The spiritus asper as used by Frege in a letter to Russell from 1904 bears resemblance to Church’s lambda. It is natural to ask how they relate to each other. An alternative approach to functional abstraction developed by Per Martin-Löf some thirty years ago allows us to describe the relationship precisely. Frege’s spiritus asper provides a way of restructuring a unary function name in Frege’s sense such that the argument place indicator occurs all the way to the right. (...) Martin-Löf’s alternative approach shows that this is only half of what lambda does. The other half is the deletion of the argument place indicator, resulting in what Frege would have called an isolated function name. (shrink)

We introduce a family of rank functions and related notions of total transcendence for Galois types in abstract elementary classes. We focus, in particular, on abstract elementary classes satisfying the condition known as tameness, where the connections between stability and total transcendence are most evident. As a byproduct, we obtain a partial upward stability transfer result for tame abstract elementary classes stable in a cardinal $\lambda$ satisfying $\lambda^{\aleph_{0}}\gt \lambda$, a substantial generalization of a result of Baldwin, Kueker, and VanDieren.

In this article, I articulate and defend an account of corporations motivated by John Searle’s discussion of them in his Making the Social World. According to this account, corporations are abstract entities that are the products of status function Declarations. They are also connected with, though not reducible to, various people and certain of the power relations among them. Moreover, these connections are responsible for corporations having features that stereotypical abstract entities lack (e.g., the abilities to take actions and make (...) profits). (shrink)

In this note some epistemological problems in general theories about living systems are considered; in particular, the question of hidden connections between different areas of experience, such as folk biology and scientific biology, and hidden connections between central concepts of theoretical biology, such as function, semiosis, closure and life.

This paper presents and discusses Simon Evnine’s hylomorphic account of fictional characters and proposes some amendments to it with the aim of explaining the functioning of fictional characters. The paper does so by relying on a case study, viz. Edgar Allan Poe’s short story Berenice. The amended hylomorphic account of fictional characters will also be capable of explaining the malfunctioning of fictional characters.

The paper begins by considering Russell's criticism of Meinong's theory of objects and Sosein that center on the notions of negation and existence. The discussion raises issues about functions, properties, predication, the "concept" of existence and relations. These lead to a consideration of recent revivals of moderate nominalism in the form of trope theories. An argument against such theories suggests a fundamental principle of ontology and a reformulation of the nominalism-realism dispute.

The paper begins by considering Russell's criticism of Meinong's theory of objects and Sosein that center on the notions of negation and existence. The discussion raises issues about functions, properties, predication, the "concept" of existence and relations. These lead to a consideration of recent revivals of moderate nominalism in the form of trope theories. An argument against such theories suggests a fundamental principle of ontology and a reformulation of the nominalism-realism dispute.

ZusammenfassungEs werden zwei Begriffe, «Prozess» und «Funktion», besprochen, welche in der heutigen Philosophie zu Grundbegriffen zweier, miteinander unvereinbarer philosophischer Systeme geworden sind, die sich beide auf die Wissenschaft stützen. In dieser hingegen werden die beiden genannten Begriffe nicht als einander ausschliessend angesehen, sondern funktionieren als Leitbegriffe zweier nebeneinder stehenden Hypothesen, welche zu verschiedenen Methoden der Forschung führen. Im ersten Teil des vorliegenden Aufsatzes wird der Begriff «Prozess» im Hinblick auf die gegenwärtige Physik untersucht und vier Grundstellungen unterschieden, die sich in (...) der Relativitätstheorie Whiteheads, in der Einsteinschen einheitlichen Feldtheorie, in der mit dieser unvereinbaren Auffassung der führenden Quantenphysiker und dem Bridgmanschen Operationismus ausprägen. Im zweiten Teil wird der Begriff «Funktion» im Hinblick auf die heutige Biologie erörtert. Die beiden oben erwähnten philosophischen Systeme zeigen aber, dass philosophisch Funktionen als Prozesse und umgekehrt Prozesse als Funktionen aufgefasst werden können. Andererseits beeinflusst jeder Begriff von «Prozess», der in der Physik entwickelt wird, die Biologie und jeder Begriff von «Funktion», der in der Biologie auftritt, hat Bedeutung für die Physik. Im Grunde genommen, sind die beiden genannten Begriffe die Grenzpunkte des Weges, den die Entwicklung der, aus der antiken Philosophie stammenden Begriffe «Sein» und «Substanz» genommen hat. Beide haben ihre berechtigte methodische Verwendung in der Wissenschaft. Vielleicht könnte die Philosophie, deren Grundfragen in den Wissenschaften eine fundamentale Rolle spielen, aus diesem Vorgehen der Wissenschaften lernen, ihre Begriffe genauer zu präzisieren, indem sie, statt ihre Thesen zu verabsolutieren, diese als Forschungshypothesen auffasst, deren Folgen zu untersuchen sind. Auch könnte man auf diese Weise dazu kommen, die philosophischen Thesen nicht als absolute, ausschliessende Gegensätze, sondern als «komplementär» aufzufassen und diese «komplementären» Gesichtspunkte für die wissenschaftliche Forschung auszuwerten. (shrink)

We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C ⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, (...) this situation leaves one no choice but to restrict the use of a certain class of implicational rules including modus ponens. (shrink)

As a result of these restrictions, an implementation of L [subscript lambda] does not need to implement full higher-order unification. Instead, an extension to first-order unification that respects bound variable names and scopes is all that is required. Such unification problems are shown to be decidable and to possess most general unifiers when unifiers exist. A unification algorithm and logic programming interpreter are described and proved correct. Several examples of using L[subscript lambda] as a meta-programming language are presented.

The functionalist approach to kinds has suffered recently due to its association with law-based approaches to induction and explanation. Philosophers of science increasingly view nomological approaches as inappropriate for the special sciences like psychology and biology, which has led to a surge of interest in approaches to natural kinds that are more obviously compatible with mechanistic and model-based methods, especially homeostatic property cluster theory. But can the functionalist approach to kinds be weaned off its dependency on laws? Dan Weiskopf has (...) recently offered a reboot of the functionalist program by replacing its nomological commitments with a model-based approach more closely derived from practice in psychology. Roughly, Weiskopf holds that the natural kinds of psychology will be the functional properties that feature in many empirically successful cognitive models, and that those properties need not be localized to parts of an underlying mechanism. I here skeptically examine the three modeling practices that Weiskopf thinks introduce such non-localizable properties: fictionalization, reification, and functional abstraction. In each case, I argue that recognizing functional properties introduced by these practices as autonomous kinds comes at clear cost to those explanations’ counterfactual explanatory power. At each step, a tempting functionalist response is parochialism: to hold that the false or omitted counterfactuals fall outside the modeler’s explanatory aims, and so should not be counted against functional kinds. I conclude by noting the dangers this attitude poses to scientific disagreement, inviting functionalists to better articulate how the individuation conditions for functional kinds might outstrip the perspective of a single modeler. (shrink)

In recent years, language has been shown to play a number of important cognitive roles over and above the communication of thoughts. One hypothesis gaining support is that language facilitates thought about abstract categories, such as democracy or prediction. To test this proposal, a novel set of semantic memory task trials, designed for assessing abstract thought non-linguistically, were normed for levels of abstractness. The trials were rated as more or less abstract to the degree that answering them required the participant (...) to abstract away from both perceptual features and common setting associations corresponding to the target image. The normed materials were then used with a population of people with aphasia to assess the relationship of abstract thought to language. While the language-impaired group with aphasia showed lower overall accuracy and longer response times than controls in general, of special note is that their response times were significantly longer as a function of a trial’s degree of abstractness. Further, the aphasia group’s response times in reporting their degree of confidence (a separate, metacognitive measure) were negatively correlated with their language production abilities, with lower language scores predicting longer metacognitive response times. These results provide some support for the hypothesis that language is an important aid to abstract thought and to metacognition about abstract thought. (shrink)

Recent scholarship emphasizes the scaffolding role of language for cognition. Language, it is claimed, is a cognition-enhancing niche (Clark, 2006), a programming tool for cognition (Lupyan and Bergen, 2016), even a neuroenhancement (Dove, 2019), and augments cognitive functions such as memory, categorization, cognitive control as well as meta-cognitive abilities (‘thinking about thinking’). Yet the notion that language enhances or augments cognition does not fit in with embodied approaches to language processing, or so we will argue. Accounts aiming to explain how (...) language enhances various cognitive functions often employ a notion of abstract representation. Yet embodied approaches to language processing have it that language processing crucially, according to some accounts even exclusively, involves embodied, modality-specific, i.e. non-abstract representations. In coming to understand a particular phrase or sentence, a prior experience has to be simulated or reenacted. The representation thus activated is embodied (modality-specific) as sensorimotor regions of the brain are thereby recruited. In the paper, we will first discuss the notion of representation, clarify what it takes for a representation to be embodied or abstract respectively, and distinguish between conceptual and (other) linguistic representations. We will then put forward a characterization of cognitive control and examine its representational infrastructure. The remainder of the paper will be devoted to arguing that language augments cognitive control. To that end, we will draw on two lines of research, which investigate how language augments cognitive control: i. research on the availability of linguistic labels, and ii. research on the active usage of a linguistic code, specifically in inner speech. Eventually, we will argue that the cognition-enhancing capacity of language can be explained once we assume that it provides us with a. abstract, non-embodied representations, and with b. abstract, sparse linguistic representations that may serve as easy-to-manipulate placeholders for fully embodied or otherwise more detailed representations. (shrink)

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

I defend the view that many biological categories are defined by homology against a series of arguments designed to show that all biological categories are defined, at least in part, by selected function. I show that categories of homology are `abnormality inclusive'—something often alleged to be unique to selected function categories. I show that classifications by selected function are logically dependent on classifications by homology, but not vice-versa. Finally, I reject the view that biologists must use considerations of selected function (...) to abstract away from variation and pathology to form a canonical description of a class of biological systems. (shrink)

I examine a major objection to the mechanistic view of concrete computation, stemming from an apparent tension between the abstract nature of computational explanation and the tenets of the mechanistic framework: while computational explanation is medium-independent, the mechanistic framework insists on the importance of providing some degree of structural detail about the systems target of the explanation. I show that a common reply to the objection, i.e. that mechanistic explanation of computational systems involves only weak structural constraints, is not enough (...) to save the standard mechanistic view of computation—it trivialises the appeal to mechanism, and thus makes the account collapse into a purely functional view. I claim, however, that the objection can be put to rest once the account is appropriately amended: computational individuation is indeed functional, while mechanistic explanation plays a role in accounting for computational implementation. Since individuation and implementation are crucial elements in a satisfying account of computation in physical systems, mechanism keeps its central importance in the theory of concrete computation. Finally, I argue that my version of the mechanistic view helps to provide a convincing reply to a powerful objection against non-semantic theories of concrete computation: the argument from the multiplicity of computations. (shrink)

. What is a logic? Which properties are preserved by maps between logics? What is the right notion for equivalence of logics? In order to give satisfactory answers we generalize and further develop the topological approach of [4] and present the foundations of a general theory of abstract logics which is based on the abstract concept of a theory. Each abstract logic determines a topology on the set of theories. We develop a theory of logic maps and show in what (...) way they induce (continuous, open) functions on the corresponding topological spaces. We also establish connections to well-known notions such as translations of logics and the satisfaction axiom of institutions [5]. Logic homomorphisms are maps that behave in some sense like continuous functions and preserve more topological structure than logic maps in general. We introduce the notion of a logic isomorphism as a (not necessarily bijective) function on the sets of formulas that induces a homeomorphism between the respective topological spaces and gives rise to an equivalence relation on abstract logics. Therefore, we propose logic isomorphisms as an adequate and precise notion for equivalence of logics. Finally, we compare this concept with another recent proposal presented in [2]. (shrink)

We reply to Artiga and Martinez’s claim according to which the organizational account of cross-generation functions implies a backward looking interpretation of etiology, just as standard etiological theories of function do. We argue that Artiga and Martinez’s claim stems from a fundamental misunderstanding about the notion of “closure”, on which the organizational account relies. In particular, they incorrectly assume that the system, which is relevant for ascribing cross-generation organizational function, is the lineage. In contrast, we recall that organizational closure refers (...) to a relational description of a network of mutual dependencies, abstracted from time, in which production relations are irrelevant. From an organizational perspective, ascribing a function to an entity means locating it in the abstract system that realizes closure. In particular, the position of each entity within the relational system conveys an etiological explanation of its existence, because of its dependence on the effects exerted by other entities subject to closure. Because of the abstract relational nature of closure, we maintain that the organizational account of functions does not endorse a backward looking interpretation of etiology. As a consequence, it does not fall prey of epiphenomenalism. (shrink)

Reification is to abstraction as disease is to health. Whereas abstraction is singling out, symbolizing, and systematizing, reification is neglecting abstractive context, especially functional, historical, and analytical-level context. William James and John Dewey provide similar and nuanced arguments regarding the perils and promises of abstraction. They share an abstraction-reification account. The stages of abstraction and the concepts of “vicious abstractionism,” “/the/ psychologist’s fallacy,” and “the philosophic fallacy” in the works of these pragmatists are here (...) analyzed in detail. For instance, in 1896 Dewey exposes various fallacies associated with reifying dualistic reflex arc theory. The conclusion prescribes treatments (pluralism and assumption archaeology) for de-reifying ill models (i.e., universalized, narrowed, and ontologized models) in contemporary scientific fields such as cognitive science and biology. (shrink)

In the following I take issue with the allegation that liberalism must inevitably be guilty of ‘abstract individualism’. I treat Michael Sandel’s well-known claim that there are ‘loyalties and convictions whose moral force consists partly in the fact that living by them is inseparable from understanding ourselves as the particular persons we are’ as representative of this widely held view. Specifically, I argue: (i) that Sandel’s account of the manner in which ‘constitutive’ loyalties function as reasons for action presupposes the (...) possibility of there being (what I call) ‘underivable particular obligations’, but that such obligations are, in fact, a logical impossibility; and (ii) that Sandel’s account of the self as necessarily ‘encumbered’ presupposes an account of personal identity which confuses identification with definition, and which is, therefore, fundamentally flawed. (shrink)

This volume explores the roles and uses of abstraction in scientific and artistic practice. Conceived as an interdisciplinary dialogue between experts across histories and philosophies of art and science, this collection of essays draws on the shared premise that abstraction is a rich and generative process, not reducible to the mere omission of details in a representation. When scientists attempt to make sense of complex natural phenomena, they often produce highly abstract models of them. In the history and (...) philosophy of art, there is a long tradition of debate on the function of abstraction, and - more recently - its relation with theories of depiction. Adopting a process-oriented perspective, the chapters in this volume explore the epistemic potential of a diversity of practices of abstracting. The systematic analysis of a wide range of historical cases, from early twentieth-century abstractionist painting to contemporary abstract photography, and from nineteenth-century physics to recent research in biology and neurosciences, invites the reader to reflect on the material lives of abstraction through concrete artefacts, experimental practices and theoretical and aesthetic achievements. Abstraction in Science and Art: Philosophical Perspectives will be of interest to scholars and advanced students working in aesthetics, philosophy of science, and epistemology, as well as to historians of science and art, and to practicing artists and scientists interested in exploring foundational questions at the heart of the creative practice of abstracting. (shrink)

Evolutionary psychology tends to be associated with a massively modular cognitive architecture. On this framework of human cognition, an assembly of specialized information processors called modules developed under selection pressures encountered throughout the phylogenic history of hominids. The coordinated activity of domain-specific modules carries out all the processes of belief fixation, abstract reasoning, and other facets of central cognition. Against the massive modularity thesis, I defend an account of systemic functional adaptedness, according to which non-modular systems emerged because of (...) adaptive problems imposed by the intrinsic physiology of the evolving human brain. The proposed reformulation of evolutionary theorizing draws from neural network models and Cummins’ (1975) account of systemic functions to identify selection pressures that gave rise to non-modular, domain-general mechanisms in cognitive architecture. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 9.3 (2002) 237-241 [Access article in PDF] Practical, Functional, and Natural Kinds Nick Haslam Keywords: Classification, essentialism, natural kinds, practical kinds. I am grateful to the two commentators for giving my paper their serious attention, and for writing such stimulating, clarifying, and challenging responses. In a brief response I can only begin to discuss a select few issues, although both commentaries could generate a (...) great deal of profitable exchange.Zachar's commentary elaborates his practical kinds model, discusses several of the graded series of kinds proposed in my taxonomy of psychiatric categories, and disputes some aspects of my treatment of natural kinds. Zachar and I have no quarrel on his first point. I recognize his practical kinds model as a general theory of psychiatric classification rather than simply as a description of one type of category, the "practical kind." It was perhaps bad form to pilfer a term from Zachar's model and give it a more circumscribed role in my own, although by doing so I intended both to acknowledge the importance of the concept and to situate it among some of its alternatives.All the same, I stand by the account of practical kinds developed in my paper, even if it reflects a narrower sense than Zachar's. In my sense, practical kinds are pragmatically drawn distinctions imposed on continuous dimensions, whereas to Zachar all psychiatric categories are at least to some degree practical. He therefore proposes a broad "continuum" of practical kinds. The difficulty that I have with this proposal is that such a continuum implies a fundamental unity among psychiatric categories: categories are all to be understood first and foremost in pragmatic terms and differences in kind between them in internal structure are to be neglected. In my view, although the pragmatic bases of psychiatric classification are vitally important, and perhaps inadequately formulated in my paper, the neglect of internal structure and of possible breaks in the continuum of kinds are real limitations of the practical kinds model. Although Zachar is partially justified in claiming that his view is pluralistic, allowing as it does for variability in degrees of practicality, by failing to acknowledge distinctly different kinds of categories in the psychiatric domain, his view is less pluralistic than I believe it should be.One example of what I take to be this neglect of structural differences is a conflation of two sorts of practicality in Zachar's work. On the one hand, certain categories such as hypertension or obesity are defined on pragmatic grounds, a binary distinction being drawn in the absence of an internal discontinuity, because individuals identified as category members are adjudged to [End Page 237] be at significantly elevated risk. On the other hand, some categories just happen to have high practical utility. Zachar argues that schizotaxia, for example, is practical because it affords a variety of scientific and clinical inferences.It seems to me that these sorts of practicality—or perhaps these sorts of relations to practicality—are importantly different. Hypertension is defined as a category because of its practical utility—because a certain blood pressure threshold marks an inflection in actuarial risk of other illnesses—and might therefore be said to have "front-end" or constitutive practicality. Schizotaxia, which taxometric research shows to be a discrete kind (Haslam, 2003), is not defined and identified primarily on the basis of its relation to an external criterion, but on the basis of its internal structure. Its features cohere in a way that indicates a category with a determinate prevalence. It has "back-end" or consequential practicality to the degree that this category enables useful predictions. These two proposed forms of practicality are equally important: both mean that categories will be pragmatically valuable. However, they are also different, being characteristic of different kinds of categories and perhaps even negatively related. Kinds with front-end practicality, that is, may tend to have a more restricted range of practical implications, defined as they are in relation to specific external criteria. Kinds with back-end practicality, in contrast, may enable a wider array of predictions to the extent that... (shrink)

Deep learning developers typically rely on deep learning software frameworks (DLSFs)—simply described as pre-packaged libraries of programming components that provide high-level access to deep learning functionality. New DLSFs progressively encapsulate mathematical, statistical and computational complexity. Such higher levels of abstraction subsequently make it easier for deep learning methodology to spread through mimesis (i.e., imitation of models perceived as successful). In this study, we quantify this increase in abstraction and discuss its implications. Analyzing publicly available code from Github, we (...) found that the introduction of DLSFs correlates both with significant increases in the number of deep learning projects and substantial reductions in the number of lines of code used. We subsequently discuss and argue the importance of abstraction in deep learning with respect to ephemeralization, technological advancement, democratization, adopting timely levels of abstraction, the emergence of mimetic deadlocks, issues related to the use of black box methods including privacy and fairness, and the concentration of technological power. Finally, we also discuss abstraction as a symptom of an ongoing technological metatransition. (shrink)

Overlaps in form and meaning between morphologically related words have led to ambiguities in interpreting priming effects in studies of lexical organization. In Semitic languages like Arabic, however, linguistic analysis proposes that one of the three component morphemes of a surface word is the CV-Skeleton, an abstract prosodic unit coding the phonological shape of the surface word and its primary syntactic function, which has no surface phonetic content (McCarthy, J. J. (1981). A prosodic theory of non-concatenative morphology, Linguistic Inquiry, 12 (...) 373-418). The other two morphemes are proposed to be the vocalic melody, which conveys additional syntactic information, and the root, which defines meaning. In three experiments using masked, cross-modal, and auditory-auditory priming we examined the role of the vocalic melody and the CV-Skeleton as potential morphemic units in the processing and representation of Arabic words. Prime/target pairs sharing the vocalic melody but not the CV-Skeleton consistently failed to prime. In contrast, word pairs sharing only the CV-Skeleton primed reliably throughout, with the amount of priming being as large as that observed between word pattern pairs sharing both vocalic melody and CV-Skeleton. Priming between morphologically related words can be observed when there is no overlap either in meaning or in surface phonetic form. (shrink)

Awareness is a two-place determinable relation some determinates of which are seeing, hearing, etc. Abstract objects are items such as universals and functions, which contrast with concrete objects such as solids and liquids. It is uncontroversial that we are sometimes aware of concrete objects. In this paper I explore the more controversial topic of awareness of abstract objects. I distinguish two questions. First, the Existence Question: are there any experiences that make their subjects aware of abstract objects? Second, the Grounding (...) Question: if an experience makes its subject aware of an abstract object, in virtue of what does it do so? I defend the view that intuitions, specifically mathematical intuitions, sometimes make their subjects aware of abstract objects. In defending this view, I develop an account of the ground of intuitive awareness. (shrink)

λ-calculi are of interest to logicians and computer scientists but have largely escaped philosophical commentary, perhaps because they appear narrowly technical or uncontroversial or both. I argue that even within logic λ-expressions need to be understood correctly, as functors signifying functions in intension within a categorical or typed language. λ-expressions are not names but pure viable binders generating functors, and as such they are of use in giving explicit definitions. But λ is applicable outside logic and computer science, anywhere where (...) the notions of complex whole, substitution, abstraction and structure make sense. To illustrate this, two domains are considered. One is somewhat frivolous: the study of flags; the other is very serious: manufacturing engineering. In each case we can employ λ-abstraction to describe substitutions within a structure, and in the latter case there is even a practical need for such a notation. (shrink)

In addition to their core explanatory and predictive assumptions, scientific models include simplifying assumptions, which function as idealizations, approximations, and abstractions. There are methods to investigate whether simplifying assumptions bias the results of models, such as robustness analyses. However, the equally important issue – the focus of this paper – has received less attention, namely, what are the methodological and epistemic strengths and limitations associated with different simplifying assumptions. I concentrate on one type of simplifying assumption, the use of mega (...) parameters as abstractions in ecological models. First, I argue that there are two kinds of mega parameters qua abstractions, sufficient parameters and aggregative parameters, which have gone unnoticed in the literature. The two are associated with different heuristics, holism and reductionism, which many view as incompatible. Second, I will provide a different analysis of abstractions and the associated heuristics than previous authors. Reductionism and holism and the accompanying abstractions have different methodological and epistemic functions, strengths, and limitations, and the heuristics should be viewed as providing complementary research perspectives of cognitively limited beings. This is then, third, used as a premise to argue for epistemic and methodological pluralism in theoretical ecology. Finally, the presented taxonomy of abstractions is used to comment on the current debate whether mechanistic accounts of explanation are compatible with the use of abstractions. This debate has suffered from an abstract discussion of abstractions. With a better taxonomy of abstractions the debate can be resolved. (shrink)

Recently, Caleiro, Gon¸calves and Martins introduced the notion of behaviorally algebraizable logic. The main idea behind their work is to replace, in the traditional theory of algebraizability of Blok and Pigozzi, unsorted equational logic with multi-sorted behavioral logic. The new notion accommodates logics over many-sorted languages and with non-truth-functional connectives. Moreover, it treats logics that are not algebraizable in the traditional sense while, at the same time, shedding new light to the equivalent algebraic semantics of logics that are algebraizable (...) according to the original theory. In this paper, the notion of an abstract multi-sorted π-institution is introduced so as to transfer elements of the theory of behavioral algebraizability to the categorical setting. Institutions formalize a wider variety of logics than deductive systems, including logics involving multiple signatures and quantifiers. The framework developed has the same relation to behavioral algebraizability as the classical categorical abstract algebraic logic framework has to the original theory of algebraizability of Blok and Pigozzi. (shrink)

Hailed by the Bulletin of the American Mathematical Society as "easy to use and a pleasure to read," this research monograph is recommended for students and professionals interested in model theory and definability theory. The sole prerequisite is a familiarity with the basics of logic, model theory, and set theory. 1974 edition.

In lieu of an abstract, here is a brief excerpt of the content:Changing Functions, Moral Responsibility, and Mental IllnessCraig Edwards (bio)Keywordsmental illness, responsibility, character, dysfunction, personhoodI thank both Wakefield and Tomasini for their illuminating comments. Both commentaries are thought provoking and warrant a full response. However, as always, space is limited and I must make the all-too-predictable apology for not addressing both commentaries in full. Wakefield's contribution more directly engages with, and challenges, my claims, and so I focus on addressing (...) his concerns.ClarificationsWakefield correctly notes that I am interested in how mental illness (and illness generally) operates to remove moral responsibility for one's actions. Despite this, it seems at several points that he and I are talking about two different, albeit related, concepts of mental illness. 'Mental illness' is used to both explain and excuse certain behaviors, but these two functions, explanatory and exculpable, do not always operate simultaneously. As we discover biological explanations for apparently immoral behaviors, the question arises as to whether the explanation should remove the immorality and liability for punishment. The 'sick role' can be divided into two aspects. One is the role of deserving and warranting medical treatment. The other is the negation of moral responsibility. Wakefield's own example, pedophilia, involves the first sense of the sick role but not the second. Wakefield's use of this example is unusual, because it deftly highlights the limitation of his HD account. Pedophilia is a mental disorder in the sense of warranting treatment, and is a mental illness under Wakefield's model, but it is not something that negates moral responsibility. There is a sense of the term 'mental illness'—an important and, as I argue, an objective sense—that is relevant to establishing one's moral responsibility for such behaviors.In addressing my account of mental illness as though it contained two distinct answers, 'mental illness as dysfunction of rational agency, or 'mental illness as moral judgment,' it is unclear whether Wakefield takes them to be conjunctive or alternative. Hence it is worth reiterating in point form the structure of my account:1. Illness involves dysfunction;2. The 'proper function' of a bodily or psychological mechanism is determined by the purpose that we impose upon that mechanism (within the constraints of our biological needs);3. Dysfunction of rational agency is necessary, but not sufficient, for 'mental illness' in the normative sense relevant to negating moral responsibility; and [End Page 105]4. The distinction between 'mental illness' (in the above sense) and the many dysfunctions of rational agency for which we are morally responsible, turns upon (objective) normative facts rather than features internal to the dysfunctions themselves.Functions and ValueWakefield misses the point when he criticizes my comment that, although bodily mechanisms are fairly uniformly valued, there is substantial historical and cross-cultural variation in the way people value personhood. He notes—accurately, but irrelevantly—that people almost always place great value on their capacity for rational agency, probably more so than many aspects of their physical health. My comment, taken in context, has nothing to do with how much people value personhood, but has everything to do with what kinds of purposes people want their mental and physical processes to achieve. A heart has the same function for a Londoner today as it did for a Japanese peasant a thousand years ago, and although it is possible for us to want it to achieve other purposes, any culture that seriously imputes a different set of vital functions on the heart is likely to be rather disappointed. By contrast, our species has experienced vast changes in the demands we make of our rational and intellectual capacities—dysfunctions like dyslexia and alcoholism were irrelevant before the availability of written communication and alcohol.Wakefield's HD account is unable to deal with the relevance of such change. The link between evolutionary function and illness is tenuous in any event. Evolutionary explanations of specific mechanisms are often untestable, simply positing some evolutionary purpose that happens to fit our understanding of what the mechanism does. If we were to discover that alcoholism evolved as a means of increasing birthrates, or (perhaps more plausibly) that anxiety disorders occur among those for whom... (shrink)

The costs of and returns from actions are varied and individually concrete dimensions, combined in heterogeneous ways. The many needs of the body also fluctuate. Making action selection efficiently track some ultimate goal, whether fitness or another utility function, itself requires representational abstraction. Therefore, predictive brains need abstract value representations.

We devise imperative programming languages for verified real number computation where real numbers are provided as abstract data types such that the users of the languages can express real number computation by considering real numbers as abstract mathematical entities. Unlike other common approaches toward real number computation, based on an algebraic model that lacks implementability or transcendental computation, or finite-precision approximation such as using double precision computation that lacks a formal foundation, our languages are devised based on computable analysis, a (...) foundation of rigorous computation over continuous data. Consequently, the users of the language can easily program real number computation and reason about the behaviours of their programs, relying on their mathematical knowledge of real numbers without worrying about artificial roundoff errors. As the languages are imperative, we adopt precondition–postcondition-style program specification and Hoare-style program verification methodologies. Consequently, the users of the language can easily program a computation over real numbers, specify the expected behaviour of the program, including termination, and prove the correctness of the specification. Furthermore, we suggest extending the languages with other interesting continuous data, such as matrices, continuous real functions, et cetera.Abstract taken directly from the thesis.E-mail: [email protected]: https://sewonpark.com/thesis. (shrink)

In finite type arithmetic, the real numbers are represented by rapidly converging Cauchy sequences of rational numbers. Ulrich Kohlenbach introduced abstract types for certain structures such as metric spaces, normed spaces, Hilbert spaces, etc. With these types, the elements of the spaces are given directly, not through the mediation of a representation. However, these abstract spaces presuppose the real numbers. In this paper, we show how to set up an abstract type for the real numbers. The appropriateness of our construction (...) works in tandem with the bounded functional interpretation. (shrink)

A distinction between different notions of “structure” and “function” is suggested for interpreting the overwhelming amount of data on microbiome structure and function. Sequence data, biochemical agents, interaction networks, taxonomic communities, and their dynamics can be linked to potential or actual biochemical activities, causal roles, and selected effects, respectively. This conceptual clarification has important methodological consequences for how to interpret existing data and approach open questions in contemporary microbiome research practice. In particular, the field will have to start thinking about (...) notions of function more directly. Also see the video abstract here https://youtu.be/j5pq5uGld1k. (shrink)