It is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, (...) is derivable from the other axioms. The set of remaining axioms is independent. Finally, it is shown that if both the left-hand and right-hand distributive laws for relative multiplication are included in the set of axioms, then two of Tarski’s other axioms become redundant, namely the second involution law and the distributive law for converse. The set of remaining axioms is independent and equivalent to Tarski’s axiom system. (shrink)

IntroductionMentalizing is a key aspect of social cognition. Several researchers assume that mentalization has two systems, an explicit one and an implicit one. In schizophrenia, several studies have confirmed the deficit of explicit mentalizing, but little data are available on non-explicit mentalizing. However, increasing research activity can be detected recently in implicit mentalizing. The aim of this systematic review and meta-analysis is to summarize the existing results of implicit mentalizing in schizophreniaMethodsA systematic search was performed in four major databases: MEDLINE, (...) EMBASE, Cochrane Central Register of Controlled Trials, Web of Science. Eleven publications were selected. Five studies were found to be eligible for quantitative synthesis, and 9 studies were included in qualitative synthesis.ResultsThe meta-analysis revealed significantly lower accuracy, slower reaction time during implicit mentalizing in patients with schizophrenia. The systematic review found different brain activation pattern, further alterations in visual scanning, cue fixation, face looking time, and difficulties in perspective taking.DiscussionOverall, in addition to the deficit of explicit mentalization, implicit mentalization performance is also affected in schizophrenia, if not to the same extent. It seems likely that some elements of implicit mentalization might be relatively unaffected, but the effectiveness is limited by certain neurocognitive deficits. These alterations in implicit mentalizing can also have potential therapeutic consequences.Systematic Review Registration:https://www.crd.york.ac.uk/prospero/, identifier: CRD42021231312. (shrink)

We make comments on some problems Erdős and Hajnal posed in their famous problem list. Let X be a graph on $\omega _1$ with the property that every uncountable set A of vertices contains a finite set s such that each element of $A-s$ is joined to one of the elements of s. Does then X contain an uncountable clique? We prove that both the statement and its negation are consistent. Do there exist circuitfree graphs $\{X_n:n<\omega \}$ on $\omega (...) _1$ such that if $A\in [\omega _1]^{\aleph _1}$, then $\{n<\omega :X_n\cap [A]^2=\emptyset \}$ is finite? We show that the answer is yes under CH, and no under Martin’s axiom. Does there exist $F:[\omega _1]^2\to 3$ with all three colors appearing in every uncountable set, and with no triangle of three colors. We give a different proof of Todorcevic’ theorem that the existence of a $\kappa $ -Suslin tree gives $F:[\kappa ]^2\to \kappa $ establishing $\kappa \not \to [\kappa ]^2_{\kappa }$ with no three-colored triangles. This statement in turn implies the existence of a $\kappa $ -Aronszajn tree. (shrink)

István Hajnal is one of the most remarkable historians and a forerunner of research on the history of communication. He developed his radical theories on the connections between writing as a technique and social structure mainly in the first half of the twentieth century. He emphasized, in a unique way, the importance of technology for social development arguing that the transformation of social structures and the individual within stand in a mutual and interdependent relation with various technological systems. While (...) doing so he reconsidered Max Weber's concepts of traditionalism and rationalism from a so to speak Heideggerian angle. (shrink)

Whereas a growing bulk of work has demonstrated that both adults and children are sensitive to frequently occurring word sequences, little is known about the potential role of meaning in the processing of such multiword chunks. Here, we take a first step toward assessing the contribution of meaningfulness in the processing of multiword sequences, using items that varied in chunk meaningfulness. In a phrasal-decision study, we compared reaction times for triads of three-word sequences, corresponding to idiomatic expressions, compositional phrases, and (...) phrasal fragments, while controlling for phrase and substring frequencies. Chunk meaningfulness, as assessed by a separate subjective rating study, was found to speed up decision times for all three types of strings: The more meaningful a multiword sequence was judged to be, the faster it was processed, independently of whether it was idiomatic, compositional in nature, or a phrasal fragment. These results highlight the importance of taking meaning into account when considering the processing of multiword chunks, consistent with predictions of construction-based approaches to language. (shrink)

When do two sentences say the same thing, that is, express the same content? We defend two-component (2C) semantics: the view that propositional contents comprise (at least) two irreducibly distinct constituents, (1) truth-conditions, and (2) subject-matter. We contrast 2C with one-component (1C) semantics, focusing on the view that subject-matter is reducible to truth- conditions. We identify exponents of this view and argue in favor of 2C. An appendix proposes a general formal template for propositional 2C semantics.

Berkeley’s likeness principle is the claim that “an idea can be like nothing but an idea”. The likeness principle is intended to undermine representationalism: the view (that Berkeley attributes to thinkers like Descartes and Locke) that all human knowledge is mediated by ideas in the mind which represent material objects. Yet, Berkeley appears to leave the likeness principle unargued for. This has led to several attempts to explain why Berkeley accepts it. In contrast to ‘metaphysical’ and ‘epistemological’ interpretations available in (...) the literature, in this paper I defend a ‘conceptual’ interpretation. I argue that Berkeley accepts the likeness principle on the basis of (i) his commitment to the transparency of ideas, and (ii) his account of resemblance which he sets out in his works on vision. Thus, I provide an explanation for Berkeley’s reasons for accepting the likeness principle which, appropriately, focuses on his views concerning ideas and likeness. (shrink)

What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...) As a counterproposal, then, we define a large fragment of predicate logic characterized by its use of only bounded quantification. This so-called guarded fragment enjoys the above nice properties, including decidability, through an effectively bounded finite model property. (These are new results, obtained by generalizing notions and techniques from modal logic.) Moreover, its own internal finite variable hierarchy turns out to work well. Finally, we shall make another move. The above analogy works both ways. Modal operators are like quantifiers, but quantifiers are also like modal operators. This observation inspires a generalized semantics for first-order predicate logic with accessibility constraints on available assignments (cf. N´emeti 1986, 1992) which moves the earlier quantifier restrictions into the semantics. This provides a fresh look at the landscape of possible predicate logics, including candidates sharing various desirable features with basic modal logic – in particular, its decidability. (shrink)

Margaret Macdonald was at the institutional heart of analytic philosophy in Britain in the mid-twentieth century. Yet, her views on the nature of philosophical theories diverge quite considerably from those of many of her contemporaries. In this paper, I focus on her 1953 article ‘Linguistic Philosophy and Perception’, a provocative paper in which Macdonald argues that the value of philosophical theories is more akin to that of poetry or art than science or mathematics. I do so for two reasons. First, (...) because it reveals just how far Macdonald’s meta- philosophical views diverged from those of many of her contemporaries. Second, because the discussion in LPP pre-empts recent literature on the nature of philosophical inquiry and the efficacy of philosophical arguments. Indeed, Macdonald’s paper is just as likely to provoke discussion today as it was in the 1950s. (shrink)

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

This paper provides a philosophical evaluation of the concept of handedness prevalent but largely unspoken in the scientific literature. This literature defines handedness as the preference or ability to use one hand rather than the other across a range of common activities. Using the philosophical discipline of phenomenology, I articulate and critique this conceptualization of handedness. Phenomenology shows defining a concept of handedness by focusing on hand use leads to a right hand biased concept. I argue further that a phenomenological (...) model based in spatial orientation rather than hand use provides a more inclusive concept of handedness. (shrink)

We give two theories, Th1 and Th2, which are explicitly definable over each other , but are not definitionally equivalent. The languages of the two theories are disjoint.

We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...) for every natural number k there is an equation in E containing more than k distinct variables and all the operation symbols, if 2 < n < ω. Completely analogous statement holds for the case n ω. This improves Monk's famous non-finitizability theorem for which we give here a simple proof. We prove analogous nonfinitizability properties of the larger varieties SNrnCAn + k. We prove that the complementation-free subreducts of RCAn do not form a variety. We also investigate the reason for the above “non-finite axiomatizability” behaviour of RCAn. We look at all the possible reducts of RCAn and investigate which are finitely axiomatizable. We obtain several positive results in this direction. Finally, we summarize the results and remaining questions in a figure. We carry through the same programme for RPEAn and for RRA. By looking into the reducts we also investigate what other kinds of natural algebras of relations are possible with more positive behaviour than that of the well known ones. Our investigations have direct consequences for the logical properties of the n-variable fragment Ln of first order logic. The reason for this is that RCAn and RPEAn are the natural algebraic counterparts of Ln while the varieties SNrnCAn + k are in connection with the proof theory of Ln. This paper appears in two parts. The first part contains the non-finite axiomatizability results. The present second part contains finite axiomatizations of some fragments together with a figure summarizing the finite and non-finite axiomatizability results in this area and the problems left open. (shrink)

Since its original publication in 1975, this groundbreaking work has awakened millions of people to the existence of "speciesism"—our systematic disregard of nonhuman animals—inspiring a worldwide movement to transform our attitudes to animals and eliminate the cruelty we inflict on them. In Animal Liberation, author Peter Singer exposes the chilling realities of today’s "factory farms" and product-testing procedures—destroying the spurious justifications behind them, and offering alternatives to what has become a profound environmental and social as well as moral issue. (...) An important and persuasive appeal to conscience, fairness, decency, and justice, it is essential reading for the supporter and the skeptic alike. (shrink)

It is argued that causal understanding originates in experiences of acting on objects. Such experiences have consistent features that can be used as clues to causal identification and judgment. These are singular clues, meaning that they can be detected in single instances. A catalog of 14 singular clues is proposed. The clues function as heuristics for generating causal judgments under uncertainty and are a pervasive source of bias in causal judgment. More sophisticated clues such as mechanism clues and repeated interventions (...) are derived from the 14. Research on the use of empirical information and conditional probabilities to identify causes has used scenarios in which several of the clues are present, and the use of empirical association information for causal judgment depends on the presence of singular clues. It is the singular clues and their origin that are basic to causal understanding, not multiple instance clues such as empirical association, contingency, and conditional probabilities. (shrink)

In this important new book in the IPPP series, a group of leading thinkers in psychiatry, psychology, and philosophy offer alternative perspectives that address both the scientific and clinical aspects of psychiatric validation, emphasizing throughout their philosophical and historical considerations.

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events and when we lack them. The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in (...) the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering. (shrink)

We give a novel application of algebraic logic to first order logic. A new, flexible construction is presented for representable but not completely representable atomic relation and cylindric algebras of dimension n (for finite n > 2) with the additional property that they are one-generated and the set of all n by n atomic matrices forms a cylindric basis. We use this construction to show that the classical Henkin-Orey omitting types theorem fails for the finite variable fragments of first order (...) logic as long as the number of variables available is > 2 and we have a binary relation symbol in our language. We also prove a stronger result to the effect that there is no finite upper bound for the extra variables needed in the witness formulas. This result further emphasizes the ongoing interplay between algebraic logic and first order logic. (shrink)

We shall show that certain natural and interesting intervals in the lattice of varieties of representable relation algebras embed the lattice of all subsets of the natural numbers, and therefore must have a very complicated lattice-theoretic structure.

Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, (...) Glymour and Halvorson. (shrink)

William Molyneux was born in Dublin, studied in Trinity College Dublin, and was a founding member of the Dublin Philosophical Society (DPS), Ireland’s counterpart to the Royal Society in London. He was a central figure in the Irish intellectual milieu during the Early Modern period and – along with George Berkeley and Edmund Burke – is one of the best-known thinkers to have come out of that context and out of Irish thought more generally. In 1688, when Molyneux wrote the (...) letter to Locke in which he posed the now famous question about a man born blind made to see, he was an active member of the DPS and was on familiar terms with several other key figures in Irish philosophy at the time. For the most part, Irish thinkers in the seventeenth and eighteenth centuries answered “no” to Molyneux’s question of whether a blind man made to see could distinguish, by sight alone, between a cube and a sphere. (shrink)

This book examines the complex and varied ways in which fictions relate to the real world, and offers a precise account of how imaginative works of literature can use fictional content to explore matters of universal human interest. While rejecting the traditional view that literature is important for the truths that it imparts, the authors also reject attempts to cut literature off altogether from real human concerns. Their detailed account of fictionality, mimesis, and cognitive value, founded on the methods of (...) analytical philosophy, restores to literature its distinctive status among cultural practices. The authors also explore metaphysical and skeptical views, prevalent in modern thought, according to which the world itself is a kind of fiction, and truth no more than a social construct. They identify different conceptions of fiction in science, logic, epistemology, and make-believe, and thereby challenge the idea that discourse per se is fictional and that different modes of discourse are at root indistinguishable. They offer rigorous analyses of the roles of narrative, imagination, metaphor, and "making" in human thought processes. Both in their methods and in their conclusions, Lamarque and Olsen aim to restore rigor and clarity to debates about the values of literature, and to provide new, philosophically sound foundations for a genuine change of direction in literary theorizing. (shrink)

This is an abstract of our paper \A characterisation of Floyd-provable programs" submitted to Theoretical Computer Science. ! denotes the set of natural numbers. Y =d fyi : i 2 !g is the set of variable symbols. L denotes the set of classical rst order formulas of type t possibly with free variables , where t is the similarity type of arithmetic, i.e. it consists of \+; ; 0; 1" with arities \2; 2; 0; 0".

Theorem 1 states a negative result about the classical semantics j= ! of program schemes. Theorem 2 investigates the reason for this. We conclude that Theorem 2 justies the Henkin-type semantics j= for which the opposite of the present Theorem 1 was proved in [1]{[3] and also in a dierent form in part III of [5]. The strongest positive result on j= is Corollary 6 in [3].

P.F. Strawson's essay traces some formal characteristics of logic and grammar to their roots in general features of thought and experience.

The problem of whether Lambek Calculus is complete with respect to (w.r.t.) relational semantics, has been raised several times, cf. van Benthem (1989a) and van Benthem (1991). In this paper, we show that the answer is in the affirmative. More precisely, we will prove that that version of the Lambek Calculus which does not use the empty sequence is strongly complete w.r.t. those relational Kripke-models where the set of possible worlds,W, is a transitive binary relation, while that version of the (...) Lambek Calculus where we admit the empty sequence as the antecedent of a sequent is strongly complete w.r.t. those relational models whereW=U×U for some setU. We will also look into extendability of this completeness result to various fragments of Girard's Linear Logic as suggested in van Benthem (1991), p. 235, and investigate the connection between the Lambek Calculus and language models. (shrink)

In September 2008, the European Organization for Nuclear Research (CERN) scientists successfully switched on the historic biggest physics device, the Large ...

Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...) to other classes of algebras of logic, for example quasi-polyadic algebras and substitution-cylindrification algebras with and without equality, relation algebras, and special Boolean monoids. The results of op. cit. mentioned above are special cases of our general theorems. We point out an error in the proof of the Henkin-Monk-Tarski representation theorem for atomic, equality-free, quasi-polyadic algebras with rectangular atoms. The error consists in the implicit assumption of a property that does not, in general, hold. We then give a correct proof of their theorem. Henkin and Tarski also introduced the notion of a rich cylindric algebra and proved in op. cit. that every rich cylindric algebra of finite dimension satisfying certain special identities is representable. We introduce a modification of the notion of a rich algebra that, in our opinion, renders it more natural. In particular, under this modification richness becomes a density notion. Moreover, our notion of richness applies not only to algebras with equality, such as cylindric algebras, but also to algebras without equality. We show that a finite dimensional algebra is rich iff it is rectangularly dense and quasi-atomic; moreover, each of these conditions is also equivalent to a very natural condition of point density . As a consequence, every finite dimensional rich algebra of logic is representable. We do not have to assume the validity of any special identities to establish this representability. Not only does this give an improvement of the Henkin-Tarski representation theorem for rich cylindric algebras, it solves positively an open problem in op. cit. concerning the representability of finite dimensional rich quasi-polyadic algebras without equality. (shrink)

In my contribution to this Concise Collection on Margaret Cavendish, I focus on teaching Cavendish’s work in the context of philosophy (and, more specifically, Early Modern Philosophy). I have three aims. First, to explain why teaching women from philosophy’s history is crucially important to the discipline. Second, to outline my own reflections on teaching Cavendish’s philosophy. Third, to defend a specific claim about the benefits of teaching Cavendish to philosophy students; namely, that introducing biographical detail alongside philosophical ideas enriches the (...) learning experience. (shrink)