The much-anticipated anthology on Plato’s_Timaeus_—Plato’s singular dialogue on the creation of the universe, the nature of the physical world, and the place of persons in the cosmos—examining all dimensions of one of the most important books in Western Civilization: its philosophy, cosmology, science, and ethics, its literary aspects and reception. Contributions come from leading scholars in their respective fields, including Sir Anthony Leggett, 2003 Nobel Laureate for Physics. Parts of or earlier versions of these papers were first presented at the (...) _Timaeus_ Conference, held at the University of Illinois at Urbana–Champaign in September of 2007._ To this day, Plato’s _Timaeus_ grounds the form of ethical and political thinking called Natural Law—the view that there are norms in nature that provide the patterns for our actions and ground the objectivity of human values. Beyond the intellectual content of the dialogue’s core, its literary frame is also the source of the myth of Atlantis, giving the West the concept of the “lost world.” From Platonic space to Presocratic vortices, from Philosopher-Kings to Craftsman-Gods and from modern physics to the myth of Atlantis, _One Book, The Whole Universe_ presents in one volume the most up-to-date and penetrating scholarship on Plato’s _Timaeus_ by some of the greatest minds alive today. Contributors__ _Ann Bergren Gábor Betegh Sean Carroll Alan Code Zina Giannopoulou Verity Harte Thomas Kjeller Johansen Charles H. Kahn Anthony J. Leggett Anthony A. Long Stephen Menn Richard D. Mohr Kathryn A. Morgan Alexander P.D. Mourelatos Ian Mueller Thomas M. Robinson Barbara M. Sattler Allan Silverman Jon Solomon Anthony Vidler Matthias Vorwerk Donald Zeyl. (shrink)

Economics has developed into one of the most specialised social sciences. Yet at the same time, it shares its subject matter with other social sciences and humanities and its method of analysis has developed in close correspondence with the natural and life sciences. This book offers an up to date assessment of economics in relation to other disciplines. -/- This edited collection explores fields as diverse as mathematics, physics, biology, medicine, sociology, architecture, and literature, drawing from selected contributions to the (...) 2005 Annual Conference of the European Society for the History of Economic Thought (ESHET). There is currently much discussion at the leading edges of modern economics about openness to other disciplines, such as psychology and sociology. But what we see here is that economics has drawn on (as well as contributed to) other disciplines throughout its history. In this sense, in spite of the increasing specialisation within all disciplines, economics has always been an open discipline and the chapters in this volume provide a vivid illustration for this. -/- Open Economics is a testament to the intellectual vibrancy of historical research in economics. It presents the reader with a historical introduction to the disciplinary context of economics that is the first of its kind, and will appeal to practising economists and students of the discipline alike, as well as to anybody interested in economics and its position in the scientific and social scientific landscape. -/- Table of Contents -/- Introduction: Economics in relation to other disciplines Richard Arena, Sheila Dow and Matthias Klaes Part I. Economics in relation to the humanities and social sciences 1. The social science of economics Brian J. Loasby 2. Economics and literature Bruna Ingrao 3. Happiness: what Kahneman could have learnt from Pietro Verri Pier Luigi Porta Part II. Economics in relation to the life and natural sciences 4. Newtonian physics, experimental moral philosophy and the shaping of political economy Sergio Cremaschi 5. Evolutionary biology and economic behaviour: re-visiting Veblen's instinct of workmanship Mark Harrison 6. Medicine and economics in pre-classical economics Alain Clément and Ludovic Desmedt Part III. Economics and mathematics 7. Mathematics as the role model for neoclassical economics Nicola Giocoli 8. The role of econometric method in economic analysis: A reassessment of the Keynes-Tinbergen debate, 1938-43 Giovanna Garrone and Roberto Marchionatti IV. Economics and architecture 9. Economics and architecture Maurice Lagueux 10. Economic policies and urban development in Latin America Michele Alacevich and Andrea Costa V. Economics and geography 11. ‘Space’ in economic thought Giovanna Vertova 12. Economics, geography and colonialism in the writings of William Petty Hugh Goodacre Part VI. Economics and sociology 13. Economics and sociology: Gustav Schmoller and Werner Sombart on social differentiation Joachim Zweynert 14. Is Homo Oeconomicus a 'bad guy'? Isabelle This Saint-Jean -/- . (shrink)

Figurative elements in language have their own particularities, including words that deviate from their generally accepted definition to amplify our language or to paraphrase an issue. It is still...

First-order Gödel logics are a family of finite- or infinite-valued logics where the sets of truth values V are closed subsets of [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics GV (sets of those formulas which evaluate to 1 in every interpretation into V). It is shown that GV is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V is uncountable. Complete (...) axiomatizations for each of these cases are given. The r.e. prenex, negation-free, and existential fragments of all first-order Gödel logics are also characterized. (shrink)

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

Research on the cognitive abilities involved in decision making has shown that, under objective risk conditions (i.e., when explicit information about possible outcomes and risks is available), superior decisions are especially predicted by executive functions and exact number processing skills, also referred to as objective numeracy. So far, decision-making research has mainly focused on exact number processing skills, such as performing calculations or transformations of symbolic numbers. There is evidence that such exact numeric skills are based on approximate number processing (...) (ANP) skills, which enable quick and accurate processing of non-symbolic numbers (e.g. Chen and Li, 2014). Very few studies, however, have investigated ANP skills in the context of risky decision making and have analyzed direct associations among the aforementioned sub functions. Possible interactions between the closely related skills have not been considered. The current study (N = 128) examines interactions of ANP skills with executive functions and objective numeracy, in predicting risky choice behavior. ANP skills are represented by the accuracy in a dot-comparison task. Decision making is measured by two versions of the Game of Dice Task (GDT), which place different emphases on the reflection of potential risks. The results show two-way as well as three-way interactions between the measures of ANP skills, executive functions, and objective numeracy in predicting risky decisions in both GDT versions. The riskiest decisions were most frequently made in case of low scores in all of the three competencies, while good performance in any one of them resulted in significant reductions of disadvantageous decisions. The findings indicate that high ANP skills can positively affect choice behavior in individuals who have weaknesses in reflectively attributed skills, namely executive functions and objective numeracy. Potential compensatory effects and mechanisms of ANP in decision making are discussed. (shrink)

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the (...) number of truth values, and it is shown that this bound is tight. (shrink)

Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ - (...) and $\tau $ -formulas and using the translation of quantifiers into $\varepsilon $ - and $\tau $ -terms to intermediate logics. It is shown that conservativity over the propositional base logic also holds for such intermediate ${\varepsilon \tau }$ -calculi. The “extended” first $\varepsilon $ -theorem holds if the base logic is finite-valued Gödel–Dummett logic, and fails otherwise, but holds for certain provable formulas in infinite-valued Gödel logic. The second $\varepsilon $ -theorem also holds for finite-valued first-order Gödel logics. The methods used to prove the extended first $\varepsilon $ -theorem for infinite-valued Gödel logic suggest applications to theories of arithmetic. (shrink)

The scientific study of consciousness emerged as an organized field of research only a few decades ago. As empirical results have begun to enhance our understanding of consciousness, it is important to find out whether other factors, such as funding for consciousness research and status of consciousness scientists, provide a suitable environment for the field to grow and develop sustainably. We conducted an online survey on people’s views regarding various aspects of the scientific study of consciousness as a field of (...) research. 249 participants completed the survey, among which 80% were in academia, and around 40% were experts in consciousness research. Topics covered include the progress made by the field, funding for consciousness research, job opportunities for consciousness researchers, and the scientific rigor of the work done by researchers in the field. The majority of respondents (78%) indicated that scientific research on consciousness has been making progress. However, most participants perceived obtaining funding and getting a job in the field of consciousness research as more difficult than in other subfields of neuroscience. Overall, work done in consciousness research was perceived to be less rigorous than other neuroscience subfields, but this perceived lack of rigor was not related to the perceived difficulty in finding jobs and obtaining funding. Lastly, we found that, overall, the global workspace theory was perceived to be the most promising (around 28%), while most non-expert researchers (around 22% of non-experts) found the integrated information theory (IIT) most promising. We believe the survey results provide an interesting picture of current opinions from scientists and researchers about the progresses made and the challenges faced by consciousness research as an independent field. They will inspire collective reflection on the future directions regarding funding and job opportunities for the field. (shrink)

This paper contributes to the (re-)conceptualisation of responsible innovation by proposing an evolutionary economic approach that focuses on the role of consumers in the innovation process. After a discussion of the philosophical foundations and ethical implications of this approach, which bears an explanatory potential that has not been adequately considered in previous discussions of responsible innovation, we present a first step towards capturing the important but often neglected role of consumers in innovation processes (including responsible innovation): We propose an agent-based (...) model that incorporates a multidimensional space of characteristics in which new products or services are represented by more than the mere aspect of price and quality. Instead, innovations are denoted by a large set of characteristics, including also negative or harmful ones. The model is used to illustrate that consumers’ heterogeneity and bounded rationality – even if considered in a simple manner – indeed play a crucial role in the creation and diffusion of responsible innovation which can and should be used for further work in this field and for possible extensions of the model. (shrink)

A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.

This handbook pursues an integrated communication approach. Drawing on the various fields of organizational communication and their relevance for CSR, it addresses innovative topics such as big data, social media, and the convergence of communication channels, as well as the roles they play in a successfully integrated CSR communication program. Further aspects covered include the analysis of sector-specific, cross-cultural, and ethical challenges related to the effective communication of CSR. This handbook is unique in its consistent focus on integrated communication. It (...) is of interest not only for the scientific discourse, but will also benefit those corporations that not only seek to operate in a socially responsible manner, but also to communicate their efforts to their various stakeholders. Besides its significant value for researchers and professionals, the book can also be used as a reference for undergraduate and graduate students interested in successful CSR communication. (shrink)

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...) the exclusion of the opposite truth value describe the same situation.). (shrink)

Jan Krajíček posed the following problem: Is there is a generalization result in the theory of real closed fields of the form: If A is provable in length k for all n ϵ ω , then A is provable? It is argued that the answer to this question depends on the particular formulation of the “theory of real closed fields.” Four distinct formulations are investigated with respect to their generalization behavior. It is shown that there is a positive answer to (...) Krajíček's question for 1. the axiom system RCF of Artin-Schreier with Gentzen's LK as underlying logical calculus, 2. RCF with the variant LK B of LK allowing introduction of several quantifiers of the same type in one step, 3. LK B and the first-order schemata corresponding to Dedekind cuts and the supremum principle. A negative answer is given for 4. any system containing the schema of extensionality. (shrink)

Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the only one with an r.e. entailment relation.

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, and (...) allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively. (shrink)

In this volume, a diverse group of world experts in personality assessment showcase a range of different viewpoints on response distortion. Contributors consider what it means to "fake" a personality assessment, why and how people try to obtain particular scores on personality tests, and what types of tests people can successfully manipulate. The authors present and discuss the usefulness of a range of traditional and cutting-edge methods for detecting and controlling the practice of faking. These methods include social desirability scales, (...) warnings, affective neutralization, unidimensional and multidimensional pairwise preferences, decision trees, linguistic analysis, situational measures, and methods based on item response theory. The wide range of viewpoints presented in this book are then summarized, synthesized, and evaluated. The authors make practical recommendations and suggest areas for future research. Anyone who wonders whether people exaggerate or lie outright on personality tests -- or questions what psychologists can and should do about it -- will find in this book stimulating questions and useful answers. (shrink)

It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.

The generalization properties of algebraically closed fields $ACF_p$ of characteristic $p > 0$ and $ACF_0$ of characteristic 0 are investigated in the sequent calculus with blocks of quantifiers. It is shown that $ACF_p$ admits finite term bases, and $ACF_0$ admits term bases with primality constraints. From these results the analogs of Kreisel's Conjecture for these theories follow: If for some $k$ , $A(1 + \cdots + 1)$ ( $n$ 1's) is provable in $k$ steps, then $(\forall x)A(x)$ is provable.

Consider a group of people whose preferences satisfy the axioms of one of the current versions of utility theory, such as von Neumann-Morgenstern (1944), Savage (1954), or Bolker-Jeffrey (1965). There are political and economic contexts in which it is of interest to find ways of aggregating these individual preferences into a group preference ranking. The question then arises of whether methods of aggregation exist in which the group’s preferences also satisfy the axioms of the chosen utility theory, and in which (...) at the same time the aggregation process satisfies certain plausible conditions (e.g., the Pareto conditions below). (shrink)

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various ways can (...) be approximated by finite-valued logics. It is shown that the minimal m-valued logic for which a given calculus is strongly sound can be calculated. It is also investigated under which conditions propositional logics can be characterized as the intersection of (effectively given) sequences of finite-valued logics. (shrink)

The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB ( LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introduction of cuts into a proof. The algorithmic solvability of this problem can be reduced to the question of k-l-compressibility: "Given a proof of length k , and l ≤ k : Is (...) there is a proof of length ≤ l ?" When restricted to proofs with universal or existential cuts, this problem is shown to be (1) undecidable for linear or tree-like LK-proofs (corresponds to the undecidability of second order unification), (2) undecidable for linear LKB-proofs (corresponds to the undecidability of semi-unification), and (3) decidable for tree-like LKB -proofs (corresponds to a decidable subprob- lem of semi-unification). (shrink)

All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.

It is shown how the schema of equivalence can be used to obtain short proofs of tautologies A , where the depth of proofs is linear in the number of variables in A .

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...) logic of linear discrete time with gaps follows. (shrink)

The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can (...) be computed from the calculus. (shrink)

Infants can see someone pointing to one of two buckets and infer that the toy they are seeking is hidden inside. Great apes do not succeed in this task, but, surprisingly, domestic dogs do. However, whether children and dogs understand these communicative acts in the same way is not yet known. To test this possibility, an experimenter did not point, look, or extend any part of her body towards either bucket, but instead lifted and shook one via a centrally pulled (...) rope. She did this either intentionally or accidentally, and did or did not address her act to the subject using ostensive cues. Young 2-year-old children but not dogs understood the experimenter’s act in intentional conditions. While ostensive pulling of the rope made no difference to children’s success, it actually hindered dogs’ performance. We conclude that while human children may be capable of inferring communicative intent from a wide variety actions, so long as these actions are performed intentionally, dogs are likely to be less flexible in this respect. Their understanding of communicative intention may be more dependent upon bodily markers of communicative intent, including gaze, orientation, extended limbs, and vocalisations. This may be because humans have come under selective pressure to develop skills for communicating with absent interlocutors – where bodily co-presence is not possible. (shrink)

In “Agreeing to Disagree” [1], Robert Aumann proves that a group of agents who once agreed about the probability of some proposition for which their current probabilities are common knowledge must still agree, even if those probabilities reflect disparate observations. Perhaps one saw that a card was red and another saw that it was a heart, so that as far as that goes, their common prior probability of 1/52 for its being the Queen of hearts would change in the one (...) case to 1/26, and in the other to 1/13. But if those are indeed their current probabilities, it cannot be the case that both know them, and both know that both know them, etc., etc. (shrink)

We show that Bayesian ex post aggregation is unstable with respect to refinements. Suppose a group of Bayesians use ex post aggregation. Since it is a joint problem, each agent’s problem is captured by the same model, but probabilities and utilities may vary. If they analyze the same situation in more detail, their refined analysis should preserve their preferences among acts. However, ex post aggregation could bring about a preference reversal on the group level. Ex post aggregation thus depends on (...) how much information is used and may keep oscillating (‘‘flipping’’) as one keeps adding more information. (shrink)

Successful transitions to a sustainable bioeconomy require novel technologies, processes, and practices as well as a general agreement about the overarching normative direction of innovation. Both requirements necessarily involve collective action by those individuals who purchase, use, and co-produce novelties: the consumers. Based on theoretical considerations borrowed from evolutionary innovation economics and consumer social responsibility, we explore to what extent consumers’ scope of action is addressed in the scientific bioeconomy literature. We do so by systematically reviewing bioeconomy-related publications according to (...) the extent to which consumers are regarded as passive vs. active, and different domains of consumer responsibility. We find all aspects of active consumption considered to varying degrees but observe little interconnection between domains. In sum, our paper contributes to the bioeconomy literature by developing a novel coding scheme that allows us to pinpoint different aspects of consumer activity, which have been considered in a rather isolated and undifferentiated manner. Combined with our theoretical considerations, the results of our review reveal a central research gap which should be taken up in future empirical and conceptual bioeconomy research. The system-spanning nature of a sustainable bioeconomy demands an equally holistic exploration of the consumers’ prospective and shared responsibility for contributing to its coming of age, ranging from the procurement of information on bio-based products and services to their disposal. (shrink)

INTERVIEW Matthias BormuthAn Intellectual Affair – Meeting Hannah Arendt: An Interview with Richard Bernstein.

INTERVIEW Matthias BormuthAn Intellectual Affair – Meeting Hannah Arendt: An Interview with Richard Bernstein.

The thematic survey of traditional literature uncovered a pressing need to study the M-L figure as a phenomenon in its own right. A design was constructed intending to evoke the figure's full phenomenal appearance. Instead of framing a highly determinate structure wherein a specific question is posed, E presented the figure to naive Ss, simply asking them to describe it. The purpose was to ascertain what naive Ss would perceive if not encumbered by a prior set. In addition, five experiential (...) questions about the descriptive task were included, aiming to elucidate and render intelligible the factual perceptions. The results showed that the M-L figure appears physiognomically. Typical responses exhibiting stylistic variation pointed to the dialectic between perceiver and perceived thing. A second finding was that the perception of equal horizontal lines as unequal emerged as a predominant, but only one of several possible ways of resolving the M-L figure's many perceptual possibilities. In fact, the data revealed a trend that elucidates the conditions which make possible the "M-L effect." Finally, "direction-orientation," a phenomenal variable elucidated by Merleau-Ponty's notions about the body and perception, emerged as the most characteristic way of perceiving the experimental figure. (shrink)

Hans Vaihinger and the Stiftung Nietzsche-Archiv. The Letters to Richard Oehler. Hans Vaihinger’s letters to Richard Oehler document the ideological constellation in the context of the First World War. Unconcealed enthusiasm for the war, associated national-chauvinist resentment, and pronounced anti-communism immediately after the war clearly emerge. At first sight, this may be surprising, since Vaihinger is generally regarded as a progressive liberal pacifist. As this article attempts to make clear, however, it is also evident in Vaihinger’s case that (...) the First World War and its immediate aftermath led – at least temporarily – to quite questionable intellectual attitudes even among declared pacifists. In this respect, Vaihinger’s letters to Nietzsche’s cousin, librarian at the Nietzsche Archive in Weimar and later convinced National Socialist Richard Oehler are evaluated as revealing documents of contemporary history. (shrink)

The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come. Contributors Paul Benacerraf, George Boolos, John P. Burgess, Charles S. Chihara, Michael Detlefsen, Michael Dummett, Hartry Field, Kit Fine, (...) Bob Hale, Richard G. Heck, Jnr., Geoffrey Hellman, Penelope Maddy, Karl-Georg Niebergall, Charles D. Parsons, Michael D. Resnik, Matthias Schirn, Stewart Shapiro, Peter Simons, W.W. Tait, Crispin Wright. (shrink)

What is the cash value of Richard Rorty’s philosophy and politics of religion? This paper analyzes the political promise of Rorty’s shift from atheism to anticlericalism in the last decade of his life. It seeks to deliver primarily a concise summary of this shift, and of its transformative motivation. Then a critique of this shift is followed by the suggestion of a friendly amendment: its extension towards a pragmatic pluralism. The outlined Rortyan conception of a serene, and, at the (...) same time robust, politics of religion is proposed as a promising answer to the question of how secular liberal citizens should react to the “return of the gods.”. (shrink)

In this paper, I shall discuss several topics related to Frege’s paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege’s notion of evidence and its interpretation by Jeshion, the (...) introduction of the course-of-values operator and Frege’s attitude towards Axiom V, in the expression of which this operator occurs as the key primitive term. Axiom V says that the course-of-values of the function f is identical with the course-of-values of the function g if and only if f and g are coextensional. In the third section, I intend to show that in Die Grundlagen der Arithmetik (1884) Frege hardly could have construed Hume’s Principle (HP) as a primitive truth of logic and used it as an axiom governing the cardinality operator as a primitive sign. HP expresses that the number of Fs is identical with the number of Gs if and only if F and G are equinumerous. In the fourth section, I argue that Wright falls short of making a convincing case for the alleged analyticity of HP. In the final section, I canvass Heck’s arguments for his contention that Frege knew he could deduce the simplest laws of arithmetic from HP without invoking Axiom V. I argue that they do not carry conviction. I conclude this section by rejecting an interpretation concerning HP suggested by MacFarlane. (shrink)

In Die Grundlagen der Arithmetik, Frege attempted to introduce cardinalnumbers as logical objects by means of a second-order abstraction principlewhich is now widely known as ``Hume's Principle'' (HP): The number of Fsis identical with the number of Gs if and only if F and G are equinumerous.The attempt miscarried, because in its role as a contextual definition HP fails tofix uniquely the reference of the cardinality operator ``the number of Fs''. Thisproblem of referential indeterminacy is usually called ``the Julius Caesar (...) problem''.In this paper, Frege's treatment of the problem in Grundlagen is critically assessed. In particular, I try to shed new light on it by paying special attention to the framework of his logicism in which it appears embedded. I argue, among other things, that the Caesar problem, which is supposed to stem from Frege's tentative inductive definition of the natural numbers, is only spurious, not genuine; that the genuine Caesar problem deriving from HP is a purely semantic one and that the prospects of removing it by explicitly defining cardinal numbers as objects which are not classes are presumably poor for Frege. I conclude by rejecting two closely connected theses concerning Caesar put forward by Richard Heck: (i) that Frege could not abandon Axiom V because he could not solve the Julius Caesar problem without it; (ii) that (by his own lights) his logicist programme in Grundgesetze der Arithmetik failed because he could not overcome that problem. (shrink)

In this paper, I shall discuss several topics related to Frege's paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege's notion of evidence and its interpretation by Jeshion, the (...) introduction of the course-of-values operator and Frege's attitude towards Axiom V, in the expression of which this operator occurs as the key primitive term. Axiom V says that the course-of-values of the function f is identical with the course-of-values of the function g if and only if f and g are coextensional. In the third section, I intend to show that in Die Grundlagen der Arithmetik Frege hardly could have construed Hume's Principle as a primitive truth of logic and used it as an axiom governing the cardinality operator as a primitive sign. HP expresses that the number of Fs is identical with the number of Gs if and only if F and G are equinumerous. In the fourth section, I argue that Wright falls short of making a convincing case for the alleged analyticity of HP. In the final section, I canvass Heck's arguments for his contention that Frege knew he could deduce the simplest laws of arithmetic from HP without invoking Axiom V. I argue that they do not carry conviction. I conclude this section by rejecting an interpretation concerning HP suggested by MacFarlane. (shrink)

In this article, I try to shed some new light onGrundgesetze§10, §29–§31 with special emphasis on Frege’s criteria and proof of referentiality and his treatment of the semantics of canonical value-range names. I begin by arguing against the claim, recently defended by several Frege scholars, that the first-order domain inGrundgesetzeis restricted to value-ranges, but conclude that there is an irresolvable tension in Frege’s view. The tension has a direct impact on the semantics of the concept-script, not least on the semantics (...) of value-range names. I further argue that despite first appearances truth-value names play a distinguished role as semantic “target names” for “test names” in the criteria of referentiality and do not figure themselves as “test names” regarding referentiality. Accordingly, I show in detail that Frege’s attempt to demonstrate that by virtue of his stipulations “regular” value-range names have indeed been endowed with a unique reference, can plausibly be regarded as a direct application of the context principle. In a subsequent section, I turn to some special issues involved in §10. §10 is closely intertwined with §31 and in my and Richard Heck’s view would have been better positioned between §30 and §31. In a first step, I discuss the piecemeal strategy which Frege applies when he attempts to bestow a unique reference on value-range names in §3, §10–§12. In a second step, I critically analyze his tentative, but predictably unsuccessful proposal to identify all objects whatsoever, including those already clad in the garb of value-ranges, with their unit classes. In conclusion, I present two arguments for my claim that Frege’s identification of the True and the False with their unit classes in §10 is illicit even if both the permutation argument and the identifiability thesis that he states in §10 are regarded as formally sound. The first argument is set out from the point of view of the syntax of his formal language. It suggests though that a reorganization of the exposition of the concept-script would have solved at least one of the problems to which the twin stipulations in §10 give rise. The second argument rests on semantic considerations. If it is sound, it may call into question, if not undermine the legitimacy of the twin stipulations. (shrink)