principle concerns the reorganization of regulation systems, through a coherent response to the medicine. This model is backed by a large number of published studies from our laboratory and others, by toxicological evidence such as the emerging fields of (...) ‘hormesis’, of neuropharmacology, and of systems biology. The immune system is just one example of the possible application of this law of similitude, which constitutes the true ‘heart’ of the homeopathic idea, and again ethically justifies the attempt to apply it to experimental pharmacology. (shrink)

In this article I suggest that in the Soviet period Central Asians cultivated and conceptualized Islam as an episteme. They did this by reaching beyond alienating categories offered to them by the state. I argue that the constitution of an Islamic culture was made possible, among other things, by Central Asians’ encounters with the past, most notably with what they perceived as an Islamic past. We observe the curious phenomenon of Central Asians’ continuous interaction with the Islamic historical sites that (...) escaped the bulldozers of the Soviet campaigns of religious repression. For some, encounters with the past might be accidental. For many others, the exploration of the past represented a purposive, self-conscious, and reiterated emotional act. I show that Central Asians in the Soviet period—even if at school they were taught little about, and were usually offered a distorted vision of, the Islamic history of their region—were still able to access their past through the surviving architectural presence of Islam. Monumental sites, however, were not enough for Muslims to understand the past and use it to construct their own identity. Such artifacts acquired meaning through an interpretive framework provided by Sufi narratives about saints and their miracles. Therefore, shrines represented for Central Asia a collective memory space, i.e., a place in which the past was preserved for mobilization in the present through narrative. (shrink)