We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite structures, and use the construction to show that the Grothendieck ring of the complex numbers contains as a subring the ring of (...) integer polynomials in continuum many variables. We prove the existence of a universal strong Euler characteristic on a structure. We investigate the dependence of the Grothendieck ring on the theory of the structure and give a few counter-examples. Finally, we relate some open problems and independence results in bounded arithmetic to properties of particular Grothendieck rings. (shrink)

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and (...) conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find this comprehensive treatment an excellent guide to this expanding interdisciplinary area. (shrink)

Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in (...) proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject. (shrink)

Biologists and philosophers of science have recently called for an extension of evolutionary theory. This so-called ‘extended evolutionary synthesis’ seeks to integrate developmental processes, extra-genetic forms of inheritance, and niche construction into evolutionary theory in a central way. While there is often agreement in evolutionary biology over the existence of these phenomena, their explanatory relevance is questioned. Advocates of EES posit that their perspective offers better explanations than those provided by ‘standard evolutionary theory’. Still, why this would be the case (...) is unclear. Usually, such claims assume that EES’s superior explanatory status arises from the pluralist structure of EES, its different problem agenda, and a growing body of evidence for the evolutionary relevance of developmental phenomena. However, what is usually neglected in this debate is a discussion of what the explanatory standards of EES actually are, and how they differ from prevailing standards in SET. In other words, what is considered to be a good explanation in EES versus SET? To answer this question, we present a theoretical framework that evaluates the explanatory power of different evolutionary explanations of the same phenomena. This account is able to identify criteria for why and when evolutionary explanations of EES are better than those of SET. Such evaluations will enable evolutionary biology to find potential grounds for theoretical integration. (shrink)

The larger part of Yearbook 6 of the Institute Vienna Circle constitutes the proceedings of a symposium on Alfred Tarski and his influence on and interchanges with the Vienna Circle, especially those on and with Rudolf Carnap and Kurt Gödel. It is the first time that this topic has been treated on such a scale and in such depth. Attention is mainly paid to the origins, development and subsequent role of Tarski's definition of truth. Some contributions are primarily historical, others (...) analyze logical aspects of the concept of truth. Contributors include Anita and Saul Feferman, Jan Wolenski, Jan Tarski and Hans Sluga. Several Polish logicians contributed: Gzegorczyk, Wójcicki, Murawski and Rojszczak. The volume presents entirely new biographical material on Tarski, both from his Polish period and on his influential career in the United States: at Harvard, in Princeton, at Hunter, and at the University of California at Berkeley. The high point of the analysis involves Tarski's influence on Carnap's evolution from a narrow syntactical view of language, to the ontologically more sophisticated but more controversial semantical view. Another highlight involves the interchange between Tarski and Gödel on the connection between truth and proof and on the nature of metalanguages. The concluding part of Yearbook 6 includes documentation, book reviews and a summary of current activities of the Institute Vienna Circle. Jan Tarski introduces letters written by his father to Gödel; Paolo Parrini reports on the Vienna Circle's influence in Italy; several reviews cover recent books on logical empiricism, on Gödel, on cosmology, on holistic approaches in Germany, and on Mauthner. (shrink)

Józef M. Bocheński began his philosophical career as an eclectic philosopher, then switched to Thomism and finally became a representative of the analytic school. As a Thomist he wanted to reform this orientation by the resources of modern formal logic. This tendency culminated in the establishment of the Cracow Circle (established in 1936) whose members were Bocheński, Jan F. Drewnowski, Jan Salamucha, and Bolesław Sobociński. However, the program of the Cracow Circle was rejected by most Thomists who considered traditional logic (...) as an entirely sufficient device of philosophy. Bocheński was very disappointed by this attitude of his Thomist fellows. His evolution toward analytic philosophy, free of any ideological pressure, can be regarded as his reaction to the conservatism of Thomism. (shrink)

Complex vocal learning, the capacity to imitate new sounds, underpins the evolution of animal vocal cultures and song dialects and is a key prerequisite for human speech and song. Due to its relevance for the understanding of cultural evolution and the biology and evolution of language and music, the trait has gained much scholarly attention. However, while we have seen tremendous progress with respect to our understanding of its morphological, neurological and genetic aspects, its peculiar phylogenetic distribution has remained elusive. (...) Intriguingly, animals as distinct as hummingbirds and humpback whales share well-developed vocal learning capacity in common with humans, while this ability is quite limited in nonhuman primates. Yet, solving this ‘vocal learning conundrum’ may shed light on the constraints ancestral humans overcame to unleash their vocal capacities. To this end I consider major constraints and functions that have been proposed. I highlight an especially promising ecological constraint, namely the spatial dimensionality of the environment. Based on an informal comparative review, I suggest that complex vocal learning is associated with three-dimensional habitats such as air and water. I argue that this is consistent with recent theoretical advances—i.e., the coercion-avoidance and dimensionality hypotheses—and with the long-standing hypothesis that mate choice is a major driver of the evolution and origin of complex vocal learning. However, I stress that multiple functions may apply and that quantitative phylogenetic comparative methods should be employed to finally resolve the issue. (shrink)

Research on the relation between sound and meaning in language has reported substantial evidence for implicit associations between articulatory–acoustic characteristics of phonemes and emotions. In the present study, we specifically tested the relation between the acoustic properties of a text and its emotional tone as perceived by readers. To this end, we asked participants to assess the emotional tone of single stanzas extracted from a large variety of poems. The selected stanzas had either an extremely high, a neutral, or an (...) extremely low average formant dispersion. To assess the average formant dispersion per stanza, all words were phonetically transcribed and the distance between the first and second formant per vowel was calculated. Building on a long tradition of research on associations between sound frequency on the one hand and non‐acoustic concepts such as size, strength, or happiness on the other hand, we hypothesized that stanzas with an extremely high average formant dispersion would be rated lower on items referring to Potency (dominance) and higher on items referring to Activity (arousal) and Evaluation (emotional valence). The results confirmed our hypotheses for the dimensions of Potency and Evaluation, but not for the dimension of Activity. We conclude that, at least in poetic language, extreme values of acoustic features of vowels are a significant predictor for the emotional tone of a text. (shrink)

This is a paper about The Causal Self-Referential Theory of Perception. According to The Causal Self-Referential Theory as developed by above all John Searle and David Woodruff Smith, perceptual content is satisfied by an object only if the object in question has caused the perceptual experience. I argue initially that Searle's account cannot explain the distinction between hallucination and illusion since it requires that the state of affairs that is presented in the perceptual experience must exist in order for the (...) perception to be veridical. Smith's account is interestingly different in that the descriptive content, i.e. the content that presents the perceptual object as having certain properties, does not determine the object of the experience. His account consequently does not require that the state of affairs that is presented in perception exists in order for the perception to have an object. Smith argues instead that perceptual reference is determined by a specific kind of demonstrative content. In this paper it is argued that Smith's account of demonstrative content is too indeterminate and in certain circumstances prescribes the wrong object. It is subsequently argued that the theory of demonstrative content can be modified so as to avoid these consequences. This modification involves deriving the conditions of satisfaction of seeing an object from the conditions of satisfaction of seeing the shape of the object, where the shape of the object is conceived of as a particularized property, what is also called a ‘trope’. (shrink)

We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite structures, and use the construction to show that the Grothendieck ring of the complex numbers contains as a subring the ring of (...) integer polynomials in continuum many variables. We prove the existence of a universal strong Euler characteristic on a structure. We investigate the dependence of the Grothendieck ring on the theory of the structure and give a few counter-examples. Finally, we relate some open problems and independence results in bounded arithmetic to properties of particular Grothendieck rings. (shrink)

We introduce a cyclic proof system for the two-way alternation-free modal μ-calculus. The system manipulates one-sided Gentzen sequents and locally deals with the backwards modalities by allowing analytic applications of the cut rule. The global effect of backwards modalities on traces is handled by making the semantics relative to a specific strategy of the opponent in the evaluation game. This allows us to augment sequents by so-called trace atoms, describing traces that the proponent can construct against the opponent’s strategy. The (...) idea for trace atoms comes from Vardi’s reduction of alternating two-way automata to deterministic one-way automata. Using the multi-focus annotations introduced earlier by Marti and Venema, we turn this trace-based system into a path-based system. We prove that our system is sound for all sequents and complete for sequents not containing trace atoms. (shrink)

The aim of this paper is twofold: The general aim is to shed light on the structure of species discoveries new to biology by bringing together a practice-oriented philosophy of science perspective with a philosophy of language perspective. The more specific aim is to argue that and to show how the overall structure of biological species discoveries comprises aspects of both institutional and non-institutional reality. The author proceeds as follows: he shows that placing the focus on the topic of scientific (...) discoveries enables us to circumvent two long-standing problems. He analyzes three fictional cases of discoveries in order to bring about a greater sensitivity for the concept of discovery. He takes a closer look at a real example – the discovery of a deep-sea anglerfish – and identifies the main structural features of species discovery processes in biology. In order to connect these results with Searle’s account of institutional reality, he provides an overview of the conceptual apparatus needed here. In bringing Searle’s account together with the structural features of species discoveries developed before, he shows to what extent declarative speech acts play a central role in species discovery processes in biology. (shrink)

ABSTRACT Backwards-looking operators Saarinen, E. [1979. “Backwards-Looking Operators in Tense Logic and in Natural Language.” In Essays on Mathematical and Philosophical Logic, edited by J. Hintikka, I. Niiniluoto, and E. Saarinen, 341–367. Dordrecht: Reidel] that have the material in their scope depend on higher intensional operators, are known to increase the expressivity of some intensional languages and have thus played a central role in debates about approaches to intensionality in terms of implicit parameters vs. variables explicitly quantifying over them. The (...) current contribution takes a look at these operators from a type-logical perspective. It is shown that extending Gallin's translation from intensional type logic to two-sorted type theory so as to include a version of Yanovich's backwards-looking operators, does not increase the expressive power of formulae with exclusively intensional parameters. The result, which makes use of a theorem by Zimmermann : 65–77]), is illustrated by pertinent examples from the literature. The paper closes by indicating alternative strategies of incorporating backwards-looking operators. (shrink)

‘The mathematisation of time has limits,’ writes Derrida in ‘Ousia and Gramme.’ Taking this quote in all possible senses, this paper considers Derrida’s definition of limit as gramme, trace, and ap...

INTRODUCTION This study arose from involvement with the works of Thomas Aquinas (/5-) that was not only intensive, but also extensive in the time devoted to ...

The book is a collection of the author¿s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the (...) history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

. This papers examines formal properties of logical squares and their generalizations in the form of hexagons and octagons. Then, several applications of these constructions in philosophical analysis are elaborated. They concern contingency (accidentality), possibility, permission, axiological concepts (bonum and malum), the generalized Hume thesis (deontic and epistemic modalities), determinism, truth and consistency (in various senses. It is shown that relations between notions used in various branches of philosophy fall into the same formal scheme.

Research on the relationship between corporate environmental performance and corporate financial performance has consistently grown and is gaining widespread attention. Given the vast body of CEP–CFP studies, recently scholars have begun to take stock of the cumulative results. However, no study so far has meta-analyzed the findings yielded by event studies assessing the stock market reactions to corporate environmental performance-related events. This paper sets out to close this gap by synthesizing previous empirical results regarding the stock market impact of positive (...) and negative CEP-related events. Results indicate a positive relationship across studies in terms of positive market reactions to positive events and negative reactions to negative events. Furthermore, the findings show that the market reactions are stronger for negative events than for positive events. Finally, this study examines whether methodological artifacts may explain the differences in the findings of the analyzed event studies. (shrink)

In this volume specialists of medieval music and philosophy put the medieval 'musica' into the context of ideas and institutions in which it existed. The significance of 'musica' cannot be understood from a modern point of view since 'music' does not match the medieval 'musica'.

This is an essay on McDowell’s naturalism. It is, pace some commentators, argued that McDowell’s naturalism does not end up in any strange metaphysical positions in the philosophy of mind, because second nature non-reductively supervenes on first nature and have causal powers. Pace certain other commentators, it is also argued that McDowell can be read as drawing a clear line between ethical platonism, and his own naturalized platonism, but only at the cost of landing in standard naturalism.

[A dialogue between Kant and Bolzano on mathematical knowledge.].