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)

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)

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)

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)

Frames, i.e., recursive attribute-value structures, are a general format for the decomposition of lexical concepts. Attributes assign unique values to objects and thus describe functional relations. Concepts can be classified into four groups: sortal, individual, relational and functional concepts. The classification is reflected by different grammatical roles of the corresponding nouns. The paper aims at a cognitively adequate decomposition, particularly, of sortal concepts by means of frames. Using typed feature structures, an explicit formalism for the characterization of cognitive (...) frames is developed. The frame model can be extended to account for typicality effects. Applying the paradigm of object-related neural synchronization, furthermore, a biologically motivated model for the cortical implementation of frames is developed. Cortically distributed synchronization patterns may be regarded as the fingerprints of concepts. (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)

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)

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.

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)

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)

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)

Several articles have recently appeared arguing that there really are no viable alternatives to mechanistic explanation in the biological sciences (Kaplan and Bechtel; Kaplan and Craver). We argue that mechanistic explanation is defined by localization and decomposition. We argue further that systems neuroscience contains explanations that violate both localization and decomposition. We conclude that the mechanistic model of explanation needs to either stretch to now include explanations wherein localization or decomposition fail or acknowledge that there are counterexamples (...) to mechanistic explanation in the biological sciences. (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 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)

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)

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)

Kant is gaining popularity in business ethics because the categorical imperative rules out actions such as deceptive advertising and exploitative working conditions, both of which treat people merely as means to an end. However, those who apply Kant in this way often hold businesses themselves morally accountable, and this conception of collective responsibility contradicts the kind of moral agency that underlies Kant's ethics. A business has neither inclinations nor the capacity to reason, so it lacks the conditions necessary for constraint (...) by the moral law. Instead, corporate policies ought to be understood as analogous to legal constraints. They may encourage or discourage certain actions, but they cannot determine a person's maxim - which for Kant is the focus of moral judgment. Because there is no collective intention apart from any intentions of the individual agents who act as members of the corporation, an organization itself has no moral obligations. This poses a dilemma: either apply the categorical imperative to the actions of particular businesspeople and surrender the notion of collective responsibility, or apply a different moral theory to the actions of businesses themselves. Given the diffusion of responsibility in a bureaucracy, the explanatory usefulness of collective responsibility may force business ethicists to abandon Kant's moral philosophy. (shrink)

The concept of technical function is a key concept to describe technical artifacts and artifacts-to-be-designed. Engineers often give such descriptions in terms of functional decomposition models, which represent relationships between functions and sets of other functions. Despite the importance of the concept of function there is no consensus among engineers about its meaning. Models of functional decomposition are likewise conceptually divergent. Although this conceptual diversity hampers information exchange between engineers, they accept and maintain it. Engineers do not, by (...) and large, engage in a focused debate to establish commonly shared functional conceptualizations. This contrasts with science where both debates on the adequacy of key conceptualizations and convergence toward shared conceptualizations are common. This book investigates the side-by-side usage of different functional decomposition models in engineering. It explains this phenomenon by applying and extending the analysis of theory choice in terms of methodological incommensurability to engineering functional decomposition, rather than to science. This analysis shows that engineers’ usage of competing functional decomposition models is rational from a practical point of view. This book furthermore investigates the communication problems that the side-by-side usage of different models engenders and presents a strategy that supports the exchange and re-use of functional information between engineers. (shrink)

In this paper we develop a differential analogue of o-minimal cell decomposition for the theory CODF of closed ordered differential fields. Thanks to this differential cell decomposition we define a well-behaving dimension function on the class of definable sets in CODF. We conclude this paper by proving that this dimension is closely related to both the usual differential transcendence degree and the topological dimension associated, in this case, with a natural differential topology on ordered differential fields.

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)

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)

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.

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)

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.

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.

The core of human cooperation is people's ability to perform joint actions. Frequently, this requires effectively decomposing a joint task into individual subtasks, for example, when jointly shopping at the market to buy food. Surprisingly, little is known about how collaborators balance the costs of establishing a joint strategy for such decompositions and its expected benefits for a joint goal. We created a new online task that required pairs of randomly matched participants to jointly collect colored items. We then systematically (...) varied the cognitive costs and benefits of applying a color‐splitting strategy. The results showed that pairs adopted a color‐splitting strategy more often when necessary to lower cognitive costs. However, once the strategy was jointly adopted, it continued to be used even when the cost–benefits changed. Our results provide first insights on how people decompose joint tasks into individual components and how decomposition strategies may evolve into conventions. (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”?

The paper discusses a four-valued propositional logic FOUR≤, similar to Belnap's logic, which can be used to describe incomplete or inconsistent knowledge. In addition to the two classical logical values tt, ff, FOUR≤ features also two nonclassical values: ⊥, representing incomplete information, and ⊤, representing inconsistency. The nonclassical values are incomparable, and together with the classical ones they form a diamond-shaped lattice L4 known from Belnap's logic, which underlies the semantics of FOUR≤. The set of connectives contains those of Belnap's (...) logic, together with an additional operator representing the lattice order, which decisively increases the expressive power of the logic. In the paper we develop a complete decompositional deduction system in Rasiowa-Sikorski style for FOUR≤. (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?

Strong cell decomposition property has been proved in non-valuational weakly o-minimal expansions of ordered groups. In this note, we show that all o-minimal traces have strong cell decomposition property. Also after introducing the notion of irrational nonvaluational cut in arbitrary o-minimal structures, we show that every expansion of o-minimal structures by irrational nonvaluational cuts is an o-minimal trace.

I attempt to complement my earlier critiques of human sociobiology, by offering an account of how evolutionary ideas might legitimately be employed in the study of human social behavior. The main emphasis of the paper is the need to integrate studies of proximate mechanisms and their ontogenesis with functional/evolutionary research. Human psychological complexity makes it impossible to focus simply on specific types of human behavior and ask for their functional significance. For any of the kinds of behavior patterns that have (...) occupied human sociobiologists, the underlying proximate mechanisms are very likely to be linked to a broad spectrum of types of behavior, and we cannot expect that natural selection will have acted directly on any individual element from this spectrum. I illustrate this general point with a specific example, considering the traditional sociobiological account of human incest-avoidance and outlining an alternative approach to the phenomena. The example is intended to show the possibility of a more rigorous and sophisticated successor to human sociobiology, which I call "human behavioral ecology". (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)

Several articles have recently appeared arguing that there really are no viable alternatives to mechanistic explanation in the biological sciences. This claim is meant to hold both in principle and in practice. The basic claim is that any explanation of a particular feature of a biological system, including dynamical explanations, must ultimately be grounded in mechanistic explanation. There are several variations on this theme, some stronger and some weaker. In order to avoid equivocation and miscommunication, in section 1 we will (...) argue that mechanistic explanation is defined by localization and decomposition. In section 2 we will argue that systems neuroscience contains explanations that violate both localization and decomposition on any non-trivial construal of these concepts. Therefore, in section 3 we conclude the mechanistic model of explanation either needs to stretch to now include explanations wherein localization or decomposition fail, or acknowledge that there are counter-examples to mechanistic explanation in the biological sciences. We will also consider consequences and possible replies on the part of the mechanist in section 3. (shrink)

Michael Dummett has long argued that Frege is committed to recognizing a distinction between two sorts of analysis of propositional contents: 'analysis', which reveals the entities that one must grasp in order to apprehend a given propositional content; and 'decomposition', which is used in recognizing the validity of certain inferences. Whereas any propositional content admits of a unique ultimate 'analysis' into simple constituents, it also admits of distinct 'decompositions', no one of which is ultimately privileged over the others. I (...) argue that although Russell accepts this distinction between analysis and decomposition, Frege does not. In particular, I consider claims which Dummett makes regarding how 'analysis' and 'decomposition' are related to two different models Frege at least suggests in discussing the composition of thoughts, the part/whole model and the function/argument model; and I argue that in each case, while Russell accepts views which Dummett attributes to Frege, Frege does not. (shrink)

This paper examines the underdetermination between the Ptolemaic, Copernican, and the Tychonic theories of planetary motions and its attempted resolution by Kepler. I argue that past philosophical analyses of the problem of the planetary motions have not adequately grasped a method through which the underdetermination might have been resolved. This method involves a procedure of what I characterize as decomposition and identification. I show that this procedure is used by Kepler in the first half of the Astronomia Nova, where (...) he ultimately claims to have refuted the Ptolemaic theory, thus partially overcoming the underdetermination. Finally, I compare this method with other views of scientific inference such as bootstrapping. (shrink)

In this paper we argue that an operational organism concept can help to overcome the structural deficiency of mathematical models in biology. In our opinion, the structural deficiency of mathematical models lies mainly in our inability to identify functionally relevant biological characters in biological systems, and not so much in a lack of adequate mathematical representations of biological processes. We argue that the problem of character identification in biological systems is linked to the question of a properly formulated organism concept. (...) Lastly, we demonstrate how a decomposition of an organism into independent characters in the context of a specific biological process--such as adaptation by means of natural selection--depends on the dynamical properties and invariance conditions of the equations that describe this process. (shrink)

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)