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Thepartialstructures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model‐theoretic techniques in the philosophy (...) of science. However, my concerns arise independently of the more controversial assumptions that Cartwright and Suárez have employed. (shrink)

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The semantic approach to scientific representation is now long established as a favourite amongst philosophers of science. One of the foremost strains of this approach—the model-theoretic approach —is to represent scientific theories as families of models, all of which satisfy or ‘make true’ a given set of constraints. However some authors have criticised the approach on the grounds that certain scientific theories are logically inconsistent, and there can be no models of an inconsistent set of constraints. Thus it would seem (...) that the MTA fails to represent inconsistent scientific theories at all, and this raises concerns about the way it represents in general. In a series of papers and a recent book da Costa and French have developed a variant of the MTA approach which they call ‘partialstructures’, and which they claim can accommodate inconsistent theories. I assess this claim, looking to two theories which have been called ‘inconsistent’: Bohr’s theory of the atom and classical electrodynamics. (shrink)

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Thepartialstructures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model-theoretic techniques in the philosophy (...) of science. However, my concerns arise independently of the more controversial assumptions that Cartwright and Suárez have employed. (shrink)

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I show that extant attempts to capture and generalize empirical adequacy in terms ofpartialstructures fail. Indeed, the motivations for the generalizations in thepartialstructures approach are better met by the generalizations via approximation sets developed in “Generalizing Empirical Adequacy I”. Approximation sets also generalizepartialstructures.

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In Science andPartial Truth it was argued that inconsistencies in scientific reasoning may be accommodated by the combination ofpartialstructures and quasi-truth, together with a notion of ‘representational belief’. In this paper I shall examine whether this framework can be extended to the reasonings and beliefs of other cultures, focusing in particular on the witchcraft beliefs of Azande. I shall argue that these beliefs are akin to the theoretical beliefs of Western science but that the (...) most appropriate way of representing the latter — and hence also the former — is via the framework ofpartialstructures and quasi-truth. In this way I hope to steer a plausible path between ‘imperialist’ and ‘relativist’ approaches. (shrink)

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In this work we show that every structure [MATHEMATICAL SCRIPT CAPITAL A] can be expanded to apartial structure [MATHEMATICAL SCRIPT CAPITAL A]* with universal functions for the class of polynomials on [MATHEMATICAL SCRIPT CAPITAL A]*. We can embed [MATHEMATICAL SCRIPT CAPITAL A]* monomorphically in a total structure [MATHEMATICAL SCRIPT CAPITAL A]º that preserves universal functions of [MATHEMATICAL SCRIPT CAPITAL A]* and that is universal among suchstructures, i.e. [MATHEMATICAL SCRIPT CAPITAL A]º can be homomorphically embedded in every (...) total structure that preserves universal functions of [MATHEMATICAL SCRIPT CAPITAL A]*. Universal functions are the starting point for developing recursion theoretic tools in an [MATHEMATICAL SCRIPT CAPITAL A]* that satisfies some simple additional conditions. (shrink)

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The theory of rankedpartialstructures allows a reinterpretation of several of the standard results of model theory and first-order logic and is intended to provide a proof-theoretic method which allows for the intuitions of model theory. A version of the downward Löwenheim-Skolem theorem is central to our development. In this paper we will present the basic theory of rankedpartialstructures and their logic including an appropriate version of the completeness theorem.

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Based on da Costa's and French's notions ofpartialstructures and pragmatic truth, this paper examines two possible characterizations of the concept of empirical adequacy, one depending on the notion ofpartial isomorphism, the other on the hierarchy ofpartial models of phenomena, and both compatible with an empiricist view. These formulations can then be employed to illuminate certain aspects of scientific practice.An empirical theory must single out a specific part of the world, establish reference to (...) that part, and say—by way of contingent, substantial claim about the world—that its models fit that. Now, how exactly can this be done? Bas C. van Fraassen. (shrink)

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In Tsuji 1997 the concept of Jeffrey-Keynes algebras was introduced in order to construct a paraconsistent theory of decision under uncertainty. In the present paper we show that these algebras can be used to develop a theory of decision under uncertainty that measures the degree of belief on the quasi (orpartial) truth of the propositions. As applications of this new theory of decision, we use it to analyze Popper's paradox of ideal evidence and to indicate a possible way (...) of formalizing Keynes' theory of economic action. (shrink)

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The notion of empirical adequacy has received recent philosophical attention, especially within the framework of the semantic approach. Empirical adequacy, as explicated in the semantic approach, concerns the relationship between empirical substructures and some phenomena. The aim here is to differentiate this notion of empirical adequacy from one concerning the relationship between data and phenomena. Distinguishing each notion of empirical adequacy emphasizes different aspects of scientific practice—one concerning theory-development from the basis of an established theory, the other concerning theory-development from (...) the basis of data-fitting, where established theory may not foster further development. To illustrate this contrast, an example from financial economics is considered. (shrink)

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Wigner famously referred to the `unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics, I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa'spartialstructures programme.

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Scientific change has two important dimensions: conceptual change and structural change. In this paper, I argue that the existence of conceptual change brings serious difficulties for scientific realism, and the existence of structural change makes structural realism look quite implausible. I then sketch an alternative account of scientific change, in terms ofpartialstructures, that accommodates both conceptual and structural changes. The proposal, however, is not realist, and supports a structuralist version of van Fraassen’s constructive empiricism (structural empiricism).

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It is shown that if is an o-minimal structure such that is a dense total order and ≾ is a parameter-definablepartial order on M, then ≾ has an extension to a definable total order.

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Adapting a claim of Kracht (Theor Comput Sci 354:131–141, 2006), we establish a characterization of the typablepartial applicativestructures.

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I show that thepartial truth of a sentence in apartial structure is equivalent to the truth of that sentence in an expansion of a structure that corresponds naturally to thepartial structure. Further, a mapping is apartial homomorphism/partial isomorphism between twopartialstructures if and only if it is a homomorphism/isomorphism between their correspondingstructures. It is a corollary that thepartial truth of a sentence in a (...) class='Hi'>partial structure is equivalent to the truth of a specific Ramsey sentence in a corresponding structure. Hence thepartialstructures approach can be expressed in standard first or second-order model theory, and it can be captured in the received view on scientific theories as developed by Carnap and Hempel. (shrink)

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This paper elaborates on the following correspondence theorem (which has been defended and formally proved elsewhere): if theory T has been empirically successful in a domain of applications A, but was superseded later on by a different theory T* which was likewise successful in A, then under natural conditions T contains theoretical expressions which were responsible for T’s success and correspond (in A) to certain theoretical expressions of T*. I illustrate this theorem at hand of the phlogiston versus oxygen theories (...) of combustion, and the classical versus relativistic theories of mass. The ontological consequences of the theorem are worked out in terms of the indirect reference andpartial truth. The final section explains how the correspondence theorem may justify a weak version of scientific realism without presupposing the no-miracles argument. (shrink)

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We show, for various classes of totally orderedstructures, including o‐minimal and weakly o‐minimalstructures, that every definablepartial order on a subset of extends definably in to a total order. This extends the result proved in for and o‐minimal.

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This paper argues that the future of capabilities approach lies on the theoretical development of the democratic political structure. For this purpose, we take into account Martha Nussbaum’s late theoretical works. Firstly, we argue that the capability approach can be divided into two main models: the top down and the bottom up. Nussbaum, for example, endorses a top-down model, which it begins from an abstractive theory ofpartial justice and then draws the issue of institutional implementation. On the other (...) hand, Amartya Sem advocates the bottom-up model, which starts from the immanent demands of justice from public sphere and then up to normative and abstract questions (like his “idea of justice”). In the second part of this paper, we present Nussbaum’spartial theory of justice, arguing that it is mainly composed by four issues: (a) the elaboration of the list of capabilities, (b) the process of normative evaluation, (c) arguments for stability, (d) the implementation of the model. About this last topic, we argue in the third part that the current theoretical advance of the capabilities approach lies on the issue of the democratic political structure. In other words, the future of capabilities approach depends on the interaction between its own theory and a theory of democracy. Finally, in the last section we provide a re-elaboration of Nussbaum’s threshold level of capabilities (the list) in order to make it more adherent with the democratic political structure. (shrink)

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In this paper we show that any reasoning process in which conclusions can be both fallible and corrigible can be formalized in terms of two approaches: (i) syntactically, with the use of defeasible reasoning, according to which reasoning consists in the construction and assessment of arguments for and against a given claim, and (ii) semantically, with the use ofpartialstructures, which allow for the representation of less than conclusive information. We are particularly interested in the formalization of (...) scientific reasoning, along the lines traced by Lakatos’ methodology of scientific research programs. We show how current debates in cosmology could be put into this framework, shedding light on a very controversial topic. (shrink)

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This paper presents a new language for isomorphic representations of legalknowledge in featurestructures. The language includes predefinedstructures based on situation theory for common-sense categories, andpredefinedstructures based on Van Kralingens frame-based conceptualmodelling language for legal rules. It is shown that the flexibility of thefeature-structure formalism can exploited to allow for structure-preservingrepresentations of non-primitive concepts, and to enable various types ofinteraction and cross- reference between language elements. A fragment of theDutch Opium Act is used to illustrate how modelling (...) and reasoning proceed in practice. (shrink)

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Newton da Costa and Steven French have argued that the concept ofpartial truth plays an important role in our understanding of significant aspects of scientific practice: from the status of scientific theories through the understanding of inconsistency in science to the nature of induction. In this paper, I use the concept ofpartial truth and the associated framework ofpartialstructures to offer a formulation of the concept of visual evidence, and I examine some of (...) the roles that this notion plays in scientific activity. (shrink)

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In this paper we give an axiomatisation of the concept of a computability structure withpartial sequences on a many‐sorted metricpartial algebra, thus extending the axiomatisation given by Pour‐El and Richards in [9] for Banach spaces. We show that every Banach‐Mazur computablepartial function from an effectively separable computable metricpartial Σ‐algebraAto a computable metricpartial Σ‐algebraBmust be continuous, and conversely, that every effectively continuouspartial function with semidecidable domain and which preserves the (...) computability of a computably enumerable dense set must be computable. Finally, as an application of these results we give an alternative proof of the first main theorem for Banach spaces first proved by Pour‐El and Richards. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

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Marilyn Strathern’s arguments against the possibility of feminist research bringing about a paradigm shift in social anthropology have led to a number of responses. Regarding one argument she presents, her own writings suggest a response: the argument that feminist research cannot bring about such a shift, because it is only concerned with part of society. A foray into the history of British social anthropology is of value for appreciating this argument and the response.

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This paper studies a distinction that was proposed in previous works between total andpartial adjectives. In pairs of adjectives such as safe–dangerous, clean–dirty and healthy–sick, the first (“total”) adjective describes lack of danger, dirt, malady, etc., while the second (“partial”) adjective describes the existence of such properties. It is shown that the semantics of adjective phrases with modifiers such as almost, slightly, and completely is sensitive to whether the adjective is total orpartial. The interpretation of (...) such modified constructions is accounted for using a novel scale structure for total andpartial adjectives. It is proposed that the standard value of a total adjective is always fixed as the lower bound of the correspondingpartial adjective. By contrast, the standard value ofpartial adjectives can take any point on thepartial scale. The effects of this theoretical distinction on the behavior of modified constructions are studied in detail, and their ramifications for the semantic theory of adjectives are discussed. Some other phenomena are surveyed that show evidence for total andpartial adjectival constructions with various comparatives and exceptive phrases. (shrink)

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One important role of belief systems is to allow us to represent information about a certain domain of inquiry. This paper presents a formal framework to accommodate such information representation. Three cognitive models to represent information are discussed: conceptual spaces, state-spaces, and the problem spaces familiar from artificial intelligence. After indicating their weakness to deal withpartial information, it is argued that an alternative, formulated in terms ofpartialstructures, can be provided which not only captures the (...) positive features of these models, but also accommodates the partiality of information ubiquitous in science and mathematics. (shrink)

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This paper provides a defence of the account ofpartial resemblances between properties according to which such resemblances are due topartial identities of constituent properties. It is argued, first of all, that the account is not only required by realists about universals à la Armstrong, but also useful (of course, in an appropriately re-formulated form) for those who prefer a nominalistic ontology for material objects. For this reason, the paper only briefly considers the problem of how to (...) conceive of the structural universals first posited by Armstrong in order to explainpartial resemblances, and focuses instead on criticisms that have been levelled against the theory (by Pautz, Eddon, Denkel and Gibb) and that apply regardless of one’s preferred ontological framework. Thepartial identity account is defended from these objections and, in doing so, a hitherto quite neglected connection—between the debate aboutpartial similarity aspartial identity and that concerning ontological finitism versus infinitism—is looked at in some detail. (shrink)

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In a recent paper, Suárez and Cartwright return to the example of London and London's construction of a model for superconductivity and raise a number of concerns against the account of this construction presented in French and Ladyman and elsewhere. In this discussion note, we examine the challenge they raised and offer our responses.

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Philosophers and scientists have maintained that causation, correlation, andpartial correlation are essentially related. These views give rise to various rules of causal inference. This essay considers the claims of several philosophers and social scientists for causal systems with dichotomous variables. In section 2 important commonalities and differences are explicated among four major conceptions of correlation. In section 3 it is argued that whether correlation can serve as a measure of A's causal influence on B depends upon the conception (...) of causation being used and upon certain background assumptions. In section 4 five major kinds ofpartial correlation are explicated, and some of the important relations are established among two conceptions ofpartial correlation, the conception of screening off, the conception of partitioning, and the measures of causal influence which have been suggested by advocates of path analysis or structural equation methods. In section 5 it is argued that whether any of these five conceptions ofpartial correlation can serve as a measure of causal influence depends upon the conception of causation being used and upon certain background assumptions.The important conclusion is that each of the approaches (considered here) to causal inference for causal systems with dichotomous variables stands in need of important qualifications and revisions if they are to be justified. (shrink)

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Theories ofpartial reference have been developed in order to retrospectively interpret rather stubborn past scientific theories like Newtonian dynamics and the phlogiston theory in a realist way, i.e., as approximately true. This is done by allowing for a term to refer to more than one entity at the same time and by providing semanticstructures that determine the truth values of sentences containing partially referring terms. Two versions of theories ofpartial reference will be presented, a (...) conjunctive (by Hartry Field, 1973) and a disjunctive one (by Christina McLeish, 2006). In this paper, I will analyze them with regard to modal and epistemic aspects of those theories. It will be argued that a) theories ofpartial reference are (surprisingly) compatible with the rigidity of natural kind terms but face a weaker form of the so called “no-failures-of-reference-problem” and b) that the disjunctive account ofpartial reference suffers from a serious weakness: the impossibility of discriminating between descriptions that fix the reference of a term and those merely associated with it leads to the unacceptable result that past scientific theories containing such partially referring terms will come out as epistemically necessary, i.e., as a priori true. (shrink)

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A strong reducibility relation betweenpartial numberings is introduced which is such that the reduction function transfers exactly the numbers which are indices under the numbering to be reduced into corresponding indices of the other numbering. The degrees ofpartial numberings of a given set with respect to this relation form an upper semilattice.In addition, Ershov’s completion construction for total numberings is extended to thepartial case: every partially numbered set can be embedded in a set which (...) results from the given set by adding one point and which is enumerated by a total and complete numbering. As is shown, the degrees of complete numberings of the extended set also form an upper semilattice. Moreover, both semilattices are isomorphic.This is not so in the case of the usual, weaker reducibility relation forpartial numberings which allows the reduction function to transfer arbitrary numbers into indices. (shrink)

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This paper argues that ontic structural realism (OSR) faces a dilemma: either it remains on the general level of realism with respect to the structure of a given theory, but then it is, like epistemic structural realism, only apartial realism; or it is a complete realism, but then it has to answer the question how the structure of a given theory is implemented, instantiated or realized and thus has to argue for a particular interpretation of the theory in (...) question. This claim is illustrated by examining how OSR fares with respect to the three main candidates for an ontology of quantum mechanics, namely many worlds-type interpretations, collapse-type interpretations and hidden variable-type interpretations. The result is that OSR as such is not sufficient to answer the question of what the world is like if quantum mechanics is correct. (shrink)

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Partial reasons are considerations in favor of something that, taken individually, are not sufficient to establish an obligation. I consider the extent to whichpartial reasons are reasons, and why they cannot be reduced to or identified with pro tanto reasons. I lay out two approaches to the content of reasons, the flat theory and the structured theory. I argue that parts of reasons are notpartial reasons, by showing that natural ways to represent parts of reasons (...) in the flat theory and the structured theory lead to overgeneration problems with regard topartial reasons. I then formulate two notions ofpartial reasons: one based on a notion ofpartial support, which is in turn captured by the notions of full support andpartial content, and one based on the notion of in exact verification. I show under which conditions the two notions ofpartial reasons (based onpartial content, and based on inexact verification) coincide. (shrink)

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Interest surges in a distinctively metaphysical notion of ground. But a Schism has emerged between Orthodoxy’s view of ground as inducing a strictpartial order structure on reality and Heresy’s rejection of this view. What’s at stake is the structure of reality (for proponents of ground), or even ground itself (for those who think this Schism casts doubt upon its coherence). I defend Orthodoxy against Heresy.

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PurposeDrawing upon the stimulus-organism-response model, this paper aims to investigate the effects of stores’ environmental components on Chinese consumers’ emotions and intentions to purchase luxury brands.Design/Methodology/ApproachData were collected from Chinese consumers who have purchased luxury brands from retail stores.Partial least squares-structural equation modeling and fuzzy-set qualitative comparative analysis were employed for data analysis.FindingsThe results of PLS-SEM indicated that three dimensions of the store environment directly and significantly influenced Chinese consumers’ emotions. However, fsQCA revealed greater heterogeneity among respondents by (...) highlighting stores’ environmental components and Chinese consumers’ emotions.Originality/ValueThis study makes significant contributions to the marketing literature by examining the S-O-R model alongside fsQCA approach to conditionally predict outcomes in a luxury brand context. The present study may be one of the first to examine the effects of stores’ environmental components on Chinese consumers’ emotions and purchase intentions, applying both symmetrical test and asymmetrical test approaches to determine significant components of the store environment as well as component combinations that predict Chinese consumers’ emotions and purchase intentions. (shrink)

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In this article we characterize a countable ordinal known as the big Veblen number in terms of natural well-partially ordered tree-likestructures. To this end, we consider generalized trees where the immediate subtrees are grouped in pairs with address-like objects. Motivated by natural ordering properties, extracted from the standard notations for the big Veblen number, we investigate different choices for embeddability relations on the generalized trees. We observe that for addresses using one finite sequence only, the embeddability coincides with (...) the classical tree-embeddability, but in this article we are interested in more general situations. We prove that the maximal order type of some of these new embeddability relations hit precisely the big Veblen ordinal ϑΩΩ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\vartheta \Omega^{\Omega}}$$\end{document}. Somewhat surprisingly, changing a little bit the well-partially ordered addresses, the maximal order type hits an ordinal which exceeds the big Veblen number by far, namely ϑΩΩΩ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\vartheta \Omega^{\Omega^\Omega}}$$\end{document}. Our results contribute to the research program on classifying properties of natural well-orderings in terms of order-theoretic properties of the functions generating the orderings. (shrink)

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We argue for asymmetries between positive and negative partiality. Specifically, we defend four claims: i) there are forms of negative partiality that do not have positive counterparts; ii) the directionality of personal relationships has distinct effects on positive and negative partiality; iii) the extent of the interactions within a relationship affects positive and negative partiality differently; and iv) positive and negative partiality have different scope restrictions. We argue that these asymmetries point to a more fundamental moral principle, which we call (...) Morality’s Harmonious Propensity. According to this principle, morality has a propensity toward preserving positive relationships and dissolving negative ones. (shrink)

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