Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular.

LetL(K) denote the lattice (ordered by inclusion) of quasivarieties contained in a quasivarietyK and letD 2 denote the variety of distributive (0, 1)-lattices with 2 additional nullary operations. In the present paperL(D 2) is described. As a consequence, ifM+N stands for the lattice join of the quasivarietiesM andN, then minimal quasivarietiesV 0,V 1, andV 2 are given each of which is generated by a 2-element algebra and such that the latticeL(V 0+V1), though infinite, still admits an easy and nice description (...) (see Figure 2) while the latticeL(V 0+V1+V2), because of its intricate inner structure, does not. In particular, it is shown thatL(V 0+V1+V2) contains as a sublattice the ideal lattice of a free lattice with free generators. Each of the quasivarietiesV 0,V 1, andV 2 is generated by a 2-element algebra inD 2. (shrink)

This paper was presented at the Seminar of the Section of Logic, In- stitute of Mathematics Nicholas Copernicus University, held by Professor Jerzy Kotas, Torun, March 1975. An altered version of the paper will be published in Studia Logica.

The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.

Things and Their Place in Theories Our talk of external things, our very notion of things, is just a conceptual apparatus that helps us to foresee and ...

Explores the nature and types of mystical experience and discusses the value of mysticism for humanity.

W. V. Quine is one of the most eminent philosophers alive today. Now in his mid-eighties he has produced a sharp, sprightly book that encapsulates the whole of his philosophical enterprise, including his thinking on all the key components of his epistemological stance--especially the value of logic and mathematics. New readers of Quine may have to go slowly, fathoming for themselves the richness that past readers already know lies between these elegant lines. For the faithful there is much to ponder. (...) In this short book, based on lectures delivered in Spain in 1990, Quine begins by locating his work historically. He provides a lightning tour of the history of philosophy (particularly the history of epistemology), beginning with Plato and culminating in an appreciative sketch of Carnap's philosophical ambitions and achievements. This leads, in the second chapter, to an introduction to Quine's attempt to naturalize epistemology, which emphasizes his continuities with Carnap rather than the differences between them. The next chapters develop the naturalistic story of the development of science to take account of how our conceptual apparatus is enhanced so that we can view the world as containing re-identifiable objects. Having explained the role of observation sentences in providing a checkpoint for assessing scientific theories, and having despaired of constructing an empirical criterion to determine which sentences are meaningful, Quine in the remaining chapters takes up a variety of important issues about knowledge. He concludes with an extended treatment of his views about reference and meaning and his attitudes toward psychological and modal notions. The presentation is distinctive, and the many small refinements of detail and formulation will fascinate all who know Quine's philosophy. (shrink)

We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.

First, we prove that the lattice of all structural strengthenings of a given strongly finite consequence operation is both atomic and coatomic, it has finitely many atoms and coatoms, each coatom is strongly finite but atoms are not of this kind — we settle this by constructing a suitable counterexample. Second, we deal with the notions of hereditary: algebraicness, strong finitisticity and finite approximability of a strongly finite consequence operation. Third, we formulate some conditions which tell us when the lattice (...) of all structural strengthenings of a given strongly finite consequence operation is finite, and subsequently we give some applications of them. (shrink)

The aim of the paper is to prove the result announced by the title.

While the idea of philosophy as conceptual analysis has attracted many adherents and undergone a number of variations, in general it suffers from an authority problem with two dimensions. First, it is unclear why the analysis of a concept should have objective authority: why explicating what we mean should express how things are. Second, conceptual analysis seems to lack intersubjective authority: why philosophical analysis should apply to more than a parochial group of individuals. I argue that Hegel’s conception of social (...) ontology, focused on his concept of “ethical life” (Sittlichkeit), helps to explain how concepts (and their explication) have both objective and intersubjective authority in the social domain. Hegel claims that modern institutions are the product of self-conscious purposes, so that they are conceptually constituted. Concepts do not just represent these objects and so depend on a contingent relation to them. As many contemporary social ontologists agree, this means that our concepts of these institutions are uniquely epistemically “transparent.” They have objective authority. Concepts have intersubjective authority in the modern world as well, according to Hegel. However, I show that this feature of Hegel’s account does not rely on the solution to a philosophical problem. Rather, since the concepts of modern ethical life are “essentially contested,” their content depends on the practical and political agreement of modern subjects. This means that concepts can only have objective authority if some prior intersubjective agreement has been reached. The role of philosophy as conceptual analysis is thus importantly dependent on political developments. (shrink)

In his “Kant and Finitism” Tait attempts to connect his analysis of finitist arithmetic with Kant’s perspective on arithmetic. The examination of this attempt is the basis for a distinctive view on the dramatic methodological shift from Kant to Dedekind and Hilbert. Dedekind’s 1888 essay “Was sind und was sollen die Zahlen?” gives a logical analysis of arithmetic, whereas Hilbert’s 1899 book “Grundlagen der Geometrie” presents such an analysis of geometry or, as Hilbert puts it, of our spatial intuition. This (...) shift in the late ninteenth century required a radical expansion of logic: first by the inclusion of principles for “systems” and “mappings”, but second by a structuralist broadening of axioms and inferential principles. The interaction of mathematics and logic in mathematical logic opened, around 1920, fields of investigation with enormous impact on the philosophy of mathematics, promoting a deeper integration of mathematical practice and philosophical reflection. (shrink)

We present some equivalent conditions for a quasivariety \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {K}}$$\end{document} of structures to be generated by a single structure. The first such condition, called the embedding property was found by A.I. Mal′tsev in [6]. It says that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf A}, {\bf B} \in \mathcal {K}}$$\end{document} are nontrivial, then there exists \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf C} \in \mathcal{K}}$$\end{document} (...) such that A and B are embeddable into C. One of our equivalent conditions states that the set of quasi-identities valid in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{K}}$$\end{document} is closed under a certain Gentzen type rule which is due to J. Łoś and R. Suszko [5]. (shrink)

P. KOnig: Einleitung - P. ZIche: Idiographik und allgemeine Wissenschaftlichkeit - Windelband und die Wissenschaftsreflexion um 1900 - G. HArtung: Ein Philosoph korrigiert sich selbst - Wilhelm Windelbands Abkehr vom Relativismus - O. SChlaudt: Philosophie am Leitfaden der Empirie. WIndelbands relativistisches Programm - S. KUft: Windelbands Konzeption von Transzendentalphilosophie und ihr Bezug zur Kulturphilosophie - R. BOnito Oliva: Windelband. KUlturphilosophie und Kulturkrise - P. KOnig: Teleologie und Geschichte bei Wilhelm Windelband - J. BOhr: Im Fortschreiben der Probleme: Windelbands 19. JAhrhundert (...) - T.-H. CHang: Der Wertbegriff beiWilhelm Windelband und sein Konzept der Problemgeschichte - T. KUbalica: Die Geschichte der Philosophie als Problemgeschichte - J. MEhlich: Windelbands Praludien und das Silberne Zeitalter in Russland - G. SChluter: Windelbands italienische Kontakte und Bezugnahmen - D. STefanelli: Notizen uber Karl Vossler und die "Sudwestdeutsche Schule" - C. ZAnfi: Geschichte, Natur und Leben: Windelband und Bergson in der Historismus-Debatte - J.-I. LIndén: Der beseelte Geist: Dilthey als Kritiker der badischen Schule - H. GUndlach: Windelbands Ringen mit der Psychologie - Anhang: Wilhelm Windelband: Blaue Hefte zur Psychologie. (shrink)

In classes of algebras such as lattices, groups, and rings, there are finite algebras which individually generate quasivarieties which are not finitely axiomatizable (see [2], [3], [8]). We show here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras. Moreover, we show that the lattice join of two finitely axiomatizable quasivarieties, each generated by a finite Heyting or topological Boolean algebra, respectively, need not be finitely axiomatizable. Finally, we solve problem 4 asked (...) in Rautenberg [10]. (shrink)

If within the borders of human life the truth is, as Vico has said, what is made, then the task of a student of human life can be and should be to find out from what human beings have made what manner of makers they are and what sorts of production their circumstance allows.

Using ideas from Murskii [3], Tokarz [4] and Wroski [7] we construct some strongly finite consequence operation having 2%0 standard strengthenings. In this way we give the affirmative answer to the following question, stated in Tokarz [4]: are there strongly finite logics with the degree of maximality greater than 0?

The categorical dualities presented are: (first) for the category of bi-algebraic lattices that belong to the variety generated by the smallest non-modular lattice with complete (0,1)-lattice homomorphisms as morphisms, and (second) for the category of non-trivial (0,1)-lattices belonging to the same variety with (0,1)-lattice homomorphisms as morphisms. Although the two categories coincide on their finite objects, the presented dualities essentially differ mostly but not only by the fact that the duality for the second category uses topology. Using the presented dualities (...) and some known in the literature results we prove that the Q-lattice of any non-trivial variety of (0,1)-lattices is either a 2-element chain or is uncountable and non-distributive. (shrink)

We prove that each proper ideal in the lattice of axiomatic, resp. standard strengthenings of the intuitionistic propositional logic is of cardinality 20. But, each proper ideal in the lattice of structural strengthenings of the intuitionistic propositional logic is of cardinality 220. As a corollary we have that each of these three lattices has no atoms.

The aim of this paper is to propose a criterion of finite detachment-substitutional formalization for normal modal systems. The criterion will comprise only those normal modal systems which are finitely axiomatizable by means of the substitution, detachment for material implication and Gödel rules.

We prove that each intermediate or normal modal logic is strongly complete with respect to a class of finite Kripke frames iff it is tabular, i.e. the respective variety of pseudo-Boolean or modal algebras, corresponding to it, is generated by a finite algebra.

Professor Ryszard Wójcicki once asked whether the degree of maximality of the consequence operationC determined by the theorems of the intuitionistic propositional logic and the detachment rule for the implication connective is equal to ? The aim of the present paper is to give the affirmative answer to the question. More exactly, it is proved here that the degree of maximality ofC — the — fragment ofC, is equal to , for every such that.

In the Transcendental Aesthetic (TA), Kant is typically held to make negative assertations about “things in themselves,” namely that they are not spatial or temporal. These negative assertions stand behind the “neglected alternative” problem for Kant’s transcendental idealism. According to this problem, Kant may be entitled to assert that spatio-temporality is a subjective element of our cognition, but he cannot rule out that it may also be a feature of the objective world. In this paper, I show in a new (...) way how Kant’s view (focusing on his conclusions about space) is not subject to this objection, by showing that he does not make the denial about mind-independent reality that he is typically held to make. The argument develops consequences of a new reading of Kant’s expression “an sich selbst” (‘in itself’; ‘in themselves’). I argue that “an sich selbst” or “per se” has a special, judgment-level role, so that this expression does not form new noun-terms adjectivally. It follows that the conceptual unit of Kant’s “Conclusions” in the TA is simply “things” (Dinge), since “things in themselves” is not a nominal expression; Kant adopts the Wolffian ontological use of “thing” as the basic kind-term for any existent. The arguments that things per se are not in space are arguments that space cannot be a necessary property or relations of things as a kind. I show that this does not involve the positive claim about mind-independent reality that inspires the neglected alternative objection. (shrink)

Let q(K) denote the least quasivariety containing a given class K of algebraic structures. Mal'cev [3] has proved that q(K) = ISP r(K)(1). Another description of q(K) is given in Grätzer and Lakser [2], that is, q(K) = ISPP u(K)2. We give here other proofs of these results. The method which enables us to do that is borrowed from prepositional logics (cf. [1]).

Blame is multifarious. It can be passionate or dispassionate. It can be expressed or kept private. We blame both the living and the dead. And we blame ourselves as well as others. What’s more, we blame ourselves, not only for our moral failings, but also for our non-moral failings: for our aesthetic bad taste, gustatory self-indulgence, or poor athletic performance. And we blame ourselves both for things over which we exerted agential control (e.g., our voluntary acts) and for things over (...) which we lacked such control (e.g., our desires, beliefs, and intentions). I argue that, despite this manifest diversity in our blaming practices, it’s possible to provide comprehensive account of blame. Indeed, I propose a set of necessary and sufficient conditions that aims to specify blame’s extension in terms of its constitution as opposed to its function. And I argue that this proposal has a number of advantages beyond accounting for blame in all its disparate forms. For one, it can account for the fact that one’s having had control over whether one was to φ is a necessary condition for one’s being fittingly blamed for having φ-ed. For another, it can account for why, unlike fitting shame, fitting blame is always deserved, which in turn explains why there is something morally problematic about ridding oneself of one’s fitting self-blame (e.g., one’s fitting guilt). (shrink)