For a long time, regularity accounts of causation have virtually vanished from the scene. Problems encountered within other theoretical frameworks have recently induced authors working on causation, laws of nature, or methodologies of causal reasoning – as e.g. May (Kausales Schliessen. Eine Untersuchung über kausale Erklärungen und Theorienbildung. Ph.D. thesis, Universität Hamburg, Hamburg, 1999), Ragin (Fuzzy-set social science. Chicago: University of Chicago Press, 2000), Graßhoff and May (Causal regularities. In W. Spohn, M. Ledwig, & M. Esfeld (Eds.), Current issues (...) in causation (pp. 85–114). Paderborn: Mentis, 2001), Swartz (The concept of physical law (2nd ed.). http://www.sfu.ca/philosophy/physical-law/, 2003), Halpin (Erkenntnis, 58, 137–168, 2003) – to direct their attention back to regularity theoretic analyses. In light of the latest proposals of regularity theories, the paper at hand therefore reassesses the criticism raised against regularity accounts since the INUS theory of causation of Mackie (The cement of the universe. A study of causation. Oxford: Clarendon Press, 1974). It is shown that most of these objections target strikingly over-simplified regularity theoretic sketches. By outlining ways to refute these objections it is argued that the prevalent conviction as to the overall failure of regularity theories has been hasty. (shrink)

In this paper, we propose a regularity theory of causation. The theory aims to be reductive and to align with our pre‐theoretic understanding of the causal relation. We show that our theory can account for a wide range of causal scenarios, including isomorphic scenarios, omissions, and scenarios which suggest that causation is not transitive.

Regularity theories of causation assert that causal or nomic notions are to be reduced into “mere” frequencies of particular, non-nomic, co-located qualities and matters of fact. In this essay, I present a critical exploration of Armstrong and Strawson’s explanatory arguments against regularity theories. The shortcomings of these older arguments for nomic realism are identified and a revamped version which is immune to such problems is outlined and defended. I argue that anti-realism suffers substantial disconfirmation due to its comparative (...) inability to unify empirical regularities in the absence of any probabilistic counterweights. I also show that realist theories are much more probable than their anti-realist competitors both individually and in aggregate. This is shown to be the case with even the most humble of observational data. This revamped argument is Bayesian in character; it is immune to the criticisms of Beebee, Everitt, Loewer, and van Fraassen ; and it is empiricist friendly to boot. (shrink)

In The Secret Connexion1 Galen Strawson argues against the traditional interpretation of Hume, according to which Hume’s theory of meaning leads him to a regularity theory of causation. In actual fact, says Strawson, ‘Hume believes firmly in some sort of natural necessity’ (p. 277). What Hume denied was that we are aware of causal connections outrunning regular succession, and that we have a ‘positively or descriptively contentful conception’ of such powers (p. 283); he did not deny that (...) there are such powers, or that they are what we are talking about when we talk about causation. Strawson has four central lines of argument. His ‘most direct evidence’ (p. 2) against a regularity interpretation consists of (1) passages where Hume refers to hidden powers underlying the regularities of which we are aware. Strawson’s broader motivations for rejecting the traditional interpretation are (2) that the regularity theory is in itself quite absurd, and (3) that it is incompatible with Hume’s ‘non-committal scepticism’. And the method which he uses to defend his interpretation against pressure from the theory of ideas is (4) to develop some comments of Hume’s on ‘relative’ ideas into something like a further theory of content to supplement the theory of ideas. Strawson develops almost the strongest case I can imagine for his claims. I shall try to explain why he leaves me unconvinced. (shrink)

This article takes stock of the regularity theory of causation. It considers three challenges to the theory: the problem of joint effects, the problems of redundant causation, and omission‐involving causation. The former is often cited as a special, and especially challenging, problem for regularity theories. But the force of this problem has been greatly overstated. The threat to regularity theories instead comes from the latter two.

Classically, any structure for a signature ${\rm{\Sigma }}$ may be completed to a model of a desired regular theory ${T}}$ by means of the chase construction or small object argument. Moreover, this exhibits ${\rm{Mod}}\left$ as weakly reflective in ${\rm{Str}}\left$.We investigate this in the constructive setting. The basic construction is unproblematic; however, it is no longer a weak reflection. Indeed, we show that various reflectivity principles for models of regular theories are equivalent to choice principles in the ambient set (...) class='Hi'>theory. However, the embedding of a structure into its chase-completion still satisfies a conservativity property, which suffices for applications such as the completeness of regular logic with respect to Tarski models.Unlike most constructive developments of predicate logic, we do not assume that equality between symbols in the signature is decidable. While in this setting, we also give a version of one classical lemma which is trivial over discrete signatures but more interesting here: the abstraction of constants in a proof to variables. (shrink)

A regularity theory of causation analyses type-level causation in terms of Boolean difference-making. The essential ingredient that helps this theoretical framework overcome the problems of Hume’s and Mill’s classical accounts is a principle of non-redundancy: only Boolean dependency structures from which no elements can be eliminated track causation. The first part of this paper argues that the recent regularity theoretic literature has not consistently implemented this principle, for it disregarded an important type of redundancies: structural redundancies. Moreover, (...) it is shown that a regularity theory needs to be underwritten by a hitherto neglected metaphysical background assumption stipulating that the world's causal makeup is not ambiguous. Against that background, the second part then develops a new regularity theory that does justice to all types of redundancies and, thereby, provides the first all-inclusive notion of Boolean difference-making. (shrink)

Fred Dretske's "Knowledge and the Flow of Information" is an extended attempt to develop a philosophically useful theory of information. Dretske adapts central ideas from Shannon and Weaver's mathematical theory of communication, and applies them to some traditional problems in epistemology. In doing so, he succeeds in building for philosophers a much-needed bridge to important work in cognitive science. The pay-off for epistemologists is that Dretske promises a way out of a long-standing impasse -- the Gettier problem. He (...) offers an alternative model of knowledge as information-based belief, which purports to avoid the problems justificatory accounts face. This essay looks closely at Dretske's theory. I argue that while the information-theoretic framework is attractive, it does not provide an adequate account of knowledge. And there seems to be no way of tightening the theory without introducing some version of a theory of justification -- the very notion Dretske's theory was designed to avoid. (shrink)

A regularity theory of causation analyses type-level causation in terms of Boolean difference-making. The essential ingredient that helps this theoretical framework overcome the problems of Hume’s and Mill’s classical accounts is a principle of non-redundancy: only Boolean dependency structures from which no elements can be eliminated track causation. The first part of this article argues that the recent regularity-theoretic literature has not consistently implemented this principle, for it disregarded an important type of redundancies: structural redundancies. Moreover, it (...) is shown that a regularity theory needs to be underwritten by a hitherto neglected metaphysical background assumption stipulating that the world’s causal makeup is not ambiguous. Against that background, the second part then develops a new regularity theory that does justice to all types of redundancies and, thereby, provides the first all-inclusive notion of Boolean difference-making. (shrink)

The majority of the currently flourishing theories of actual causation are located in a broadly counterfactual framework that draws on structural equations. In order to account for cases of symmetric overdeterminiation and preemption, these theories resort to rather intricate analytical tools, most of all, to what Hitchcock has labeled explicitly nonforetracking counterfactuals. This paper introduces a regularity theoretic approach to actual causation that only employs material conditionals, standard Boolean minimization procedures, and a stability condition that regulates the behavior of (...) causal models under model expansions. Notwithstanding its lightweight analytical toolbox, this regularity theory performs at least as well as the structural equations accounts with their heavy appliances. (shrink)

The regularization of chiral gauge theories is reviewed from the “overlap” point of riew. This is a brief and biased review containing no references.

This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF ${(\mathcal{L})}$ (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here ${\mathcal{L}}$ is a language with a distinguished linear order <, and REF ${(\mathcal {L})}$ consists of formulas of the form $$\exists x \forall y_{1} < x \ldots \forall y_{n} < x \varphi (y_{1},\ldots ,y_{n})\leftrightarrow \varphi^{ < x}(y_1, \ldots ,y_n),$$ where φ is an (...) ${\mathcal{L}}$ -formula, φ theory T in a countable language ${\mathcal{L}}$ with a distinguished linear order:Some model of T has an elementary end extension with a first new element.T ⊢ REF ${(\mathcal{L})}$ .T has an ω 1-like model that continuously embeds ω 1.For some regular uncountable cardinal κ, T has a κ-like model that continuously embeds a stationary subset of κ.For some regular uncountable cardinal κ, T has a κ-like model ${\mathfrak{M}}$ that has an elementary extension in which the supremum of M exists.Moreover, if κ is a regular cardinal satisfying κ = κ <κ , then each of the above conditions is equivalent to: T has a κ + -like model that continuously embeds a stationary subset of κ. (shrink)

We define a hierarchy on the regular types of an ω-stable nonmultidimensional theory, using generalised notions of algebraic and strongly minimal formulae. As an application we show that any resplendent model of an ω-stable finite-dimensional theory is saturated.

We propose a set theory, called NRFST, in which the Cantorian axiom of infinity is negated, and a new notion of infinity is introduced via non standard methods, i. e. via adequate notions of standard and internal, two unary predicates added to the language of ZF. After some initial results on NRFST, we investigate its relative consistency with respect to ZF and Kawai's WNST.

Regularity theories of causation are guided by the idea that causes are collectively sufficient for their effects. Following Mackie [1974], that idea is typically refined to distinguish collections that include redundant members from those that do not. Causes must be collectively sufficient for their effects without redundancy. While Mackie was surely right that the regularity theory must distinguish collections that are in some sense minimally sufficient for an effect from those that include unnecessary hangers-on, I believe that (...) redundancy is the wrong mark of that distinction. I propose a way to develop the regularity theory without it. Instead of distinguishing minimal from mere sufficiency in terms of redundancy, we should look to the influence that events have in the world. Causes, so construed, must have just enough collective influence to ensure that an effect occurs. I argue that such an account provides a uniform solution to the problem of epiphenomena and to a pair of related problems that aris.. (shrink)

This paper discusses the role of levels and level-bound theoretical terms in neurobiological explanations under the presupposition of a regularity theory of constitution. After presenting the definitions for the constitution relation and the notion of a mechanistic level in the sense of the regularity theory, the paper develops a set of inference rules that allow to determine whether two mechanisms referred to by one or more accepted explanations belong to the same level, or to different levels. (...) The rules are characterized as underlying level distinctions in neuroscience research. (shrink)

This new and important study of semantic change examines how new meanings arise through language use, especially the various ways in which speakers and writers experiment with uses of words and constructions in the flow of strategic interaction with addressees. In the last few decades there has been growing interest in exploring systemicities in semantic change from a number of perspectives including theories of metaphor, pragmatic inferencing, and grammaticalization. Like earlier studies, these have for the most part been based on (...) data taken out of context. This book is the first detailed examination of semantic change from the perspective of historical pragmatics and discourse analysis. Drawing on extensive corpus data from over a thousand years of English and Japanese textual history, Traugott and Dasher show that most changes in meaning originate in and are motivated by the associative flow of speech and conceptual metonymy. (shrink)

We continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } (...) \right\}$ of countable models of the theory of a fixed Baldwin–Shi hypergraph with $\mathfrak{M}_\beta \preccurlyeq \mathfrak{M}_\gamma $ if and only if the dimension of $\mathfrak{M}_\beta $ is at most the dimension of $\mathfrak{M}_\gamma $ and that each countable model is isomorphic to some $\mathfrak{M}_\beta $. We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on a large body of work, we use these structures to give an example of a pseudofinite, ω-stable theory with a nonlocally modular regular type, answering a question of Pillay in [11]. (shrink)

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to (...) prove the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory. (shrink)

Many philosophers insist that the most plausible solution to the exclusion problem is to adopt the so-called ‘autonomy approach’, which denies either upward or downward causation between mental and physical properties. But the question of whether the autonomy approach is compatible with respectable theories of causation has seldom been discussed in the literature. This paper considers two influential theories of causation, the counterfactual account and the regularity account. I argue that neither the counterfactual theory nor the regularity (...) theory can support the autonomy approach – while the counterfactual approach fails to block downward causation, the regularity approach is unable to refute upward causation. (shrink)

BackgroundRegularity effect can affect performance in prospective memory, but little is known on the cognitive processes linked to this effect. Moreover, its impacts with regard to aging remain unknown. To our knowledge, this study is the first to examine regularity effect in PM in a lifespan perspective, with a sample of young, intermediate, and older adults.Objective and designOur study examined the regularity effect in PM in three groups of participants: 28 young adults, 16 intermediate adults, and 25 older (...) adults. The task, adapted from the Virtual Week, was designed to manipulate the regularity of the various activities of daily life that were to be recalled. We examine the role of several cognitive functions including certain dimensions of executive functions, short-term memory, and retrospective episodic memory to identify those involved in PM, according to... (shrink)

The underlying structures that are common to the world's languages bear an intriguing connection with early emerging forms of “core knowledge”, which are frequently studied by infant researchers. In particular, grammatical systems often incorporate distinctions that reflect those made in core knowledge. Here, I argue that this connection occurs because non-verbal core knowledge systematically biases processes of language evolution. This account potentially explains a wide range of cross-linguistic grammatical phenomena that currently lack an adequate explanation. Second, I suggest that developmental (...) researchers and cognitive scientists interested in knowledge representation can exploit this connection to language by using observations about cross-linguistic grammatical tendencies to inspire hypotheses about core knowledge. (shrink)

In this paper I formulate Minimal Requirements for Candidate Predictions in quantum field theories, inspired by viewing the standard model as an effective field theory. I then survey standard effective field theory regularization procedures, to see if the vacuum expectation value of energy density ) is a quantity that meets these requirements. The verdict is negative, leading to the conclusion that \ is not a physically significant quantity in the standard model. Rigorous extensions of flat space quantum field (...) theory eliminate \ from their conceptual framework, indicating that it lacks physical significance in the framework of quantum field theory more broadly. This result has consequences for problems in cosmology and quantum gravity, as it suggests that the correct solution to the cosmological constant problem involves a revision of the vacuum concept within quantum field theory. (shrink)

The underlying structures that are common to the world's languages bear an intriguing connection with early emerging forms of “core knowledge” (Spelke & Kinzler, 2007), which are frequently studied by infant researchers. In particular, grammatical systems often incorporate distinctions (e.g., the mass/count distinction) that reflect those made in core knowledge (e.g., the non-verbal distinction between an object and a substance). Here, I argue that this connection occurs because non-verbal core knowledge systematically biases processes of language evolution. This account potentially explains (...) a wide range of cross-linguistic grammatical phenomena that currently lack an adequate explanation. Second, I suggest that developmental researchers and cognitive scientists interested in (non-verbal) knowledge representation can exploit this connection to language by using observations about cross-linguistic grammatical tendencies to inspire hypotheses about core knowledge. (shrink)

In his recent book The Secret Connection (Clarendon 1989), Galen Strawsonadvances what he calls 'a simple and devastating objection' to the regularitytheory of causation. I will argue that his objection, far from beingdevastating, has no force at all; and further, that if it did have force, itwould tell equally against Strawson's own preferred alternative to theregularity theory.

The thesis focuses on a quite recent research field lying in between Descriptive Set Theory and Automata Theory (for infinite objects). In both areas, one is often concerned with subsets of the Cantor space or of its homeomorphic copies. In Descriptive Set Theory, such subsets are usually stratified in topological hierarchies, like the Borel hierarchy, the Wadge hierarchy and the difference hierarchy; in Automata Theory, such sets are studied in terms of regularity, that is, the (...) property of being recognised by an automaton or, equivalently, of being expressible in Monadic Second-Order Logic. This double point of view leads to many interesting questions about the interplay and relationship between topological complexity and regularity. While we have a complete picture of what happens in the case of automata on words, the case of automata on trees is still a terra incognita. Some results have already been obtained for particular classes of languages, like Buchi languages, deterministic languages, ¨ and unambiguous languages. In this thesis we instead drop any restriction and prove some new results concerning arbitrary regular tree languages which belong to low levels of the Borel hierarchy and of the Wadge hierarchy. (shrink)

Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indetermi nacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI al gebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties are discussed. Moreover, the (...) relationships among neutrosophic regular filter, fuzzy filters and anti-grouped neutrosophic filters are prese nted, and the results are proved: a neutrosophic filter (fuzzy filter) is a neutrosophic regular filter (fuzzy regular filter), if and only if it is both a neutrosophic closed filter (fuzzy closed filter) and an anti-grouped neutrosophic filter (fuzzy anti-grouped filter). (shrink)

The purpose of this study is to assess the intention of typically developing peers towards learning in the classroom with students with Autism Spectrum Disorder. In developing countries, such as Ghana, the body of literature on the relationship between students with disabilities and typically developing peers has been sparsely studied. Using Ajzen's theory of planned behaviour as a theoretical framework for this study, 516 typically developing students completed four scales representing belief constructs, attitudes, subjective norms, and perceived behavioural controls, (...) hypothesised to predict behavioural intention. The data were subjected to a t-test, analysis of variance, and structural equation modelling. The modelling confirmed the combining ability of attitude, subjective norms, and perceived behavioural controls to predict intention. We conclude by revealing the need for policymakers to consider designing programmes aimed towards promoting social relationships between students with ASD and typically developing peers. (shrink)

In earlier work by the first and second authors, the equivalence of a finite square principle $\square^{\mathrm{fin}}_{\lambda,D}$ with various model-theoretic properties of structures of size $\lambda $ and regular ultrafilters was established. In this paper we investigate the principle $\square^{\mathrm{fin}}_{\lambda,D}$—and thereby the above model-theoretic properties—at a regular cardinal. By Chang’s two-cardinal theorem, $\square^{\mathrm{fin}}_{\lambda,D}$ holds at regular cardinals for all regular filters $D$ if we assume the generalized continuum hypothesis. In this paper we prove in ZFC that, for certain regular filters (...) that we call $\mathit{doubly}^{+}$ regular, $\square^{\mathrm{fin}}_{\lambda,D}$ holds at regular cardinals, with no assumption about GCH. Thus we get new positive answers in ZFC to Open Problems 18 and 19 in Chang and Keisler’s book Model Theory. (shrink)