One of the themes that has been widely addressed in both the implicit learning and statistical learning literatures is that of rule learning. While it is widely agreed that the extraction of regularities from the environment is a fundamental facet of cognition, there is still debate about the nature of rule learning. Rey and colleagues show that the comparison between human and non‐human primates can contribute important insights to this debate.

Machamer, Darden, and Craver argue that causal explanations explain effects by describing the operations of the mechanisms which produce them. One of this paper’s aims is to take advantage of neglected resources of Mechanism to rethink the traditional idea that actual or counterfactual natural regularities are essential to the distinction between causal and non-causal co-occurrences, and that generalizations describing natural regularities are essential components of causal explanations. I think that causal productivity and regularity are by no means the same (...) thing, and that the Regularists are mistaken about the roles generalizations play in causal explanation. Humean, logical empiricist, and other Regularist accounts of causal explanation have had the unfortunate effect of distracting philosophers’ from important non-explanatory scientific uses of laws and lesser generalizations which purport to describe natural regularities. My second aim is to characterize some of these uses, illustrating them with examples from neuroscientific research. (shrink)

Comparativism—the view that mass ratios are not grounded in absolute masses—faces a challenge by Baker which suggests that absolute masses are empirically meaningful. Regularity comparativism uses a liberalized version of the Mill-Ramsey-Lewis Best Systems Account to have both the laws of Newtonian gravity and the absolute mass scale supervene on a comparativist Humean mosaic as a package deal. I discuss three objections to this view and conclude that it is untenable. The most severe problem is that once we have (...) reduced away the absolute masses, there is nothing that stops us from also reducing the mass ratios. (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)

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)

The regularities in nature, simply by being regularities, call for explanation. There are only two ways in which we could, with any plausibility, try to explain them. One way would be to suppose that they are imposed on the world by God. The other would be to suppose that they reflect the presence of laws of nature, conceived of as forms of natural necessity. But the only way of making sense of the notion of a law of nature, thus conceived, (...) is by construing a law as the causing of the associated regularity, and the only remotely plausible account of such causing would be in terms of the agency of God. So, by whichever route, we are led to the conclusion that the regularities are brought about by God. So the presence of the regularities in nature provides us with a strong case for accepting the existence of God. (shrink)

The goal of this paper is to sketch an empiricist metaphysics of laws of nature. The key idea is that there are regularities without regularity-enforcers. Differently put, there are natural laws without law-makers _of a distinct metaphysical kind_. This sketch will rely on the concept of a natural pattern and more significantly on the existence of a network of natural patterns in nature. The relation between a regularity and a pattern will be analysed in terms of mereology. Here (...) is the road map. In section 2, I will briefly discuss the relation between empiricism and metaphysics, aiming to show that an empiricist metaphysics is possible. In section 3, I will offer arguments against stronger metaphysical views of laws. Then, in section 4 I will motivate nomic objectivism. In section 5, I will address the question ‘what is a regularity?’ and will develop a novel answer to it, based on the notion of a natural pattern. In section 6, I will raise the question: ‘what is a law of nature?’, the answer to which will be: a law of nature is a regularity that is characterised by the unity of a _natural_ pattern. (shrink)

This article addresses the question of whether we should conceive of mechanisms as productive of change in a regular way. I argue that, if mechanisms are characterized as fully regular, on the one hand, then not enough processes will count as mechanisms for them to be interesting or useful. If no appeal to regularity is made at all in their characterization, on the other hand, then mechanisms can no longer be useful for grounding prediction and supporting intervention strategies. I (...) conclude that, if the New Mechanistic Philosophy is to be successful, a stochastic characterization of mechanisms must be adopted. (shrink)

During the course of about ten years, Wittgenstein revised some of his most basic views in philosophy of mathematics, for example that a mathematical theorem can have only one proof. This essay argues that these changes are rooted in his growing belief that mathematical theorems are ‘internally’ connected to their canonical applications, i.e. , that mathematical theorems are ‘hardened’ empirical regularities, upon which the former are supervenient. The central role Wittgenstein increasingly assigns to empirical regularities had profound implications for all (...) of his later philosophy; some of these implications (particularly to rule following) are addressed in the essay. (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)

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 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)

Can stable regularities be explained without appealing to governing laws or any other modal notion? In this paper, I consider what I will call a ‘Humean system’—a generic dynamical system without guiding laws—and assess whether it could display stable regularities. First, I present what can be interpreted as an account of the rise of stable regularities, following from Strevens [2003], which has been applied to explain the patterns of complex systems (such as those from meteorology and statistical mechanics). Second, since (...) this account presupposes that the underlying dynamics displays deterministic chaos, I assess whether it can be adapted to cases where the underlying dynamics is not chaotic but truly random—that is, cases where there is no dynamics guiding the time evolution of the system. If this is so, the resulting stable, apparently non-accidental regularities are the fruit of what can be called statistical necessity rather than of a primitive physical necessity. (shrink)

Say that α is an n-strongly c. e. real if α is a sum of n many strongly c. e. reals, and that α is regular if α is n-strongly c. e. for some n. Let Sn be the set of all n-strongly c. e. reals, Reg be the set of regular reals and CE be the set of c. e. reals. Then we have: S1 ⊂ S2 ⊂ · · · ⊂ Sn ⊂ · · · ⊂ ⊂ Reg (...) ⊂ CE. This gives a hierarchy of the c. e. reals. We also study the regularity of the d. c. e. reals. (shrink)

It has recently been argued that Harvey Brown and Oliver Pooley’s ‘dynamical approach’ to special relativity should be understood as what might be called an ontologically and ideologically relationalist approach to Minkowski geometry, according to which Minkowski geometrical structure supervenes upon the symmetries of the best-systems dynamical laws for a material world with primitive topological or differentiable structure. Fleshing out the details of some such primitive structure, and a conception of laws according to which Minkowski geometry could so supervene, has (...) been referred to by some as the ‘constructivist project’. Here, it is explained that Nick Huggett’s work on ‘regularity relationalism’ provides a framework for such an approach, and a relativistic version of Huggett’s regularity relationalism is outlined for that purpose. Finally, by way of examples, it is shown that this approach fails in the simplest cases. Still, reasons are given for which this should not necessarily discourage an advocate of this interpretation of the dynamical approach. _1_ Introduction to the Dynamical Approach _2_ Huggett’s Regularity Relationalism _3_ The Dynamical Approach as a Form of Regularity Relationalism _4_ A Simple Way to Set the Stage _5_ A First Attempt _5.1_ Complex-valued planewave solutions _5.2_ Real-valued planewave solutions _6_ More General Solutions _7_ Summary and Reflections. (shrink)

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)

Timothy Williamson has claimed to prove that regularity must fail even in a nonstandard setting, with a counterexample based on tossing a fair coin infinitely many times. I argue that Williamson’s argument is mistaken, and that a corrected version shows that it is not regularity which fails in the non-standard setting but a fundamental property of shifts in Bernoulli processes.

Wittgenstein has a role for pointing out with grammar. Pointing is available as a potential resource in justifying and explaining grammar, the regular use of words. This chapter explores some of the foundational issues that frame the idea that pointing can play this role. It concentrates on the role of pointing in justifying the use of words and provides the beginnings of an account of how Wittgenstein's discussion in the opening sections of Philosophical Investigations can be integrated with on‐going philosophical (...) enquiry. The autonomy of grammar is a metaphysical thesis. Wittgenstein has a role for pointing that can contribute to an explanation and justification of linguistic regularities. The idea of grammar as linguistic regularity cuts across the received mythology of grammar as a body of norms, norms for the use of words. The idea of philosophical explanation surviving as an enterprise in Wittgenstein's work is contentious. (shrink)

Emotional regularity is the degree to which a person maintains and returns to a set of emotional states over time. The present investigation examined associations between emotional regularity and extant emotion measures as well as psychologically relevant dimensions of personality, health, and real-world occupational outcomes. Participants included 598 U.S. adults who provided daily experience sampling reports on their emotional states for approximately two months. Results suggest that emotional regularity was related to, but distinct from, well-established measures of (...) emotion including emotional intensity, variability, covariation, inertia, granularity, and emodiversity. Furthermore, emotional regularity significantly predicted measures of personality, psychological health, and occupational outcomes even when accounting for extant emotion measures and sociodemographic covariates. Finally, it explained modest (7.5%) improvement (in terms of cross-validated RSq.) over baseline models containing emotional intensity, variability, and sociodemographic covariates. These findings suggest that emotional regularity may provide an important indicator of healthy emotional functioning and may be a promising area for further scientific discovery. (shrink)

Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this (...) popular view is the result of two mistakes. The first mistake, which this essay calls the “numerical fallacy,” is to assume that a distinction that isn't represented by different numbers isn't represented at all in a mathematical representation. In this case, the essay claims that although the real numbers do not make all relevant distinctions, the full mathematical structure of a probability function does. The second mistake is that the hyperreals make too many distinctions. They have a much more complex structure than credences in ordinary propositions can have, so they make distinctions that don't exist among credences. While they might be useful for generating certain mathematical models, they will not appear in a faithful mathematical representation of credences of ordinary propositions. (shrink)

Regularity is the thesis that all contingent propositions should be assigned probabilities strictly between zero and one. I will prove on cardinality grounds that if the domain is large enough, a regular probability assignment is impossible, even if we expand the range of values that probabilities can take, including, for instance, hyperreal values, and significantly weaken the axioms of probability.

For regular sets in Euclidean space, previous work has identified twelve ‘basic’ computability notions to which many previous notions considered in literature were shown to be equivalent. With respect to those basic notions we now investigate on the computability of natural operations on regular sets: union, intersection, complement, convex hull, image, and pre-image under suitable classes of functions. It turns out that only few of these notions are suitable in the sense of rendering all those operations uniformly computable.

Former discussions of biological generalizations have focused on the question of whether there are universal laws of biology. These discussions typically analyzed generalizations out of their investigative and explanatory contexts and concluded that whatever biological generalizations are, they are not universal laws. The aim of this paper is to explain what biological generalizations are by shifting attention towards the contexts in which they are drawn. I argue that within the context of any particular biological explanation or investigation, biologists employ two (...) types of generations. One type identifies causal regularities exhibited by particular kinds of biological entities. The other type identifies how these entities are distributed in the biological world. (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)

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)

Regularization may be used as an alternative to dimensionality reduction when the number of variables in a model is much larger than the number of available observations. In a recent study from our group regularized regression was employed to quantify brain functional connectivity in a sample of healthy controls using a brain parcellation and resting state fMRI images. Here regularization is applied to evaluate resting state connectivity abnormalities at the voxel level in a sample of patients with schizophrenia. Specifically, ridge (...) regression is implemented with different degrees of regularization. Results are compared to those delivered by the weighted global brain connectivity method, which is based on averaged bivariate correlations and from the non-redundant connectivity method, a dimensionality reduction approach that applies supervised principal component regressions. Ridge regression is able to detect a larger set of abnormally connected regions than both GBC and NRC methods, including schizophrenia related connectivity reductions in fronto-medial, somatosensory and occipital structures. Due to its multivariate nature, the proposed method is much more sensitive to group abnormalities than the GBC, but it also outperforms the NRC, which is multivariate too. Voxel based regularized regression is a simple and sensitive alternative for quantifying brain functional connectivity. (shrink)

In reply to certain cosmological arguments for theism, critics regularly argue that the causal principle ex nihilo nihil fit may be false. Various theistic counter-replies to this challenge have emerged. One type of strategy is to double down on ex nihilo nihil fit. Another, very different strategy of counter-reply is to grant for the sake of argument that the principle is false, while maintaining that sound cosmological arguments can be formulated even with this concession in place. Notably, one can employ (...) a weaker opening premise formulated in modal terms, proceeding for instance from the proposition that for any contingent object coming into existence it is at least possible that it have a cause. My aim here is to try out a related strategy for weakening the relevant opening premise. Granting that it is possible for a contingent object to come into existence out of nothing without a cause, I proceed from the extremely modest claim that the obtaining of exceptionless longstanding contingent regularities demands an explanation. As such, the contingent regularity that empirically accessible macro-level contingent objects do not pop into existence causelessly demands explanation. And as it turns out, that explanation will have to be in terms of an object or objects possessed of at least some of the traditional divine attributes. (shrink)

Prediction of daily rainfall is important for flood forecasting, reservoir operation, and many other hydrological applications. The artificial intelligence algorithm is generally used for stochastic forecasting rainfall which is not capable to simulate unseen extreme rainfall events which become common due to climate change. A new model is developed in this study for prediction of daily rainfall for different lead times based on sea level pressure which is physically related to rainfall on land and thus able to predict unseen rainfall (...) events. Daily rainfall of east coast of Peninsular Malaysia was predicted using SLP data over the climate domain. Five advanced AI algorithms such as extreme learning machine, Bayesian regularized neural networks, Bayesian additive regression trees, extreme gradient boosting, and hybrid neural fuzzy inference system were used considering the complex relationship of rainfall with sea level pressure. Principle components of SLP domain correlated with daily rainfall were used as predictors. The results revealed that the efficacy of AI models is predicting daily rainfall one day before. The relative performance of the models revealed the higher performance of BRNN with normalized root mean square error of 0.678 compared with HNFIS, BART, xgBoost, and ELM. Visual inspection of predicted rainfall during model validation using density-scatter plot and other novel ways of visual comparison revealed the ability of BRNN to predict daily rainfall one day before reliably. (shrink)

This paper examines the incompleteness of collective preference. We provide a series of Arrovian impossibility theorems without completeness. First, we consider the notion of regularity introduced by Eliaz and Ok (2006, Games and Economic Behavior 56, 61–86); it is an appropriate richness property for strict preference when preference is allowed to be incomplete. We examine the implication of imposing regularity on collective preference. Second, we propose responsiveness, a variation of positive responsiveness. This axiom requires that some changes in (...) individual preferences make an alternative weakly better than another. Third, we consider coherency conditions for collective preferences; this conditionally requires the existence of comparable pairs in a certain manner. We prove an impossibility result for each condition using Arrovian axioms. (shrink)

This essay proposes a reductive account of robust macro-regularities. On the view proposed, regularities can earn their elite scientific status by featuring in good summaries of restricted regions in the space of physical possibilities: our “modal neighborhoods.” I argue that this view vindicates “nomic foundationalism”, while doing justice to the practice of invoking physically contingent generalizations in higher-level explanations. Moreover, the view suggests an explanation for the particular significance of robust macro-regularities: we rely on summaries of our modal neighborhoods when (...) reasoning hypothetically about “agentially accessible” possibilities. (shrink)

This paper focuses on the view that rationality requires that our credences be regular. I go through different formulations of the requirement, and show that they face several problems. I then formulate a version of the requirement that solves most of, if not all, these problems. I conclude by showing that an argument thought to support the requirement as traditionally formulated actually does not; if anything, the argument, slightly modified, supports my version of the requirement.Send article to KindleTo send this (...) article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.REGULARITY REFORMULATEDVolume 9, Issue 4Weng Hong TangDOI: https://doi.org/10.1017/epi.2012.23Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. REGULARITY REFORMULATEDVolume 9, Issue 4Weng Hong TangDOI: https://doi.org/10.1017/epi.2012.23Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. REGULARITY REFORMULATEDVolume 9, Issue 4Weng Hong TangDOI: https://doi.org/10.1017/epi.2012.23Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

BackgroundPhysical activity has a significant health impact worldwide and has been linked to a lower risk of the common cold.ObjectiveThe aim of this study was to estimate the form of PA among Chinese adults and the correlation between PA and number of the common cold in China's eastern, central, and western areas.DesignA cross-sectional study.SettingChina's eastern, central, and western regions from 30 November 2020 to 30 March 2021.PatientsA total of 1,920 healthy participants, who aged over 18 years old, with Internet access, (...) were enrolled, and then self-reported PA behaviors and number of the common cold were collected.MeasurementsThe authors calculated preference, intensity, frequency, and duration of PA in Chinese based on gender, age, and broad occupational categories and explored the potential effect between these factors and the common cold.ResultsApproximately 20.4% of participants reported not participating in sports regularly. Except for gender, there were significant differences in PA preference and intensity among the remaining individuals. However, intensity shows a U-shaped dose-response relationship with colds, whereas the frequency and duration have an inverse dose-response relationship. High intensity combined with high frequency increased colds the most. Nevertheless, non-exercise groups always have the most colds in each comparison.LimitationsThe result may be vulnerable to recall bias.ConclusionIntensity showed that U-shape, frequency, and duration showed inverse response to the number of colds last year, but age, sex, and occupation had no significant effects. High intensity and high frequency mixed increased colds the most, regardless of duration. (shrink)

We study the Full Bayesian Updating rule for convex capacities. Following a route suggested by Jaffray (IEEE Transactions on Systems, Man and Cybernetics 22(5):1144–1152, 1992), we define some properties one may want to impose on the updating process, and identify the classes of (convex and strictly positive) capacities that satisfy these properties for the Full Bayesian Updating rule. This allows us to characterize two parametric families of convex capacities: ${(\varepsilon,\delta)}$ -contaminations (which were introduced, in a slightly different form, by Huber (...) (Robust Statistics, Wiley, New York, 1981)) and ${\varepsilon}$ -contaminations. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is (...) speaking of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

How regular do mechanisms need to be, in order to count as mechanisms? This paper addresses two arguments for dropping the requirement of regularity from the definition of a mechanism, one motivated by examples from the sciences and the other motivated by metaphysical considerations regarding causation. I defend a broadened regularity requirement on mechanisms that takes the form of a taxonomy of kinds of regularity that mechanisms may exhibit. This taxonomy allows precise explication of the degree and (...) location of regular operation within a mechanism, and highlights the role that various kinds of regularity play in scientific explanation. I defend this regularity requirement in terms of regularity’s role in individuating mechanisms against a background of other causal processes, and by prioritizing mechanisms’ ability to serve as a model of scientific explanation, rather than as a metaphysical account of causation. It is because mechanisms are regular, in the expanded sense described here, that they are capable of supporting the kinds of generalizations that figure prominently in scientific explanations. (shrink)

We show how the Full Bayesian Significance Test (FBST) can be used as a model selection criterion. The FBST was presented by Pereira and Stern as a coherent Bayesian significance test. Key Words: Bayesian test; Evidence; Global optimization; Information; Model selection; Numerical integration; Posterior density; Precise hypothesis; Regularization. AMS: 62A15; 62F15; 62H15.

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)

The notion of internalization put forth by Roger Shepard continues to be appealing and challenging. He suggests that we have internalized, during our evolutionary development, environmental regularities, or constraints. Internalization solves one of the hardest problems of perceptual psychology: the underspecification problem. That is the problem of how well-defined perceptual experience is generated from the often ambiguous and incomplete sensory stimulation. Yet, the notion of internalization creates new problems that may outweigh the solution of the underspecification problem. To support this (...) claim, I first examine the concept of internalization, breaking it down into several distinct interpretations. These range from well-resolved dynamic regularities to ill-resolved statistical regularities. As a function of the interpretation the researcher selects, an empirical test of the internalization hypothesis may be straightforward or it may become virtually impossible. I then attempt to cover the range of interpretations by drawing on examples from different domains of visual event perception. Unfortunately, the experimental tests regarding most candidate regularities, such as gravitational acceleration, fail to support the concept of internalization. This suggests that narrow interpretations of the concept should be given up in favor of more abstract interpretations. However, the latter are not easily amenable to empirical testing. There is nonetheless a way to test these abstract interpretations by contrasting internalization with the opposite concept: externalization of body dynamics. I summarize evidence for such a projection of body constraints onto external objects. Based on the combined evidence of well-resolved and ill- resolved regularities, the value of the notion of internalization has to be reassessed. Key Words: event perception; evolution; internalization. (shrink)

For the computability of subsets of real numbers, several reasonable notions have been suggested in the literature. We compare these notions in a systematic way by relating them to pairs of ‘basic’ ones. They turn out to coincide for full-dimensional convex sets; but on the more general class of regular sets, they reveal rather interesting ‘weaker/stronger’ relations. This is in contrast to single real numbers and vectors where all ‘reasonable’ notions coincide.

We discuss the close relationship between structural theorems in (generalized) stability theory, and graph regularity theorems.

According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements in a (...) collection without counting them), or on the ability to approximate quantities (i.e., to assess anapproximatequantity of the elements in a collection without counting them), or both, fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm. In the final section, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics. (shrink)

J. P lonka at WSP in Opole, in 1980 and 1981. We shall consider algebras o type : T ! N; E, R, S denote the set of all identities of type and the set of all regular identities of type , respectively . If is a set of identities of type , then E() denotes the set of all identities which can be proved from ; R() = \ R, S() = \ S. denotes the variety generated by . (...) Similarly, for a given variety V of algebras of type we shall consider varieties R and S dened by the set R of all regular identities satised in V and the set S of all symmetric identities satised in V , respectively. (shrink)

This paper is devoted to showing certain connections between normal modal logics and those strictly regular modal logics which have as a theorem. We extend some results of E. J. Lemmon (cf. [66]). In particular we prove that the lattice of the strictly regular modal logics with the axiom is isomorphic to the lattice of the normal modal logics.

The relationship between regularity and chance, or necessity and contingency, is a common concern of classical pragmatists. The metaphysical quality of this issue flows into the construction of postmodern discourse, although in a very different framework and, paradoxically, under the auspices of the anti-metaphysics that such a discourse claims. This paper proposes at first a brief reconstruction of the chance and regularity issue in postmodernism; then Peirce’s cosmological-metaphysical theory of chance, namely his ‘tychism,’ is recalled as a fruitful (...) suggestion to avoid the conceptual split between chance and regularity. Subsequently, considering the family resemblances between postmodernism and Rorty’s neo-pragmatism, the insistence upon history and contingency that stands out in his work will be tackled as a ‘postmodern tychism’ that, in fact, does not fit too-easy readings according to which he would have turned pragmatism into an extreme form of irrationalism and radical moral relativism. In particular, this paper aims to enlighten Rorty’s effort to re-propose, with new and more refined philosophical tools, the great challenge posed by the classical pragmatists: namely, the challenge to translate the pathos of contingency into an anti-dogmatic ethos, that is a cultural stance that might be able to combine the rejection of absolutes with the commitment to construct meanings and values hosting argumentative interpersonal and intercultural practices as the ‘rule’ of our moral history. (shrink)

This is a continuation of [3]. We deal with algebras of type : T ! N. Assume that V is a variety of type . Let p = x be a strongly nonregular identity satised in V , i.e. x; y are variables of p and x =6 y . For a variety K 2 L; E; R; S or RS denotes the set of all, regular, symmetric or regular and symmetric identities satised in K, respectively.

We show that every dominating analytic set in the Baire space has a dominating closed subset. This improves a theorem of Spinas [15] saying that every dominating analytic set contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. In [15], a subset of the Baire space is called u-regular if either it is not dominating or it contains the branches of a uniform tree, (...) and it was proved that Σ21-Kσ-regularity implies Σ21-u-regularity. Here we show that these properties are in fact equivalent. Since the proof of analytic u-regularity uses a game argument it was clear that determinacy implies u-regularity of all sets. Here we show that an inaccessible cardinal is enough to construct a model for projective u-regularity, namely it holds in Solovay's model. Finally we show that forcing with uniform trees is equivalent to Laver forcing. (shrink)

We show that many singular cardinals λ above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle $\square _{\lambda ,D}^{\mathit{fin}}$ introduced in [3]. For such ultrafilters D and cardinals λ there are models of size λ for which Mλ / D is not λ⁺⁺-universal and elementarily equivalent models M and N of size λ for which Mλ / D and Nλ / D are non-isomorphic. The question of the existence of such ultrafilters and models was (...) raised in [1]. (shrink)

In this paper I examine a recent argument that regularity approaches to causation can easily solve the problem of pre-emption. If this argument were successful it would neatly solve the problem of pre-emption—a problem that many still consider to be a central unsolved problem for accounts of causation. The argument is surprising in that the conclusion goes against the common consensus that regularity accounts of causation cannot solve the problem of pre-emption, at least without major amendments. This consensus (...) was one of the reasons for the decline in popularity of the regularity approach and the rise in popularity (for a few decades at least) of the counterfactual approach. In its fullest form the recent argument is due to Strevens (Causation and explanation, topics in contemporary philosophy. MIT Press, Cambridge, MA, 2007). He claims, "Mackie's account supplies, without any of the complex amendments now standard in counterfactual theories, a completely satisfactory treatment of the standard cases of pre-emption". This paper examines this argument and refutes it. I argue that Mackie's account really does fail to solve the problem of pre-emption; it fails to account for even the standard cases of pre-emption in the literature. (shrink)