Recently Feferman has outlined a program for the development of a foundation for naive category theory. While Ernst has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook (...) recipe’ is used for constructing categories, and it is explicitly shown with a formalized argument that this “foundationless” naive category theory therefore contains a paradox similar to the Russell paradox of naive set theory. (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)

Notions such as śūnyatā, catuṣkoṭi, and Indra's net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nāgārjuna considered two levels of reality: one called conventional reality, and the other ultimate reality. Within this framework, śūnyatā refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuṣkoṭi refers to the claim (...) that four truth values, including contradiction, are admissible in reasoning. Indra's net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions that are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of śūnyatā. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of catuṣkoṭi. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

Linnebo and Pettigrew present some objections to category theory as an autonomous foundation. They do a commendable job making clear several distinct senses of ‘autonomous’ as it occurs in the phrase ‘autonomous foundation’. Unfortunately, their paper seems to treat the ‘categorist’ perspective rather unfairly. Several infelicities of this sort were addressed by McLarty. In this note I address yet another apparent infelicity.

The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided (...) into 5 sections. We first show that already in the set theoretical framework, there are different dimensions to the expression foundations of. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory. (shrink)

The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based definitions can (...) be abstracted in purely arrow-theoretic way for abstract category theory. In short, the language of elements & distinctions is the conceptual language in which the category of sets is written, and abstract category theory gives the abstract arrows version of those definitions. (shrink)

This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in category theory is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal (...) profile of $\Omega$-logical validity, and thus the generic invariance of mathematical truth, modal coalgebras are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility. (shrink)

In this paper, we develop a mathematical model of awareness based on the idea of plurality. Instead of positing a singular principle, telos, or essence as noumenon, we model it as plurality accessible through multiple forms of awareness (“n-awareness”). In contrast to many other approaches, our model is committed to pluralist thinking. The noumenon is plural, and reality is neither reducible nor irreducible. Nothing dies out in meaning making. We begin by mathematizing the concept of awareness by appealing to the (...) mathematical formalism of higher category theory. The beauty of higher category theory lies in its universality. Pluralism is categorical. In particular, we model awareness using the theories of derived categories and (infinity, 1)-topoi which will give rise to our meta-language. We then posit a “grammar” (“n-declension”) which could express n-awareness, accompanied by a new temporal ontology (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? Another question which could be re-conceptualized in our model is one of soteriology related to this pluralism: what is a self in this context? A new model of “personal identity over time” is thus introduced. (shrink)

Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic (...) treatment of concrete universals along with a new concept to abstractly model the functions of a brain. (shrink)

This paper shows how the universals of category theory in mathematics 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. The paper also shows how the always-self-predicative universals of category theory provide the "opposite bookend" to the never-self-predicative universals of iterative set theory and thus (...) that the paradoxes arose from having one theory (e.g., Frege's Paradise) where universals could be either self-predicative or non-self-predicative (instead of being always one or always the other). (shrink)

The following text is divided in four parts. The first presents the inner relation between the phenomenological concept of intentionality and space in a general mathematical sense. Following this train of though the second part brie_ly characterizes the use of the geometrical concept of manifold (Mannigfaltigkeit) in Husserl’s work. In the third part we present some examples of the use of the concept in Husserl’s analyses of space, time and intersubjectivity, pointing out some dif_iculties in his endeavor. In the fourth (...) and _inal part we offer some points of coincidence between phenomenology and category theory suggesting that the latter can work as a formal frame for ontology in the former. Our thesis is that intentionality operates in different levels as a morphism, functor and natural transformation. (shrink)

The following text is divided in four parts. The first presents the inner relation between the phenomenological concept of intentionality and space in a general mathematical sense. Following this train of though the second part brie_ly characterizes the use of the geometrical concept of manifold (Mannigfaltigkeit) in Husserl’s work. In the third part we present some examples of the use of the concept in Husserl’s analyses of space, time and intersubjectivity, pointing out some dif_iculties in his endeavor. In the fourth (...) and _inal part we offer some points of coincidence between phenomenology and category theory suggesting that the latter can work as a formal frame for ontology in the former. Our thesis is that intentionality operates in different levels as a morphism, functor and natural transformation. (shrink)

Notions such as Sunyata, Catuskoti, and Indra's Net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nagarjuna considered two levels of reality: one called conventional reality and the other ultimate reality. Within this framework, Sunyata refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuskoti refers to the claim (...) that four truth values, along with contradiction, are admissible in reasoning. Indra's Net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions which are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of Sunyata. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of Catuskoti. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's Net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

In this article, the authors try to answer the following questions: How can an object/instance seen for the first time extend a category or update a concept? How is it possible to determine the reference of a concept that represents a behaviour? In the first case, the authors discuss the learning of inferential linguistic competence used to update a concept through an approach based on prototype theory. In the second case, the authors discuss the learning of referential linguistic (...) competence used to determine the reference of a concept (i.e., determination of an actual behaviour) through an approach based on embodied cognition. The authors show how combining prototype-based and embodied categorization in Wittgenstein’s rule-following praxis (the individual and community dimension), linguistic learning of a concept (inferential competence), and determination of its reference (referential competence) can be traced back to the same model. Keywords Action, Categorization, Embodied Cognition, Embodiment, Linguistic Inferential Competence, Linguistic Referential Competence, Perception, Prototype Theory, Reference, Sign. (shrink)

This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the (...) implicit foundation, confining our presentation to elementary results such as function extensionality, the derivation of weak connections and path induction, the groupoid structure of types, and the Eckmman–Hilton duality. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes (...) have exactly the same members, they are identical. In this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

We investigated, experimentally, the contention that the folk view, or naïve theory, of time, amongst the population we investigated is dynamical. We found that amongst that population, ~ 70% have an extant theory of time that is more similar to a dynamical than a non-dynamical theory, and ~ 70% of those who deploy a naïve theory of time deploy a naïve theory that is more similar to a dynamical than a non-dynamical theory. Interestingly, while (...) we found stable results across our two experiments regarding the percentage of participants that have a dynamical or non-dynamical extant theory of time, we did not find such stability regarding which particular dynamical or non-dynamical theory of time they take to be most similar to our world. This suggests that there might be two extant theories in the population—a broadly dynamical one and a broadly non-dynamical one—but that those theories are sufficiently incomplete that participants do not stably choose the same dynamical theory as being most similar to our world. This suggests that while appeals to the ordinary view of time may do some work in the context of adjudicating disputes between dynamists and non-dynamists, they likely cannot do any such work adjudicating disputes between particular brands of dynamism. (shrink)

In this paper it is shown how simple texts that can be parsed in a Lambek Categorial Grammar can also automatically be provided with a semantics in the form of a Discourse Representation Structure in the sense of Kamp [1981]. The assignment of meanings to texts uses the Curry-Howard-Van Benthem correspondence.

Samuel Alexander was one of the first realists of the twentieth century to defend a theory of categories. He thought that the categories are genuinely real and grounded in the intrinsic nature of Space-Time. I present his reduction of the categories in terms of Space-Time, articulate his account of categorial structure and completeness, and offer an interpretation of what he thought the nature of the categories really were. I then argue that his theory of categories has some advantages (...) over competing theories of his day, and finally draw some important lessons that we can learn from his realist yet reductionist theory of categories. (shrink)

Recently, it has been objected that naïve realism is inconsistent with an empirically well-supported claim that mental states of the same fundamental kind as ordinary conscious seeing can occur unconsciously (SFK). The main aim of this paper is to establish the following conditional claim: if SFK turns out to be true, the naïve realist can and should accommodate it into her theory. Regarding the antecedent of this conditional, I suggest that empirical evidence renders SFK plausible but not obvious. For (...) it is possible that what is currently advocated as unconscious perception of the stimulus is in fact momentaneous perceptual awareness (or residual perceptual awareness) of the stimulus making the subject prone to judge in some way rather than another, or to act in some way rather than another. As to the apodosis, I show that neither the core of naïve realism nor any of its main motivations is undermined if SFK is assumed. On the contrary, certain incentives for endorsing naïve realism become more tempting on this assumption. Since the main motivations for naïve realism retain force under SFK, intentionalism is neither compulsory nor the best available explanation of unconscious perception. (shrink)

In this paper, I explore a line of argument against one form of realism about fictional characters : abstract artifact theory, the view according to which fictional characters like Harry Potter are part of our reality, but, they are abstract objects created by humans, akin to the institution of marriage and the game of soccer. I will defend artifactualism against an objection that Mark Sainsbury considers decisive against it: the category-mistake objection. The objection has it that artifactualism attributes (...) to people who produce and process sentences and thoughts about Harry Potter massive error, indeed, a category mistake about what kind of thing Harry Potter is; for an abstract object isn’t the sort of thing that can wear glasses, ride a double-decker bus, attend school. Given problems with this objection, artifactualism, I shall conclude, remains a tenable contender. (shrink)

This paper elaborates on an argument in my book *Perception*. It has two parts. In the first part, I argue against what I call "basic" naive realism, on the grounds that it fails to accommodate what I call "internal dependence" and it requires an empirically implausible theory of sensible properties. Then I turn Craig French and Ian Phillips’ modified naïve realism as set out in their recent paper "Austerity and Illusion". It accommodates internal dependence. But it may retain (...) the empirically implausible theory of sensible properties. And it faces other empirical problems. Representationalism about experiences avoids those problems and is to be preferred. (shrink)

Neo-Russellians like Salmon and Braun hold that: the semantic contents of sentences are structured propositions whose basic components are objects and properties, names are directly referential terms, and a sentence of the form ‘n believes that S’ is true in a context c iff the referent of the name n in c believes the proposition expressed by S in c. This is sometimes referred to as ‘the Naive Russellian theory’. In this talk, I will discuss the Naive (...) Russellian theory primarily in connection with a problem known as Schiffer’s puzzle. Schiffer first presented the puzzle as an argument against the Naive Russellian theory. Schiffer’s argument proceeds in two steps. In step one, Schiffer argues that the Naive Russellian theory is committed to two principles regarding de re belief; the special-case consequence and Frege’s constraint. Then, in step two, Schiffer argues that the special-case consequence is not consistent with Frege’s constraint. Salmon and Braun reply to Schiffer’s argument that although the Naive Russellian theory is committed to Frege’s constraint, it is not committed to the special-case consequence. However, in this paper, I will argue with a new Schiffer-case that even if the Naive Russellian theory is not committed to the special-case consequence, it is still not consistent with Frege’s constraint. Concluding, I will discuss the possibility to reject Frege’s constraint within the Naive Russellian theory. (shrink)

The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the biomathematician Robert Rosen in 1958. In this theoretical proposal, Rosen suggests using the mathematical concept of “category” and the correlative concept of “natural equivalence” in mathematical modeling applied to living beings. Our questions are the following: According to Rosen, to what extent does the mathematical notion of category give access to more “natural” formalisms in the modeling of living (...) beings? Is the so -called “naturalness” of some kinds of equivalences (which the mathematical notion of category makes it possible to generalize and to put at the forefront) analogous to the naturalness of living systems? Rosen appears to answer “yes” and to ground this transfer of the concept of “natural equivalence” in biology on such an analogy. But this hypothesis, although fertile, remains debatable. Finally, this paper makes a brief account of the later evolution of Rosen’s arguments about this topic. In particular, it sheds light on the new role played by the notion of “category” in his more recent objections to the computational models that have pervaded almost every domain of biology since the 1990s. (shrink)

It is widely acknowledged that categories play significant roles in the appreciation of artworks. This paper argues that the correct categories of artworks are institutionally established through social processes. Section 1 examines the candidates for determining correct categories and proposes that this question should shift the focus from category membership to appreciative behaviour associated with categories. Section 2 draws on Francesco Guala’s theory of institutions to show that categories of artworks are established as rules-in-equilibrium. Section 3 reviews the (...) explanatory benefits of this institutional theory of the correct category. [Winner of the 2022 Debates in Aesthetics Essay Prize]. (shrink)

This paper sets out a novel response to the ‘screening off problem’ for naïve realism. The aim is to resist the claim (which many naïve realists accept) that the kind of experience involved in hallucinating also occurs during perception, by arguing that there are causal constraints that must be met if an hallucinatory experience is to occur that are never met in perceptual cases. Notably, given this response, it turns out that, contra current orthodoxy, naïve realists need not adopt any (...) particular view about the psychological nature of hallucinatory experience to handle the screening off problem. Consequently, room opens up for naïve realists to endorse whatever theory of hallucinatory experience seems to best capture the distinctive nature of such episodes. (shrink)

I begin by describing what I call simple naïve realism. Then I describe relevant empirical results. Next, I develop two new empirical arguments against simple naive realism. Then I briefly look at two new, more complex forms of naïve realism: one due to Keith Allen and the other due to Heather Logue and Ori Beck. I argue that they are not satisfactory retreats for naive realists. The right course is to reject naive realism altogether. My stalking horse (...) is contemporary naive realism but there is a larger, positive lesson: new empirical results support a brain-based theory of sensory consciousness. (shrink)

Naïve realism, often overlooked among philosophical theories of perception, has in recent years attracted a surge of interest. Broadly speaking, the central commitment of naïve realism is that mind-independent objects are essential to the fundamental analysis of perceptual experience. Since the claims of naïve realism concern the essential metaphysical structure of conscious perception, its truth or falsity is of central importance to a wide range of topics, including the explanation of semantic reference and representational content, the nature of phenomenal consciousness, (...) and the basis of perceptual justification and knowledge. One of the greatest difficulties surrounding discussions of naïve realism, however, has been lack of clarity concerning exactly what affirming or denying it entails. In particular, it is sometimes unclear how naïve realism is related to the claim that perceptual experience is in some sense direct or unmediated, and also to what extent the view is compatible with another widely discussed thesis in the philosophy of perception, the claim that perceptual experiences are states with representational content. In this essay, I discuss how recent work on these issues helps to clarify both the central commitments of naïve realism, as well as its relation to representationalist theories of perception. Along the way, I will attempt to shed light on the different ways in which each approach tries to address the various theoretical challenges facing a philosophical theory of perception, and also to assess the prospects for views that attempts to combine features of each approach. (shrink)

The project of a 'naive physics' has been the subject of attention in recent years above all in the artificial intelligence field, in connection with work on common-sense reasoning, perceptual representation and robotics. The idea of a theory of the common-sense world is however much older than this, having its roots not least in the work of phenomenologists and Gestalt psychologists such as K hler, Husserl, Schapp and Gibson. This paper seeks to show how contemporary naive physicists (...) can profit from a knowledge of these historical roots of their discipline, which are shown to imply above alla critique of the set-theory-based models of reality typically presupposed by contemporary work in common-sense ontology [1]. (shrink)

It’s generally thought that we naively or pre-theoretically represent the future to be open. While philosophers have modelled future openness in different ways, it’s unclear which, if any, captures our naïve sense that the future is open. In this paper we focus on just one way the future might count as being open: by being nomically open, and empirically investigate whether our naïve representation of the future as open is partly constituted by representing the future as nomically open. We also (...) investigate the connection between our naïve representation of the future as open, and our representation of time. One of the purported advantages of the growing block theory of time is that it captures our naive sense that the future is open, and the past closed. We investigate whether there is an explanatory connection between people representing the future to be nomically open and representing our world to be a growing block and reflect on the implications of our findings for theorising about future openness and temporal ontology. (shrink)

This paper seeks to resolve a fairly simple question in ethics: Why do seemingly reasonable people disagree about ethical problems? My paper seeks both to analyze this question and attempts to find a solution. My premise is that disagreement happens because of differences in hierarchical value ranking, or quite simply because some problems are more important to some people than others. Theories of choice, however, influenced by concepts such as "freedom of choice," conceal the hierarchical nature of our choices, leading (...) to confusion over the nature and degree of our ethical disagreements. I propose then that ethical disagreements can be reduced when we understand hierarchy as an essential element in moral choice theory. (shrink)

This paper defends the idea that phenomenological approaches to self-consciousness can enrich the current analytic philosophy of perception, by showing how phenomenological discussions of minimal self-consciousness can enhance our understanding of the phenomenology of conscious perceptual experiences. As a case study, I investigate the nature of the relationship between naïve realism, a contemporary Anglophone theory of perception, and experiential minimalism (or, the ‘minimal self’ view), a pre-reflective model of self-consciousness originated in the Phenomenological tradition. I argue that naïve realism (...) is not only compatible with, but can be supplemented with experiential minimalism in a novel way. The suggestion is that there are reasons to combine naïve realism and experiential minimalism. My focus here will be on drawing a connection between the notion of minimal self and two core theoretical commitments of naïve realism, relationalism and transparency. (shrink)

Perception plays a central and wide-ranging role in the philosophy of Margaret Cavendish. In this paper, I argue that Cavendish holds a naïve realist theory of perception. The case draws on what Cavendish has to say about perceptual presentation, the role of sympathy in experience, the natures of hallucination and of illusion, and the individuation of kinds. While Cavendish takes perception to have representational content, I explain how this is consistent with naïve realism. In closing, I address challenges to (...) the interpretation, one of which turns on whether Cavendish allows for action at a distance. I argue that she does. (shrink)

Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a (...) serious problem: an internalized version of Cut can be proved for a Curry-like sentence. We also evaluate a number of possible ways of escaping this difficulty. (shrink)

The viability of a naïve realist theory of memory was a lively debate for philosophers of mind in the first half of the twentieth century. More recently, though, naïve realism has been largely abandoned as a non-starter in the memory literature, with representationalism being the standard view held by philosophers of memory. But rather than being carefully argued, the dismissal of naïve realism is an assumption that sits at the back of much recent theorizing in the philosophy of memory. (...) In this paper, we identify three reasons why philosophers of memory have felt compelled to outright reject naïve realism. We argue that none of those reasons are successful. Thus, far from being a non-starter, we argue that naïve realism is a theoretical perspective that needs to be given serious consideration in current philosophy of memory debates. (shrink)

This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential account of conditionals offered by Crupi and Iacona. As will be shown, in a first-order language that contains a naïve truth predicate and a suitable conditional, one can define a validity predicate in accordance with the thesis that the inference from a conjunction of premises to a conclusion is valid when the corresponding conditional is true. The validity (...) predicate so defined significantly increases our expressive resources and provides a coherent formal treatment of paradoxical arguments. (shrink)

This paper describes a method for the analysis of the evolutionary path of a complex, dynamic, and contingent social phenomenon in an empirical setting. Given empirical evidence of a surprising or anomalous fact, which contradicts the prediction of the wide-acknowledged theory, the goal is to formulate a plausible explanation based on the context of occurrence, taking a holistic and historical point of view. The procedure begins by translating theoretical propositions into grammar rules to describe patterns of either individual action (...) or interaction that may occur within the hypothesized social system. The result is a category of social process in which the objects are types of decision-making events carried by a stable community of actors over time, and the relationships between them are state transitions revealed in the sequences of event outcomes. Therefore, structural comparison between pairs of representative instances result in an extension of the category of social processes, relying on the configurations of contextual conditions that enable the occurrence of the new event outcome in specific empirical settings. (shrink)

Husserl and Cassirer stand, according to their own self-understanding, as key 20th century figures in the cultivation of Enlightenment’s principles and views on humanity, culture, and history. In a word, they both understand European culture and history as a story of progress (§ 1). As I see it, central in a culture and its dynamics is its system of values, and a grounded understanding of the issue of progress presupposes an adequate theory of the standing or constitution as well (...) as of the givenness and transvaluation of values. Neither Husserl nor Cassirer, however, actually advanced any such theory. We are still in need of one in order to account for culture’s formation and dynamics in history. Next, I briefly review Husserl’s and Cassirer’s available problematic views on values (§ 2). Then, in § 3, I examine some of the central problems in the traditional approaches to culture and to values. In § 4, I appeal to Köhler’s very interesting Gestalt theoretical approach to values and pinpoint some of its problems. Next, in § 5, I suggest how we could start the research from below, from the level of the organism, which could eventually shed some new light on the problem of value constitution and givenness. Finally, in § 6, I attempt to sketch an explanation for how we can use this new approach to values in order to understand actual cultural formation and its historicity, in a way that goes further than the whiggish philosophy of history. (shrink)

We introduce the category of mereotopology Mtop as an alternative category to that of topology Top, stating ontological consequences throughout. We consider entities such as boundaries utilizing Brentano’s thesis and holes utilizing homotopy theory with a rigorous proof of Hausdorff Spaces satisfying [GEM]TC axioms. Lastly, we mention further areas of study in this category.

In this paper we propose a very general de nition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide a new (...) semantical account for abstract logical systems, particularly for many-valued and paraconsistent logics. (shrink)

Conspiracies are, by definition, a group activity; to conspire requires two or more people working together towards some end, typically in secret. Conspirators have intentions; this is borne out by the fact they want some end and are willing to engage in action to achieve. Of course, what these intentions are can be hard to fathom: historians have written a lot about the intentions of the assassins of Julius Caesar, for example; did they want to restore the Republic; was Marcus (...) Brutus lusting after power; was it an attempt to curb the ambitions of the plebeian class, who saw in Caesar someone not unlike themselves? If intentions can be hard to infer, who is a knowing conspirator and who is a dupe is almost as tricky to parse. Not all purported members of a conspiracy are conspirators, even if they aid and abet the conspiracy. Take, for example, the notorious lax engineer who the conspirators know will sign off on substandard building compliance measures, making it all the easier for them to plant their controlled demolitions. On some account of causal or even moral responsibility the lax engineer would then be responsible for the subsequent event, the one the conspirators desired. Yet it also seems clear that even if she is responsible in some sense for the culminating event of the conspiracy, it is clear that they did not conspire. Or, at least, we would like to think so, although should the authorities find out about the lax engineer’s involvement, they may well be considered part of the conspiracy, especially if the conspirators do their best to hide their own involvement or identities. (shrink)

This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory.

The idea of a responsible cosmopolitan state (RCS) represents a recent attempt to reconcile the utopianism of cosmopolitan political theory and the practical constraints arising from the current realities of politics among territorial and largely self-interested states. I show in the chapter that the neorealist and/or geopolitical challenge rests on a misconception about what cosmopolitanism is meant to provide, because immediate practical advice is only a part of what normative political theory may bring to the table. Besides the (...) notion of self-interest which can be interpreted in different ways, it is mainly the action-modifying role of norms (especially international/supranational law) which may gradually change the game. Since the sustenance of state capacities is often preconditioned by events which take place beyond state borders, shared rules of conduct allow for more effective coordination in cases where collective action is required. Although the idea of a RCS primarily targets foreign policy priorities of smaller/weaker states (not-great-powers), it may turn out that collective action problems arising from empirical realities of the 21st century increasingly put great powers under pressure to accept such self-imposed constraints and comply with them. In the final part of the paper, however, I explain why this ‘cosmopolitan optimism’ needs to be aware of its own limitations, singling out the problems of internal motivation of actors in world politics and the deeper meaning of sovereignty which precludes an easy switch to the language of dispersed, pooled, or relational sovereignty. I conclude by arguing that if we are to take cosmopolitan ideals seriously, the RCS most likely represents a transitional stage on the route towards a centralised global political authority. (shrink)

The precondition of any feminist politics – a usable category of ‘woman’ – has proved to be difficult to construct, even proposed to be impossible, given the ‘problem of exclusion’. This is the inevitable exclusion of at least some women, as their lives or experiences do not fit into the necessary and sufficient condition(s) that denotes group membership. In this paper, I propose that the problem of exclusion arises not because of inappropriate category membership criteria, but because of (...) the presumption that categories can only be organised by identity relations or shared properties among their members. This criterion of sameness as well as the characterisation of this exclusion as essentialism attests to a metaphysics that is not conducive to resistance and liberatory projects. Following a strain of hybrid thinking in feminist and post-colonial theory, I outline an alternative pluralist logic that confronts oppressive binaries that impede theory work in gender, sexuality, and race theory, and limit political action and resistance. The problem of exclusion is neither irresolvable nor is it essentialism. Instead it is a denial of subjectivity due to pseudodualistic self/Other dichotomies that can be resisted by adopting a new categorial logic. While this paper focuses on the specific problem of formulating a category of ‘woman’, it has implications for other areas of gender, critical race, and postcolonial theory. Rather than working toward an inclusive category founded on sameness, theorists need to develop independent and positive categories grounded in difference. Our current categorial logic does not permit such a project, and therefore a new metaphysics must be adopted. (shrink)

Analytical categories of scientific cultures have typically been used both exclusively and universally. For instance, when styles of scientific research are employed in attempts to understand and narrate science, styles alone are usually employed. This article is a thought experiment in interweaving categories. What would happen if rather than employ a single category, we instead investigated several categories simultaneously? What would we learn about the practices and theories, the agents and materials, and the political-technological impact of science if we (...) analyzed and applied styles, paradigms, and models simultaneously? I address these questions in general and for a specific case study: a brief history of systematics. (shrink)

According to non-conceptualist interpretations, Kant held that the application of concepts is not necessary for perceptual experience. Some have motivated non-conceptualism by noting the affinities between Kant's account of perception and contemporary relational theories of perception. In this paper I argue (i) that non-conceptualism cannot provide an account of the Transcendental Deduction and thus ought to be rejected; and (ii) that this has no bearing on the issue of whether Kant endorsed a relational account of perceptual experience.