This article discusses the relation between empirical and normative approaches in bioethics. The issue of dwarf tossing, while admittedly unusual, is chosen as a point of departure because it challenges the reader to look with fresh eyes upon several central bioethical themes, including human dignity, autonomy, and the protection of vulnerable people. After an overview of current approaches to the integration of empirical and normative ethics, we consider five ways that the empirical and normative can be brought together to speak (...) to the problem of dwarf tossing: prescriptive applied ethics, theoretical ethics, critical applied ethics, particularist ethics and integrated empirical ethics. We defend a position of critical applied ethics that allows for a two-way relation between empirical and normative theories. Against efforts fully to integrate the normative and the empirical into one synthesis, we propose that the two should stand in tension and relation to one another. The approach we endorse acknowledges that a social practice can and should be judged both by the gathering of empirical data and by normative ethics. Critical applied ethics uses a five stage process that includes: (a) determination of the problem, (b) description of the problem, (c) empirical study of effects and alternatives, (d) normative weighing and (e) evaluation of the effects of a decision. In each stage, we explore the perspective from both the empirical (sociological) and the normative ethical point of view. We conclude by applying our five-stage critical applied ethics to the example of dwarf tossing. (shrink)

Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the (...) subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time. (shrink)

Why do we remember the past and not the future? What does it mean for time to "flow"? Do we exist in time or does time exist in us? In lyric, accessible prose, Carlo Rovelli invites us to consider questions about the nature of time that continue to puzzle physicists and philosophers alike. For most readers this is unfamiliar terrain. We all experience time, but the more scientists learn about it, the more mysterious it remains. We think of it (...) as uniform and universal, moving steadily from past to future, measured by clocks. Rovelli tears down these assumptions one by one, revealing a strange universe where at the most fundamental level time disappears. He explains how the theory of quantum gravity attempts to understand and give meaning to the resulting extreme landscape of this timeless world. Weaving together ideas from philosophy, science and literature, he suggests that our perception of the flow of time depends on our perspective, better understood starting from the structure of our brain and emotions than from the physical universe. (shrink)

Facts happen at every interaction, but they are not absolute: they are relative to the systems involved in the interaction. Stable facts are those whose relativity can effectively be ignored. In this work, we describe how stable facts emerge in a world of relative facts and discuss their respective roles in connecting quantum theory and the world. The distinction between relative and stable facts resolves the difficulties pointed out by the no-go theorem of Frauchiger and Renner, and is consistent with (...) the experimental violation of the Local Friendliness inequalities of Bong et al.. Basing the ontology of the theory on relative facts clarifies the role of decoherence in bringing about the classical world and solves the apparent incompatibility between the ‘linear evolution’ and ‘projection’ postulates. (shrink)

This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last (...) century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality. (shrink)

The concept of dignity is notoriously vague. In this paper it is argued that the reason for this is that there are three versions of dignity that are often confused. First we will take a short look at the history of the concept of dignity in order to demonstrate how already from Roman Antiquity two versions of dignity can be distinguished. Subsequently, the third version will be introduced and it will be argued that although the three versions of dignity hang (...) together, they should also be clearly distinguished in order to avoid confusion. The reason for distinguishing the three versions is because all three of them are only partially effective. This will be demonstrated by taking the discussion about voluntary ‘dying with dignity’ as an example. Inspired by both Paul Ricoeur’s concept of ethics and the ethics of care a proposition will be done as to how the three versions of dignity may sustain each other and help achieve what neither one of the versions can do on its own. (shrink)

According to the implicit commitment thesis, once accepting a mathematical formal system S, one is implicitly committed to additional resources not immediately available in S. Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in S itself. It has recently become clear, however, that such reading of the implicit commitment thesis cannot be compatible with well-established positions (...) in the foundations of mathematics which consider a specific theory S as self-justifying and doubt the legitimacy of any principle that is not derivable in S: examples are Tait’s finitism and the role played in it by Primitive Recursive Arithmetic, Isaacson’s thesis and Peano Arithmetic, Nelson’s ultrafinitism and sub-exponential arithmetical systems. This casts doubts on the very adequacy of the implicit commitment thesis for arithmetical theories. In the paper we show that such foundational standpoints are nonetheless compatible with the implicit commitment thesis. We also show that they can even be compatible with genuine soundness extensions of S with suitable form of reflection. The analysis we propose is as follows: when accepting a system S, we are bound to accept a fixed set of principles extending S and expressing minimal soundness requirements for S, such as the fact that the non-logical axioms of S are true. We call this invariant component the semantic core of implicit commitment. But there is also a variable component of implicit commitment that crucially depends on the justification given for our acceptance of S in which, for instance, may or may not appear reflection principles for S. We claim that the proposed framework regulates in a natural and uniform way our acceptance of different arithmetical theories. (shrink)

One of the world's most renowned theoretical physicists, Carlo Rovelli has entranced millions of readers with his singular perspective on the cosmos. In Helgoland, Rovelli examines the enduring enigma of quantum theory. The quantum world Rovelli describes is as beautiful as it is unnerving. Helgoland is a treeless island in the North Sea where the 21-year-old Werner Heisenberg first developed quantum theory, setting off a century of scientific revolution. Full of alarming ideas (ghost waves, distant objects that seem to (...) be magically connected, cats that appear both dead and alive), quantum physics has led to countless discoveries and technological advancements. Today our understanding of the world is based on this theory, yet it is still profoundly mysterious. As scientists and philosophers continue to fiercly debate the theory's meaning, Rovelli argues that its most unsettling contradictions can be explained by seeing the world as fundamentally made of relationships, not substances. We and everything around us exist only in our interactions with one another. This bold idea suggests new directions for understanding the structure of reality and even the nature of consciousness. Rovelli makes learning about quantum mechanics an almost psychedelic experience. Shifting our perspective once again, he takes us on a riveting journey through the universe so we can better understand our place in it. (shrink)

In his 1956 book ‘The Direction of Time’, Hans Reichenbach offered a comprehensive analysis of the physical ground of the direction of time, the notion of physical cause, and the relation between the two. I review its conclusions and argue that at the light of recent advances in physics Reichenbach analysis provides the best account for the physical underpinning of these notions. I integrate results in cosmology, and on the physical underpinning of records and agency into Reichenbach’s account, and discuss (...) which questions it leaves open. (shrink)

Human beings are getting fatter and sicker. As we question what we eat and why we eat it, this book argues that living well involves consuming a raw vegan diet. With eating healthfully and eating ethically being simpler said than done, this book argues that the best solution to health, environmental, and ethical problems concerning animals is raw veganism―the human diet. The human diet is what humans are naturally designed to eat, and that is, a raw vegan diet of fruit, (...) tender leafy greens, and occasionally nuts and seeds. While veganism raises challenging questions over the ethics of consuming animal products, while also considering the environmental impact of the agriculture industry, raw veganism goes a step further and argues that consuming cooked food is also detrimental to our health and the environment. Cooking foods allows us to eat food that is not otherwise fit for human consumption and in an age that promotes eating foods in ‘moderation’ and having ‘balanced’ diets, this raises the question of why we are eating foods that should only be consumed in moderation at all, as moderation clearly implies they aren’t good for us. In addition, from an environmental perspective, the use of stoves, ovens and microwaves for cooking contributes significantly to energy consumption and cooking in general generates excessive waste of food and resources. Thus, this book maintains that living well and living a noble life, that is, good physical and moral health, requires consuming a raw vegan diet. Exploring the scientific and philosophical aspects of raw veganism, this novel book is essential reading for all interested in promoting ethical, healthful, and sustainable diets. (shrink)

We discuss the principles for a primitive, object-linguistic notion of consequence proposed by ) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a notion (...) of logical consequence: we study the corresponding theory of validity by showing that it is conservative over a wide range of base theories: this result is achieved via a well-behaved form of local reduction. The theory of logical consequence is based on a restriction of the introduction rule for the consequence predicate. To unrestrictedly maintain this principle, we develop a conception of object-linguistic consequence, which we call grounded consequence, that displays a restriction of the structural rule of reflexivity. This construction is obtained by generalizing Saul Kripke’s inductive theory of truth. Grounded validity will be shown to satisfy several desirable principles for a naïve, self-applicable notion of consequence. (shrink)

Testable predictions of quantum mechanics are invariant under time reversal. But the evolution of the quantum state in time is not so, neither in the collapse nor in the no-collapse interpretations of the theory. This is a fact that challenges any realistic interpretation of the quantum state. On the other hand, this fact raises no difficulty if we interpret the quantum state as a mere calculation device, bookkeeping past real quantum events.

What is morally valuable—if anything at all—in entrepreneurship? Existing normative takes can be broadly categorized as belonging to two main views: a backward and a forward-looking approach. The former sees entrepreneurial activity as a permissible emergent product of individuals’ interactions within the boundaries of people’s existing rights; the latter looks at entrepreneurship in the broader context of market processes and emphasizes its role in generating Pareto-improvements in social welfare. In this paper, I suggest that certain instances of entrepreneurship can be (...) intrinsically valuable when they constitute Millian Experiments in Living, that is when entrepreneurial ventures are the expression of an entrepreneur’s conception of the good. Engaging in entrepreneurial activity which reflects one’s conception of the good helps individuals in cultivating their individuality and originality by means of subjecting their normative beliefs to empirical scrutiny, thus allowing one to confirm, revise, or refine them. (shrink)

In this paper we argue that Sen's defence of liberal democracy suffers from a moralistic and pro-liberal bias that renders it unable to take pluralism as seriously as it professes to do. That is because Sen’s commitment to respecting pluralism is not matched by his account of how to individuate the sorts of preferences that ought to be included in democratic deliberation. Our argument generalises as a critique of the two most common responses to the fact of pluralism in contemporary (...) (i.e. post-Rawls) liberalism: a broadly procedural understanding of autonomy and the idea of deliberative democracy. That is to say, the difficulties with pluralism we identify can be traced back to the particular version of Kantian deontology prevalent in contemporary liberalism, and to the equally prevalent aspiration to ground political legitimacy in a moralised consensus. (shrink)

On the basis of historical and textual evidence, this paper claims that after his Tractatus, Wittgenstein was actually influenced by Einstein's theory of relativity and, the similarity of Einstein's relativity theory helps to illuminate some aspects of Wittgenstein's work. These claims find support in remarkable quotations where Wittgenstein speaks approvingly of Einstein's relativity theory and in the way these quotations are embedded in Wittgenstein's texts. The profound connection between Wittgenstein and relativity theory concerns not only Wittgenstein's “verificationist” phase , but (...) also Wittgenstein's later philosophy centred on the theme of rule‐following. (shrink)

Since the crisis of Fordism, capitalism has been characterised by the ever more central role of knowledge and the rise of the cognitive dimensions of labour. This is not to say that the centrality of knowledge to capitalism is new per se. Rather, the question we must ask is to what extent we can speak of a new role for knowledge and, more importantly, its relationship with transformations in the capital/labour relation. From this perspective, the paper highlights the continuing validity (...) of Marx's analysis of the knowledge/power relation in the development of the division of labour. More precisely, we are concerned with the theoretical and heuristic value of the concepts of formal subsumption, real subsumption and general intellect for any interpretation of the present change of the capital/labour relation in cognitive capitalism. In this way, we show the originality of the general intellect hypothesis as a sublation of real subsumption. Finally, the article summarises key contradictions and new forms of antagonism in cognitive capitalism. (shrink)

This is a profound study of Aristotle's concept of phronesis, or practical wisdom. Carlo Natali critically reconsiders Aristotle's famous doctrine of contemplations, relating it to contemporary theories of the good life.

In what follows I consider the apparent contrast between two kinds of theories of context: a theory of objective context - exemplified in the works of Kaplan and Lewis - and a theory of subjective context -exemplified in the works of McCarthy and Giunchiglia. I consider then some difficulties for the objective theory. I don't give any formalization; instead I give some theoretical points about the problem. A possible result could be the abandon of the double indexing for a development (...) a multi-context theory (I give an example of a case). However other results could be possible and a challenge is posed to solve problems using the best results from each tradition of research. (shrink)

We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘\-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules are all valid in fixed-point models; the second by ‘\-like’ theories first introduced by Solomon Feferman, that lose this property but reflect the classicality of the metatheory in which Kripke’s construction is carried out. We show that (...) to any natural system in one cluster—corresponding to natural variations on induction schemata—there is a corresponding system in the other proving the same sentences true, addressing a problem left open by Halbach and Horsten and accomplishing a suitably modified version of the project sketched by Reinhardt aiming at an instrumental reading of classical theories of self-applicable truth. (shrink)

Shannon's notion of relative information between two physical systems can function as foundation for statistical mechanics and quantum mechanics, without referring to subjectivism or idealism. It can also represent a key missing element in the foundation of the naturalistic picture of the world, providing the conceptual tool for dealing with its apparent limitations. I comment on the relation between these ideas and Democritus.

Biological diversity would apparently seem the most intuitive and easily studied of all the ecological concepts. However, in practice biodiversity has suffered from great number of definitions that vary with the specific needs of the different researchers, thus making it extremely confusing as an ecological concept. In this paper, I shortly review the concept of biodiversity showing that there exists a substantial ambiguity among ecologists as far as biodiversity conceptualization and evaluation is concerned. I conclude that, due to this major (...) disagreement on its very nature, biodiversity may be defined simply as a set of multivariate summary statistics for quantifying different characteristics of community structure. (shrink)

No detailed description available for "Conventionalism in logic".

One way to study and understand the notion of truth is to examine principles that we are willing to associate with truth, often because they conform to a pre-theoretical or to a semi-formal characterization of this concept. In comparing different collections of such principles, one requires formally precise notions of inter-theoretic reduction that are also adequate to compare these conceptual aspects. In this work I study possible ways to make precise the relation of conceptual equivalence between notions of truth associated (...) with collections of principles of truth. In doing so, I will consider refinements and strengthenings of the notion of relative truth-definability proposed by Fujimoto (2010): in particular I employ suitable variants of notions of equivalence of theories considered in Visser (2006) and Friedman & Visser (2014) to show that there are better candidates than mutual truth-definability for the role of sufficient condition for conceptual equivalence between the semantic notions associated with the theories. In the concluding part of the paper, I extend the techniques introduced in the first and show that there is a precise sense in which ramified truth (either disquotational or compositional) does not correspond to iterations of comprehension. (shrink)

The author deals with the lost works of Empedocles, an often neglected subject, in the frame of the discussion concerning the number of the poems and their main features. He reviews the traces of the Passage of Xerxes, of the Medical Discourse, and of the Proem to Apollo among the fragments and witnesses, taking his cue from textual aspects and dealing with the contents, the significance of each of these writings in Empedocles’ culture and thought and their multifarious relationships with (...) his times. As to the Passage, he tries to reconcile the contrasting interpretations so far proposed (historical or religious poem). Concerning B111, the only relic from the Medical Discourse, he explains why its contents are incompatible with the Physical Poem and the Purifications. He analyzes the Proem to Apollo in several perspectives (text, witnesses, contents also from the epistemological point of view, literary genre). He assigns fragments 131–134 and 142 to the Proem, drawing one of his arguments from the comparison with the third Homeric Hymn to Apollo, and also suggesting a relationship with an intellectual cult of the sun. Formal features help to ascribe each fragment to the relevant poem. Close similarities between fragments do not necessarily mean that they come from the same writing: Empedocles is wont to allude to one poem of his while composing another. The author concludes that the striving for a reductio ad unum of the Acragantine’s output, also evident in the attempt by a number of scholars to make only one poem out of the Περὶ φύσεως and the Καθαρμοί, has often led researchers to take for granted that none of the fragments preserved might belong to the lost works. (shrink)

In this paper, I discuss some of Maximilian de Gaynesford’s arguments regarding indexicals. Although I agree with his treatment of the first singular personal pronoun as a prototype of demonstrative expressions, I challenge his refusal to treat indexicals as complex demonstratives. To offer an alternative to this refusal I try to develop a common ground from different theories that consider indexicals as linguistic constructions that embed a nonlinguistic element, following an original idea in Frege’s latest writings. These views form the (...) backdrop on which we can put forward the claim of treating all indexicals as complex demonstratives. In the central part of the paper, I criticize each of de Gaynesford’s arguments against the reduction of indexicals to complex demonstratives. Besides, I propose a new definition of the concept of “demonstration” as a nonlinguistic feature of all indexicals in their referential uses, to contrast de Gaynesford’s rejection of the idea that demonstrations are an essential feature of indexicals. Eventually, I strengthen my claim by distinguishing indexicals from proper names and definite descriptions on the ground that only perceptual indexicals necessarily require an accompanying demonstration. However, the main point of the paper is a negative one, that is the rejection of de Gaynesford’s arguments against the reduction of indexicals to complex demonstratives. More work is needed to reach a positive conclusion on this topic. (shrink)

In this paper I offer a defence of a Russellian analysis of the referential uses of incomplete (mis)descriptions, in a contextual setting. With regard to the debate between a unificationist and an ambiguity approach to the formal treatment of definite descriptions (introduction), I will support the former against the latter. In 1. I explain what I mean by "essentially" incomplete descriptions: incomplete descriptions are context dependent descriptions. In 2. I examine one of the best versions of the unificationist “explicit” approach (...) given by Buchanan and Ostertag. I then show that this proposal seems unable to treat the normal uses of misdescriptions. I then accept the challenge of treating misdescriptions as a key to solving the problem of context dependent descriptions. In 3. I briefly discuss Michael Devitt’s and Joseph Almog’s treatments of referential descriptions, showing that they find it difficult to explain misdescriptions. In 4. I suggest an alternative approach to DD as contextuals, under a normative epistemic stance. Definite descriptions express (i) what a speaker should have in mind in using certain words in a certain context and (ii) what a normal speaker is justified in saying in a context, given a common basic knowledge of the lexicon. In 5. I define a procedure running on contextual parameters (partiality, perspective and approximation) as a means of representing the role of pragmatics as a filter for semantic interpretation. In 6. I defend my procedural approach against possible objections concerning the problem of the boundaries between semantics and pragmatics, relying on the distinction between semantics and theory of meaning. (shrink)

We introduce and study some local versions of o-minimality, requiring that every definable set decomposes as the union of finitely many isolated points and intervals in a suitable neighbourhood of every point. Motivating examples are the expansions of the ordered reals by sine, cosine and other periodic functions.

The project of growing meat artificially represents for some the next best thing to humanity. If successful, it could be the solution to several problems, such as feeding a growing global population while reducing the environmental impact of raising animals for food and, of course, reducing the amount and degree of animal cruelty and suffering that is involved in animal farming. In this paper, I argue that the issue of the morality of such a project has been framed only in (...) terms of the best consequences for the environment, animals, and humans, or in terms of deontic principles. I argue that to appreciate how deep and difficult this issue is, it is necessary to consider it in terms of a virtue-oriented approach. Such an approach will reveal aspects that are not apparent, not contemplated by typical approaches, but are essential to our understanding of the morality of lab-grown meat. As I argue, evaluating the issue from a virtue-oriented perspective suggests that the project of in vitro meat should not be supported because it stems from unvirtuous motivations. (shrink)

The view that the subject matter of epistemology is the concept of knowledge is faced with the problem that all attempts so far to define that concept are subject to counterexamples. As an alternative, this article argues that the subject matter of epistemology is knowledge itself rather than the concept of knowledge. Moreover, knowledge is not merely a state of mind but rather a certain kind of response to the environment that is essential for survival. In this perspective, the article (...) outlines an answer to four basic questions about knowledge: What is the role of knowledge in human life? What is the relation between knowledge and reality? How is knowledge acquired? Is there any a priori knowledge? (shrink)

The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the (...) effectiveness of mathematics in natural science. (shrink)

The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick, to which a ‘third way’ has been recently added, the philosophy of mathematical practice. In this paper the limitations of these trends in the philosophy of mathematics are pointed out, and it is argued that they are due to the fact that all of them are based on a top-down approach, that is, an approach which explains the nature of mathematics in terms of some (...) general unproven assumption. As an alternative, a bottom-up approach is proposed, which explains the nature of mathematics in terms of the activity of real individuals and interactions between them. This involves distinguishing between mathematics as a discipline and the mathematics embodied in organisms as a result of biological evolution, which however, while being distinguished, are not opposed. Moreover, it requires a view of mathematical proof, mathematical definition and mathematical objects which is alternative to the top-down approach. (shrink)

As a response to the semantic and logical paradoxes, theorists often reject some principles of classical logic. However, classical logic is entangled with mathematics, and giving up mathematics is too high a price to pay, even for nonclassical theorists. The so-called recapture theorems come to the rescue. When reasoning with concepts such as truth/class membership/property instantiation, (These are examples of concepts that are taken to satisfy naive rules such as the naive truth schema and naive comprehension, and that therefore are (...) compatible with a solution to paradox cast in the logics considered below. Other notions of similar kind can be added to the list.) if one is interested in consequences of the theory that only contain mathematical vocabulary, nothing is lost by reasoning in the nonclassical framework. This article shows that this claim is highly misleading, if not simply false. Under natural assumptions, some well-established approaches to recapture are incorrect. (shrink)

Choice can be defined in thermodynamical terms, and shown to have a thermodynamic cost: choosing between a binary alternative at temperature T dissipates an energy $$E\ge kT\ln 2$$.

The present article discusses the relationship between might ( potentia ) and power ( potestas ) as it has unfolded throughout the modern age, from Thomas Hobbes to Carl Schmitt. Hobbes indicates the way forward for a progressive linguistic and conceptual coincidence of potentia and potestas : the goal of Hobbesian political philosophy (the search for peace and security) necessitates the reduction of potentia to potestas through the elimination of the content of actus . Schmitt accepts this reduction, by assigning (...) priority to potestas : the image of modern technology as a privileged dimension of potentia—potestas comes together as the modern state. Instead of taking the route of potentia understood as an opening-up to new possibilities and as human self-affirmation, the language of potentia—potestas has triggered a process, which is that of a naturalization of power relations, that is based on and justified by the social inequality arising from the differing extent of ownership of the instruments of technological production. (shrink)

In the last 2500 years, since the beginnings in ancient Greece of the literary genre we call “history,” the relationship between history and law has been very close. True, the Greek word historia is derived from medical language, but the argumentative ability it implied was related to the judicial sphere. History, as Arnaldo Momigliano emphasized some years ago, emerged as an independent intellectual activity at the intersection of medicine and rhetoric. Following the example of the former, the historian analyzed specific (...) cases and situations looking for their natural causes; following the prescriptions of the latter—a technique, or an art, born in tribunals—he communicated the results of his inquiry.2Within the classical tradition, historical writing had to display a feature the Greeks called enargeia, and the Romans, evidential in narrtatione: the ability to convey a vivid representation of characters and situations. The historian, like the lawyer, was expected to make a convincing argument by communicating the illusion of reality, not by exhibiting proofs collected either by himself or by others.3 Collecting proofs was, until the mid-eighteenth century, an activity practiced by antiquarians and erudite, not by historians.4 When, in his Traité des differentes sortes de preuves qui servent à établir la vérité he l’histoire , the erudite Jesuit Henri Griffet compared the historian to a judge who carefully evaluates proofs and witnesses, he was expressing a still-unaddressed intellectual need. Only a few years later Edward Gibbon published his Decline and Fall of the Roman Empire, the first work that effectively combined historical narrative with an antiquarian approach.5 2. See Arnaldo Momigliano, ”History between Medicine and Rhetoric,” Ottavo contributo alla storia degli studi classici e del mondo antico, trans. Riccardo Di Donato , pp. 14-25.3. See Ginzburg, “Montrer et citer.”4. See Momigliano, “Ancient History and the Antiquarian,” Contributo alla storia degli studi classici , pp. 67-106.5. See Henri Griffet, Traité des differentes sortes de preuves qui servent à établir la vérité de l’histoire, 2d ed. . Allen Johnson, in his Historian and Historical Evidence , speaks of the Traité as “the most significant book on method after Mabillon’s De re diplomatic” . See also Momigliano, “Ancient History and the Antiquarian,” p. 81, and Ginzburg, “Just One Witness.” On Gibbon, see Momilgiano, Sesto contributo alla storia degli studi classici e del mondo antico , pp. 231-84. Carlo Ginzburg is Franklin D. Murphy Professor of Italian Renaissance Studies at the University of California, Los Angeles. His two most recent books are Ecstasies: Deciphering the Witches’ Sabbath and Il giudice e lo storico. (shrink)

In his book The Value of Science Poincaré criticizes a certain view on the growth of mathematical knowledge: “The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new ones, but to the continuous evolution of zoological types which develop ceaselessly and end by becoming unrecognizable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past” (Poincaré (...) 1958, p. 14). The view criticized by Poincaré corresponds to Frege’s idea that the development of mathematics can be described as an activity of system building, where each system is supposed to provide a complete representation for a certain mathematical field and must be pitilessly torn down whenever it fails to achieve such an aim. All facts concerning any mathematical field must be fully organized in a given system because “in mathematics we must always strive after a system that is complete in itself” (Frege 1979, p. 279). Frege is aware that systems introduce rigidity and are in conflict with the actual development of mathematics because “in history we have development; a system is static”, but he sticks to the view that “science only comes to fruition in a system” because “only through a system can we achieve complete clarity and order” (Frege 1979, p. 242). He even goes so far as saying that “no science can be so enveloped in obscurity as mathematics, if it fails to construct a system” (Frege 1979, p. 242). By ‘system’ Frege means ‘axiomatic system’. In his view, in mathematics we cannot rest content with the fact that “we are convinced of something, but we must strive to obtain a clear insight into the network of inferences that support our conviction”, that is, to find “what the primitive truths are”, because “only in this way can a system be constructed” (Frege 1979, p. 205). The primitive truths are the principles of the axiomatic system. Frege’s stress on the role of systems also determines his views on the growth of mathematical knowledge.. (shrink)