We characterize the classifiability of a countable first-order theory T in terms of the solvability of the potential-isomorphism problem for models of T.

We relate the classifiability of a complete finitary first-order theory in the sense of S. SHELAH to the determinacy of the class of -saturated models in the sense of stationary logic.

We analyze the relationship between evolutionary theory and classification of higher taxa in the work of three ichthyologists: Albert C.L.G. Günther (1830–1914), Edward Drinker Cope (1840–1897), and Theodore Gill (1837–1914). The progress of ichthyology in the early years following the Origin has received little attention from historians, and offers an opportunity to further evaluate the extent to which evolutionary theorizing influenced published views on systematic methodology. These three ichthyologists held radically different theoretical views. The apparent commensurability of claims (...) about relationships among groups of fishes belies differences in what the relationships actually were supposed to be. As well, interpreting classification as genealogical did not lead to agreement about taxonomic methodology; instead, applying evolutionary theory raised new axes of disagreement. (shrink)

Stakeholder theory is widely accepted but elementary aspects remain indeterminate as the term ‘stakeholder’ is an essentially contested concept, being variously describable, internally complex and open in character. Such contestability is highly problematic for theory development and empirical testing. The extent of essential contestability, previously unknown, is demonstrated in this paper through a bounded systematic review of 593 different stakeholder theory definitions. As an essentially contested concept, the solution does not lie in a universal stakeholder definition, but (...) in debating the boundaries of stakeholder identification. To this end, this paper presents the first major attempt at sorting, filtering and ordering stakeholder theory and stakeholder definitions to produce a comprehensive, multi-dimensional classification of stakeholder theory. The constructs of the classification model juxtapose existing stakeholder theories and contributions from across the multi-contextual applications of stakeholder theory, thereby providing an invaluable overview of what we know about stakeholder theory in one model. The classification model is then tested with positive results. The paper concludes with a comprehensive discussion of the implications of classification stakeholder theory definitions, which has for future research. (shrink)

We study the complexity of the classification problem for countable models of set theory (). We prove that the classification of arbitrary countable models of is Borel complete, meaning that it is as complex as it can conceivably be. We then give partial results concerning the classification of countable well‐founded models of.

In lieu of an abstract, here is a brief excerpt of the content:Classification and Explanation in Aristotle’s Theory of DefinitionGreg Bayer1. introductiona problem lies at the heart of Aristotle’s theory of definition. On the one hand, Aristotle says in Topics VI.4 that “the one who defines well must define by means of genus1 and differentia” (141b25–7); indeed his view of definition most often seems to be confined to its role of picking out the definiendum by indicating the (...) class it belongs to—what can be called its “class definition.”2 But on the other hand, in Posterior Analytics II.2 he makes the pronouncement that “knowing what something is ” is the same as knowing why it is ” (90a31–2), and then goes on in II.2 and 8 to argue that definition is an, “explanation” or “explanatory principle.” How can these two notions of definition be reconciled?Short of giving the full Aristotelian solution to this problem, I hope here to suggest one way in which Aristotle’s notion of class definition—especially the reformed version presented in De Partibus Animalium I.2–4—can be shown to relate to his notion of explanatory definition in APo II. The link is his notion of scientific, “problems,” as discussed in APo II. 14 and elsewhere.3 It will turn out that a class definition in effect presents a scientific problem to the scientist which can best be solved by an explanation—ultimately by an “explanatory definition”—accounting for the attributes that form the basis of [End Page 487] class membership. Or more succinctly: the class definition presents a problem that the explanatory definition solves. Further, although the discussion in PA I is meant to be a reform of the simpler but unworkable method of arriving at the genus-differentia formula based upon, “division,” I intend to argue that an important ancillary benefit of the reformed method is that it is capable of articulating scientific problems in a much clearer way than division can. In fact, it seems very well suited to the task of presenting problems and hence to the task of searching for explanatory definitions.2. scientific problemsIn APo II. 14, Aristotle begins to outline the proper procedure for formulating scientific problems. We are told that “in order to obtain problems, we must pick out the sections 4 and divisions” of the subject we are investigating, about which we are formulating a problem (98a1–3). That is, we must learn to pick out each genus in the hierarchy of genera the subject belongs to by learning to identify the attributes associated with each of these genera. This will enable us to account for each attribute we find in the subject under investigation in terms of the genus the attribute is primarily associated with. As Aristotle explains: “Let A stand for animal, B for [an attribute] of every animal, and C, D, and E some particular animal [species]; it is clear why B belongs to D—because of A” (98a9–11).This, in a sense, shows one way a scientific problem—Why does attribute B belong to D?—can be “solved”: by finding the right “division” of D that accounts for its having B. But what is important to note here is that, in fact, our investigation only begins with this process of finding the right genus. This is simply how we “obtain” the problem, strictly speaking, not the means for ultimately solving it. Indeed the problem of accounting for why an attribute belongs to a given subject is not even completely formulated until we are able to determine the proper “division,” or genus, the attribute universally belongs to. Then we can ask the more fundamental question of why the attribute belongs to this genus, i.e., why B belongs to genus A. Now this question can be analyzed further, in terms of the other attributes of the genus. Any genus (or infima species) is, in effect, designated by a regular concomitance of the many attributes that identify it—i.e., attributes that universally co-occur in it. So the scientific problem we are formulating, regarding why a certain attribute belongs to a certain subject, ultimately should be reformulated in this way: Why does... (shrink)

Oulis pointed out that there is a great deal of interest in specific mechanisms relating to mental disorders and that these mechanisms should play a role in classification. Although specific mechanisms are important, more attention should be given to general theories. The following example from Salmon illustrates the difference.

This book is an essay on the epistemology of classifications. Its main purpose is not to provide an exposition of an actual mathematical theory of classifications, that is, a general theory which would be available to any kind of them: hierarchical or non-hierarchical, ordinary or fuzzy, overlapping or non-overlapping, finite or infinite, and so on, establishing a basis for all possible divisions of the real world. For the moment, such a theory remains nothing but a dream. Instead, (...) the authors essentially put forward a number of key questions. Their aim is rather to reveal the “state of art” of this dynamic field and the philosophy one may eventually adopt to go further. To this end they present some advances made in the course of the last century, discuss a few tricky problems that remain to be solved, and show the avenues open to those who no longer wish to stay on the wrong track. Researchers and professionals interested in the epistemology and philosophy of science, library science, logic and set theory, order theory or cluster analysis will find this book a comprehensive, original and progressive introduction to the main questions in this field. (shrink)

In this paper it is argued that qualitative theories (Q-theories) can be used to describe the statistical structure of cross classified populations and that the notion of verisimilitude provides an appropriate tool for measuring the statistical adequacy of Q-theories. First of all, a short outline of the post-Popperian approaches to verisimilitude and of the related verisimilitudinarian non-falsificationist methodologies (VNF-methodologies) is given. Secondly, the notion of Q-theory is explicated, and the qualitative verisimilitude of Q-theories is defined. Afterwards, appropriate measures for (...) the statistical verisimilitude of Q-theories are introduced, so to obtain a clear formulation of the intuitive idea that the statistical truth about cross classified populations can be approached by falsified Q-theories. Finally, it is argued that some basic intuitions underlying VNF-methodologies are shared by the so-called prediction logic, developed by the statisticians and social scientists David K. Hildebrand, James D. Laing and Howard Rosenthal. (shrink)

Newcomb-like problems are classified by the payoff table of their act-state pairs, and the causal structure that gives rise to the act-state correlation. Decision theories are classified by the one or more points of intervention whose causal role is taken to be relevant to rationality in various problems. Some decision theories suggest an inherent conflict between different notions of rationality that are all relevant. Some issues with causal modeling raise problems for decision theories in the contexts where Newcomb problems arise.

The volume presents phenomena of classification and categorisation in ancient and modern cultures and provides an overview of how cultural practices and cognitive systems interact when individuals or larger groups conceptually organize their world. Scientists of antiquity studies, anthropologists, linguists etc. will find methods to reconstruct early concepts of men and nature from a synchronic and diachronic comparative perspective.

Ontic structural realism constitutes a promising take on scientific realism, one that avoids the well‐known issues that realist stances have with underdetermination and theory change. In its most radical versions, ontic structural realism proposes a type of eliminativism about theoretical entities, ascribing ontological commitment only to the structures, and not to the objects appearing in our theories. More moderate versions of ontic structural realism have also been proposed, allowing for ‘thin’ objects in the ontology. This work connects these takes (...) on structural realism with the independent notion that there are two categorically different kinds of scientific theories, namely those that deal with interactions and those that deal with structural constraints – what are known as interaction and framework theories, respectively. By taking this classification seriously, one can arrive at a selective version of ontic structural realism which is better adapted to our scientific knowledge, in which eliminativist ontic structural realism constitutes a natural fit to framework theories, whereas the moderate version is connected to interaction theories. (shrink)

A theory is stable up to Δ if any Δ-type over a model has a few extensions up to complete types. We prove that a theory has no the independence property iff it is stable up to some Δ, where each equation image has no the independence property.

To assist in the evaluation process when determining architectures for new robots and intelligent systems equipped with artificial emotions, it is beneficial to understand the systems that have been built previously. Other surveys have classified these systems on the basis of their technological features. In this survey paper, we present a classification system based on a model similar to that used in psychology and philosophy for theories of emotion. This makes possible a connection to thousands of years of discourse (...) on the topic of emotion. Five theories of emotion are described based on an emotion theory model proposed by Power and Dalgleish. The paper provides classifications using a model of 10 new questions, for 14 major research projects that describe implementations or designs for systems that use artificial emotions for either robotics or general artificial intelligence. We also analyze the trends in the usage of various theories and complexity changes over time. (shrink)

Otto Neurath’s early work on the classification of systems of hypotheses in optics provided some of the key insights of Neurath’s later philosophy of science. The chapter investigates how Neurath developed his theory of theory-classification in response to inconsistencies he stumbled upon while studying the historical theories. Neurath’s empiricism and thoroughgoing fallibilism informed his mapping of the group of theories, locating “elementary notions” of theories and taking into account the “blurred margins” of theories. To replace false (...) dichotomies the project provided a finer-grained analysis of theories and could be utilized to locate unconceived alternatives of a domain. The first sections discuss the close links between Neurath’s optical essays, his notion of an “auxiliary motive,” and his attack on pseudorationalism in the “Lost Wanderers of Descartes” paper. The last sections provide a comparison of the two essays, with an extended table of the elementary notions Neurath listed, and discuss Neurath’s two-tier methodology for historical reconstruction. (shrink)

In this article, we explore the heuristic power of the theoretical distinction between framework and interaction theories applied to the case of General Relativity. According to the distinction, theories and theoretical elements can be classified into two different groups, each with clear ontological, epistemic and functional content. Being so, to identify the group to which a theory belongs would suffice to know a priori its prospects and limitations in these areas without going into a detailed technical analysis. We make (...) the exercise here with General Relativity, anticipate its ontological, epistemic and functional content and show afterwords that such expectations are justified in this case, being consistent with formal issues of General Relativity. With this, we attempt to make a case for the use of the distinction as a powerful tool for scientific and philosophical analysis. (shrink)

Using a classical life history model (the Smith & Fretwell model of the evolution of offspring size), it is demonstrated that even in the presence of overwhelming empirical support, the testability of predictions derived from evolutionary models can give no guarantee that the underlying fitness concept is sound. Non-awareness of this problem may cause considerable justified but avoidable criticism. To help understanding the variable use of fitness in evolutionary models and recognizing potentially problematic areas which need careful consideration, a hierarchical (...) classification of definitions of fitness used in evolutionary models is presented. As a conclusion, it is advocated to use the term fitness more conscientiously than currently often practised and to think more about ways to develop fitness-free evolutionary theories compatible with Darwin's ideas. (shrink)

Characterizing how activity in the central and autonomic nervous systems corresponds to distinct emotional states is one of the central goals of affective neuroscience. Despite the ease with which individuals label their own experiences, identifying specific autonomic and neural markers of emotions remains a challenge. Here we explore how multivariate pattern classification approaches offer an advantageous framework for identifying emotion-specific biomarkers and for testing predictions of theoretical models of emotion. Based on initial studies using multivariate pattern classification, we (...) suggest that central and autonomic nervous system activity can be reliably decoded into distinct emotional states. Finally, we consider future directions in applying pattern classification to understand the nature of emotion in the nervous system. (shrink)

We investigate a theory of Frege structures extended by the Myhill-Flagg hierarchy of implications. We study its relation to a property theory with an approximation operator and we give a proof theoretical analysis of the basic system involved. MSC: 03F35, 03D60.