During the 1960s Paul F. Lazarsfeld, co-founder of the renowned Columbia school, worked to promote a useful new research methodology. This paper analyses these activities. In a series of papers, Lazarsfeld demonstrated that the roots of empirical research, the useful methodology he developed, lie in the work of early European scholars. Building on his belief that quantification does not need numbers, he showed that Hermann Conring, with his “classificatory statistics,” had predated Frédéric Le Play and his “ family budgets” and (...) Adolphe Quételet and his “probability statistics” by almost two centuries. In another paper he highlighted the importance of Max Weber’s empirical studies on agrarian and industrial workers within the frame of his life work. His seminars at Columbia University with Robert K. Merton and at the Sorbonne with Raymond Boudon opened up transatlantic cooperation on empirical research between New York and Paris for decades to come. (shrink)

1. The aim of the present article is not to compare Hume’s and Husserl’s philosophy or to trace Hume’s influence on Husserl’s phenomenology in detail. Such tasks would clearly exceed the limits of...

We show that \, the basic theory of bounded arithmetic corresponding to the complexity class \, proves the \ axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the \ iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, \ can also prove the integer division axiom, and the \-translation of induction and minimization for sharply bounded formulas. Similar consequences hold for the related theories \ and \. As a side (...) result, we also prove that there is a well-behaved \ definition of modular powering in \\). (shrink)

We study the notion of conservative translation between logics introduced by (Feitosa & D’Ottaviano2001). We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most (...) nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal. (shrink)

The elementary arithmetic operations +,·,≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${+,\cdot,\le}$$\end{document} on integers are well-known to be computable in the weak complexity class TC0, and it is a basic question what properties of these operations can be proved using only TC0-computable objects, i.e., in a theory of bounded arithmetic corresponding to TC0. We will show that the theory VTC0 extended with an axiom postulating the totality of iterated multiplication proves induction for quantifier-free formulas in the language ⟨+,·,≤⟩\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle{+,\cdot,\le}\rangle}$$\end{document}, and more generally, minimization for Σ0b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma_{0}^{b}}$$\end{document} formulas in the language of Buss’s S2. (shrink)

The article analyses the reception of Hume’s moral philosophy in the lectures and manuscripts of Edmund Husserl and in the published lectures of Franz Brentano, on which Husserl originally based his views. I first present the reasons that led Brentano to appreciate Hume’s sentimentalist background in moral philosophy and to criticize Hume’s relativism. I then show how Husserl, following the critique of psychologism in his Logical Investigations, builds on this starting point and attempts to show a possible contradictory nature of (...) Hume’s moral relativism. Finally, I consider whether Hume’s doctrine contains phenomenological insights that Husserl overlooks. (shrink)

D’Aquino et al. (J Symb Log 75(1):1–11, 2010) have recently shown that every real-closed field with an integer part satisfying the arithmetic theory IΣ4 is recursively saturated, and that this theorem fails if IΣ4 is replaced by IΔ0. We prove that the theorem holds if IΣ4 is replaced by weak subtheories of Buss’ bounded arithmetic: PV or $${\Sigma^b_1-IND^{|x|_k}}$$. It also holds for IΔ0 (and even its subtheory IE 2) under a rather mild assumption on cofinality. On the other hand, it (...) fails for the extension of IOpen by an axiom expressing the Bézout property, even under the same assumption on cofinality. (shrink)

We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic logics. We state a broad condition under which the admissibility problem is coNEXP-hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC) is in coNE, thus obtaining a sharp complexity estimate for admissibility in these systems.

The name the “Prague school of Brentano” refers to three generations of thinkers who temporarily or permanently lived in Prague, bound together by teacher/student relationships, and who accepted the main views of Franz Brentano’s philosophy. This chapter discusses central aspects of the philosophical work done in the School.

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson’s theory R. To this end, we borrow tools from model theory — specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of ∃∀ theories interpretable in (...) existential theories in the process. (shrink)

The concept ofmimēsiswas ‘shared by most authors, philosophers and educated audiences in the classical period, in antiquity as a whole, and even later’, although it has probably never been developed into a well-articulated theory. As far as we can judge from the extant evidence, the meaning of the expressions μίμησις and μιμέομαι differs from author to author and sometimes even from passage to passage. Ancient Greek views onmimēsishave often been discussed in modern scholarship, mainly within the field of history of (...) art, and it has been demonstrated repeatedly that the traditional English translation ‘imitation’ is not always appropriate for the ancient texts and that in many contexts it is rather misleading. In the following study I aim to focus on this concept as it was employed in the oldest Greek cosmological and philosophical theories. As a rule, the study of these theories is complicated by their fragmentary state of preservation and by their distortion through the specifically Platonic views that were dominant among the later doxographers. I shall suggest that the Platonizing tendency still prevalent today, which tends to translate and interpretmimēsisas ‘imitation’ or ‘copy’, should be carefully revised in the light of the Hippocratic evidence and specifically in view ofDe victu, probably the oldest authentic, non-fragmentary, and non-Platonic document attesting the concept ofmimēsis. (shrink)

We show that IPC, K4, GL, and S4, as well as all logics inheriting their admissible rules, have independent bases of admissible rules.

We show that $$ VTC ^0$$, the basic theory of bounded arithmetic corresponding to the complexity class $$\mathrm {TC}^0$$, proves the $$ IMUL $$ axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the $$\mathrm {TC}^0$$ iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, $$ VTC ^0$$ can also prove the integer division axiom, and (by our previous results) the $$ RSUV $$ -translation of induction and minimization for sharply (...) bounded formulas. Similar consequences hold for the related theories $$\Delta ^b_1\text{- } CR $$ and $$C^0_2$$. As a side result, we also prove that there is a well-behaved $$\Delta _0$$ definition of modular powering in $$I\Delta _0+ WPHP (\Delta _0)$$. (shrink)

We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV)), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP, APP, MA, AM) in PV₁ + dWPHP(PV).

We show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several applications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy to the collapse of the polynomial-time hierarchy.

We develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok–Esakia (...) theorem and the theory of modal companions to systems of multiple-conclusion rules or (finitary structural global) consequence relations, and a characterization of splittings in the lattices of consequence relations over monomodal or superintuitionistic logics with the finite model property. (shrink)

This paper focuses on Aristotle’s methodology of science and its application to the study of the human soul. My aim is to contrast two significantly different methodological approaches and to formulate two pairs of premises that Aristotle employs in two clearly differentiated and independent fields of study, namely in his zoological works and in the works of practical philosophy. Acknowledging these principles, as I suggest, may shed a new light on the methodological difficulties that Aristotle indicates in the introductory chapters (...) of his De anima. (shrink)

Despite Aristotle's family background and his undeniable impact on ancient Greek medicine, the influence of medicine on Aristotle's philosophy is controversial and far from universally acknowledged. The aim of this volume is to re-examine the influence of medical knowledge and literature on Aristotle's work, in particular to explore the connections with the Hippocratic writings. The volume encourages further exploration of this interdisciplinary area and offers new insights by presenting a series of case studies that examine in detail specific debates within (...) the Aristotelian corpus in relation to the medical literature. (shrink)

The paper discusses the sharp semantic shifts of the Greek expressions psychê and sôma between the Archaic and Classical era. Concerning the documentary evidence of the medical, rhetorical and philosophical literature at the end of the 5th century BC, I argue that speculations on human health and disease attested in some of the Hippocratic treatises involved a specificnotionofthebody-souldistinctionandalsothatthisnotionprovides an important contrast to the definitionofphilosophyasatherapyofsoul.

The purpose of this article is to provide a multi-perspective examination of one of the most important contemporary security issues: weaponized, and especially lethal, artificial intelligence. This technology is increasingly associated with the approaching dramatic change in the nature of warfare. What becomes particularly important and evermore intensely contested is how it becomes embedded with and concurrently impacts two social structures: ethics and law. While there has not been a global regime banning this technology, regulatory attempts at establishing a ban (...) have intensified along with acts of resistance and blocking coalitions. This article aims to reflect on the prospects and limitations, as well as the ethical and legal intensity, of the emerging regulatory framework. To allow for such an investigation, a power-analytical approach to studying international security regimes is utilized. (shrink)

International Relations's intellectual history is almost always treated as a history of ideas in isolation from both those discursive and political economies which provide its disciplinary and wider context. This paper contributes to this wider analysis by focusing on the impact of the field's discursive economy. Specifically, using Foucaultian archaeologico-genealogical strategy of problematization to analyse the emergence and disciplinary trajectories of Constructivism in IR, this paper argues that Constructivism has been brought gradually closer to its mainstream Neo-utilitarian counterpart through a (...) process of normalization, and investigates how it was possible for Constructivism to be purged of its early critical potential, both theoretical and practical. The first part of the paper shows how the intellectual configuration of Constructivism and its disciplinary fortunes are inseparable from far-from-unproblematic readings of the Philosophy of Social Science: the choices made at this level are neither as intellectually neutral nor as disciplinarily inconsequential as they are presented. The second and third parts chart the genealogies of Constructivism, showing how its overall normalization occurred in two stages, each revolving around particular practices and events. The second part concentrates on older genealogies, analysing the politics of early classificatory practices regarding Constructivism, and showing how these permitted the distillation and immunization of Constructivism – and thus of the rest of the mainstream scholarship which it was depicted as compatible with – against more radical Postmodernist/Post-structuralist critiques. Finally, the third part focuses attention on recent genealogies, revealing new attempts to reconstruct and reformulate Constructivism: here, indirect neutralization practices such as the elaboration of ‘Pragmatist’ Constructivism, as well as the direct neutralization such as the formulation of ‘Realist’ Constructivism, are key events in Constructivism's normalization. These apparently ‘critical’ alternatives that aim to ‘provide the identity variable’ in fact remain close to Neo-utilitarianism, but their successful representation as ‘critical’ help neutralize calls for greater openness in mainstream IR. Rather than a simple intellectual history, it is this complex process of reading and producing that counts as ‘Constructivism’, which explains both the normalization of Constructivism and the continued marginalization of Postmodernist/Post-structuralist approaches in mainstream IR's infra-disciplinary balance of intellectual power. (shrink)

The study aims to show that the Kantian distinction of synthetic and analytical resolution of the courts is originally epistemic and not purely logical. Proof of this proposition is done so that in the first step are distinguished two types of synthetic and analytical predicate relation to the subject - logical-semantic and epistemic. Furthermore, the examples demonstrated that Kant was familiar cases in courts, which are found only logico-semantic synthetic or analytic connection of concepts in trials. Consequently, Kant care for (...) them and are therefore not in terms classifiable Critique of Pure Reason, Kant even offers a way to understand its logic and Prolegomena. Based on various Kant notes offered by Article resolution three types of synthetic courts and courts of two kinds of analysis. The final part of the article is devoted to a brief outline of the relationship of epistemic and epistemic-synthetic-analytic courts, because the courts are due to which Kant its resolution synthetic and analytical courts instituted . Shown is both preferred synthesis of ideas before analysis, first, how Kant based his teachings on unum, verum, bonum featured specific tasks analysis concepts. article is supplemented by a short reflection on Kant's definition of the principle of the dispute and by showing a significant difference between Kant and Bolzano definition of analytic courts, whose oversight can lead to misunderstanding the context in which resolution synthetic and analytical courts in Kant belongs. (shrink)

We show that the quantified propositional proof systems Gi are polynomially equivalent to their restricted versions that require all cut formulas to be prenex Σqi . Previously this was known only for the treelike systems G*i. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

International Relations's intellectual history is almost always treated as a history of ideas in isolation from both those discursive and political economies which provide its disciplinary and wider context. This paper contributes to this wider analysis by focusing on the impact of the field's discursive economy. Specifically, using Foucaultian archaeologico-genealogical strategy of problematization to analyse the emergence and disciplinary trajectories of Constructivism in IR, this paper argues that Constructivism has been brought gradually closer to its mainstream Neo-utilitarian counterpart through a (...) process of normalization, and investigates how it was possible for Constructivism to be purged of its early critical potential, both theoretical and practical. The first part of the paper shows how the intellectual configuration of Constructivism and its disciplinary fortunes are inseparable from far-from-unproblematic readings of the Philosophy of Social Science: the choices made at this level are neither as intellectually neutral nor as disciplinarily inconsequential as they are presented. The second and third parts chart the genealogies of Constructivism, showing how its overall normalization occurred in two stages, each revolving around particular practices and events. The second part concentrates on older genealogies, analysing the politics of early classificatory practices regarding Constructivism, and showing how these permitted the distillation and immunization of Constructivism – and thus of the rest of the mainstream scholarship which it was depicted as compatible with – against more radical Postmodernist/Post-structuralist critiques. Finally, the third part focuses attention on recent genealogies, revealing new attempts to reconstruct and reformulate Constructivism: here, indirect neutralization practices such as the elaboration of ‘Pragmatist’ Constructivism, as well as the direct neutralization such as the formulation of ‘Realist’ Constructivism, are key events in Constructivism's normalization. These apparently ‘critical’ alternatives that aim to ‘provide the identity variable’ in fact remain close to Neo-utilitarianism, but their successful representation as ‘critical’ help neutralize calls for greater openness in mainstream IR. Rather than a simple intellectual history, it is this complex process of reading and producing that counts as ‘Constructivism’, which explains both the normalization of Constructivism and the continued marginalization of Postmodernist/Post-structuralist approaches in mainstream IR's infra-disciplinary balance of intellectual power. (shrink)

We study the extension 123) of the theory S21 by instances of the dual weak pigeonhole principle for p-time functions, dWPHPx2x. We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a strengthening of Wilkie's witnessing theorem for S21+dWPHP. We construct a propositional proof system WF , which captures the Π1b-consequences of S21+dWPHP. We also show that WF p-simulates the Unstructured Extended Nullstellensatz proof system of Buss et al. 256). We prove that (...) dWPHP is equivalent to a statement asserting the existence of a family of Boolean functions with exponential circuit complexity. Building on this result, we formalize the Nisan–Wigderson construction in a conservative extension of S21+dWPHP. (shrink)

We develop an arithmetical theory and its variant , corresponding to “slightly nonuniform” . Our theories sit between and , and allow evaluation of log-depth bounded fan-in circuits under limited conditions. Propositional translations of -formulas provable in admit L-uniform polynomial-size Frege proofs.

We prove that the sharply bounded arithmetic T02 in a language containing the function symbol ⌊x /2y⌋ is equivalent to PV1.

We prove that all axiomatic extensions of the full Lambek calculus with exchange can be axiomatized by formulas on the level of the substructural hierarchy.

We show that the universally axiomatized, induction-free theory equation image is a sequential theory in the sense of Pudlák's 5, in contrast to the closely related Robinson's arithmetic.

The goal of the present article is to describe the Brentanian background of several topics concerning judgments and assertions in Husserl’s Logical Investigations. Why did Husserl abandon Brentano’s theory of two judgmental forces? Is the “is true/false” to be understood as an expression of judgmental force or as a logical predication? Is a “common expression” of the objective validity of judgment equivalent with our expression of our belief in that validity? Does the linguistic sign of the logical force manifest this (...) force or not? In order to provide a better understanding of Husserl’s approach, the paper also discusses his earlier views on these issues in recently published manuscripts from the early 1890s and in his Logic Lectures from the year 1896. (shrink)

We investigate the substitution Frege () proof system and its relationship to extended Frege () in the context of modal and superintuitionistic propositional logics. We show that is p-equivalent to tree-like , and we develop a “normal form” for -proofs. We establish connections between for a logic L, and for certain bimodal expansions of L.We then turn attention to specific families of modal and si logics. We prove p-equivalence of and for all extensions of , all tabular logics, all logics (...) of finite depth and width, and typical examples of logics of finite width and infinite depth. In most cases, we actually show an equivalence with the usual system for classical logic with respect to a naturally defined translation.On the other hand, we establish exponential speed-up of over for all modal and si logics of infinite branching, extending recent lower bounds by P. Hrubeš. We develop a model-theoretical characterization of maximal logics of infinite branching to prove this result. (shrink)

We formalize the construction of Paterson’s variant of the Ajtai–Komlós–Szemerédi sorting network of logarithmic depth in the bounded arithmetical theory , under the assumption of the existence of suitable expander graphs. We derive a conditional p-simulation of the propositional sequent calculus in the monotone sequent calculus.

By a well-known result of Cook and Reckhow [S.A. Cook, R.A. Reckhow, The relative efficiency of propositional proof systems, Journal of Symbolic Logic 44 36–50; R.A. Reckhow, On the lengths of proofs in the propositional calculus, Ph.D. Thesis, Department of Computer Science, University of Toronto, 1976], all Frege systems for the classical propositional calculus are polynomially equivalent. Mints and Kojevnikov [G. Mints, A. Kojevnikov, Intuitionistic Frege systems are polynomially equivalent, Zapiski Nauchnyh Seminarov POMI 316 129–146] have recently shown p-equivalence of (...) Frege systems for the intuitionistic propositional calculus in the standard language, building on a description of admissible rules of IPC by Iemhoff [R. Iemhoff, On the admissible rules of intuitionistic propositional logic, Journal of Symbolic Logic 66 281–294]. We prove a similar result for an infinite family of normal modal logics, including K4, GL, S4, and. (shrink)