Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called “determination through universals” based on universal mapping properties. A recently developed (...) “heteromorphic” theory about adjoints suggests a conceptual structure, albeit abstract and atemporal, for how new relatively autonomous behavior can emerge within a system obeying certain laws. The focus here is on applications in the life sciences (e.g., selectionist mechanisms) and human sciences (e.g., the generative grammar view of language). (shrink)

Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called "internalization through a universal" based on universal mapping properties. A (...) recently developed "heteromorphic" theory of adjoint functors allows the concepts to be more easily applied empirically. This suggests a conceptual structure, albeit abstract, to model a range of selectionist mechanisms (e.g., in evolution and in the immune system). Closely related to adjoints is the notion of a "brain functor" which abstractly models structures of cognition and action (e.g., the generative grammar view of language). (shrink)

Boolean logic deals with {0, 1}-observables and yes–no events, as many-valued logic does for continuous ones. Since every measurement has an error, continuity ensures that small measurement errors on elementary observables have small effects on compound observables. Continuity is irrelevant for {0, 1}-observables. Functional completeness no longer holds when n-ary connectives are understood as [0, 1]-valued maps defined on [0, 1] n . So one must envisage suitable selection criteria for [0, 1]-connectives. Łukasiewicz implication has a well known characterization as (...) the only continuous connective \ satisfying the following conditions: \= y\Rightarrow}\) and \ . Then syntactic consequence can be defined purely algorithmically using the Łukasiewicz axioms and Modus Ponens. As discussed in this paper, to recover a strongly complete semantics one may use differential valuations. (shrink)

This paper summarizes and extends the transmodal argument for the existence of universals (developed in full detail in "Universals"). This argument establishes not only the existence of universals, but also that they exist necessarily, thereby confirming the ante rem view against the post rem and in re views (and also anti-existentialism against existentialism). Once summarized, the argument is extended to refute the trope theory of properties and is also shown to succeed even if possibilism is assumed. A nonreductionist theory (...) of universals and properties is then outlined, and it is sketched how to reap the benefits of possibilism and Meinongianism in an actualist setting. (shrink)

The properties of DNA -- DNA as universal property -- DNA as intellectual property -- DNA as national property -- DNA as personal property -- DNA as academic property -- DNA as taxable propety.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Mapping Gendered Ecologies: Engaging with and Beyond Ecowomanism and Ecofeminism by K. Melchor Quick Hall and Gwyn KirkCecilia Herles (bio)K. Melchor Quick Hall and Gwyn Kirk, Mapping Gendered Ecologies: Engaging with and Beyond Ecowomanism and Ecofeminism. Lanham, MD: Rowman & Littlefield, 2021. ISBN- 978-1-7936-3946-2K. Melchor Quick Hall and Gwyn Kirk are leading feminist authors who have beautifully woven together an inspiring and diverse collection of essays (...) in the anthology, Mapping Gendered Ecologies: Engaging with and beyond Ecowomanism and Ecofeminism. What does it take to gather together some of the most eloquent voices of activists, teachers, farmers, artists, and organizers in an anthology focused on engaging with and beyond ecowomanism and ecofeminism, and what could this cultivate? I find Hall and Kirk's reflections on the process and their approach to collaboration illustrate some of the tools needed to address complex issues of disasters, the global pandemic, climate justice, white supremacy, gender oppression, and practices of domination. Their approach is to build relationships, acknowledge vulnerability, and appreciate differences in experiences. It seems fitting that this project initially began with Margo Okazawa-Rey who connected Hall and Kirk together. Okazawa-Rey's introduction generated the openness needed to bring this collection to fruition. Mapping as the thematic image of this collection is found in destructive boundary-making, the violence of enslavement, wars, and the dumping of contaminants in the environment. Mapping is also evident in the physical, temporal, and evolving locations in which Okazawa-Rey's work of sustaining community and recognizing interconnections across locations opens up the time and spaces to envision peace.This collection marks a shift away from the elitism of academic spaces by illuminating connections between community and university, and actively resisting against patriarchal notions of what counts as expertise and scholarship. The anthology draws attention to personal experiences as fundamentally relevant to perspectives about place, location, and [End Page 97] belonging and relations with land, water, sky and nonhumans. It begins with an autobiographical account by Hall who brilliantly weaves together her life story with her analytical insight in illustrating how Black geographies show spaces as often hard to map and in flux for the marginalized. In "Darkness All around Me: Black Waters, Land, Animals, and Sky" Hall notes how she is unable to discuss her understanding and relationship with Nature outside of being a Black Woman. When she poses the question, "how would our maps be different if they were rooted in the histories and realities of people of color?" (23) Hall pivots mapping to the contingent, unstable complexities that mark Black people's relations with land and food. In doing so, Hall reveals compelling insights into trauma, anxieties, and relationships with land and water in shifting landscapes. Connecting to the mission of Soul Fire Farm, to resist the US food apartheid and mobilize towards food justice, Hall reveals the possibilities for reparative healing properties in agricultural activities at Soul Fire Farm. Hall's narrative about racialized hierarchies recognizes how human hierarchies are connected to human-nonhuman animal divisions, raising the question of "How might we imagine freeing ourselves and other animals from the systems that seek to devalue us as (human and nonhuman) beings?" (27). Hall intervenes and challenges geographical mapping centered in white frameworks rooted in claims of stolen territories and measured in segregation and displacement. Pointing to Black shoals, Black food geographies, and Afrofuturism, to name a few, Hall is marking potential paths to shared liberation. Although Hall does not identify strongly as ecofeminist nor ecowomanist, this provides a promising direction for ecowomanist and ecofeminist inquiries, speaking to the need to explore what it takes for shared liberation. This direction also has the potential to offer insight into an alternative mapping for disability justice. Hall's acknowledgement of "being out of place" connects to the disability justice work of Sunaura Taylor (2014) and Leah Lakshmi Piepzna-Samarasinha (2018) in the mapping of access in describing surroundings and focusing on interconnectedness.In Kirk's autobiographical account, "Roots, Branches, Wings" she points to how Margo Okazawa-Rey (2020) introduced her to philosopher Alan Rosenberg's (1998) distinction between knowing and understanding. In contrast to knowing facts that... (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)

Comparative constructions form two classes, those that permit direct comparisons (comparisons of measurements as in Seymour is taller than he is wide) and those that only allow indirect comparisons (comparisons of relative positions on separate scales as in Esme is more beautiful than Einstein is intelligent). In contrast with other semantic theories, this paper proposes that the interpretation of the comparative morpheme remains the same whether it appears in sentences that compare individuals directly or indirectly. To develop a unified account, (...) I suggest that all comparisons (whether in terms of height, intelligence or beauty) involve a scale of universal degrees that are isomorphic to the rational (fractional) numbers between 0 and 1. Crucial to a unified treatment, the connection between the individuals being compared and universal degrees involves two steps. First individuals are mapped to a value on a primary scale that ranks individuals with respect to the gradable property (whether it be height, beauty or intelligence). Second, the value on the primary scale is mapped to a universal degree that encodes the value’s relative position on the primary scale. Direct comparison results if measurements such as seven feet participate in the primary scale (as in Seven feet is tall). Otherwise the result is an indirect comparison. (shrink)

There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are shown to start (...) with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of Sets are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences. (shrink)

Saunders Mac Lane famously remarked that "Bourbaki just missed" formulating adjoints in a 1948 appendix (written no doubt by Pierre Samuel) to an early draft of Algebre--which then had to wait until Daniel Kan's 1958 paper on adjoint functors. But Mac Lane was using the orthodox treatment of adjoints that only contemplates the object-to-object morphisms within a category, i.e., homomorphisms. When Samuel's treatment is reconsidered in view of the treatment of adjoints using heteromorphisms or hets (object-to-object morphisms between objects in (...) different categories), then he, in effect, isolated the concept of a left representation solving a universal mapping problem. When dualized to obtain the concept of a right representation, the two halves only need to be united to obtain an adjunction. Thus Samuel was only a now-simple dualization away for formulating adjoints in 1948. Apparently, Bodo Pareigis' 1970 text was the first and perhaps only text to give the heterodox "new characterization" (i.e., heteromorphic treatment) of adjoints. Orthodox category theory uses various relatively artificial devices to avoid formally recognizing hets--even though hets are routinely used by the working mathematician. Finally we consider a "philosophical" question as to whether the most important concept in category theory is the notion of an adjunction or the notion of a representation giving a universal mapping property (where adjunctions arise as the special case of a bi-representation of dual universal mapping problems). (shrink)

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in (...) exploring the foundations of multialgebras applied to the study of logic systems. It is well known from universal algebra that, for every signature \, there exist algebras over \ which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of \-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms. Equivalently, the forgetful functor, from the category of \-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor \, from the category of \-multialgebras to Set, does not have a left adjoint. In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices, there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that \ does not have a left adjoint. (shrink)

Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction. (...) Semiadjunctions (essentially a formulation of universal mapping properties using hets) can then be combined in a new way to define the notion of a brain functor that provides an abstract model of the intentionality of perception and action (as opposed to the passive reception of sense-data or the reflex generation of behavior). (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory of (...) categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in (...) exploring the foundations of multialgebras applied to the study of logic systems. -/- It is well known from universal algebra that, for every signature Sigma, there exist algebras over Sigma which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of Sigma-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms (or propositional formulas, in the context of logic). Equivalently, the forgetful functor, from the category of Sigma-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor U, from the category of Sigma-multialgebras to Set, does not have a left adjoint. -/- In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices (which selects how a homomorphism approaches indeterminacies), there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that U does not have a left adjoint. (shrink)

Sensibility, in any of its myriad realms – moral, physical, aesthetic, medical and so on – seems to be a paramount case of a higher-level, intentional property, not a basic property. Diderot famously made the bold and attributive move of postulating that matter itself senses, or that sensibility (perhaps better translated ‘sensitivity’ here) is a general or universal property of matter, even if he at times took a step back from this claim and called it a “supposition.” Crucially, sensibility (...) is here playing the role of a ‘booster’: it enables materialism to provide a full and rich account of the phenomena of conscious, sentient life, contrary to what its opponents hold: for if matter can sense, and sensibility is not a merely mechanical process, then the loftiest cognitive plateaus are accessible to materialist analysis, or at least belong to one and the same world as the rest of matter. This was noted by the astute anti-materialist critic, the Abbé Lelarge de Lignac, who, in his 1751 Lettres à un Amériquain, criticized Buffon for “granting to the body [la machine, a common term for the body at the time] a quality which is essential to minds, namely sensibility.” This view, here attributed to Buffon and definitely held by Diderot, was comparatively rare. If we look for the sources of this concept, the most notable ones are physiological and medical treatises by prominent figures such as Robert Whytt, Albrecht von Haller and the Montpellier vitalist Théophile de Bordeu. We then have, or so I shall try to sketch out, an intellectual landscape in which new – or newly articulated – properties such as irritability and sensibility are presented either as an experimental property of muscle fibers, that can be understood mechanistically (Hallerian irritability, as studied recently by Hubert Steinke and Dominique Boury) or a property of matter itself (whether specifically living matter as in Bordeu and his fellow montpelliérains Ménuret and Fouquet, or matter in general, as in Diderot). I am by no means convinced that it is one and the same ‘sensibility’ that is at issue in debates between these figures (as when Bordeu attacks Haller’s distinction between irritability and sensibility and claims that ‘his own’ property of sensibility is both more correct and more fundamental in organic beings), but I am interested in mapping out a topography of the problem of sensibility as property of matter or as vital force in mid-eighteenth-century debates – not an exhaustive cartography of all possible positions or theories, but an attempt to understand the ‘triangulation’ of three views: a vitalist view in which sensibility is fundamental, matching up with a conception of the organism as the sum of parts conceived as little lives (Bordeu et al.); a mechanist, or ‘enhanced mechanist’ view in which one can work upwards, step by step from the basic property of irritability to the higher-level property of sensibility (Haller); and, more eclectic, a materialist view which seeks to combine the mechanistic, componential rigour and explanatory power of the Hallerian approach, with the monistic and metaphysically explosive potential of the vitalist approach (Diderot). It is my hope that examining Diderot in the context of this triangulated topography of sensibility as property sheds light on his famous proclamation regarding sensibility as a universal property of matter. (shrink)

We define a type theory MLM, which has proof theoretical strength slightly greater then Rathjen's theory KPM. This is achieved by replacing the universe in Martin-Löf's Type Theory by a new universe V having the property that for every function f, mapping families of sets in V to families of sets in V, there exists a universe inside V closed under f. We show that the proof theoretical strength of MLM is $\geq \psi_{\Omega_1}\Omega_{{\rm M}+\omega}$ . This is slightly greater (...) than $|{\rm KPM}|$ , and shows that V can be considered to be a Mahlo-universe. Together with [Se96a] it follows $|{\rm MLM}|=\psi_{\Omega_1}(\Omega_{{\rm M}+\omega})$. (shrink)

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. The (...) role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

There are three outstanding issues raised by my critics in this volume. The first concerns the nature and status of universals (John Heil). The second is ‘the essential problem’, which is the issue of how to distinguish the essential properties of natural kinds from their accidental ones, and the related question of whether we really need to believe in the essences of natural kinds (Stephen Mumford). The third is that of strong versus weak dispositional essentialism (Alexander Bird), or equivalently, (...) whether there is any place for categorical properties in an essentialist metaphysic (John Heil). This paper addresses these three issues. (shrink)

A famous proposed solution to the one over many problem is found in Plato. For example, it appears in The Parmenedies and is introduce by Zeno arguing that . . . if being is many, it must be both like and unlike, and that this is impossible, for neither can the like be unlike, nor the unlike like-is that your position? and Socrates responds: do you not further think that there is an idea of likeness in itself, and another idea (...) of unlikeness, which is the opposite of likeness, and that in these two, you and I and all other things to which we apply the term many, participate-things which participate in likeness become in that degree and manner like; and so far as they participate in unlikeness become in that degree unlike, or both like and unlike in the degree in which they participate in both? And may not all things partake of both opposites, and be both like and unlike, by reason of this participation? Where is the wonder? and the discussion moves on to the interesting question that.. (shrink)

We prove that if an incomplete computably enumerable set has the the universal splitting property then it is low2. This solves a question from Ambos-Spies and Fejer [1] and Downey and Stob [7]. Some technical improvements are discussed.

Universals are properties that are shared by multiple objects. In classical South Asia, Brahmanical thinkers from Vyākaraṇa, Nyāya, Vaiśeṣika, and Mīmāṃsā text traditions were realists about universals, while most Buddhists were nominalists. In this paper, my aim is to reconstruct the early Nyāya-Vaiśeṣika theory of universals, with special emphasis on the arguments of the Nyāya philosopher Uddyotakara (6th century CE) against a Buddhist strand of resemblance nominalism. I show that Uddyotakara's contribution to this debate is twofold. First, he is (...) possibly the first Naiyāyika to adopt a sparse theory of universals, a theory according to which it is necessary to posit only those universals which explain how objects resemble each other in the most fundamental or irreducible respects. On the other hand, he offers a few arguments for realism, which are explicitly motivated by a causal constraint on intentionality. (shrink)

If the contemporary rebirth of the ontological argument had its conception in Norman Malcolm's discovery of a second Anselmian argument it had its full-term delivery as a healthy philosophical progeny with Alvin Plantinga's sophisticated modal version presented in the tenth chapter of The Nature of Necessity. This latter argument has been the centre of a huge body of literature over the last fifteen years, and deservedly so. One is impressed that this version of Anselm's jewel is valid and sound if (...) any is. (shrink)

A universally acknowledged, core property of language is its complexity, at each level of structure – sounds, words, phrases, clauses, utterances, and higher levels of discourse. How does this complexity originate and develop in a language? We cannot fully answer this question from spoken languages, since they are all thousands of years old or descended from old languages. However, sign languages of deaf communities can arise at any time and provide empirical data for testing hypotheses related to the emergence of (...) language complexity. An added advantage of the signed modality is a direct correspondence between visible physical articulations and linguistic structures, providing a more transparent view of linguistic complexity and its emergence (Sandler 2012). These essential characteristics of sign languages allow us to address the issue of emerging complexity by documenting the use of the body for linguistic purposes. We look at three types of discourse relations of increasing complexity motivated by research on spoken languages – additive, symmetric and asymmetric (Mann and Thompson 1988; Sanders, Spooren, and Noordman 1992), Each relation type can connect units at two different levels: within propositions (simpler) and across propositions (more complex). We hypothesized that these relations provide a measure for charting the time course of emergence of complexity, from simplest to most complex, in a new sign language. We test this hypothesis on Israeli Sign Languages (ISL), a young language, some of whose earliest users are still available for recording. Taking advantage of the unique relation in sign languages between bodily articulations and linguistic form, we study fifteen ISL signers from three different generations, and demonstrate that the predictions indeed hold. We also find that younger signers tend to converge on more systematic marking of relations, that they use fewer articulators for a given linguistic function than older signers, and that the form of articulations becomes reduced, as the language matures. Mapping discourse relations to the bodily expression of linguistic components across age groups reveals how simpler, less constrained, and more gesture-like expressions, become language. (shrink)

In this paper I examine Grace A. de Laguna’s theory of universals in its historical context and in relation to contemporary debates in analytic metaphysics. I explain the central features of her theory, arguing that her theory should be classified as a form of immanent realism and as a powers ontology. I then show in what ways her theory affords a theory of modality in terms of potentialities and discuss some of its consequences along the way.

Iconicity is a fundamental property of spoken and signed languages. However, quantitative analysis of sound-meaning association in Chinese has not been extensively developed, and little is known about the impact of sound symbolism in children’s literature. As sound symbolism is supposed to be a universal cognitive phenomenon, this research seeks to investigate whether iconic structures of Mandarin are embodied in native Chinese speakers’ language experience. The paper describes a case study of Chinese storybooks with the goal of testing whether (...) phonosemantic association is prominent between name sounds and character features. A quantitative method was used to investigate the distribution of different phonological units in character denomination depending on their physical and emotional traits. The results show that phonemes and syllable combination patterns are closely related to perceivable character features. By comparing schematic mapping in Chinese with other languages, the study illuminates a cross-linguistic tendency in addition to a Chinese-specific iconic relation between sound and meaning. (shrink)

Since the publication of David Lewis's ''New Work for a Theory of Universals,'' the distinction between properties that are fundamental – or perfectly natural – and those that are not has become a staple of mainstream metaphysics. Plausible candidates for perfect naturalness include the quantitative properties posited by fundamental physics. This paper argues for two claims: (1) the most satisfying account of quantitative properties employs higher-order relations, and (2) these relations must be perfectly natural, for otherwise the (...) perfectly natural properties cannot play the roles in metaphysical theorizing as envisaged by Lewis. (shrink)

Many philosophers have declared that everything which exists is a particular. There is a weak interpretation of this doctrine which I believe to be a true proposition, and a strong one which I believe to be false.

Do properties have intrinsic properties of their own? If so, which second-order properties are intrinsic? This paper introduces two competing views about second-order intrinsicality: generalism, according to which the intrinsic–extrinsic distinction cuts across all orders of properties and applies to the properties of properties as well as the properties of objects, and objectualism, according to which intrinsicality is a feature exclusive to the properties of objects. The case for generalism is then surveyed (...) along with some proposals for distinguishing intrinsic second-order properties from extrinsic ones. After addressing these broad questions about the nature of second-order intrinsicality, the Problem of Accidental Intrinsic Properties of Properties is introduced and put to work as a case study for the significance of second-order intrinsicality. The connection between this problem and the metaphysics of quantitative properties is then examined. (shrink)

Many philosophers have declared that everything which exists is a particular. There is a weak interpretation of this doctrine which I believe to be a true proposition, and a strong one which I believe to be false.

It has been maintained by such philosophers as Quine and Goodman that purely ‘extensional’ language suffices for all the purposes of properly formalized scientific discourse. Those entities that were traditionally called ‘universals’ — properties, concepts, forms, etc. — are rejected by these extensionalist philosophers on the ground that ‘the principle of individuation is not clear’. It is conceded that science requires that we allow something tantamount to quantification over non-particulars (or, anyway, over things that are not material objects, not (...) space-time points, not physical fields, etc.), but, the extensionalists contend, quantification over sets serves the purposes nicely. The ‘ontology’ of modern science, at least as Quine formalizes it, comprises material objects (or, alternatively, space-time points), sets of material objects, sets of sets of material objects,... but no properties, concepts,or forms. Let us thus examine the question: Can the principle of individuation for properties ever be made clear? (shrink)

Things are particulars and their qualities are universals, but do universals have an existence distinct from the particular things describable by those terms? And what must be their nature if they do? This book provides a careful and assured survey of the central issues of debate surrounding universals, in particular those issues that have been a crucial part of the emergence of contemporary analytic ontology. The book begins with a taxonomy of extreme nominalist, moderate nominalist, and realist positions on (...) class='Hi'>properties, and outlines the way each handles the phenomena of predication, resemblance, and abstract reference. The debate about properties and philosophical naturalism is also examined. Different forms of extreme nominalism, moderate nominalism, and minimalist realism are critiqued. Later chapters defend a traditional realist view of universals and examine the objections to realism from various infinite regresses, the difficulties in stating identity conditions for properties, and problems with realist accounts of knowledge of abstract objects. In addition, the debate between Platonists and Aristotelians is examined alongside a discussion of the relationship between properties and an adequate theory of existence. The book's final chapter explores the problem of individuating particulars. The book makes accessible a difficult topic without blunting the sophistication of argument required by a more advanced readership. (shrink)

Both philosophers of perception and analytic metaphysicians apply the tropes/universals distinction when considering the ontological status of visual properties. One way of arguing in favor of the trope interpretation of visual properties is to claim that the way in which we visually experience properties makes it plausible to characterize them as tropes. In this paper, I argue for a different position, namely that the way in which we visually experience properties provides a serious challenge for the (...) trope interpretation, but not for an interpretation in terms of universals. More specifically, I claim that the trope interpretations of visual properties have problems accounting for the fact that ordinary, veridical visual experiences can present the properties of two objects as strictly similar. (shrink)

This book articulates and defends Fregean realism, a theory of properties based on Frege's insight that properties are not objects, but rather the satisfaction conditions of predicates. Robert Trueman argues that this approach is the key not only to dissolving a host of longstanding metaphysical puzzles, such as Bradley's Regress and the Problem of Universals, but also to understanding the relationship between states of affairs, propositions, and the truth conditions of sentences. Fregean realism, Trueman suggests, ultimately leads to (...) a version of the identity theory of truth, the theory that true propositions are identical to obtaining states of affairs. In other words, the identity theory collapses the gap between mind and world. This book will be of interest to anyone working in logic, metaphysics, the philosophy of language or the philosophy of mind. (shrink)

. The deep structural properties of a quantum information theoretic approach to formal languages and universal computation, as well as those of the topology problem of defining the presentation of the Mapping Class Group of a smooth, compact manifold are shown to be grounded in the common categorical features of the two problems.

What all contemporary so-called aristotelian realists have in common has been identified by David Armstrong as the principle of instantiation. This principle has been put forward in different versions, but all of them have the following simple consequence in common: uninstantiated universals do not exist. Such entities are for the lotus-eating Platonist to countenance, but not for any sort of moderate realist. I shall argue that this principle, in any guise, is not the best way to differentiate aristotelianism from Platonism. (...) In its place, I shall suggest that the best way to differentiate the two versions of realism from each other is by means of a far more powerful idea: naturalism. And the surprising conclusion given this means of differentiation will be that contrary to the usual proclamations, Platonism will be the more naturalistic theory, whereas aristotelianism will come to be seen for what it really is, namely, non-naturalistic. (shrink)

There is substantial controversy about the nature of both particulars and properties. Some philosophers think that the categories of particular and property are fundamental, that at least some of the things in both are in no way derived from or dependent on things in another category. These philosophers are Realists about both particulars and properties. Nominalists think of particulars as fundamental and of properties as non‐fundamental, with the latter being derived from the former. This chapter explores why (...) someone might go in for Realism about properties. If one insists that universals are just properties that could be exemplified by more than one thing, Class and Resemblance Nominalism turn out to be committed to universals. Ostrich Nominalism is much larger qualitatively, since UP‐Realism has only two fundamental kinds, whereas Ostrich Nominalism has n fundamental kinds. Ostrich Nominalists must posit a very large number of metaphysically fundamental sorts of things: spheres, cubes, blue things, red things, etc. (shrink)

This article attempts to make sense of property contingentism, the view that the metaphysical nature of properties is contingent. That is, it is contingent whether properties are universals or tropes or some other kind of entity. The article argues that even if one thinks that necessities are exhausted by conceptual truths and a posteriori necessities, the sort of methodology that can lead one to endorse contingentism in various domains in metaphysics does not give us good grounds to suppose (...) that the nature of properties is contingent. (shrink)

Certain realists about properties and relations identify them with universals. Furthermore, some hold that for a wide range of meaningful predicates, the semantic contribution to the propositions expressed by the sentences in which those predicates figure is the universal expressed by the predicate. I here address ontological issues raised by predicates first introduced to us via works of fiction and whether the universal realist should accept that any such predicates express universals. After assessing arguments by Braun, D. (...) and Sawyer, S. for fictional universal anti-realism, I propose a novel, Kripke-inspired argument for the same conclusion. I ultimately defend the claim that while this argument presents the strongest case for fictional universal anti-realism, it is nonetheless unsound. I conclude that nothing stands in the way of accepting that some fictional predicates express fictional universals. (shrink)

Proponents of the dispositional theory of properties typically claim that their view is not one that offers a realist, governing conception of laws. My first aim is to show that, contrary to this claim, if one commits to dispositionalism then one does not automatically give up on a robust, realist theory of laws. This is because dispositionalism can readily be developed within a Platonic framework of universals. Second, I argue that there are good reasons for realist dispositionalists to favour (...) a Platonic view. This is because the alternative Aristotelian version of dispositionalism, on which universals are immanent entities, is unstable for various reasons. My final aim is to address a common criticism facing Platonic theories of laws, which is the problem of how external entities can play an explanatory role where the world’s law-like patterns of behaviour are concerned. I argue that the Platonists’ response to the one over many problem can help to shed light on this matter, and a possible solution is sketched, one which makes use of the notions of essence, constitution and ontological dependence. (shrink)