This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

Is reality three-dimensional and becoming real (Presentism), or is reality four-dimensional and becoming illusory (Eternalism)? Both options raise difficulties. I argue that we do not need to be trapped by this dilemma. There is a third possibility: reality has a more complex temporal structure than either of these two naive options. Fundamental becoming is real, but local and unoriented. A notion of present is well defined, but only locally and in the context of approximations.

Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role at all. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must “forget time”, and how this can be done in the classical and in the quantum theory. The idea is to (...) develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time. (shrink)

The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe “handles” though which systems couple: they represent real relational structures to which the experimentalist has access in measurement by supplying one of the relata in the measurement procedure itself. This observation leads to a physical interpretation for the ubiquity of gauge: it (...) is a consequence of a relational structure of physical quantities. (shrink)

Quantum mechanics is not about 'quantum states': it is about values of physical variables. I give a short fresh presentation and update on the *relational* perspective on the theory, and a comment on its philosophical implications.

This book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th- to 20th-Century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantial part of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann was the (...) man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies is documented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific upheaval, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientific revolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved: others are still at the level of likely but unproven conjectures. The main text of this biography is written almost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject. (shrink)

A solution to the issue of time in quantum gravity is proposed. The hypothesis that time is not defined at the fundamental level (at the Planck scale) is considered. A natural extension of canonical Heisenberg-picture quantum mechanics is defined. It is shown that this extension is well defined and can be used to describe the "non-Schrödinger regime," in which a fundamental time variable is not defined. This conclusion rests on a detailed analysis of which quantities are the physical observables of (...) the theory; a main technical result of the paper is the identification of a class of gauge-invariant observables that can describe the (observable) evolution in the absence of a fundamental definition of time. The choice of the scalar product and the interpretation of the wave function are carefully discussed. The physical interpretation of the extreme "no time" quantum gravitational physics is considered. (shrink)

At least since Kuhn’s Structure, philosophers have studied the influence of social factors in science’s pursuit of truth and knowledge. More recently, formal models and computer simulations have allowed philosophers of science and social epistemologists to dig deeper into the detailed dynamics of scientific research and experimentation, and to develop very seemingly realistic models of the social organization of science. These models purport to be predictive of the optimal allocations of factors, such as diversity of methods used in science, size (...) of groups, and communication channels among researchers. In this paper we argue that the current research faces an empirical challenge. The challenge is to connect simulation models with data. We present possible scenarios about how the challenge may unfold. (shrink)

In this paper I analyze four so-called “principles of expertise”; that is, good epistemic practices that are normatively motivated by the epistemological literature on expert judgment. I highlight some of the problems that the four principles of expertise run into, when we try to implement them in concrete contexts of application (e.g. in science committees). I suggest some possible alternatives and adjustments to the principles, arguing in general that the epistemology of expertise should be informed both by case studies and (...) by the literature on the use of experts in science practice. (shrink)

Truth-theoretic deflationism holds that truth is simple, and yet that it can fulfil many useful logico-linguistic roles. Deflationism focuses on axioms for truth: there is no reduction of the notion of truth to more fundamental ones such as sets or higher-order quantifiers. In this paper I argue that the fundamental properties of reasonable, primitive truth predicates are at odds with the core tenets of classical truth-theoretic deflationism that I call fix, express, and quantify. Truth may be regarded as a broadly (...) logical, sui generis notion. However, this has little to do with the original aims of the deflationary theory of truth. (shrink)

The book is a comprehensive introduction to the work of the Estonian-German biologist Jakob von Uexküll. After a first introductory chapter by Morten Tønnessen and a second chapter on Uexküll's life and philosophical background, it contains four chapters devoted to the analysis of his main works; they are followed by a vast eighth chapter which deals with the influence Uexküll had on other philosophers and scientists, and by a conclusions focused on the possibility of updating Uexküll's work. The monograph combines (...) a careful reconstruction of the historical context in which the Uexküllian concepts emerged (the debate between mechanism and vitalism, contemporary scientific studies) and a thorough analysis of the philosophical contents of the Uexküllian views. As far as the key issue is concerned, Uexküll's notion of Umwelt refers to the perceptive and operative world which surrounds animal species; it is a subjective species-specific construction which provides living organisms with great security and behaviour stability. Moreover, the relationship that the animal carries out with its environment proves to be a complex system of semiotic interactions: its behaviour is not a set of mechanical reactions, but the result of a spontaneous attribution of meaning to the outside world, whose environmental elements are actively interpreted by the subject. The environment of animal species becomes a field of meaning, an exceedingly complex subjective elaboration; this can lessen the distance between animals and men, crediting both with the cognitive ability to grasp meanings and to use signs. (shrink)

The Heythrop Journal, Volume 63, Issue 5, Page 869-885, September 2022.

In the paper we investigate typed axiomatizations of the truth predicate in which the axioms of truth come with a built-in, minimal and self-sufficient machinery to talk about syntactic aspects of an arbitrary base theory. Expanding previous works of the author and building on recent works of Albert Visser and Richard Heck, we give a precise characterization of these systems by investigating the strict relationships occurring between them, arithmetized model constructions in weak arithmetical systems and suitable set existence axioms. The (...) framework considered will give rise to some methodological remarks on the construction of truth theories and provide us with a privileged point of view to analyze the notion of truth arising from compositional principles in a typed setting. (shrink)

The existence of a close connection between results on axiomatic truth and the analysis of truth-theoretic deflationism is nowadays widely recognized. The first attempt to make such link precise can be traced back to the so-called conservativeness argument due to Leon Horsten, Stewart Shapiro and Jeffrey Ketland: by employing standard Gödelian phenomena, they concluded that deflationism is untenable as any adequate theory of truth leads to consequences that were not achievable by the base theory alone. In the paper I highlight, (...) as Shapiro and Ketland, the irreducible nature of truth axioms with respect to their base theories. But, I argue, this does not immediately delineate a notion of truth playing a substantial role in philosophical or scientific explanations. I first offer a refinement of Hartry Field’s reaction to the conservativeness argument by distinguishing between metatheoretic and object-theoretic consequences of the theory of truth and address some possible rejoinders. In the resulting picture, truth is an irreducible tool for metatheoretic ascent. How robust is this characterizaton? I test it by considering: a recent example, due to Leon Horsten, of the alleged explanatory role played by the truth predicate in the derivation of Fitch’s paradox; an essential weakening of theories of truth analyzed in the first part of the paper. (shrink)

From antiquity several philosophers have claimed that the goal of natural science is truth. In particular, this is a basic tenet of contemporary scientific realism. However, all concepts of truth that have been put forward are inadequate to modern science because they do not provide a criterion of truth. This means that we will generally be unable to recognize a scientific truth when we reach it. As an alternative, this paper argues that the goal of natural science is plausibility and (...) considers some characters of plausibility. (shrink)

The first book of NE is organised on the model of investigating definitions described in the second Book of the Posterior Analytics, although, of course, with some adaptation due to the subject matter. It first establishes if the object exists and looks for the meaning of the terms used in common language to indicate it, next considers some necessary qualities of the object and then concludes with a definition of the object. We find there a dialectical syllogism of definition, and (...) not the procedure in three steps described in NE VII 1, sometimes called 'the method of ethics'. In fact, the method described in NE VII 1 does not apply to the first book of the NE. Its relevance for the NE has been somehow exaggerated. (shrink)

The Conventionality of Simultaneity espoused by Reichenbach, Grunbaum, Edwards, and Winnie is herein extended to mechanics and electrodynamics. The extension is seen to be a special case of a generally covariant formulation of physics, and therefore consistent with Special Relativity as the geometry of flat space-time. Many of the quantities of classical physics, such as mass, charge density, and force, are found to be synchronization dependent in this formulation and, therefore, in Reichenbach's terminology, "metrogenic." The relationship of these quantities to (...) 4-vectors and their physical significance is discussed. (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)

Following the invitation of the editors of Foundations of Physics, I give here a personal assessment of string theory, from the point of view of an outsider, and I compare it with the theory, methods, and expectations of my own field.

In twentieth-century continental philosophy, German philosophical anthropology can be seen as a sort of conceptual laboratory devoted to human/animal research, and, in particular, to the discontinuity between human and non-human animals. Its main notion—the idea of the special position of humans in nature—is one of the first philosophical attempts to think of the specificity of humans as a natural and qualitative difference from non-human animals. This school of thought correctly rejects both the metaphysical and/or religious characterisations of humans, and the (...) positivistic gradualism, that sees the human being as an animal endowed with a greater degree of certain faculties. At the same time, German philosophical anthropology still takes it for granted that such natural-qualitative novelty is unique in the realm of the living, that in correspondence with humans there is the hiatus, the discontinuity par excellence. The semiotic side of this view is the distinction between signs and symbols developed by Ernst Cassirer and Susanne Langer: animal signs would be mere proxies for perceptive elements or stimuli, whereas only human symbols could convey complex representation of objects and situations. The goal of this contribution is to criticise the alleged uniqueness of the hiatus and its semiotic implications through the opposite approach of the diffuse discontinuities. This approach that focuses on the semiotic traits of different species-specific environments can be traced back to Jakob von Uexküll’s biosemiotical phenomenology, which thinks of discontinuities as a normal phenomenon of animal life. (shrink)

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 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 so-called “intentional object” occupies a central position in the debates about intentionality in Brentano and the Brentano School. How does it relate to the correlate, the content, or the intended, possibly external, transcendent object? Does it perhaps even coincide with one of these? There was no clear consensus on this neither in Brentano’s time nor today. In order to develop a new perspective on the problem of the intentional object, I would like to introduce a deliberately radical interpretation and (...) related terminological change: what if we were to avoid any talk of “object” in this context altogether? Perhaps this could help avoid the ambiguities and misunderstandings associated with talk of “intentional objects.” In my contribution I would like to sketch such an interpretation and consider whether this attempt could be useful to reframe the debate. (shrink)

The purpose of this study is to examine the relationship between contextual work-related factors on the one hand, in terms of job demands (i.e., risk factors) and job resources (i.e., protective factors), and work-family conflict in teachers on the other. Building on the Job Demands-Resources (JD-R) model, we hypothesized that job demands, namely qualitative and quantitative workload, are positively associated with work-family conflict in teachers. Moreover, in line with the buffer hypothesis of the JD-R, we expected job resources, in terms (...) of support from supervisor, job autonomy, and participation in decision making, to affect this association, which is expected to be stronger when job resources are low. The study was conducted in an Italian secondary school. Overall, 122 teachers completed a self-report questionnaire aimed at determining work-family conflict, as well as job demands and resources. The hypothesized relationships were tested using moderated multiple regression. The results of this study largely support our predictions. First, both aspects of workload were positively associated with work-family conflict. Secondly, job resources, including support from supervisor and participation in decision making, buffered this association, which was stronger when resources were low. On the contrary, job autonomy did not buffer the association between workload and work-family conflict. Overall, the results of this study are consistent with the Job Demands-Resources model and contribute to to the understanding of work–family conflict among teachers. More specifically, our study suggests that teachers with high levels of job resources, namely support from supervisor and participation in decision making, can effectively cope with job demands, in terms of both qualitative and quantitative workload, thus preventing negative consequences such as conflict between work and family domains. Interventions aimed at preventing work-family conflict among teachers should encourage organizations to optimize the balance between job demands and resources, as well as the identification and training of the workers at risk of work-family conflict. (shrink)

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)

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 the article Husserl’s view of the infinite around 1890 is analysed. I give a survey of his mathematical background and other important influences (especially Bolzano). The article contains a short exposition on Husserl's distinction between proper and symbolic presentations in the "Philosophie der Arithmetik" and between finite and infinite symbolic collections. Subsequently Husserl’s conception of surrogate presentations in his treatise "Zur Logik der Zeichen (Semiotik)" is discussed. In this text Husserl gives a detailed account of infinity, using surrogate presentations. (...) The conclusion is that with surrogates we can only operate according to blind psychological rules. (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)

Winner of the 2000-2002 outstanding publication award of the Section on Environment and Technology of the American Sociological Association.Risk as we now know ...

The aim of this paper is to refute the hypothesis that the observer’s consciousness is necessary in the quantum mechanics measurement process. In order to achieve our target, we propose and investigate a variation of the Schrödinger’s cat thought experiment called “DAP”, short for “Dead-Alive Physicist”, in which a human being replaces the cat. This strategy enables us to logically disprove the consistency of the above hypothesis, and to oblige its supporters either to be trapped in solipsism or to rely (...) on an alternative interpretation of quantum mechanics in which the conscious observer plays the sole role of acknowledging the experimental results. Our analysis hence provides support to clarify the relationship between the observer and the objects of her/his experimental observation; this and a few other implications are discussed in the fourth section and in the conclusions. (shrink)

The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of (...) our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, De Vidi and Solomon's proposal of formulating the verification thesis as Φ → ¬¬KΦ. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models. (shrink)

In attempting to explain or deal with negative workplace behaviours such as workplace bullying, the notion of ‘workplace psychopaths’ has recently received much attention. Focusing on individual aspects of negative workplace behaviour is at odds with more systemic approaches that recognise the contribution of individual, organisational and societal influences, without seeking to blame a person(s) for their behaviour or personality disorder. Regarding a coworker as a psychopath is highly stigmatising, and given the relatively low prevalence of psychopathy in the community, (...) is likely to be incorrect. Sources promoting the notion of workplace psychopathy provide lists of diagnostic criteria and appear to encourage the perception that it is common. This research examines how lay persons use behavioural criteria consistent with psychopathy and the label ‘psychopath’ in relation to a coworker. 307 Australian workers completed an online survey concerning their experience of workplace bullying, which also asked them to rate a coworker’s behaviour on a range of scales to assess perceptions of psychopathy. Rates of psychopathy, when using labels and behavioural criteria, were found to be much higher than scientific estimates of prevalence, for both participants who had been bullied and those who had not. A higher proportion of non-bullied participants classified a coworker as a psychopath when using the label ‘psychopath’, compared to when using behavioural criteria. The notion that there are psychopaths in every workplace should be treated with caution to ensure that the potential for ‘misdiagnosis’ and stigmatisation do not cause further harm in situations of unacceptable workplace behaviours. (shrink)

The paper attempts to give a solution to the Fitch's paradox though the strategy of the reformulation of the paradox in temporal logic, and a notion of knowledge which is a kind of ceteris paribus modality. An analogous solution has been offered in a different context to solve the problem of metaphysical determinism.

Core principles of mereology have been questioned by appealing to time travel scenarios. This paper questions the methodology of employing time travel scenarios to argue against mereology. We show some time travel scenarios are structurally equivalent to more standard ones not involving time travel; and that the three main theories about persistence through time can each solve both the time travel scenario as well as the structurally similar classical scenario. Time travel scenarios that are not similar to more standard arguments (...) are instead problematic because they are open to different, incompatible interpretations. We conclude that compared to the classical arguments against mereological principles, time travel scenarios do not add anything new. (shrink)

Die Nietzscheforschung der letzten Jahrzehnte hat ein besonders Augenmerk auf den Einfluß gerichtet, den Kant auf Nietzsches Philosophie ausgreübt hat, inbesondere auf seine Wissenschafts- und erkenntnis-Kritik. Die Revision des Wahrheitsbegriffs seitens Nietzsches kommt so ans Tageslicht. Forscher wie J. Simon und F. Kaulbach haben unterstrichen, daß Nietzsche die schon von Kant angelegte Übertragung der Wahrheit aus dem Theoretischen ins Praktische vollzogen hat. In seiner geplanten Doktorarbeit im Jahr 1868 Die Teologie seit Kant greift Nietzsche F.A. Langes und K. Fischers Auslegungen (...) auf, deren Einfluß auch in seinen späteren Werken noch wahrnehmbar ist. Insbesondere entnimmt er Kant die Gegenüberstellung von menschlicher und tierischer Welt, der dann seine offene Kritik am kantischen "Anthropomorphismus" folgt. Nietzsche nimmt so mit Kant Stellung.In the last decades, many Nietzsche scholars have begun to attend Kant's influence on Nietzsche's philosophy, particularly on his criticism of science and of knowledge. This is how Nietzsche's reexamination of the concept of truth emerges. Scholars such as J. Simon and F. Kaulbach have stressed how Nietzsche has completed the displacement of truth - already formulated by Kant - from the level of theoretical reflection to the level of pragmatical reflection. In the planned Doktorarbeit of 1868, Die Teleologie seit Kant, Neitzsche uses Kant interpretations of F. A. Lange and K. Fischer, whose influence can still be found in the works of the maturity. It is mainly from Kant that Nietzche derives the opposition between human world and animal world. Such an opposition turns into an open criticism of what he considers the Kantian anthropomorphism. Thus, Nietzsche's position can be summarised as a movement mit Kant gegen Kant. (shrink)

Reuben Hersh is a champion of maverick philosophy of mathematics. He maintains that mathematics is a human activity, intelligible only in a social context; it is the subject where statements are capable in principle of being proved or disproved, and where proof or disproof bring unanimous agreement by all qualified experts; mathematicians' proof is deduction from established mathematics; mathematical objects exist only in the shared consciousness of human beings. In this paper I describe my several points of agreement and few (...) points of disagreement with Hersh's views. (shrink)

The article examines the development of Husserl’s early philosophy from his Habilitationsschrift (1887) to the Philosophie der Arithmetik (1891). -/- An attempt will be made at reconstructing the lost Habilitationsschrift (of which only the first chapter survives, which we know as Über den Begriff der Zahl). The examined sources show that the original version of the Habilitationsschrift was by far broader than the printed version, and included most topics of the PA. -/- The article contains an extensive and detailed comparison (...) of these texts to illustrate the changes in Husserl’s position before and after February 1890. This date is taken as a turning point in his development, because of Husserl’s announcement in a letter to Carl Stumpf that he was mistaken in his basic assumption, i.e. that the (psychological) analysis of the concept of Anzahl would yield a foundation for arithmetic. Some interesting conclusions in this respect can also be drawn from an unpublished lecture that Husserl held in the WS 1889/90, in which he anticipates aspects of his position hitherto deemed to belong to the last phases of the PA. (shrink)

ellucci, C., Existential instantiation and normalization in sequent natural deduction, Annals of Pure and Applied Logic 58 111–148. A sequent conclusion natural deduction system is introduced in which classical logic is treated per se, not as a special case of intuitionistic logic. The system includes an existential instantiation rule and involves restrictions on the discharge rules. Contrary to the standard formula conclusion natural deduction systems for classical logic, its normal derivations satisfy both the subformula property and the separation property and (...) allow to establish a version of the midsequent theorem and Herbrand's theorem. (shrink)

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)