ZusammenfassungIm Zuge des „empirical turn“ der Medizin- und Bioethik ist von verschiedenen Autoren in den vergangenen Jahren die Idee einer „evidenzbasierten Ethik“ diskutiert worden. Die Analogie zwischen evidenzbasierter Medizin und „evidenzbasierter Ethik“ soll in diesem Beitrag kritisch diskutiert und dabei gezeigt werden, dass der Ausdruck „evidenzbasierte Ethik“ irreführend ist. Zentraler Ausgangspunkt der Kritik ist die unterschiedliche Bedeutung, die empirische Informationen für das medizinisch-klinische Urteil zum einen und das ethische Urteil in der Medizin zum anderen haben. Im medizinisch-klinischen Urteil können mit (...) Hilfe empirischer Informationen hypothetische Handlungsnormen generiert werden, welche auf den der Medizin inhärenten Zwecksetzungen basieren. Bei Fragen der Ethik in der Medizin hingegen sind die Handlungsziele selbst Gegenstand des Urteils; diese aber können allein aus empirischem Wissen heraus nicht zureichend bestimmt werden. Die Diskussion um die Möglichkeit einer „evidenzbasierten Ethik“ eröffnet weiterhin aufschlussreiche Perspektiven in Bezug auf empirische Forschung und den Umgang mit empirischen Informationen in der Angewandten Ethik und das Aufgabenfeld der Medizinethik. (shrink)

Due to Gӧdel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments –Warren (2020), Murzi and Topey (2021)– for the idea that the natural deduction rules (...) for the first-order universal quantifier are categorical, i.e., they uniquely determine its semantic intended meaning. Both of them make use of McGee’s open-endedness requirement and the second one uses in addition Garson’s (2013) local models for defining the validity of these rules. I argue that the success of both these arguments is relative to their semantic or infinitary assumptions, which could be easily discharged if the introduction rule for the universal quantifier is taken to be an infinitary rule, i.e. non-compact. Consequently, I reconsider the use of the ω-rule and I show that the addition of the ω-rule to the standard formalizations of first-order logic is categorical. In addition, I argue that the open-endedness requirement does not make the first-order Peano Arithmetic categorical and I advance an argument for its categoricity based on the inferential conservativity requirement. (shrink)

A syntactic machinery is developed for π-institutions based on the notion of a category of natural transformations on their sentence functors. Rules of inference, similar to the ones traditionally used in the sentential logic framework to define the best known sentential logics, are, then, introduced for π-institutions. A π-institution is said to be rule-based if its closure system is induced by a collection of rules of inference. A logical matrix-like semantics is introduced for rule-based π-institutions and a version of Bloom's (...) Lemma and Bloom's Theorem are proved for rule-based π-institutions. (shrink)

Adopting a different method from the previous scholars, this article deduces the remaining 23 valid syllogisms just taking the syllogism AEE-4 as the basic axiom. The basic idea of this study is as follows: firstly, make full use of the trichotomy structure of categorical propositions to formalize categorical syllogisms. Then, taking advantage of the deductive rules in classical propositional logic and the basic facts in the generalized quantifier theory, we deduce the remaining 23 valid categorical syllogisms by (...) taking just one syllogism (that is, AEE-4) as the basic axiom. This article not only reveals the reducible relations between the syllogism AEE-4 and the other 23 valid syllogisms, but also establishes a concise formal axiomatic system for categorical syllogistic logic. We hope that the results and methods will provide a good mathematical paradigm for studying other kinds of syllogistic logics, and that the project will appeal to specialists in logic, linguistic semantics, computational semantics, cognitive science and artificial intelligence. (shrink)

Categorical Monism (that is, the view that all fundamental natural properties are purely categorical) has recently been challenged by a number of philosophers. In this paper, I examine a challenge which can be based on Gabriele Contessa’s [10] defence of the view that only powers can confer dispositions. In his paper Contessa argues against what he calls the Nomic Theory of Disposition Conferral (NTDC). According to NTDC, in each world in which they exist, (categorical) properties confer specific (...) dispositions on their bearers; yet, which disposition a (categorical) property confers on its bearers depends on what the (contingent) laws of nature happen to be. Contessa, inter alia, rests his case on an intuitive analogy between cases of mimicking (in which objects do not actually possess the dispositions associated with their displayed behaviour) and cases of disposition conferral through the action of laws. In this paper, I criticize various aspects of Contessa’s argumentation and show that the conclusion he arrives at (that is, only powers can confer dispositions) is controversial. (shrink)

Categorical perception (CP) refers to how similar things look different depending on whether they are classified as the same category. Many studies demonstrate that adult humans show CP for human emotional faces. It is widely debated whether the effect can be accounted for solely by perceptual differences (structural differences among emotional faces) or whether additional perceiver-based conceptual knowledge is required. In this review, I discuss the phenomenon of CP and key studies showing CP for emotional faces. I then discuss (...) a new model of emotion which highlights how perceptual and conceptual knowledge interact to explain how people see discrete emotions in others’ faces. In doing so, I discuss how language (emotion words included in the paradigm) contribute to CP. (shrink)

An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl( $\emptyset$ )-definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU-rank.

This paper focuses on the categoricity of arithmetic and determinacy of arithmetical truth. Several ‘internal’ categoricity results have been discussed in the recent literature. Against the background of the philosophical position called internalism, we propose and investigate truth-theoretic versions of internal categoricity based on a primitive truth predicate. We argue for the compatibility of a primitive truth predicate with internalism and provide a novel argument for (and proof of) a truth-theoretic version of internal categoricity and internal determinacy with some positive (...) properties. (shrink)

Discussions about dispositional and categorical properties have become commonplace in metaphysics. Unfortunately, dispositionality and categoricity are disputed notions: usual characterizations are piecemeal and not widely applicable, thus threatening to make agreements and disagreements on the matter merely verbal—and also making it arduous to map a logical space of positions about dispositional and categorical properties in which all parties can comfortably fit. This paper offers a prescription for this important difficulty, or at least an inkling thereof. This will be (...) achieved by comparing pairs of positions and exploring their background metaphysics to discover where alleged agreements and disagreements concerning dispositionality and categoricity really lie; more specifically, the Pure Powers view and the Powerful Qualities view will be under scrutiny. Over this background, the prescription functions by isolating a successful identity-based characterization of categoricity, while abandoning the correspondent identity-based characterization of dispositionality. On the contrary, according to this prescription a property is dispositional if and only if it is solely in virtue of possessing that property that its bearer is assigned a certain dispositional profile. A crucial consequence of this prescription is that, while supporters of the Pure Powers view often characterize their position as an essentialist one, the dispositionality of properties needn’t always be a matter of essence. (shrink)

The results in this paper are in a context of abstract elementary classes identified by Shelah and Villaveces in which the amalgamation property is not assumed. The long-term goal is to solve Shelah’s Categoricity Conjecture in this context. Here we tackle a problem of Shelah and Villaveces by proving that in their context, the uniqueness of limit models follows from categoricity under the assumption that the subclass of amalgamation bases is closed under unions of bounded, -increasing chains.

ABSTRACTThe present study describes the development and validation of a facial expression database comprising five different horizontal face angles in dynamic and static presentations. The database includes twelve expression types portrayed by eight Japanese models. This database was inspired by the dimensional and categorical model of emotions: surprise, fear, sadness, anger with open mouth, anger with closed mouth, disgust with open mouth, disgust with closed mouth, excitement, happiness, relaxation, sleepiness, and neutral. The expressions were validated using emotion classification and (...) Affect Grid rating tasks [Russell, Weiss, & Mendelsohn, 1989. Affect Grid: A single-item scale of pleasure and arousal. Journal of Personality and Social Psychology, 57, 493–502]. The results indicate that most of the expressions were recognised as the intended emotions and could systematically represent affective valence and arousal. Furthermore, face angle and facial motion information influenced emot... (shrink)

Trust can be understood as a precondition for a well-functioning society or as a way to handle complexities of living in a risk society, but also as a fundamental aspect of human morality. Interactions on the Internet pose some new challenges to issues of trust, especially connected to disembodiedness. Mistrust may be an important obstacle to Internet use, which is problematic as the Internet becomes a significant arena for political, social and commercial activities necessary for full participation in a liberal (...) democracy. The Categorical Imperative lifts up trust as a fundamental component of human ethical virtues – first of all, because deception and coercion, the antitheses of trust, cannot be universalized. Mistrust is, according to Kant, a natural component of human nature, as we are social beings dependent on recognition by others but also prone to deceiving others. Only in true friendships can this tendency be overcome and give room for unconditional trust. Still we can argue that Kant must hold that trustworthy behaviour as well as trust in others is obligatory, as expressions of respect for humanity. The Kantian approach integrates political and ethical aspects of trust, showing that protecting the external activities of citizens is required in order to act morally. This means that security measures, combined with specific regulations are important preconditions for building online trust, providing an environment enabling people to act morally and for trust-based relationships. (shrink)

A classic result in the foundations of Yang-Mills theory, due to J. W. Barrett ["Holonomy and Path Structures in General Relativity and Yang-Mills Theory." Int. J. Th. Phys. 30, ], establishes that given a "generalized" holonomy map from the space of piece-wise smooth, closed curves based at some point of a manifold to a Lie group, there exists a principal bundle with that group as structure group and a principal connection on that bundle such that the holonomy map corresponds to (...) the holonomies of that connection. Barrett also provided one sense in which this "recovery theorem" yields a unique bundle, up to isomorphism. Here we show that something stronger is true: with an appropriate definition of isomorphism between generalized holonomy maps, there is an equivalence of categories between the category whose objects are generalized holonomy maps on a smooth, connected manifold and whose arrows are holonomy isomorphisms, and the category whose objects are principal connections on principal bundles over a smooth, connected manifold. This result clarifies, and somewhat improves upon, the sense of "unique recovery" in Barrett's theorems; it also makes precise a sense in which there is no loss of structure involved in moving from a principal bundle formulation of Yang-Mills theory to a holonomy, or "loop", formulation. (shrink)

This paper offers a conceptual clarification of the phenomenon commonly referred to as categorical perception of color, both in adults and in infants. First, I argue against the common notion of categorical perception as involving a distortion of the perceptual color space. The effects observed in the categorical perception research concern categorical discrimination performance and the underlying processing; they need not directly reflect the relations of color similarity and difference. Moreover, the methodology of the research actually (...) presupposes that the relations of similarity and difference do not vary with languages. The observed categorical perception effects should be conceived independently of the perceptual color space. Second, I challenge the usual opinion that the existing evidence on infant “categorical perception” allows us to conclude that infants perceptually categorize color, and in particular, that they have perceptual categories that resemble the basic color categories of English. Such conclusions rest on an unjustified interpretation of the infant “categorical perception” findings in terms of adult linguistic categorical boundaries. Based on the suggested new understanding, I propose that the phenomenon, as present in infants, should be conceived and examined as a possible explanatory factor with respect to the existing patterns of color naming in languages of the world. (shrink)

Categorization is fundamental for spatial and motion representation in both the domain of artificial intelligence and human cognition. In this paper, we investigated whether motion categorizations designed in artificial intelligence can inform human cognition. More concretely, we investigated if such categorizations (also known as qualitative representations) can inform the psychological understanding of human perception and memory of motion scenes. To this end, we took two motion categorizations in artificial intelligence, Motion‐RCC and Motion‐OPRA1, and conducted four experiments on human perception and (...) memory. Participants viewed simple motion scenes and judged the similarity of transformed scenes with this reference scene. Those transformed scenes differed in none, one, or both Motion‐RCC and Motion‐OPRA1 categories. Importantly, we applied an equal absolute metric change to those transformed scenes, so that differences in the similarity judgments should be due only to differing categories. In Experiments 1a and 1b, where the reference stimulus and transformed stimuli were visible at the same time (perception), both Motion‐OPRA1 and Motion‐RCC influenced the similarity judgments, with a stronger influence of Motion‐OPRA1. In Experiments 2a and 2b, where participants first memorized the reference stimulus and viewed the transformed stimuli after a short blank (memory), only Motion‐OPRA1 had marked influences on the similarity judgments. Our findings demonstrate a link between human cognition and these motion categorizations developed in artificial intelligence. We argue for a continued and close multidisciplinary approach to investigating the representation of motion scenes. (shrink)

This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category theory. (...) This categorical harmony is stated in terms of adjoints and says that any concept definable by iterated adjoints from general categorical operations is harmonious. Moreover, it has been shown that identity in a categorical setting is determined by an adjoint in the relevant way. Furthermore, path induction as a rule comes from this definition. Thus we arrive at an account of how path induction, as a rule of inference governing identity, can be justified on mathematically motivated grounds. (shrink)

We present in this paper an abstract categorical logic based on an abstraction of quantifier. More precisely, the proposed logic is abstract because no structural constraints are imposed on models (semantics free). By contrast, formulas are inductively defined from an abstraction both of atomic formulas and of quantifiers. In this sense, the proposed approach differs from other works interested in formalizing the notion of abstract logic and of which the closest to our approach are the institutions, which in addition (...) to be semantics free do not also impose any syntactic contingencies on the structure of formulas. To define the semantical framework in which formulas will be interpreted, we propose to follow the idea from categorical logic which defines the semantical interpretation of formulas from context and as subobjects of an object of a given category. In the spirit of Lawvere’s hyperdoctrines, we use a more abstract notion which generalizes the notion of subobject, standard in category theory: Pitt’s prop-categories. Always in the spirit of categorical logic, we propose a sequent calculus of which we show correctness and completeness for all semantical frameworks defined over any prop-categories. We then study some conditions which allow us to get this completeness result for particular classes of prop-categories. (shrink)

The paper sketches an argument against modal monism, more specifically against the reduction of physical possibility to metaphysical possibility. The argument is based on the non-categoricity of quantum logic.

A category theoretic generalization of the theory of algebraizable deductive systems of Blok and Pigozzi is developed. The theory of institutions of Goguen and Burstall is used to provide the underlying framework which replaces and generalizes the universal algebraic framework based on the notion of a deductive system. The notion of a term -institution is introduced first. Then the notions of quasi-equivalence, strong quasi-equivalence and deductive equivalence are defined for -institutions. Necessary and sufficient conditions are given for the quasi-equivalence and (...) the deductive equivalence of two term -institutions, based on the relationship between their categories of theories. The results carry over without any complications to institutions, via their associated -institutions. The -institution associated with a deductive system and the institution of equational logic are examined in some detail and serve to illustrate the general theory. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the (...) first two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the (...) first two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the (...) first two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

We develop a general covariant categorical modeling theory of natural systems’ behavior based on the fundamental functorial processes of representation and localization-globalization. In the first part of this study we analyze the process of representation. Representation constitutes a categorical modeling relation that signifies the semantic bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems is substantiated by algebraic rings of observable attributes of natural systems. In this perspective, the distinction between simple (...) and complex systems is reflected in the appropriate qualification of their corresponding rings of observables. The crucial distinguishing requirement with respect to the coordinatizing rings of observables has to do with the property of global commutativity. The global information structure representing the behavior of a complex system is modeled functorially in terms of its Spectrum functor. Due to the fact that, the fundamental process of representation is bidirectional by construction, it admits a precise categorical formulation in terms of the syntactic language of adjoint functors, constituting thus, a categorical adjunction. The left adjoint functor of this adjunction signifies the process of encoding the information related with phenomena of natural systems in terms of coordinatizing rings of observables, whereas, the right adjoint functor signifies the inverse process of information decoding, which, can be used for making predictions about the behavior of natural systems. (shrink)

We develop a general covariant categorical modeling theory of natural systems' behavior based on the fundamental functorial processes of representation and localization-globalization. In the second part of this study we analyze the semantic bidirectional process of localization-globalization. The notion of a localization system of a complex information structure bears a dual role: Firstly, it determines the appropriate categorical environment of base reference contexts for considering the operational modeling of a complex system's behavior, and secondly, it specifies the (...) global compatibility conditions of local contextual information. A localization system acts on the global information structure of a complex system, partitions it into sorts, and eventually, forces the consistent sheaf-theoretic fibering of the latter over the base category of commutative reference contexts. In this manner, the sheafification of the Spectrum functor of a complex information structure takes place by imposing on the uniform and homologous fibered structure of elements of the Spectrum presheaf the following two requirements of coherence in relation to the localization-globalization process: [i]. Compatibility of information under restriction from the global to the local level, and [ii]. Compatibility of information under extension from the local to the global level. Correspondingly, the options of local and global receive a concrete mathematical meaning with respect to a suitable notion of topology (categorical Grothendieck topology) defined on the base category of commutative reference contexts. Finally, the accurate functorial process modeling of a complex system's behavior, respecting the processes of representation and localization-globalization, is being effectuated by means of establishing a categorical dual equivalence between the category of complex information structures, and the topes of sheaves over the base category of partial or local information carriers, equipped with the categorical topology of epimorphosis families. (shrink)

We elaborate on the approach to syllogistic reasoning based on “case identification” (Stenning & Oberlander, 1995; Stenning & Yule, 1997). It is shown that this can be viewed as the formalisation of a method of proof that dates back to Aristotle, namely proof by exposition ( ecthesis ), and that there are traces of this method in the strategies described by a number of psychologists, from St rring (1908) to the present day. We hypothesised that by rendering individual cases explicit (...) in the premises, the chance that reasoners would engage in a proof by exposition would be enhanced, and thus performance improved. To do so, we used syllogisms with singular premises (e.g., this X is Y ). This resulted in a uniform increase in performance as compared to performance on the associated standard syllogisms. These results cannot be explained by the main theories of syllogistic reasoning in their current state. (shrink)

Tae Wan Kim, John Hooker, and Thomas Donaldson make an attempt, in recent articles, to solve the alignment problem. As they define the alignment problem, it is the issue of how to give AI systems moral intelligence. They contend that one might program machines with a version of Kantian ethics cast in deontic modal logic. On their view, machines can be aligned with human values if such machines obey principles of universalization and autonomy, as well as a deontic utilitarian principle. (...) Programming machines to do so might be useful, in their view, for applications such as future autonomous vehicles. Their proposal draws both on traditional logic-based and contemporary connectionist approaches, to fuse factual information with normative principles. I will argue that this approach makes demands of machines that go beyond what is currently feasible, and may extend past the limits of the possible for AI. I also argue that a deontological ethics for machines should place greater stress on the formula of humanity of the Kantian categorical imperative. On this principle, one ought never treat a person as a mere means. Recognition of what makes a person a person requires ethical insight. Similar insight is needed to tell treatment as a means from treatment as a mere means. The resources in Kim, Hooker, and Donaldson’s approach is insufficient for this reason. Hesitation regarding deployment of autonomous machines is warranted in light of these alignment concerns. (shrink)

We present three experiments using a novel problem in which participants update their estimates of propensities when faced with an uncertain new instance. We examine this using two different causal structures (common cause/common effect) and two different scenarios (agent‐based/mechanical). In the first, participants must update their estimate of the propensity for two warring nations to successfully explode missiles after being told of a new explosion on the border between both nations. In the second, participants must update their estimate of the (...) accuracy of two early warning tests for cancer when they produce conflicting reports about a patient. Across both experiments, we find two modal responses, representing around one‐third of participants each. In the first, “Categorical” response, participants update propensity estimates as if they were certain about the single event, for example, certain that one of the nations was responsible for the latest explosion, or certain about which of the two tests is correct. In the second, “No change” response, participants make no update to their propensity estimates at all. Across the three experiments, the theory is developed and tested that these two responses in fact have a single representation of the problem: because the actual outcome is binary (only one of the nations could have launched the missile; the patient either has cancer or not), these participants believe it is incorrect to update propensities in a graded manner. They therefore operate on a “certainty threshold” basis, whereby, if they are certain enough about the single event, they will make the “Categorical” response, and if they are below this threshold, they will make the “No change” response. Ramifications are considered for the “categorical” response in particular, as this approach produces a positive‐feedback dynamic similar to that seen in the belief polarization/confirmation bias literature. (shrink)

A category theoretic generalization of the theory of algebraizable deductive systems of Blok and Pigozzi is developed. The theory of institutions of Goguen and Burstall is used to provide the underlying framework which replaces and generalizes the universal algebraic framework based on the notion of a deductive system. The notion of a term π-institution is introduced first. Then the notions of quasi-equivalence, strong quasi-equivalence and deductive equivalence are defined for π-institutions. Necessary and sufficient conditions are given for the quasi-equivalence and (...) the deductive equivalence of two term π-institutions, based on the relationship between their categories of theories. The results carry over without any complications to institutions, via their associated π-institutions. The π-institution associated with a deductive system and the institution of equational logic are examined in some detail and serve to illustrate the general theory. (shrink)

In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic , which is the linear fragment of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories / of an ambient *-autonomous category . Similar structures were first introduced by M. Barr in the late 1970’s in abstract duality theory and more recently in work on game semantics for linear logic. The paper has two goals: to discuss concrete models (...) and to present various completeness theorems.As concrete examples, we present a hypercoherence model, using Ehrhard’s hereditary/anti-hereditary objects, a Chu-space model, a double gluing model over our categorical framework, and a model based on iterated double gluing over a *-autonomous category.For the multiplicative fragment of. (shrink)

In contemporary analytic metaphysics there are five theories concerning the reality of dispositional and categorical properties and their relationship: mixed view dispositionalism, pan-dispositionalism, categoricalism, identity theory, and neutral monism. Here I outline briefly a novel argument against metaphysical naturalism, one based on the idea that none of these five theories is compatible with it.

Finitely algebraizable deductive systems were introduced by Blok and Pigozzi to capture the essential properties of those deductive systems that are very tightly connected to quasivarieties of universal algebras. They include the equivalential logics of Czelakowski. Based on Blok and Pigozzi’s work, Herrmann defined algebraizable deductive systems. These are the equivalential deductive systems that are also truth-equational, in the sense that the truth predicate of the class of their reduced matrix models is explicitly definable by some set of unary equations. (...) Raftery undertook the task of characterizing the property of truth-equationality for arbitrary deductive systems. In this paper, following Raftery, we extend the notion of truth-equationality for logics formalized as $\pi$-institutions and abstract several of the results that hold for deductive systems in this more general categorical context. (shrink)

In this paper I offer two arguments designed to defend the existence of categorical reasons, which I define as those justifying considerations that obtain independently of their relation to an agent's commitments. The first argument is based on certain paradigm cases meant to reveal difficulties for practical instrumentalism—the view, as I define it here, that categorical reasons do not exist, because all reasons must serve the commitments of the agents to whom they apply. The second argument relies on (...) considerations of responsibility and blame to establish the existence of categorical reasons. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the (...) first two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

Regulations implemented by World Athletics (WA) require female athletes with differences of sexual development to suppress their blood testosterone levels in order to participate in certain women’s sporting competitions. These regulations have been justified by reference to fairness. In this paper, we reconstruct WA’s understanding of fairness, which requires a “level playing field” where no athlete should have a significant performance advantage based on factors other than talent, dedication, and hard work over an average athlete in their category. We demonstrate (...) that by placing regulations only on testosterone levels, while ignoring physical as well as socioeconomic advantages, WA consistently fails to meet its own definition of fairness. We then discuss several ways in which this definition could be met. Our analysis shows that a categorical system, in which athletes are divided into categories based on properties leading to significant performance advantages, is best suited for meeting WA’s definition of fairness. (shrink)

First, we discuss basic probability notions from the viewpoint of category theory. Our approach is based on the following four “sine quibus non” conditions: 1. (elementary) category theory is efficient (and suffices); 2. random variables, observables, probability measures, and states are morphisms; 3. classical probability theory and fuzzy probability theory in the sense of S. Gudder and S. Bugajski are special cases of a more general model; 4. a good model allows natural modifications.

This paper proposes the “conceptual pragmatism” of C. I. Lewis as a useful epistemological orientation for studying the relationship between the social and individual registers, in particular as it is set out in Bourdieu’s sociology of practice. Bourdieu’s concepts of habits based upon ‘social schematism’ and of culture as a ‘second nature,’ as well as Lewis’ conception of logical schemas constructed by humans are all formulated in the wake of Kant, and mediating between sensorial experience and the conceptual level is (...) a common issue for Lewis and the French sociologist. This paper discusses Lewis’ controversial idea of “sense meaning” in order to show his commitment to a pragmatic, interactive theory of knowledge and language. Moreover, I emphasize Lewis’ intertwining of conceptual schemas, actions, and reality as a theoretical network for reshaping analysis of the relationship between sociality and individuality according to a pragmatist perspective, and for implementing and improving Lewis’ commitment to observing, describing, and interpreting the effective functioning of conceptual schemas, one that includes an option in favor of an externalist philosophical methodology which, in principle, tallies with the methodological attitude that mostly characterizes the contemporary social sciences. (shrink)

One of the innovative approaches in contemporary philosophical ontology consists in the assumption of a plurality of ontologies based on different metaphysical presuppositions. Such presuppositions involve, among others, the identification of relevant properties for the objects of our domain as a guiding principle in uncovering what it is to be considered intrinsic and what could be the mere effect of selection preferences based on objective or subjective criteria. A remarkable example of the application of a background metaphysical theory in astrophysics (...) is the problem of selection biases in detecting cosmological objects, such as supernovae, galaxies and gamma-ray bursts. We will show that it is valuable to be aware of the importance of uncovering this type of background theory to better understand selection effects and to promote a novel approach in scientific research. (shrink)

Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non-protoalgebraic logics, paralleling the well-known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibniz operator was recently extended to cover the case of, the so-called, protoalgebraic π-institutions. In the present work, following the lead of Czelakowski, an attempt is made at lifting parts of the theory of the Suszko operator to the (...) π-institution framework. (shrink)

The notion of an ℐ -matrix as a model of a given π -institution ℐ is introduced. The main difference from the approach followed so far in CategoricalAlgebraic Logic and the one adopted here is that an ℐ -matrix is considered modulo the entire class of morphisms from the underlying N -algebraic system of ℐ into its own underlying algebraic system, rather than modulo a single fixed -logical morphism. The motivation for introducing ℐ -matrices comes from a desire to formulate (...) a correspondence property for N -protoalgebraic π -institutions closer in spirit to the one for sentential logics than that considered in CAAL before. As a result, in the previously established hierarchy of syntactically protoalgebraic π -institutions, i. e., those with an implication system, and of protoalgebraic π -institutions, i. e., those with a monotone Leibniz operator, the present paper interjects the class of those π -institutions with the correspondence property, as applied to ℐ -matrices. Moreover, this work on ℐ -matrices enables us to prove many results pertaining to the local deduction-detachment theorems, paralleling classical results in Abstract Algebraic Logic formulated, first, by Czelakowski and Blok and Pigozzi. Those results will appear in a sequel to this paper. (shrink)

In this paper we prove three theorems about first-order theories that are categorical in a higher power. The first theorem asserts that such a theory either is totally categorical or there exist prime and minimal models over arbitrary base sets. The second theorem shows that such theories have a natural notion of dimension that determines the models of the theory up to isomorphism. From this we conclude that $I(T, \aleph_\alpha) = \aleph_0 +|\alpha|$ where ℵ α = the (...) number of formulas modulo T-equivalence provided that T is not totally categorical. The third theorem gives a new characterization of these theories. (shrink)

We pursue the idea that predicate logic is a “fibred algebra” while propositional logic is a single algebra; in the context of intuitionism, this algebraic understanding of predicate logic goes back to Lawvere, in particular his concept of hyperdoctrine. Here, we aim at demonstrating that the notion of monad-relativised hyperdoctrines, which are what we call fibred algebras, yields algebraisations of a wide variety of predicate logics. More specifically, we discuss a typed, first-order version of the non-commutative Full Lambek calculus, which (...) has extensively been studied in the past few decades, functioning as a unifying language for different sorts of logical systems (classical, intuitionistic, linear, fuzzy, relevant, etc.). Through the concept of Full Lambek hyperdoctrines, we establish both generic and set-theoretical completeness results for any extension of the base system; the latter arises from a dual adjunction, and is relevant to the tripos-to-topos construction and quantale-valued sets. Furthermore, we give a hyperdoctrinal account of Girard’s and Gödel’s translation. (shrink)

Evidence-based medicine (EBM) puts forward a hierarchy of evidence for informing therapeutic decisions. An unambiguous interpretation of how to apply EBM's hierarchy has not been provided in the clinical literature. However, as much as an interpretation is provided proponents suggest a categorical interpretation. The categorical interpretation holds that all the results of randomised trials always trump evidence from lower down the hierarchy when it comes to informing therapeutic decisions. Most of the critical replies to EBM react to this (...) interpretation. While proponents of EBM can avoid some of the problems raised by critics by suitably limited the claims made on behalf of the hierarchy, further problems arise. If EBM is to inform therapeutic decisions then a considerably more restricted, and context dependent interpretation of EBM's hierarchy is needed. (shrink)

A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of ~????|???? from the premise set {????|????, ~????|????} is not (...) informative, we add ????(????|(????∨????))>0 as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the assigned (precise or interval-valued) probabilities to the sequence of conditional events (????|????,~????|????,????|(????∨????)) to the conclusion ~????|???? . Thereby, we give a probabilistic meaning to the other syllogisms of Figure II. Moreover, our semantics also allows for generalizing the traditional syllogisms to new ones involving generalized quantifiers (like Most S are P) and syllogisms in terms of defaults and negated defaults. (shrink)

In this paper I aim to make sense of our pre‐theoretic intuitions about dispositions by presenting an argument for the identity of a disposition with its putative categorical base. The various possible ontologies for dispositions are outlined. The possibility of an empirical proof of identity is dismissed. Instead an a priori argument for identity is adapted from arguments in the philosophy of mind. I argue that dispositions occupy, by analytic necessity, the same causal roles that categorical bases (...) occupy contingently and that properties with identical causal roles are identical. The validity of the argument depends upon the possibility of overdetermination of disposition manifestations being rejected. ‘Ungrounded dispositions’ are dismissed as not genuine dispositions. Identity conditions for dispositions and categorical bases are outlined. (shrink)

Here we suggest a formal using of N.A. Vasil’ev’s logical ideas in categorical logic: the idea of “accidental” assertion is formalized with topoi and the idea of the notion of nonclassical negation, that is not based on incompatibility, is formalized in special cases of monoidal categories. For these cases, the variant of the law of “excluded n-th” suggested by Vasil’ev instead of the tertium non datur is obtained in some special cases of these categories. The paraconsistent law suggested by (...) Vasil’ev is also demonstrated with linear and tensor logics but in a form weaker than he supposed. As we have, in fact, many truth-values in linear logic and topos logic, the admissibility of the traditional notion of inference in the categorical interpretation of linear and intuitionistic proof theory is discussed. (shrink)

We investigate a notion called uniqueness in power κ that is akin to categoricity in power κ, but is based on the cardinality of the generating sets of models instead of on the cardinality of their universes. The notion is quite useful for formulating categoricity-like questions regarding powers below the cardinality of a theory. We prove, for universal theories T, that if T is κ-unique for one uncountable κ, then it is κ-unique for every uncountable κ; in particular, it is (...) categorical in powers greater than the cardinality of T. (shrink)

An $\omega$-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl-definable subgroup. Every finitely based regular type in a CM-trivial $\omega$-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple $\omega$-categorical CM-trivial theory has finite SU-rank.