Online research in philosophy

Philosophers of science have offered different accounts of what it means for one scientific theory to reduce to another. I propose a more or less friendly amendment to Kenneth Schaffner’s “General Reduction-Replacement” model of scientific unification. Schaffner interprets scientific unification broadly in terms of a continuum from theory reduction to theory replacement. As such, his account leaves no place on its continuum for type irreducible and irreplaceable theories. The same is true for other accounts that incorporate Schaffner's (...) continuum, for example, those developed by Paul Churchland, Clifford Hooker, and John Bickle. Yet I believe a more general account of scientific unification should include type irreducible and irreplaceable theories in an account of their partial reduction, specifically, when there is a reduction of their tokens. Thus I propose a “Reduction-Reception-Replacement” model wherein type irreducible and irreplaceable theories are accepted or received for the purpose of unifying domains of particulars. I also suggest a link between this kind of token reduction and mechanistic explanation. (shrink)

Let A be an admissible set. A sentence of the form ∀R̄φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence if φ ∈ A (φ is $\bigvee\Phi$ , where Φ is an A-r.e. set of sentences from A; φ ∈ Lω1ω). A sentence of the form ∃R̄φ is an ∃2(A) (∃s 2(A),∃2(Lω1ω)) sentence if φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence. A class of structures is, for example, a ∀1(A) class if it is the class of models of a ∀1(A) sentence. Thus (...) ∀1(A) is a class of classes of structures, and so forth. Let Mi be the structure $\langle i, 0$. Let Γ be a class of classes of structures. We say that a sequence $J_1,\ldots,J_i,\ldots, i < \omega$, of classes of structures is a Γ sequence if $J_i \in \Gamma, i < \omega$, and there is I ∈ Γ such that M ∈ Ji if and only if [M, Mi] ∈ I, where [,] is the disjoint sum. A class Γ of classes of structures has the easy uniformization property if for every Γ sequence $J_1,\ldots,J_i, \ldots, i < \omega$, there is a Γ sequence $J'_1,\ldots,J'_i,\ldots, i < \omega$, such that $J'_i \subseteq J_i, i < \omega, \bigcup J'_i = \bigcup J_i$, and the J'i are pairwise disjoint. The easy uniformization property is an effective version of Kuratowski's generalized reduction property that is closely related to Moschovakis's (topological) easy uniformization property. We show over countable structures that ∀1(A) and ∃2(A) have the easy uniformization property if A is a countable admissible set with an infinite member, that ∀s 1(Lα) and ∃s 2(Lα) have the easy uniformization property if α is countable, admissible, and not weakly stable, and that ∀1(Lω1ω) and ∃2(Lω1ω) have the easy uniformization property. The results proved are more general. The result for ∀s 1(Lα) answers a question of Vaught (1980). (shrink)

The historical development of the electronic configuration model is traced and the status of the model with respect to quantum mechanics is examined. The successes and problems raised by the model are explored, particularly in chemical ab initio calculations. The relevance of these issues to whether chemistry has been reduced to quantum mechanics is discussed, as are some general notions on reduction.

In a scientific context, ontological commitments should be considered as supervenient over accepted scientific theories. This implies that the primarily ontological notions of reduction and emergence of entities of different kinds should be reformulated in terms of relations between existing empirical theories. For this, in turn, it is most convenient to employ a model-theoretic view of scientific theories: the identity criterion of a scientific theory is essentially given by a class of models. Accordingly, reduction and emergence are to be (...) seen as particular kinds of relations between (some) models of different theories that subsume the same (or a similar) “experiential field”. The set-theoretical notion of an echelon-set proves to be crucial for this purpose: The domains in the models of the reduced theory are echelon-sets over the domains of the reducing theory. Finally, it is argued that emergence may plausibly be interpreted as akin to but weaker than reduction. (shrink)

"New wave" reductionism aims at advancing a kind of reduction that is stronger than unilateral dependency of the mental on the physical. It revolves around the idea that reduction between theoretical levels is a matter of degree, and can be laid out on a continuum between a "smooth" pole (theoretical identity) and a "bumpy" pole (extremely revisionary). It also entails that both higher and lower levels of the reductive relationship sustain some degree of explanatory autonomy. The new wave predicts that (...) reductions of folk psychology to neuroscience will be located in the middle of this continuum; as neuroscientific evidence about mental states checks in, theoretical folk psychology will therefore be moderately revised. However, the model has conceptual problems which preclude its success in reviving reductionism, and its commitment to a syntactic approach wrecks its attempt to rescue folk psychology. Moreover, the architecture of the continuum operates on a category mistake that sneaks in an eliminativist conclusion. I argue that new wave reductionism therefore tends to be eliminativism in disguise. (shrink)

Nagel’s official model of theory-reduction and the way it is represented in the literature are shown to be incompatible with the careful remarks on the notion of reduction Nagel gave while developing his model. Based on these remarks, an alternative model is outlined which does not face some of the problems the official model faces. Taking the context in which Nagel developed his model into account, it is shown that the way Nagel shaped his (...) class='Hi'>model and, thus, its well-known deficiencies, are best conceived of as a mere by-product of his philosophical background. (shrink)

Schaffner’s model of theory reduction has played an important role in philosophy of science and philosophy of biology. Here, the model is found to be problematic because of an internal tension. Indeed, standard antireductionist external criticisms concerning reduction functions and laws in biology do not provide a full picture of the limits of Schaffner’s model. However, despite the internal tension, his model usefully highlights the importance of regulative ideals associated with the search for derivational, and embedding, (...) deductive relations among mathematical structures in theoretical biology. A reconstructed Schaffnerian model could therefore shed light on mathematical theory development in the biological sciences and on the epistemology of mathematical practices more generally. *Received November 2006; revised March 2009. †To contact the author, please write to: Philosophy Department, University of California, Santa Cruz, 1156 High St., Santa Cruz, CA 95064; e‐mail: rgw@ucsc.edu. (shrink)

In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction'' arediscussed. Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of ``reducibility''. This claimrests on some mathematical results proved in this paper.

General Relativity and the Standard Model often are touted as the most rigorously and extensively confirmed scientific hypotheses of all time. Nonetheless, these theories appear to have consequences that are inconsistent with evidence about phenomena for which, respectively, quantum effects and gravity matter. This paper suggests an explanation for why the theories are not disconfirmed by such evidence. The key to this explanation is an approach to scientific hypotheses that allows their actual content to differ from their apparent (...) content. This approach does not appeal to ceteris-paribus qualifiers or counterfactuals or similarity relations. And it helps to explain why some highly idealized hypotheses are not treated in the way that a thoroughly refuted theory is treated but instead as hypotheses with limited domains of applicability. (shrink)

In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions of (...) a reducing theory T with the definitions translating the vocabulary of a reduced theory T' to the vocabulary of T, defeasibly entails the assumptions of reduced T'. This relation of defeasible reduction offers, in the context of additional knowledge becoming available, articulation of a more flexible kind of reduction in theory development than in the classical case. Also, defeasible reduction is shown to solve the problems of entailment that classical homogeneous reduction encounters. Reduction in the defeasible sense is a practical device for studying the processes of science, since it is about highlighting different aspects of the same theory at different times of application, rather than about naive dreams concerning a metaphysical unity of science. (shrink)

It is well-known that classical models of belief are not realistic representations of human doxastic capacity; equally, models of actions involving beliefs, such as decisions based on beliefs, or changes of beliefs, suffer from a similar inaccuracies. In this paper, a general framework is presented which permits a more realistic modelling both of instantaneous states of belief, and of the operations involving them. This framework is motivated by some of the inadequacies of existing models, which it overcomes, whilst retaining (...) technical rigour in so far as it relies on known, natural logical and mathematical notions. The companion paper (Towards a “sophisticated” model of belief dynamics. Part II) contains an application of this framework to the particular case of belief revision. (shrink)

An examination of earlier views yields an account of theoretic change on which changes in theory which do involve changes in meanings of terms are classified as a special (and by no means exhaustive) case of theoretic change which, latter, is construed as a more general phenomenon. Only the general problem is given detailed consideration here. The account given considers the problem of how replacement of intensional theories by extensional ones may be treated within the general framework (...) provided. Among its results is the conclusion that rational changes in a scientific theory may be cogently construed as determined by warranted decisions that a new theory is more adequate (than the old one it replaces) with regard to purposes for which a theory is sought. (shrink)

It is shown that complex adaptations are best modelled as discrete processes represented on directed weighted graphs. Such a representation captures the idea that problems of adaptation in evolutionary biology are problems in a discrete space, something that the conventional representations using continuous adaptive landscapes does not. Further, this representation allows the utilization of well-known algorithms for the computation of several biologically interesting results such as the accessibility of one allele from another by a specified number of point mutations, the (...) accessibility of alleles at a local maximum of fitness, the accessibility of the allele with the globally maximum fitness, etc. A reduction of a model due to Kauffman and Levin to such a representation is explicitly carried out and it is shown how this reduction clarifies the biological questions that are of interest. (shrink)

In Mind in a Physical World (1998), Jaegwon Kim has recently extended his ongoing critique of `non-reductive materialist' positions in philosophy of mind by arguing that Nagel's model of reduction is the wrong paradigm in terms of which to contest the issue of psychophysical reduction, and that an altogether different model of scientific reduction – a functional model of reduction – is needed. In this paper I argue, first, that Kim's conception of the Nagelian model is (...) substantially impoverished and potentially misleading; second, that his own functional model is problematic in several respects; and, third, that the basic idea underlying his functional model can well be accommodated within a properly reinterpreted Nagelian model. I conclude with some reflections on the issue of psychophysical reduction. (shrink)

How is scientific knowledge used, adapted, and extended in deriving phenomena and real-world systems? This paper aims at developing a general account of 'applying science' within the exemplar-based framework of Data-Oriented Processing (DOP), which is also known as Exemplar-Based Explanation (EBE). According to the exemplar-based paradigm, phenomena are explained not by deriving them all the way down from theoretical laws and boundary conditions but by modelling them on previously derived phenomena that function as exemplars. To accomplish this, DOP proposes (...) to maintain a corpus of derivation trees of previous phenomena together with a matching algorithm that combines subtrees from the corpus to derive new phenomena. By using a notion of derivational similarity, a new phenomenon can be modelled as closely as possible on previously explained phenomena. I will propose an instantiation of DOP which integrates theoretical and phenomenological modelling and which generalises over various disciplines, from fluid mechanics to language technology. I argue that DOP provides a solution for what I call Kuhn's problem and that it redresses Kitcher's account of explanation. (shrink)

Meaning is a central concept of (bio)semiotics. At the same time, it is also a word of everyday language. Here, on the example of the world information, we discuss the “reduction-inflation model” of evolution of a common word into a scientific concept, to return subsequently into everyday circulation with new connotations. Such may be, in the near future, also the fate of the word meaning if, flexed through objectified semantics, will become considered an objective concept usable in semiotics. We (...) argue that reducing meaning to a technical term essentially synonymous to code and stripped of most of the original semantic field is not a necessary prerequisite for a meaningful application of the concept in semiotics and in biology. (shrink)

Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function "self-collapse"(objective reduction: OR -Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable for quantum (...) effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 milliseconds) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs. Unlike the random, "subjective reduction"( SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. (shrink)

The scientific methodology underlying model-building is critically investigated. The modeling views of Popper and Samuelson and their prototypes are critically examined in the light of the theme of the moral law of unity of knowledge and unity of the world-system configured by the meta-epistemology of organic unity of knowledge. Upon such critical examination of received methodology of model-building in economics, the extended perspective?namely of integrating the moral law derived from the divine roots as the meta-epistemology?is rigorously studied. The (...) example of the Islamic prerogative in interpreting the holistic world-system through model-building in economics is highlighted. A religio-philosophical approach is adopted to exemplify some approaches in Islamic model-building. An especial focus is placed here on grassroots types of financing and activities. The critique of these models within the existing Islamic scholarship is carried out. The result is new dimensions of macroeconomic analysis that emanate in a logical way from the meta-epistemological approach, and oppose the mainstream ideas, both in received and Islamic economic thinking as of now. (shrink)

The generic account of selection proposed by Hull et al. readily fits operant learning where, by comparison with natural selection, the process is well understood but little is known about the mechanism. Objections within psychology, that operant learning ignores internal processes, fail to recognise the general significance of behaviour-environment interactions. Variation within operant response classes requires further investigation.

Four current accounts of theory reduction are presented, first informally and then formally: (1) an account of direct theory reduction that is based on the contributions of Nagel, Woodger, and Quine, (2) an indirect reduction paradigm due to Kemeny and Oppenheim, (3) an "isomorphic model" schema traceable to Suppes, and (4) a theory of reduction that is based on the work of Popper, Feyerabend, and Kuhn. Reference is made, in an attempt to choose between these schemas, to the explanation (...) of physical optics by Maxwell's electromagnetic theory, and to the revisions of genetics necessitated by partial biochemical reductions of genetics. A more general reduction schema is proposed which: (1) yields as special cases the four reduction paradigms considered above, (2) seems to be in better accord with both the canons of logic and actual scientific practice, and (3) clarifies the problems of meaning variance and ontological reduction. (shrink)

The aim of this essay is a criticism of reductionism ? both in its ?static? interpretation (usually referred to as the layer model or level?picture of science) and in its ?dynamic? interpretation (as a theory of the growth of scientific knowledge), with emphasis on the latter ? from the point of view of Popperian fallibilism and Feyerabendian pluralism, but without being committed to the idiosyncrasies of these standpoints. In both aspects of criticism, the rejection is based on the proposal (...) of a global alternative. Hummell and Opp's research programme for the reduction of sociology to psychology is used as a starting?point and taken as the primary object of criticism. Following the introductory Section I, Section II analyses the three crucial notions of Hummell and Opp's research programme ? their explications of the notions of ?sociology?, ?psychology? and the concept of reduction itself ? and criticizes the authors? deficient ?logic of reduction?. Although the ?local? shortcomings of our authors? ?logic of reduction? do not affect reductionism as such, i.e. logically sound versions of reductionism as devised by Kemeny, Nagel, Oppenheim, Putnam, Woodger et al., it is argued that the logical soundness of sophisticated reductionism cannot compensate for its additional epistemological and methodological deficiencies. Section III analyses the ?dynamic? interpretation of reductionism as a particular developmental pattern of scientific growth. It is argued that even reductionism at its best can produce only cumulative progress, thus ?a priori? excluding scientific revolutions which are inevitably counter?inductive as well as counter?reductive. Section IV discusses the philosophical background of modern reductionism, and examines the effects both of reductionism and of anti?reductionistic pluralism on the autonomy of scientific fields. It is argued that pluralistic anti?reductionism undermines spurious claims for autonomy much more effectively than reductionism. As a ?local? improvement of the reductionistic research programme, the replacement of the predominant one?way reductionism by a less restrictive many?way reductionism is proposed. It is argued that the appropriate treatment for an allegedly backward science (say sociology) is not its reduction to an allegedly more advanced science (say psychology) but its non?reductive replacement by new theories (of the same or of another field) that do not incorporate the older ones. As a ?global? alternative to the reduction of sociology to psychology, the frontier?crossing direct application of psychological theories to sociological phenomena is proposed. A plea is made for a pluralistic science without reduction, based on intra? and interscientific criticism as the proper method for the advancement of knowledge. (shrink)

A classification of models of reduction into three categories — theory reductionism, explanatory reductionism, and constitutive reductionism — is presented. It is shown that this classification helps clarify the relations between various explications of reduction that have been offered in the past, especially if a distinction is maintained between the various epistemological and ontological issues that arise. A relatively new model of explanatory reduction, one that emphasizes that reduction is the explanation of a whole in terms of its parts (...) is also presented in detail. Finally, the classification is used to clarify the debate over reductionism in molecular biology. It is argued there that while no model from the category of theory reduction might be applicable in that case, models of explanatory reduction might yet capture the structure of the relevant explanations. (shrink)

Most philosophical accounts of causation take causal relations to obtain between individuals and events in virtue of nomological relations between properties of these individuals and events. Such views fail to take into account the consequences of the fact that in general the properties of individuals and events will depend upon mechanisms that realize those properties. In this paper I attempt to rectify this failure, and in so doing to provide an account of the causal relevance of higher-level properties. I (...) do this by critiquing one prominent model of higher-level properties—Kim’s functional model of reduction—and contrasting it with a mechanistic approach to higher-level properties and causation. (shrink)

Measurement is a process aimed at acquiring and codifying information about properties of empirical entities. In this paper we provide an interpretation of such a process comparing it with what is nowadays considered the standard measurement theory, i.e., representational theory of measurement. It is maintained here that this theory has its own merits but it is incomplete and too abstract, its main weakness being the scant attention reserved to the empirical side of measurement, i.e., to measurement systems and to the (...) ways in which the interactions of such systems with the entities under measurement provide a structure to an empirical domain. In particular it is claimed that (1) it is on the ground of the interaction with a measurement system that a partition can be induced on the domain of entities under measurement and that relations among such entities can be established, and that (2) it is the usage of measurement systems that guarantees a degree of objectivity and intersubjectivity to measurement results. As modeled in this paper, measurement systems link the abstract theory of measuring, as developed in representational terms, and the practice of measuring, as coded in standard documents such as the International Vocabulary of Metrology. (shrink)

I analyse Rueger’s application of Kim’s model of functional reduction to the relation between the thermal conductivities of metal bars at macroscopic and atomic scales. 1) I show that it is a misunderstanding to accuse the functional reduction model of not accounting for the fact that there are causal powers at the micro-level which have no equivalent at the macro-level. The model not only allows but requires that the causal powers by virtue of which a functional predicate (...) is defined, are only a subset of the causal powers of the properties filling the functional specification. 2) The fact that the micro-equation does not converge to the macro-equation in general but only under the constraint of a “solvability condition” does not show that reduction is impossible, as Rueger claims, but only that reduction requires inter-level constraints. 3) Rueger tries to analyse inter-level reduction with the conceptual means of intra-level reduction. This threatens the coherence of his analysis, given that it makes no sense to ascribe macroproperties such as thermal conductivity to entities at the atomic level. Ignoring the distinction between theses two senses of “reduction” is especially confusing because they have opposite directions: in intra-level reduction, the more detailed account reduces to the less detailed one, whereas in inter-level reduction, the less detailed theory is reduced to the more detailed one. 4) Finally I criticize Rueger’s way of using Wimsatt’s criteria for emergence in terms of non-aggregativity, to construct a concept of synchronic emergence. It is wrong to require, over and above non-aggregativity, irreducibility as a criterion for emergence. (shrink)

The standard epistemic justification for inclusiveness in political decision making is the Condorcet Jury Theorem, which states that the probability of a correct decision using majority rule increases in group size (given certain assumptions). Informally, majority rule acts as a mechanism to pool the information contained in the judgements of individual agents. I aim to extend the explanation of how groups of political agents track the truth. Before agents can pool the information, they first need to find truth-conducive information. Increasing (...) group size is also important in the initial search for truth-conducive information. (shrink)

Questions concerning the epistemological status of computer science are, in this paper, answered from the point of view of the formal verification framework. State space reduction techniques adopted to simplify computational models in model checking are analysed in terms of Aristotelian abstractions and Galilean idealizations characterizing the inquiry of empirical systems. Methodological considerations drawn here are employed to argue in favour of the scientific understanding of computer science as a discipline. Specifically, reduced models gained by Dataion are acknowledged as (...) Aristotelian abstractions that include only data which are sufficient to examine the interested executions. The present study highlights how the need to maximize incompatible properties is at the basis of both Abstraction Refinement, the process of generating a cascade of computational models to achieve a balance between simplicity and informativeness, and the Multiple Model Idealization approach in biology. Finally, fairness constraints, imposed to computational models to allow fair behaviours only, are defined as ceteris paribus conditions under which temporal formulas, formalizing software requirements, acquire the status of law-like statements about the software systems executions. (shrink)

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a la (...) luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a la (...) luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)

The ultimate goal of research into computational intelligence is the construction of a fully embodied and fully autonomous artificial agent. This ultimate artificial agent must not only be able to act, but it must be able to act morally. In order to realize this goal, a number of challenges must be met, and a number of questions must be answered, the upshot being that, in doing so, the form of agency to which we must aim in developing artificial agents comes (...) into focus. This chapter explores these issues, and from its results details a novel approach to meeting the given conditions in a simple architecture of information processing. (shrink)

The problem of getting a relativistic generalization of the CSL dynamical reduction model, which has been presented in part I, is discussed. In so doing we have the opportunity to introduce the idea of a stochastically invariant theory. The theoretical model we present, that satisfies this kind of invariance requirement, offers us the possibility to reconsider, from a new point of view, some conceptually relevant issues such as nonlocality, the legitimacy of attributing elements of physical reality to physical (...) systems and the problem of establishing causal relations between physical events. (shrink)

In this comment, I first point out some problems in McCauley's defense of the traditional conception of general analytical levels. Then I present certain reductionist arguments against explanatory pluralism that are not based on the New Wave model of intertheoretic reduction, against which McCauley is arguing. Reductionists that are not committed to this model might not have problems incorporating research on long-term diachronic processes in their analyses. In the last part of the paper, I briefly compare Robert (...) N. McCauley's conception of reduction to some other current accounts, highlighting the differences between them. (shrink)

The present paper surveys the three most prominent accounts in contemporary debates over how sound reduction should be executed. The classical Nagelian model of reduction derives the laws of the target-theory from the laws of the base theory plus some auxiliary premises (so-called bridge laws) connecting the entities of the target and the base theory. The functional model of reduction emphasizes the causal definitions of the target entities referring to their causal relations to base entities. The new-wave (...) class='Hi'>model of reduction deduces not the original target theory but an analogous image of it, which remains inside the vocabulary of the base theory. One of the fundamental motivations of both the functional and the new-wave model is to show that bridge laws can be evaded. The present paper argues that bridge laws—in the original Nagelian sense—are inevitable, i.e. that none of these models can evade them. On the one hand, the functional model of reduction needs bridge laws, since its fundamental concept, functionalization, is an inter-theoretical process dealing with entities of two different theories. Theoretical entities of different theories (in a general heterogeneous case) do not have common causal relations, so the functionalization of an entity—without bridge laws—can only be executed in the framework of its own theory. On the other hand, the so-called images of the new-wave account cannot be constructed without the use of bridge laws. These connecting principles are needed to guide the process of deduction within the base theory; without them one would not be able to recognize if the deduced structure was an image of the target theory. (shrink)

University Abstract Philosophers have sought to improve upon the logical empiricists’ model of scientific reduction. While opportunities for integration between the cognitive and the neural sciences have increased, most philosophers, appealing to the multiple realizability of mental states and the irreducibility of consciousness, object to psychoneural reduction. New Wave reductionists offer a continuum of comparative goodness of intertheoretic mapping for assessing reductions. Their insistence on a unified view of intertheoretic relations obscures epistemically significant crossscientific relations and engenders dismissive conclusions (...) about psychology. Richer, more sensitive accounts of explanatory pluralism and mechanistic explanation in science advocate multi-level approaches in cross-scientific settings and criticize the distance of the standard philosophical objections from working scientists’ practices and discoveries. The Heuristic Identity Theory, a new, scientifically informed version of the psycho-physical identity theory, incorporates these insights, showing how multiple realizability is an argument for (not against) identities in science and why, therefore, consciousness is not irreducible. (shrink)

This article considers claims that biology should seek general theories similar to those found in physics but argues for an alternative framework for biological theories as collections of prototypical interlevel models that can be extrapolated by analogy to different organisms. This position is exemplified in the development of the Hodgkin‐Huxley giant squid model for action potentials, which uses equations in specialized ways. This model is viewed as an “emergent unifier.” Such unifiers, which require various simplifications, involve the (...) types of heuristics discussed in Wimsatt’s writings on reduction, but with a twist. Here, the heuristics are used to generate emergent rather than reductive explanations. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: kfs@pitt.edu. (shrink)

Modifying images for scientific publication is now quick and easy due to changes in technology. This has created a need for new image processing guidelines and attitudes, such as those offered to the research community by Doug Cromey (Cromey 2010). We suggest that related changes in technology have simplified the task of detecting misconduct for journal editors as well as researchers, and that this simplification has caused a shift in the responsibility for reporting misconduct. We also argue that the concept (...) of best practices in image processing can serve as a general model for education in best practices in research. (shrink)

One of the main results of Gödel [4] and [5] is that, if M is a transitive set such that $\langle M, \epsilon \rangle$ is a model of ZF (Zermelo-Fraenkel set theory) and α is the least ordinal not in M, then $\langle L_\alpha, \epsilon \rangle$ is also a model of ZF. In this note we shall use the Jensen uniformisation theorem to show that results analogous to the above hold for certain subsystems of ZF. The subsystems we (...) have in mind are those that are formed by restricting the formulas in the separation and replacement axioms to various levels of the Levy hierarchy. This is all done in § 1. In § 2 we proceed to establish the exact order relationships which hold among the ordinals of the minimal models of some of the systems discussed in § 1. Although the proofs of these latter results will not require any use of the uniformisation theorem, we will find it convenient to use some of the more elementary results and techniques from Jensen's fine-structural theory of L. We thus provide a brief review of the pertinent parts of Jensen's works in § 0, where a list of general preliminaries is also furnished. We remark that some of the techniques which we use in the present paper have been used by us previously in [6] to prove various results about β-models of analysis. Since β-models for analysis are analogous to transitive models for set theory, this is not surprising. (shrink)

Multi-level discrete models of genetic networks, or the more general piecewise affine differential models, provide qualitative information on the dynamics of the system, based on a small number of parameters (such as synthesis and degradation rates). Boolean models also provide qualitative information, but are based simply on the structure of interconnections. To explore the relationship between the two formalisms, a piecewise affine differential model and a Boolean model are compared, for the carbon starvation response network in E. (...) coli . The asymptotic dynamics of both models are shown to be quite similar. This study suggests new tools for analysis and reduction of biological networks. (shrink)

As a result of the complexity inherent in some natural systems, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often find multiregional models for structured populations in which individuals are classified regarding their age and their spatial location. Dealing with such structured populations leads to high dimensional models. Moreover, in many instances the dynamics of the system is controlled by processes whose time scales are very (...) different from each other. For example, in multiregional models migration is often a fast process in comparison to the growth of the population.Approximate reduction techniques take advantage of the presence of different time scales in a system to introduce approximations that allow one to transform the original system into a simpler low dimensional system. In this way, the dynamics of the original system can be approximated in terms of that of the reduced system. This work deals with the study of that approximation. In particular, we work with a non-autonomous discrete time model previously presented in the literature and obtain different bounds for the error we incur when we describe the dynamics of the original system in terms of the reduced one. (shrink)

The functionalist conception of mental properties, together with their multiple realizability, is often taken to entail their irreducibility. It might seem that the only way to revise that judgement is to weaken the requirements traditionally imposed on reduction. However, Jaegwon Kim has recently argued that we should, on the contrary, strengthen those requirements, and construe reduction as what I propose to call “logical reduction”, a model of reduction inspired by emergentism. Moreover, Kim claims that what he calls “functional reduction” (...) allows one to reduce (at least some) mental properties by these new standards. I argue against both theses. First, I present a counterexample to the emergentist model of reduction: The model judges irreducible certain properties which are clearly reducible. Second, I contestthat functional reduction as construed by Kim satisfies the emergentist constraints. Functional reduction implies, over and above a functional definition of the reduced property, the indication of its realizers. But the latter information corresponding to the discovery of a (local) bridge law, is empirical and not purely logical. (shrink)

“Weak relevant model structures” (wr-ms) are defined on “weak relevant matrices” by generalizing Brady’s model structure ${\mathcal{M}_{\rm CL}}$ built upon Meyer’s Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry’s Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry’s Paradox.

John Bickle's Psychoneural reduction: the new wave (Cambridge, MA: MIT Press, 1998) aims to resurrect reductionism within philosophy of mind. He develops a new model of scientific reduction, geared to enhancing our understanding of how theories in neuroscience and cognitive science are interrelated. I put this discussion in context, and assess the prospects for new wave reductionism, both as a general model of scientific reduction and as an attempt to defend reductionism in the philosophy of mind.

among them Joseph Levine, David Chalmers, Frank Jackson and Jaegwon Kim?have claimed that there are conceptual grounds sufficient for ruling out the possibility of a reductive explanation of phenomenal consciousness. Their claim assumes a functional model of reduction (regarded by Kim as an alternative to the traditional Nagelian model) which requires an a priori entailment from the facts in the reduction base to the phenomena to be explained. The aim of this paper is to show that this is (...) an unreasonable requirement?a requirement that no reductive explanation in science should be expected to satisfy. I argue that the functional model is not substantively different from the Nagelian model properly understood, and that the question whether consciousness is reductively explainable?in a sense involving property identifications or in some weaker sense compatible with Nagelian reduction?is a fundamentally empirical question, not one that can be settled on conceptual grounds alone. Introduction Kim's critique of the Nagelian model of reduction The functional model of reduction Is consciousness reducible? Psychophysical reduction: concluding remarks. (shrink)

In this paper I examine Jaegwon Kim’s view that emergent properties are irreducible to the base properties on which they supervene. Kim’s view assumes a model of ‘functional reduction’ which he claims to be substantially different from the traditional Nagelian model. I dispute this claim and argue that the two models are only superficially different, and that on either model, properly understood, it is possible to draw a distinction between a property’s being reductively identifiable with its base (...) property and a property’s being reductively explainable in terms of it. I propose that we should take as the distinguishing feature of emergent properties that they be truly novel properties, i.e., ontologically distinct from the ‘base’ properties which they supervene on. This only requires that emergent properties cannot be reductively identified with their base properties, not that they cannot be reductively explained in terms of them. On this conception the set of emergent properties may well include mental properties as conceived by nonreductive physicalists. (shrink)

What is consciousness? Conventional approaches see it as an emergent property of complex interactions among individual neurons; however these approaches fail to address enigmatic features of consciousness. Accordingly, some philosophers have contended that "qualia," or an experiential medium from which consciousness is derived, exists as a fundamental component of reality. Whitehead, for example, described the universe as being composed of "occasions of experience." To examine this possibility scientifically, the very nature of physical reality must be re-examined. We must come to (...) terms with the physics of spacetime-as described by Einstein's general theory of relativity, and its relation to the fundamental theory of matter-as described by quantum theory. Roger Penrose has proposed a new physics of objective reduction: "OR," which appeals to a form of quantum gravity to provide a useful description of fundamental processes at the quantum/classical borderline.hz Within the OR scheme, we consider that consciousness occurs if an appropriately organized system is able to develop and maintain quantum coherent superposition until a specific "objective" criterion (a threshold related to quantum gravity) is reached; the coherent system then self-reduces (objective reduction: OR). We contend that this type of objective self-collapse introduces non-computability, an essential feature of consciousness which distinguishes our minds from classical computers. Each OR is taken as an instantaneous event-the climax of a self-organizing process in fundamental spacetime-and a candidate for a conscious Whitehead "occasion of experience." How could an OR process occur in the brain, be coupled to neural activities, and account for other features of consciousness? We nominate a quantum computational OR process with the requisite characteristics to be occurring in cytoskeletal microtubules within the brain's neurons. In this model, quantum-superposed states develop in microtubule subunit proteins ("tubulins") within certain brain neurons, remain coherent, and recruit more superposed tubulins until a mass-time-energy threshold (related to quantum gravity) is reached.. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical debate on the nature (...) of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of verification and validation ); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of proxy ) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of commutation ); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

John Earman's recent proposal that a substantive version of general covariance consists in the requirement that diffeomorphism invariance be a gauge symmetry is critically assessed. I argue that such a principle does not serve to differentiate general relativity from pre-relativistic theories. A model-theoretic characterization of two formulations of specially-relativistic theories is suggested. Diffeomorphisms are symmetries of only one such style of formulation and, I argue, Earman's proposal does not provide a reason to deny diffeomorphisms the status of (...) gauge transformations relative to this formulation. Carlo Rovelli's distinction between "passive" and "active" diffeomorphism invariance is also clarified. (shrink)

This paper presents an argument for the claim that historical events are unique in a nontrivial sense which entails the inapplicability of the Hempelian D-N model to historical explanations. Some previous criticisms of Hempel are shown to be general criticisms of the D-N model which can be outflanked in cases where a reduction to fundamental laws is available. I then survey grounds for denying that explanations by reasons can be effectively reduced to causal explanations, and for rejecting (...) methodological individualism. I conclude with some positive remarks concerning the structure of historical explanations and sense in which historical events are unique. (shrink)

Semantic properties are not commonly held to be part of the basic ontological furniture of the world. Consequently, we confront a problem: how to 'naturalize' semantics so as to reveal these properties in their true ontological colors? Dominant naturalistic theories address semantic properties as properties of some other (more primitive, less problematic) kind. The reductionistic flavor is unmistakable. The following quote from Fodor's Psychosemantics is probably the contemporary locus classicus of this trend. Fodor is commendably unapologetic: "I suppose that sooner (...) or later the physicists will complete the catalogue they've been compiling of the ultimate and irreducible properties of things. When they do, the likes of spin, charm, and charge will perhaps appear upon their list. But aboutness surely won't; intentionality simply doesn't go that deep. It's hard to see, in the face of this consideration, how one can be a Realist about intentionality without also being, to some extent or other, a Reductionist. If the semantic and the intentional are real properties of things, it must be in virtue of their identity with (or maybe of their supervenience on?) properties that are themselves neither intentional nor semantic. If aboutness is real, it must be really something else." (Fodor 1987, 97) Notice the shape of this explanatory project. Intentional properties will count as real in virtue of their identity with, or supervenience on, some set of lower-level physical properties. Fodor thus assumes, in effect (as do many others engaged in naturalization projects for semantics), that the program of naturalization demands a higher-to-lower, top-to-bottom, kind of explanatory strategy. This paper addresses precisely that assumption, namely, that the non-semantic properties on which semantic properties depend, belong to what are intuitively lower levels of description than the intentional level itself. It also questions the higher-to-lower explanatory scheme associated with that assumption. My discussion of this topic draws on Robert Brandom's recent work (Brandom 1994) and can be considered an analysis of Brandom's stance and its implications. The discussion should help to explain the general lack of progress in the project of naturalizing content. It should also help show why attempts to eliminate the normative vocabulary employed in specifying the practices that guide the use of a language are unlikely to succeed. I shall start by displaying the general order of explanation that characterizes typical naturalization projects, showing that even when a full reduction to physics is avoided, some important assumptions inherited from the explanatory model of physics remain. These include the demand for an array of causal explanations couched in terms of ultimate properties of the world, and the idea that such non-semantic properties should be constitutive (in a narrow or individualistic sense to be explained below) of whatever semantic properties are in question. Extending Brandom's idea that the normativity of content is not reducible to physics, I shall argue that even such residual demands are inappropriate. More positively, I suggest that, despite the deep irreducibility of the normative dimension of content, we need not consider that dimension either primitive or inexplicable. Instead, such normative aspects can be unpacked by invoking a different, lower-to-higher, explanatory scheme in which the explanans includes higher level features such as skilled know-how and social frames of action. (shrink)

One can no longer truly say that virtue theory is the neglected tradition in moral philosophy. I won’t say much about the reasons for its revival, although the reasons for its temporary , though long, decline interest me. Now there are very many things that could be said here. For example, it is often thought that virtue theory requires some sort of teleology, but with the decline of Aristotelian physics and its replacement with the mechanical philosophy of the seventeenth century, (...) notions of function and purpose were given an ever-diminishing role throughout intellectual life. (MacIntyre 1982) Alternatively, or in addition, one might see virtue theory condemned through guilt by association with Aristotle. Pursuing this line it might be predicted that a developing discontent with forms of reductionist naturalism in metaphysics might also give weight to a new respect for Aristotelian themes in ethics. But while I want to paint here with a reasonably broad brush, I want to draw the focus in a little. Thinking specifically now about the relation between virtue theory and the twentieth century, one can see various ways in which virtue theory was out of keeping with the spirit of the age. As we shall see, however, some of the criticisms seem to be somewhat at odds with each other. One general line of criticism, which has several parts to it, starts from a philosophical view about the nature of morality. The second general 2 line is harder to characterise but might be thought to derive from reflection about the model of moral agent that virtue theory offers. There are several related but distinct ways in which virtue ethics has been out of step with modern moral theory. First, a developing consensus - - though one now strongly challenged - - supposes that there are certain constraints on what is to count as moral behaviour. It presupposes that the central problem of morality is that there is a conflict, to put it crudely, between morality and self-interest.. (shrink)

I show that words with indefinite implicit complements occasion a dilemma for their model theory. There has been only two previous attempts to address this problem, one by Fodor and Fodor (1980) and one by Dowty (1981). Each requires that any word tolerating an implicit complement be treated as ambiguous between two different lexical entries and that a meaning postulate or lexical rule be given to constrain suitably the meanings of the various entries for the word. I show that (...) the positing of such an ambiguity runs counter to the facts and propose an alternative solution which does not appeal to ambiguity, meaning postulates or lexical rules. Indeed, I show that the dilemma posed by indefinite implicit complements is posed by all implicit complements and that a general solution to the problem of implicit complements follows from an independently motivated, single treatment of five other problems, that of subcategorization, that of phrasal projections of words, that of defining a model theoretic structure for phrase structure grammars, that of complement polyvalence and that of complement polyadicity. (shrink)

The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the Mouse Set Conjecture (MSC). One particular motivation for resolving (...) MSC is that it provides grounds for solving the inner model problem which dates back to 1960s. There have been some new partial results on MSC and the methods used to prove the new instances suggest a general program for solving the full conjecture. It is then our goal to communicate the ideas of this program to the community at large. (shrink)

Discriminative feature-based methods are widely used in natural language processing, but sentence parsing is still dominated by generative methods. While prior feature-based dynamic programming parsers have restricted training and evaluation to artificially short sentences, we present the first general, featurerich discriminative parser, based on a conditional random field model, which has been successfully scaled to the full WSJ parsing data. Our efficiency is primarily due to the use of stochastic optimization techniques, as well as parallelization and chart prefiltering. (...) On WSJ15, we attain a state-of-the-art F-score of 90.9%, a 14% relative reduction in error over previous models, while being two orders of magnitude faster. On sentences of length 40, our system achieves an F-score of 89.0%, a 36% relative reduction in error over a generative baseline. (shrink)

In this paper we build a prey–predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators. We will focus on a simple version with two weight classes or stage (larvae and adults) and present some (...) class='Hi'>general mathematical results. In the last part, we will assume that the dynamics of the prey is fast compared to the predator’s one to go further in the results and eventually conclude that under some conditions, cannibalism can stabilize the system: more precisely, an unstable equilibrium without cannibalism will become almost globally stable with some cannibalism. Some numerical simulations are done to illustrate this result. (shrink)

It is well known that, in the terminology of Moschovakis, Descriptive set theory (1980), every adequate normed pointclass closed under ∀ω has an effective version of the generalized reduction property (GRP) called the easy uniformization property (EUP). We prove a dual result: every adequate normed pointclass closed under ∃ω has the EUP. Moschovakis was concerned with the descriptive set theory of subsets of Polish topological spaces. We set up a general framework for parts of descriptive set theory and prove (...) results that have as special cases not only the just-mentioned topological results, but also corresponding results concerning the descriptive set theory of classes of structures. Vaught (1973) asked whether the class of cPCδ classes of countable structures has the GRP. It does. A cPC(A) class is the class of all models of a sentence of the form ¬∃K̄φ, where φ is a sentence of L∞ω that is in A and K̄ is a set of relation symbols that is in A. Vaught also asked whether there is any primitive recursively closed set A such that some effective version of the GRP holds for the class of cPC(A) classes of countable structures. There is: The class of cPC(A) classes of countable structures has the EUP if ω ∈ A and A is countable and primitive recursively closed. Those results and some extensions are obtained by first showing that the relevant classes of classes of structures, which Vaught showed normed, are in a suitable sense adequate and closed under ∃ω, and then applying the dual easy uniformization theorem. (shrink)

In this paper, I propose two theses, and then examine what the consequences of those theses are for discussions of reduction and emergence. The first thesis is that what have traditionally been seen as robust, reductions of one theory or one branch of science by another more fundamental one are a largely a myth. Although there are such reductions in the physical sciences, they are quite rare, and depend on special requirements. In the biological sciences, these prima facie sweeping reductions (...) fade away, like the body of the famous Cheshire cat, leaving only a smile. ... The second thesis is that the “smiles” are fragmentary patchy explanations, and though patchy and fragmentary, they are very important, potentially Nobel-prize winning advances. To get the best grasp of these “smiles,” I want to argue that, we need to return to the roots of discussions and analyses of scientific explanation more generally, and not focus mainly on reduction models, though three conditions based on earlier reduction models are retained in the present analysis. I briefly review the scientific explanation literature as it relates to reduction, and then offer my account of explanation. The account of scientific explanation I present is one I have discussed before, but in this paper I try to simplify it, and characterize it as involving field elements (FE) and a preferred causal model system (PCMS) abbreviated as FE and PCMS. In an important sense, this FE and PCMS analysis locates an “explanation” in a typical scientific research article. This FE and PCMS account is illustrated using a recent set of neurogenetic papers on two kinds of worm foraging behaviors: solitary and social feeding. One of the preferred model systems from a 2002 Nature article in this set is used to exemplify the FE and PCMS analysis, which is shown to have both reductive and nonreductive aspects. The paper closes with a brief discussion of how this FE and PCMS approach differs from and is congruent with Bickle’s “ruthless reductionism” and the recently revived mechanistic philosophy of science of Machamer, Darden, and Craver. (shrink)

Various scientific theories stand in a reductive relation to each other. In a recent article, we have argued that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, we present a Bayesian analysis of how GNS impacts on confirmation. We formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. (...) We then ask when a purported reduction should be accepted on epistemic grounds. To do so, we compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence. (shrink)

The main aim of our paper is to show that interpretative issues belonging to classical General Relativity (GR) might be preliminary to a deeper understanding of conceptual problems stemming from on-going attempts at constructing a quantum theory of gravity. Among such interpretative issues, we focus on the meaning of general covariance and the related question of the identity of points, by basing our investigation on the Hamiltonian formulation of GR. In particular, we argue that the adoption of a (...) peculiar gauge-fixing within the canonical reduction of ADM metric gravity may yield a new solution to the debate between substantivalists and relationists, by suggesting a \emph{tertium quid} between these two age-old positions. Such a third position enables us to evaluate the controversial relationship between entity realism and structural realism in a well-defined case study. After having indicated the possible developments of this approach in Quantum Gravity, we discuss the structuralist and holistic features of the class of spacetime models that are used in the above mentioned canonical reduction. (shrink)

Does chemistry reduce to physics? If this means ‘Can we derive the laws of chemistry from the laws of physics?’, recent discussions suggest that the answer is ‘no’. But sup posing that kind of reduction—‘epistemological reduction’—to be impossible, the thesis of ontological reduction may still be true: that chemical properties are determined by more fundamental properties. However, even this thesis is threatened by some objections to the physicalist programme in the philosophy of mind, objections that generalize to the chemical case. (...) Two objections are discussed: that physicalism is vacuous, and that nothing grounds the asymmetry of dependence which reductionism requires. Although it might seem rather surprising that the philosophy of chemistry is affected by shock waves from debates in the philosophy of mind, these objections show that there is an argumentative gap between, on the one hand, the theoretical connection linking chemical properties with properties at the sub-atomic level, and, on the other, the philosophical thesis of ontological reduction. The aim of this paper is to identify the missing premises (among them a theory of physical possibility) that would bridge this gap. Introduction: missing elements and the mystery of discreteness The refutation of physicalism A combinatorial theory of physical possibilia Combinatorialism and the Bohr model Objections The missing premises and a disanalogy with mind. (shrink)

The idea of a calculus or discrete formal system is central to traditional models of language, knowledge, logic, cognition and computation, and it has provided a unifying framework for these and other disciplines. Nevertheless, research in psychology, neuroscience, philosophy and computer science has shown the limited ability of this model to account for the flexible, adaptive and creative behavior exhibited by much of the animal kingdom. Promising alternate models replace discrete structures by structured continua and discrete rule-following by continuous (...) dynamical processes. However, we believe that progress in these alternate models is retarded by the lack of a unifying theoretical construct analogous to the discrete formal system. In this paper we outline the general characteristics of continuous formal systems (simulacra), which we believe will be a unifying element in future models of language, knowledge, logic, cognition and computation. Therefore, we discuss syntax, semantics, inference and computation in the context of continuous formal systems. In addition, we address an issue that the discrete models were inadequate to address: the gradual emergence of (approximately) discrete structures from a continuum. This is relevant to the emergence of linguistic structures, including semantics and syntax, and to the emergence of rule-like regularities in behavior. (shrink)

A Krom formula of pure quantification theory is a formula in conjunctive normal form such that each conjunct is a disjunction of at most two atomic formulas or negations of atomic formulas. Every class of Krom formulas that is determined by the form of their quantifier prefixes and which is known to have an unsolvable decision problem for satisfiability is here shown to be a conservative reduction class. Therefore both the general satisfiability problem, and the problem of satisfiability in (...) finite models, can be effectively reduced from arbitrary formulas to Krom formulas of these several prefix types. (shrink)

Abstract Theories of induction in psychology and artificial intelligence assume that the process leads from observation and knowledge to the formulation of linguistic conjectures. This paper proposes instead that the process yields mental models of phenomena. It uses this hypothesis to distinguish between deduction, induction, and creative forms of thought. It shows how models could underlie inductions about specific matters. In the domain of linguistic conjectures, there are many possible inductive generalizations of a conjecture. In the domain of models, however, (...) generalization calls for only a single operation: the addition of information to a model. If the information to be added is inconsistent with the model, then it eliminates the model as false: this operation suffices for all generalizations in a Boolean domain. Otherwise, the information that is added may have effects equivalent (a) to the replacement of an existential quantifier by a universal quantifier, or (b) to the promotion of an existential quantifier from inside to outside the scope of a universal quantifier. The latter operation is novel, and does not seem to have been used in any linguistic theory of induction. Finally, the paper describes a set of constraints on human induction, and outlines the evidence in favor of a model theory of induction. (shrink)

ABSTRACT. In this paper, we present several extensions of epistemic logic with update operators modelling public information change. Next to the well-known public announcement operators, we also study public substitution operators. We prove many of the results regarding expressivity and completeness using so-called reduction axioms. We develop a general method for using reduction axioms and apply it to the logics at hand.

While the concept of multiple realizability is widely used, it is seldom rigorously characterized. This paper defends a liberal conception of multiple realizability as sameness of type through _any_ differences in the (lower-level) conditions that give rise to instances of that type. This kind of “sameness through difference” is contrasted with another type of asymmetric dependency relation between properties, multiple _specification_. This liberal conception is then defended from objections, and it is augmented by a concept of relativized multiple realizability. The (...) last section presents a survey of the ontological, explanatory, and methodological consequences of this analysis of multiple realizability. (shrink)

The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei; the second contains proper nuclei with linear chromosomes; the third contains proper nuclei with cyclical chromosomes. The nuclei have periods which are inherited up the ordering. It is also shown that the improper nuclei can have the order type of any ordinal, (...) of the rationals, or of any other order type that can be embedded in the rationals in a certain way. (shrink)

In this paper we describe the nature and problems of business and define one aspect of the business environment. We then propose a framework based on augmented soft systems methodology and object technology that captures both the soft and hard aspects of a business environment within the context of organisational culture. We also briefly discuss cognitive informatics and its relevance to understanding problems and solutions. Pólya's work, which is based around solving mathematical problems, is considered within the context of information (...) systems development. We propose a generic reusable business object model based on general systems theory. We also show how these approaches can be integrated to provide a strategy for understanding business problems and developing integrated solutions. (shrink)

The continuity thesis of the Poznań school threshold model of the growth of scientific knowledge is considered in the light of the example of Van der Waals' and Boyle-Mariotte's laws. It is argued - using both traditional logical means and the structuralist reconstruction of the example - that the continuity thesis does not hold. A distinction between 'a historical and a systematic point of view' is introduced and it is argued that the continuity thesis of the threshold model (...) presupposes the systematic point of view. However, looking at matters from the systematic point of view need not yield the original theory, looked at from the historical point of view. Applied to the case of Van der Waals/Boyle-Mariotte laws, it turns out that the latter law is not a true idealizing special case of the former, contrary to the continuity thesis. The structuralist analysis of the example indicates that Boyle-Mariotte's law is a false factual law from the historical point of view. However, viewed from the systematic point of view, Boyle-Mariotte's law turns out to be a law which is expandable, adding the relevant new concepts, to an idealized version of Van der Waals' law. This idealizing version of Van der Waal's law in turn is a structuralist specialization of the (general) Van der Waals' law. (shrink)

We introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L ′ are two logics and μ is an asymptotic measure on finite structures, then $\scr{L}\equiv _{\text{a.e.}}\scr{L}^{\prime}(\mu)$ means that there is a class C of finite structures with μ (C)=1 (...) and such that L and L ′ define the same queries on C. We carry out a systematic investigation of $\equiv _{\text{a.e.}}$ with respect to the uniform measure and analyze the $\equiv _{\text{a.e.}}$ -equivalence classes of several logics that have been studied extensively in finite model theory. Moreover, we explore connections with descriptive complexity theory and examine the status of certain classical results of model theory in the context of this new framework. (shrink)

Summary One — Sided understanding of Aristotle led to the view that the principal aim of science is general knowledge. In modern times this view must be extended: also particular knowledge of concrete situations and objects has considerable validity for science. This kind of knowledge the author calls diagnostic. In all empirical sciences diagnostic studies form their necessary part. There are two poles in sciences concerning reality — the more and more developed general knowledge and the specialized knowledge (...) about concrete situations, persons and their cultural and technical products. These two poles are joined in a new model of science which the author presents. Between these poles there exists a mutual independence: diagnostic studies constitute a firm basis for new generalisations and the existing knowledge of laws helps towards a better understanding of concrete situations and their diagnoses. (shrink)

We prove the canonical models introduced in [D] do not exist for some graded normal logics with symmetric models, namelyKB°, KBD°, KBT°, so that we define a new kind of canonical models, the general ones, and show they exist and work well in every case.

This essay is an attempt to consider dynamic aspects of scientific theorising from a formal perspective. Our emphasis will be on the aims and methods for constructing formal models of theory dynamics which will be conceived from a general or 'theoretical' rather than 'applied' standpoint.

This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, second-order, fixed-point, and (...) infinitary logics to gain insight into phenomena in complexity theory and combinatorics. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful way to analyze the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the application of finite model theory to database theory and AI. Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the application of logic to computer science. (shrink)

In his 1966 paper "The Strategy of model-building in Population Biology", Richard Levins argues that no single model in population biology can be maximally realistic, precise and general at the same time. This is because these desirable model properties trade-off against one another. Recently, philosophers have developed Levins' claims, arguing that trade-offs between these desiderata are generated by practical limitations on scientists, or due to formal aspects of models and how they represent the world. However this (...) project is not complete. The trade-offs discussed by Levins had a noticeable effect on modelling in population biology, but not on other sciences. This raises questions regarding why such a difference holds. I claim that in order to explain this finding, we must pay due attention to the properties of the systems, or targets modelled by the different branches of science. (shrink)

Some problems rarely discussed in traditional philosophy of science are mentioned: The empirical sciences using mathematico-quantitative theoretical models are frequently confronted with several types of computational problems posing primarily methodological limitations on explanatory and prognostic matters. Such limitations may arise from the appearances of deterministic chaos and (too) high computational complexity in general. In many cases, however, scientists circumvent such limitations by utilizing reductional approximations or complexity reductions for intractable problem formulations, thus constructing new models which are computationally (...) tractable. Such activities are compared with reduction types (more) established in philosophy of science. (shrink)

This book attempts to marry truth-conditional semantics with cognitive linguistics in the church of computational neuroscience. To this end, it examines the truth-conditional meanings of coordinators, quantifiers, and collective predicates as neurophysiological phenomena that are amenable to a neurocomputational analysis. Drawing inspiration from work on visual processing, and especially the simple/complex cell distinction in early vision (V1), we claim that a similar two-layer architecture is sufficient to learn the truth-conditional meanings of the logical coordinators and logical quantifiers. As a prerequisite, (...) much discussion is given over to what a neurologically plausible representation of the meanings of these items would look like. We eventually settle on a representation in terms of correlation, so that, for instance, the semantic input to the universal operators (e.g. and, all)is represented as maximally correlated, while the semantic input to the universal negative operators (e.g. nor, no)is represented as maximally anticorrelated. On the basis this representation, the hypothesis can be offered that the function of the logical operators is to extract an invariant feature from natural situations, that of degree of correlation between parts of the situation. This result sets up an elegant formal analogy to recent models of visual processing, which argue that the function of early vision is to reduce the redundancy inherent in natural images. Computational simulations are designed in which the logical operators are learned by associating their phonological form with some degree of correlation in the inputs, so that the overall function of the system is as a simple kind of pattern recognition. Several learning rules are assayed, especially those of the Hebbian sort, which are the ones with the most neurological support. Learning vector quantization (LVQ) is shown to be a perspicuous and efficient means of learning the patterns that are of interest. We draw a formal parallelism between the initial, competitive layer of LVQ and the simple cell layer in V1, and between the final, linear layer of LVQ and the complex cell layer in V1, in that the initial layers are both selective, while the final layers both generalize. It is also shown how the representations argued for can be used to draw the traditionally-recognized inferences arising from coordination and quantification, and why the inference of subalternacy breaks down for collective predicates. Finally, the analogies between early vision and the logical operators allow us to advance the claim of cognitive linguistics that language is not processed by proprietary algorithms, but rather by algorithms that are general to the entire brain. Thus in the debate between objectivist and experiential metaphysics, this book falls squarely into the camp of the latter. Yet it does so by means of a rigorous formal, mathematical, and neurological exposition – in contradiction of the experiential claim that formal analysis has no place in the understanding of cognition. To make our own counter-claim as explicit as possible, we present a sketch of the LVQ structure in terms of mereotopology, in which the initial layer of the network performs topological operations, while the final layer performs mereological operations. The book is meant to be self-contained, in the sense that it does not assume any prior knowledge of any of the many areas that are touched upon. It therefore contains mini-summaries of biological visual processing, especially the retinocortical and ventral /what?/ parvocellular pathways computational models of neural signaling, and in particular the reduction of the Hodgkin-Huxley equations to the connectionist and integrate-and-fire neurons Hebbian learning rules and the elaboration of learning vector quantization the linguistic pathway in the left hemisphere memory and the hippocampus truth-conditional vs. image-schematic semantics objectivist vs. experiential metaphysics and mereotopology. All of the simulations are implemented in MATLAB, and the code is available from the book’s website. • The discovery of several algorithmic similarities between visison and semantics. • The support of all of this by means of simulations, and the packaging of all of this in a coherent theoretical framework. (shrink)

David Papineau’s model of scientific reduction, contrary to his intent, appears to enable a naturalist realist account of the primitive normativity involved in a biological adaptation’s being “for” this or that (say the eye’s being for seeing). By disabling the crucial anti-naturalist arguments against any such reduction, his model would support a cognitivist semantics for normative claims like “The heart is for pumping blood, and defective if it doesn’t.” No moral claim would follow, certainly. Nonetheless, by thus “pressing (...) from below” we may learn something about moral normativity. For instance, suppose non-cognitivists like Mackie are right that the semantics of normative claims should be “unified”: if the semantics of moral claims is non-cognitivist, so too is that of all normative claims. Then, assuming that a naturalist reduction does yield a sound cognitivist account of the primitive normativity, it would follow that our semantics of moral claims is cognitivist as well. (shrink)

Abstract: I argue that for psychological and social reasons, the traditional “Conflict Model” of science and religion interactions has such a strong hold on the nonexpert imagination that counterexamples and claims that interactions are simply more complex than the model allows are inadequate to undermine its power. Taxonomies, such as those of Ian Barbour and John Haught, which characterize conflict as only one among several possible relationships, help. But these taxonomies, by themselves, fail to offer an account of (...) why different relationships prevail among different communities and how they succeed one another within particular communities—that is, they contain no dynamic elements. To undermine the power of the “Conflict Model,” we should be seeking to offer alternative models for science and religion interactions that can both incorporate the range of stances articulated by scholars like Barbour and which can offer an account of the process by which differing attitudes succeed one another. As a step toward this goal, I propose a general “interacting subcultures model” and illustrate its applicability in a small number of mini-case studies from Early Modern Britain and France and with glances toward contemporary America. (shrink)

The issue of representing access control requirements continues to demand significant attention. The focus of researchers has traditionally been on developing particular access control models and policy specification languages for particular applications. However, this approach has resulted in an unnecessary surfeit of models and languages. In contrast, we describe a general access control model and a logic-based specification language from which both existing and novel access control models may be derived as particular cases and from which several approaches (...) can be developed for domain- specific applications. We will argue that our general framework has a number of specific attractions and an implication of our work is to encourage a methodological shift from a study of the particulars of access control to its generalities. (shrink)

The issue of representing access control requirements continues to demand significant attention. The focus of researchers has traditionally been on developing particular access control models and policy specification languages for particular applications. However, this approach has resulted in an unnecessary surfeit of models and languages. In contrast, we describe a general access control model and a logic-based specification language from which both existing and novel access control models may be derived as particular cases and from which several approaches (...) can be developed for domain-specific applications. We will argue that our general framework has a number of specific attractions and an implication of our work is to encourage a methodological shift from a study of the particulars of access control to its generalities. (shrink)

Although many philosophers of science have recognized the importance of modeling in contemporary science, relatively little work has been done in developing a general account of models. The most widely accepted account, put forth by advocates of the semantic conception of theories, misleadingly identifies scientific models with the models of mathematical logic. I present an alternative theory of scientific models in which models are defined by their representational relation to a physical system. I explore in some detail a particular (...) sort of model called a ‘mechanical model’ I illustrate the applicability of my approach by applying it to a problem in contemporary speech perception research. The model of models is used to analyze how competing models of the mechanisms of vowel normalization are constructed, tested, and revised. (shrink)

This paper examines the nature of theory structure in biology and considers the implications of those theoretical structures for theory reduction. An account of biological theories as interlevel prototypes embodying causal sequences, and related to each other by strong analogies, is presented, and examples from the neurosciences are provided to illustrate these middle-range theories. I then go on to discuss several modifications of Nagel''s classical model of theory reduction, and indicate at what stages in the development of reductions these (...) models might best apply. Finally I consider several implications of these analyses of theory structure and reduction for disciplinary integration in biology. (shrink)

This paper examines the idea, commonly presupposed but seldom explicitly stated in discussions of certain philosophical problems, that the objects and phenomena of the world are structured in a hierarchy of "levels", from the bottom level of microparticles to the levels of cells and biological organisms and then to the levels of creatures with mentality and social groups of such creatures. Parallel to this "layered model" of the natural world is an ordering of the sciences, with physics as our (...) "basic" science and the "special sciences" forming a ladder-like hierarchy, from chemistry to biology to psychology and the social sciences, all grounded in basic physics. Focusing on two formulations of this model, the emergentist model of C. Lloyd Morgan and the reductionist model due to Paul Oppenheim and Hilary Putnam, the paper discusses such questions as these:What makes a given level of objects "higher" or "lower" than another? What makes a given property "higher" or "lower" than another property. Are objects and properties always comparable with respect to "higher" and "lower"? Can an overarching hierarchy of entities and properties be developed that comprehends the entire natural order? The issues turn out to be quite complex, and no definitive general conclusions are reached. (shrink)

This essay analyzes and develops recent views about explanation in biology. Philosophers of biology have parted with the received deductive-nomological model of scientific explanation primarily by attempting to capture actual biological theorizing and practice. This includes an endorsement of different kinds of explanation (e.g., mathematical and causal-mechanistic), a joint study of discovery and explanation, and an abandonment of models of theory reduction in favor of accounts of explanatory reduction. Of particular current interest are philosophical accounts of complex explanations that (...) appeal to different levels of organismal organization and use contributions from different biological disciplines. The essay lays out one model that views explanatory integration across different disciplines as being structured by scientific problems. I emphasize the philosophical need to take the explanatory aims pursued by different groups of scientists into account, as explanatory aims determine whether different explanations are competing or complementary and govern the dynamics of scientific practice, including interdisciplinary research. I distinguish different kinds of pluralism that philosophers have endorsed in the context of explanation in biology, and draw several implications for science education, especially the need to teach science as an interdisciplinary and dynamic practice guided by scientific problems and explanatory aims. (shrink)

This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall (...) claim of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones (each shared with some other authors) are: (i): I defend the traditional Nagelian conception of reduction (Section 3}); (ii): I deny that the multiple realizability argument causes trouble for reductions, or ``reductionism'' (Section 4); (iii): I stress the collapse of supervenience into deduction via Beth's theorem (Section 5.1); (iv): I adapt some examples already in the literature to show supervenience without emergence and vice versa (Section 5.2). (shrink)