An analysis of two heuristic strategies for the development of mechanistic models, illustrated with historical examples from the life sciences. In Discovering Complexity, William Bechtel and Robert Richardson examine two heuristics that guided the development of mechanistic models in the life sciences: decomposition and localization. Drawing on historical cases from disciplines including cell biology, cognitive neuroscience, and genetics, they identify a number of "choice points" that life scientists confront in developing mechanistic explanations and show how different choices result in (...) divergent explanatory models. Describing decomposition as the attempt to differentiate functional and structural components of a system and localization as the assignment of responsibility for specific functions to specific structures, Bechtel and Richardson examine the usefulness of these heuristics as well as their fallibility—the sometimes false assumption underlying them that nature is significantly decomposable and hierarchically organized. When Discovering Complexity was originally published in 1993, few philosophers of science perceived the centrality of seeking mechanisms to explain phenomena in biology, relying instead on the model of nomological explanation advanced by the logical positivists (a model Bechtel and Richardson found to be utterly inapplicable to the examples from the life sciences in their study). Since then, mechanism and mechanistic explanation have become widely discussed. In a substantive new introduction to this MIT Press edition of their book, Bechtel and Richardson examine both philosophical and scientific developments in research on mechanistic models since 1993. (shrink)

This paper presents decomposition of the fourth-order Euler-type linear time-varying system as a commutative pair of two second-order Euler-type systems. All necessary and sufficient conditions for the decomposition are deployed to investigate the commutativity, sensitivity, and the effect of disturbance on the fourth-order LTVS. Some systems are commutative, and some are not commutative, while some are commutative under certain conditions. Based on this fact, the commutativity of fourth-order Euler-type LTVS is investigated by introducing the commutative requirements, theories, and (...) conditions. The fourth-order Euler-type LTVSs are investigated into commutative pairs of twice Euler-type second-order linear time-varying systems. The decomposition theories and conditions are derived, proved, and solved to simplify the use of commutativity for practical and industrial uses. Some fourth-order systems are sensitive toward change in initial conditions or parameters while others are not, and the effect due to disturbance also varies within systems. Furthermore, the stability and robustness of systems have so many issues. But we consider fourth-order Euler-type LTVS to observe, investigate, and tackle these issues. Lastly, the realization of fourth-order LTVS from cascaded two second-order systems can be laboratory experimented which is an open problem for future engineers to investigate. However, the theoretical results show a good agreement with the simulation results is considered in this work. Perhaps it might have unlimited physical applications in science and engineering as well as theoretical contribution. But beyond any reasonable doubt, the novelty is guaranteed because this study is the first of its kind that introduces the decomposition of the fourth-order Euler-type linear time-varying system as a commutative pair of two second-order Euler-type systems. Illustrative examples are presented to support the results. (shrink)

Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using a simple thought experiment, that quantum theory follows from decompositional equivalence together with Landauer’s principle. This demonstration raises within physics a question previously left to psychology: how do human—or any—observers identify or agree about what constitutes a “system of interest”?

Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras.We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as (...) a direct sum of types I, II, and III; and obtain a generalization for COEAs of Ramsay’s fourfold decomposition of a complete orthomodular lattice. (shrink)

This dissertation formulates, defends, and exemplifies a semantic approach that I call Cognitive Decompositionism. Cognitive Decompositionism is one version of lexical decompositionism, which holds that the meaning of lexical items are decomposable into component parts. Decompositionism comes in different varieties that can be characterized in terms of four binary parameters. First, Natural Decompositionism contrasts with Artful Decompositionism. The former views components as word-like, the latter views components more abstractly. Second, Convenient Decompositionism claims that components are merely convenient fictions, while Real (...) Decompositionism claims that components are psychologically real. Third, Truth-conditional Decompositionism contrasts with various non-truth-conditional theories, in particular with Quantum Semantics. And fourth, Holistic Decompositionism assumes that decompositions are circular, as opposed to Atomistic Decompositionism, which assumes that some primitive basis ultimately underlies semantic components. Cognitive Decompositionism is the conjunction of the following theses: decomposition is Artful , Psychologically Real , Quantum , and Atomistic . As I substantiate these claims, I will be responding to the anti-decompositionist theories of Fodor, Davidson, and Quine. (shrink)

Sur la décomposition des ensembles de points en parties respectivement congruentes.

This article proposes three new decompositions of inequality measures, drawn from the framework of cooperative game theory. It allows the impact of players’ interactions, rather than players’ contributions to inequality, to be taken into consideration. These innovative approaches are especially suited for the study of income inequality when the income has a hierarchical structure: the income is composed of several primary sources, with the particularity that each of them is also composed of secondary sources. We revisit the Shapley–Owen value that (...) quantifies the importance of each of these secondary sources in the overall income inequality. Our main contribution is to decompose this importance into two parts: the pure marginal contribution of the considered source and a weighted sum of pairwise interactions. We then provide an axiomatic characterization of each additive interaction decomposable (AID) coalitional value considered in this paper. We give an application of these decompositions in the context of inequality theory. (shrink)

Continuous extension cell decomposition in o-minimal structures was introduced by Simon Andrews to establish the open cell property in those structures. Here, we define strong $\mathrm{CE}$-cells in weakly o-minimal structures, and prove that every weakly o-minimal structure with strong cell decomposition has $\mathrm{SCE}$-cell decomposition if and only if its canonical o-minimal extension has $\mathrm{CE}$-cell decomposition. Then, we show that every weakly o-minimal structure with $\mathrm{SCE}$-cell decomposition satisfies $\mathrm{OCP}$. Our last result implies that every o-minimal structure (...) in which every definable open set is a union of finitely many open $\mathrm{CE}$-cells, has $\mathrm{CE}$-cell decomposition. (shrink)

I argue, through appeal to the distinction between analysis and decomposition described by Dummett, that Wittgenstein employs both of those notions in the Tractatus. I then bring this interpretation to bear upon the issue of propositional unity, where I formulate an objection to the views of both Leonard Linksy and José Zalabardo. I show that both Linsky and Zalabardo fail to acknowledge the distinction between analysis and decomposition present in the Tractatus, and that they consequently mischaracterise Wittgenstein’s position (...) with respect to propositional unity. (shrink)

This paper defends an interpretation of Gottlob Frege’s views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in multiple, distinct ways. These multiple decompositions will often have distinct logical forms. I also argue against Michael Dummett and others that Frege was committed to the sense of a predicate being a function from the sense of (...) a name (or names) to a complete thought. I defend my Frege interpretation against a puzzle often discussed in the Frege literature; namely, that the Multiple Decompositions Thesis is incompatible with Frege’s stated view that a thought is built up out of its component senses as parts. I provide textual evidence and argument that Frege thought of the part/whole relation in such a way that a whole can be analyzed into (or built up out of) parts in multiple, distinct ways, thus dissolving the puzzle. I conclude with discussion of every sort of example of multiple decompositions that can be found in Frege's work. (shrink)

Mediation analysis has been used in many disciplines to explain the mechanism or process that underlies an observed relationship between an exposure variable and an outcome variable via the inclusion of mediators. Decompositions of the total effect of an exposure variable into effects characterizing mediation pathways and interactions have gained an increasing amount of interest in the last decade. In this work, we develop decompositions for scenarios where two mediators are causally sequential or non-sequential. Current developments in this area have (...) primarily focused on either decompositions without interaction components or with interactions but assuming no causally sequential order between the mediators. We propose a new concept called natural mediated interaction effect that captures the two-way and three-way interactions for both scenarios and extends the two-way MIs in the literature. We develop a unified approach for decomposing the TE into the effects that are due to mediation only, interaction only, both mediation and interaction, neither mediation nor interaction within the counterfactual framework. Finally, we compare our proposed decomposition to an existing method in a non-sequential two-mediator scenario using simulated data, and illustrate the proposed decomposition for a sequential two-mediator scenario using a real data analysis. (shrink)

Given that there is no recent research on decomposition for global inequality, the aim of this study is to fill the gap in the literature by investigating global inequality with decomposition technique. The data of this study were compiled from the World Bank and decomposition by subgroups was conducted to evaluate the driving forces behind the evolution of inequality. Almost all the countries in the world were included in this study, and the study period spans from 2000 (...) to 2017. The analysis was carried out in several stages to evaluate the issue of North–South divide, as well as the impacts of regional and income subgroups. There are several salient findings derived from this study. First, the results show that there was a gradual decline of international inequality within the study period. Second, there was still a large disparity between the developed and developing countries, and the inequality within the developing countries has aggravated further. Third, geographical location has exerted great impacts on global inequality and East Asia contributed about 40% to the overall decline in international inequality. Fourth, decline in inequality amongst the upper-middle-income countries also contributed substantially to the fall in international inequality. The results derived from this paper can provide pertinent information for the formulation of a comprehensive and coherent strategy in coordinating international efforts and managing inequality while promoting human development under the framework of the newly established Sustainable Development Goals. (shrink)

This paper will propose a novel semantic and syntactic analysis of stative verbs, more specifically abstract state verbs like 'need', 'believe', 'know', 'own', 'owe', and 'lack'. On that analysis, such verbs have an underlying structure on which they are complex predicates consisting of the light verb HAVE and a noun for a trope-like thing (a trope or attitudinal, modal or intensional object), a structure that is also input to semantic interpretation. Thus, 'need a coat' is underlyingly 'have need (of) a (...) coat'. The analysis accounts for restrictions on adverbial modifiers of abstract states verbs and surprising constraints on explicit property-referring terms, NPs of the sort the property of needing a coat. The paper advocates a notion of a property that is fundamentally different from the notions familiar from the philosophical literature (natural, non-natural properties, abundant, sparse properties). It also suggests that that notion of a property is as innate as constraints of universal grammar, given a generative perspective. (shrink)

In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for p-adically closed fields. We work here with the notion of P-minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a P-minimal field K admits cell decomposition if and only if K has definable selection. A preprint version in French of this result appeared as a prepublication [8].

Functional decomposition is an important goal in the life sciences, and is central to mechanistic explanation and explanatory reduction. A growing literature in philosophy of science, however, has challenged decomposition-based notions of explanation. ‘Holists’ posit that complex systems exhibit context-sensitivity, dynamic interaction, and network dependence, and that these properties undermine decomposition. They then infer from the failure of decomposition to the failure of mechanistic explanation and reduction. I argue that complexity, so construed, is only incompatible with (...) one notion of decomposition, which I call ‘atomism’, and not with decomposition writ large. Atomism posits that function ascriptions must be made to parts with minimal reference to the surrounding system. Complexity does indeed falsify atomism, but I contend that there is a weaker, ‘contextualist’ notion of decomposition that is fully compatible with the properties that holists cite. Contextualism suggests that the function of parts can shift with external context, and that interactions with other parts might help determine their context-appropriate functions. This still admits of functional decomposition within a given context. I will give examples based on the notion of oscillatory multiplexing in systems neuroscience. If contextualism is feasible, then holist inferences are faulty—one cannot infer from the presence of complexity to the failure of decomposition, mechanism, and reductionism. (shrink)

A synaptic algebra is a generalization of the self-adjoint part of a von Neumann algebra. In this article we extend to synaptic algebras the type-I/II/III decomposition of von Neumann algebras, AW∗-algebras, and JW-algebras.

We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition is based on the properties of the congruence lattices of algebras. We consider four properties of lattices: atomic, atomless, locally uniform and anti-uniform. In effect, we describe a star-decomposition of a given algebra with modular congruence lattice into two or three parts associated to these properties.

Avec le Memoire sur la decomposition de la pensee, ecrit en 1804 et couronne par l'Institut en 1805, on a a faire au premier expose complet de la philosophie biranienne constituee. Maine de Biran a pris la pleine mesure des implications de sa theorie du fait primitif, et s'emploie a les faire valoir dans toute leur originalite. Nous publions ici pour la premiere fois dans son integralite le memoire couronne, et nous le faisons suivre de la version remaniee durant (...) l'annee 1805, et laissee inachevee par l'auteur. La Decomposition de la pensee est precedee du Memoire sur les rapports de l'ideologie et des mathematiques, redige a la demande de Cabanis dans le dernier trimestre de 1802. (shrink)

Recently, decomposition-based multiobjective evolutionary algorithms have good performances in the field of multiobjective optimization problems and have been paid attention by many scholars. Generally, a MOP is decomposed into a number of subproblems through a set of weight vectors with good uniformly and aggregate functions. The main role of weight vectors is to ensure the diversity and convergence of obtained solutions. However, these algorithms with uniformity of weight vectors cannot obtain a set of solutions with good diversity on some (...) MOPs with complex Pareto optimal fronts. To deal with this problem, an improved decomposition-based multiobjective evolutionary algorithm with adaptive weight adjustment is proposed. Firstly, a new method based on uniform design and crowding distance is used to generate a set of weight vectors with good uniformly. Secondly, according to the distances of obtained nondominated solutions, an adaptive weight vector adjustment strategy is proposed to redistribute the weight vectors of subobjective spaces. Thirdly, a selection strategy is used to help each subobjective space to obtain a nondominated solution. Comparing with six efficient state-of-the-art algorithms, for example, NSGAII, MOEA/D, MOEA/D-AWA, EMOSA, RVEA, and KnEA on some benchmark functions, the proposed algorithm is able to find a set of solutions with better diversity and convergence. (shrink)

Decomposition is a bracing, revisionary, and provocative inquiry into music—from Beethoven to Duke Ellington, from Conlon Nancarrow to Evelyn Glennie—as a personal and cultural experience: how it is composed, how it is idiosyncratically perceived by critics and reviewers, and why we listen to it the way we do. Andrew Durkin, best known as the leader of the West Coast–based Industrial Jazz Group, is singular for his insistence on asking tough questions about the complexity of our presumptions about music and (...) about listening, especially in the digital age. In this winning and lucid study he explodes the age-old concept of musical composition as the work of individual genius, arguing instead that in both its composition and reception music is fundamentally a collaborative enterprise that comes into being only through mediation. Drawing on a rich variety of examples—Big Jay McNeely’s “Deacon’s Hop,” Biz Markie’s “Alone Again,” George Antheil’s Ballet Mécanique, Frank Zappa’s “While You Were Art,” and Pauline Oliveros’s “Tuning Meditation,” to name only a few—Durkin makes clear that our appreciation of any piece of music is always informed by neuroscientific, psychological, technological, and cultural factors. How we listen to music, he maintains, might have as much power to change it as music might have to change how we listen. (shrink)

We study a reduct ${\mathcal{L}_*}$ of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the ${\mathcal{L}_*}$ -definable subsets of K coincide with the semi-algebraic subsets of K. Hence structures (K, ${\mathcal{L}_*}$ ) can be seen as the p-adic counterpart of the o-minimal structure of semibounded sets. We show that in this language, p-adically closed fields admit cell decomposition, using cells similar to p-adic semi-algebraic cells. (...) From this we can derive quantifier-elimination, and give a characterization of definable functions. In particular, we conclude that multiplication can only be defined on bounded sets, and we consider the existence of definable Skolem functions. (shrink)

In the framework of quantum field theory, one finds multiple load-bearing locality and causality conditions. One of the most important is the cluster decomposition principle, which requires that scattering experiments conducted at large spatial separation have statistically independent results. The principle grounds a number of features of quantum field theory, especially the structure of scattering theory. However, the statistical independence required by cluster decomposition is in tension with the long-range correlations characteristic of entangled states. In this paper, we (...) argue that cluster decomposition is best stated as a condition on the dynamics of a quantum field theory, not directly as a statistical independence condition. This redefinition avoids the tension with entanglement while better capturing the physical significance of cluster decomposition and the role it plays in the structure of quantum field theory. (shrink)

We prove that forp-optimal fields a cell decomposition theorem follows from methods going back to Denef’s paper [7]. We derive from it the existence of definable Skolem functions and strongp-minimality. Then we turn to stronglyp-minimal fields satisfying the Extreme Value Property—a property which in particular holds in fields which are elementarily equivalent to ap-adic one. For such fieldsK, we prove that every definable subset ofK×Kdwhose fibers overKare inverse images by the valuation of subsets of the value group is semialgebraic. (...) Combining the two we get a preparation theorem for definable functions onp-optimal fields satisfying the Extreme Value Property, from which it follows that infinite sets definable over such fields are in definable bijection iff they have the same dimension. (shrink)

Frege seems to hold two incompatible theses:(i) that sentences differing in structure can yet express the same sense; and (ii) that the senses of the meaningful parts of a complex term are determinate parts of the sense of the term. Dummett offered a solution, distinguishing analysis from decomposition. The present paper offers an embellishment of Dummett?s distinction by providing a way of depicting the internal structures of complex senses?determinate structures that yield distinct decompositions. Decomposition is then shown to (...) be adequate as a foundation for the informativity and analyticity of logic. (shrink)

We develop a notion of cell decomposition suitable for studying weak p-adic structures definable). As an example, we consider a structure with restricted addition.

C-minimality is a variant of o-minimality in which structures carry, instead of a linear ordering, a ternary relation interpretable in a natural way on set of maximal chains of a tree. This notion is discussed, a cell-decomposition theorem for C-minimal structures is proved, and a notion of dimension is introduced. It is shown that C-minimal fields are precisely valued algebraically closed fields. It is also shown that, if certain specific ‘bad’ functions are not definable, then algebraic closure has the (...) exchange property, and for definable sets dimension coincides with the rank obtained from algebraic closure. (shrink)

This chapter contains sections titled: Decision‐Making Procedures and Maxims in Corporate Settings The Need for Collective Responsibility in Business Ethics Applying the Categorical Imperative to Businesses Kant's Account of Moral Agency and the Categorical Imperative Must We Never Treat a Business Merely as a Means? Corporate Policies and Individual Agents Bowie's Defense of Collective Responsibility, and the Need for an Alternative Personal Responsibility within the Corporation The Choice Facing Business Ethicists: Kant or Collective Responsibility?

When solving a decision problem we want to determine an optimal policy for the decision variables of interest. A policy for a decision variable is in principle a function over its past; however, some of the past may be irrelevant and for both communicational as well as computational reasons it is important not to deal with redundant variables in the policies. In this paper we present a method to decompose a decision problem into a collection of smaller sub-problems s.t. a (...) solution to the original decision problem can be found by solving the sub-problems independently. The method is based on an operational characterization of the future variables being relevant for a decision variable, thereby also providing a characterization of those parts of a decision problem that are relevant for a particular decision. (shrink)

In this paper, we explore the effects of certain forbidden substructure conditions on preordered sets. In particular, we characterize in terms of these conditions those preordered sets which can be represented as the supremum of a well-ordered ascending chain of lowersets whose members are constructed by means of alternating applications of disjoint union and ordinal sums with chains. These decompositions are examples of ordinal decompositions in relatively normal lattices as introduced by Snodgrass, Tsinakis, and Hart. We conclude the paper with (...) an application to information systems. (shrink)

We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing decomposition (...) trees. The resulting set of acceptable formulae has many attractive features, but it remains an open question whether it continues to satisfy the crucial letter-sharing condition. (shrink)

In componential analysis, word meanings are (partly) decomposed into other meanings, and semantic and syntactic markers. Although a theory of word meaning based on such semantic decompositions remains compatible with the linguistic labor division thesis, it is not compatible with Kripke/Putnam-style indexical externalism. Instead of abandoning indexical externalism, a Separation Thesis is defended according to which lexical meaning need not enter the truth-conditional content of an utterance. Lexical meaning reflects beliefs about word meaning shared in a speaker community, and these (...) may rest on possibly erroneous world-level theories. It is argued that this type of lexical meaning is indispensable for explaining word composition processes and the rationality of metalinguistic disputes. (shrink)