Categorical Properties Research Articles

On the apparatus of differentiation DI–DV for posets

The apparatus of differentiation DI–DV was introduced by A.G. Zavadskij to classify different kind of posets, in particular, Zavadskij et al. described categorical properties of algorithms of differentiation DI and DII as Gabriel did for the algorithm of differentiation with respect to a maximal point introduced by Nazarova and Roiter. In this paper, it is presented categorical properties of the algorithms of differentiation DIII, DIV and DV for posets with involution.

Modal Status of Laws of Nature

In this paper, I defend the contingency view on the laws of nature: laws of nature hold in metaphysically contingent way. First, I present an argument to demonstrate that categorical properties exist, and point out that the contingency view follows if we accept the existence of categorical properties. Second, through the critical examination of the view that laws of nature hold in metaphysically necessary way, I point out that we should take the conceivability into consideration in deciding the range of possibility and hence we should accept the contingency view. Third, I argue that this paper's approach to appeal to the conceivability mitigate the severity of a problem with categorical properties, that is, a problem of quiddity. Finally, I argue the philosophical implication of the contingency view in relation to contemporary Humeanism. In my view, though it may sound strange, those who support contemporary Humean metaphysics should take a rationalistic stance.

A nice subclass of functionally countable spaces

A space $X$ is {functionally countable} if $f(X)$ is countable for any continuous function $f\colon X \to {\mathbb{R}}$. We will call a space $X$ {exponentially separable} if for any countable family ${\mathcal{F}}$ of closed subsets of $X$, there exists a countable set $A\subset X$ such that $A\cap \bigcap {\mathcal{G}}\neq\emptyset$ whenever ${\mathcal{G}}\subset {\mathcal{F}}$ and $\bigcap {\mathcal{G}}\neq\emptyset$. Every exponentially separable space is functionally countable; we will show that for some nice classes of spaces exponential separability coincides with functional countability. We will also establish that the class of exponentially separable spaces has nice categorical properties: it is preserved by closed subspaces, countable unions and continuous images. Besides, it contains all Lindelof $P$-spaces as well as some wide classes of scattered spaces. In particular, if a scattered space is either Lindelof or ${\omega}$-bounded, then it is exponentially separable.

Does Dispositionalism Entail Panpsychism?

According to recent arguments for panpsychism, all (or most) physical properties are dispositional, dispositions require categorical grounds, and the only categorical properties we know are phenomenal properties. Therefore, phenomenal properties can be posited as the categorical grounds of all (or most) physical properties—in order to solve the mind–body problem and/or in order avoid noumenalism about the grounds of the physical world. One challenge to this case comes from dispositionalism, which agrees that all physical properties are dispositional, but denies that dispositions require categorical grounds. In this paper, I propose that this challenge can be met by the claim that the only (fundamentally) dispositional properties we know are phenomenal properties, in particular, phenomenal properties associated with agency, intention and/or motivation. Versions of this claim have been common in the history of philosophy, and have also been supported by a number of contemporary dispositionalists (and other realists about causal powers). I will defend a new and updated version of it. Combined with other premises from the original case for panpsychism—which are not affected by the challenge from dispositionalism—it forms an argument that dispositionalism entails panpsychism.

Do Categorical Properties Confer Dispositions on Their Bearers?

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

Can the Russellian Monist Escape the Epiphenomenalist’s Paradox?

Russellian monism—an influential doctrine proposed by Russell (The analysis of matter, Routledge, London, 1927/1992)—is roughly the view that physics can only ever tell us about the causal, dispositional, and structural properties of physical entities and not their categorical (or intrinsic) properties, whereas our qualia are constituted by those categorical properties. In this paper, I will discuss the relation between Russellian monism and a seminal paradox facing epiphenomenalism, the paradox of phenomenal judgment: if epiphenomenalism is true—qualia are causally inefficacious—then any judgment concerning qualia, including epiphenomenalism itself, cannot be caused by qualia. For many writers, including Hawthorne (Philos Perspect 15:361–378, 2001), Smart (J Conscious Stud 11(2):41–50, 2004), and Braddon-Mitchell and Jackson (The philosophy of mind and cognition, Blackwell, Malden, 2007), Russellian monism faces the same paradox as epiphenomenalism does. I will assess Chalmers’s (The conscious mind: in search of a fundamental theory. Oxford University Press, New York, 1996) and Seager’s (in: Beckermann A, McLaughlin BP (eds) The Oxford handbook of philosophy of mind. Oxford University Press, New York, 2009) defences of Russellian monism against the paradox, and will put forward a novel argument against those defences.

Another look at color primitivism

This article is on a precise kind of color primitivism, ‘ostensivism.’ This is the view that it is in the nature of the colors that they are phenomenal, non-reductive, structural, categorical properties. First, I differentiate ostensivism from other precise forms of primitivism. Next, I examine the core belief ‘Revelation,’ and propose a revised version, which, unlike standard statements, is compatible with a yet unstated but plausible core belief: roughly, that there are interesting things to be discovered about the nature of the colors. Finally, I show that ostensivism is the only view on color that can accommodate both proposed core beliefs.

The category of generalized crossed modules

In the definition of a crossed module $(T,G,rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate some of its categorical properties. In particular, we study the relations between epimorphisms and the surjective morphisms, and thus generalize the corresponding results of the category of (ordinary) crossed modules. By generalizing the conjugation action, we can find out what is the superiority of the conjugation to other actions. Also, we can find out a generalized crossed module with which other actions (other than the conjugation) has the properties same as a crossed module.

Categorical properties of L-fuzzifying convergence spaces

In this paper, categorical properties of L-fuzzifying convergence spaces are investigated. It is shown that (1) the category L-FYC of L-fuzzifying convergence spaces is a strong topological universe; (2) the category L-FYKC of L-fuzzifying Kent convergence spaces, as a bireflective and bicoreflective subcategory of L-FYC, is also a strong topological universe; (3) the category L-FYLC of L-fuzzifying limit spaces, as a bireflective subcategory of L-FYKC, is a topological universe.

ON STRATIFIED LATTICE-VALUED CONVERGENCE SPACES

In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our category to the categories of stratified $L$-topological spaces and of enriched $LM$-fuzzy topological spaces.

Logarithmic link invariants of [formula omitted] and asymptotic dimensions of singlet vertex algebras

We study relationships between the restricted unrolled quantum group U‾qH(sl2) at q=eπi/r, and the singlet vertex operator algebra M(r), r≥2. We use deformable families of modules to efficiently compute (1,1)-tangle invariants colored with projective U‾qH(sl2)-modules. These invariants relate to the colored Alexander tangle invariants studied in [6,40]. It follows that the regularized asymptotic dimensions of characters of M(r), studied previously by the first two authors, coincide with the corresponding modified traces of open Hopf link invariants. We also discuss various categorical properties of M(r)-mod in connection to braided tensor categories.

Dispositional and categorical properties, and Russellian Monism

This paper has two main aims. The first is to present a general approach for understanding “dispositional” (or “structural”) and “categorical” properties; the second aim is to use this approach to criticize Russellian Monism. On the approach I suggest, what are usually thought of as “dispositional” and “categorical” properties are really just the extreme ends of a spectrum of options. The approach allows for a number of options between these extremes, and it is plausible, I suggest, that just about everything of scientific interest falls in this middle ground. I argue that Russellian Monism depends for its plausibility on the unarticulated assumption that there are no properties in the middle ground.

Unified approach to graphs and metric spaces

Abstract The paper provides a generalization of a metric with values in a general structure. Quantales and special kinds of ordered monoids are shown to be suitable for this purpose. Topological and categorical properties of spaces with such generalized metrics are studied and a special emphasis is given on paths in these spaces.

On Monotone Determined Spaces

In this paper, we investigate some basic properties, especially categorical properties, of monotone determined spaces. For a topology τ, we construct a monotone determined topology md(τ). The main results are: (1) for a space (X,τ), then md(τ) is the weakest monotone determined topology on X containing τ; (2) the category Topmd of monotone determined spaces with continuous maps is fully co-reflexive in the category Top of all topology spaces with continuous maps; (3) the category Topmd is cartesian closed.

Categorical, Homological, and Homotopical Properties of Algebraic Objects

This monograph is based on the doctoral dissertation of the author defended in the Iv. Javakhishvili Tbilisi State University in 2006. It begins by developing internal category and internal category cohomology theories (equivalently, for crossed modules) in categories of groups with operations. Further, the author presents properties of actions in categories of interest, in particular, the existence of an actor in specific algebraic categories. Moreover, the reader will be introduced to a new type of algebras called noncommutative Leibniz–Poisson algebras, with their properties and cohomology theory and the relationship of new cohomologies with well-known cohomologies of underlying associative and Leibniz algebras. The author defines and studies the category of groups with an action on itself and solves two problems of J.-L. Loday. Homotopical and categorical properties of chain functors category are also examined.

A data driven approach to understanding the organization of high-level visual cortex

The neural representation in scene-selective regions of human visual cortex, such as the PPA, has been linked to the semantic and categorical properties of the images. However, the extent to which patterns of neural response in these regions reflect more fundamental organizing principles is not yet clear. Existing studies generally employ stimulus conditions chosen by the experimenter, potentially obscuring the contribution of more basic stimulus dimensions. To address this issue, we used a data-driven approach to describe a large database of scenes (>100,000 images) in terms of their visual properties (orientation, spatial frequency, spatial location). K-means clustering was then used to select images from distinct regions of this feature space. Images in each cluster did not correspond to typical scene categories. Nevertheless, they elicited distinct patterns of neural response in the PPA. Moreover, the similarity of the neural response to different clusters in the PPA could be predicted by the similarity in their image properties. Interestingly, the neural response in the PPA was also predicted by perceptual responses to the scenes, but not by their semantic properties. These findings provide an image-based explanation for the emergence of higher-level representations in scene-selective regions of the human brain.

Key physicochemical properties of nanomaterials in view of their toxicity: an exploratory systematic investigation for the example of carbon-based nanomaterial

Currently, a noncomprehensive understanding of the physicochemical properties of carbon-based nanomaterial (CBNs), which may affect toxic effects, is still observable. In this study, an exploratory systematic investigation into the key physicochemical properties of multiwall carbon nanotube (MWCNT), single-wall carbon nanotube (SWCNT), and C60-fullerene on their ecotoxicity has been undertaken. We undertook an extensive survey of the literature pertaining to the ecotoxicity of organism representative of the trophic level of algae, crustaceans, and fish. Based on this, a set of data reporting both the physicochemical properties of carbon-based nanomaterial and the observed toxic effect has been established. The relationship between physicochemical properties and observed toxic effect was investigated based on various statistical approaches. Specifically, analysis of variance by one-way ANOVA was used to assess the effect of categorical properties (use of a dispersant or treatments in the test medium, type of carbon-based nanomaterial, i.e., SWCNT, MWCNT, C60-fullerene, functionalization), while multiple regression analysis was used to assess the effect of quantitative properties (i.e., diameter length of nanotubes, secondary size) on the toxicity values. The here described investigations revealed significant relationships among the physicochemical properties and observed toxic effects. The research was mainly affected by the low availability of data and also by the low variability of the studies collected. Overall, our results demonstrate that the here proposed and applied approach could have a major role in identifying the physicochemical properties of relevance for the toxicity of nanomaterial. However, the future success of the approach would require that the ENMs and the experimental conditions used in the toxicity studies are fully characterized.

Why space is not one-dimensional: Location may be categorical and imagistic.

In our commentary, we raise concerns with the idea that location should be considered a gestural component of sign languages. We argue that psycholinguistic studies provide evidence for location as a "categorical" element of signs. More generally, we propose that the use of space in sign languages comes in many flavours and may be both categorical and imagistic. In their target article, Goldin-Meadow & Brentari (G-M&B) discuss several observations suggesting that the use of space is imagistic and may not form part of the categorical properties of sign languages. Specifically, they point out that (1) the number of locations toward which agreeing verbs can be directed is not part of a discrete set, (2) event descriptions by users of different sign languages and hearing nonsigners exhibit marked similarities in the use of space, and (3) location as a phonological parameter is not categorically perceived by native signers. It should be noted that G-M&B acknowledge that categorical properties of location and movement may simply not have been captured yet because the proper investigative tools are not yet readily available.

Influence of category coherence and type of base-rate acquisition on property generalization

Category coherence involves identifying similarities between social categories, such as jobs and hobbies, and is primarily used for generalizing or drawing inferences about their properties. Category coherence is also used for drawing inferences from explicit information, such as base rates. For example, people generalize the properties of groups or brands from multiple sources (e.g., survey results and the share market in periodicals). However, generalizing the properties of categories using explicit base-rate information may not always involve category coherence; rather, it may involve directly analyzing base-rate information. Therefore, this study attempts to distinguish between conditions in which people use category coherence and explicit base-rate information. Specifically, we proposed that people acquiring explicit base-rate knowledge—described as a percentage—would generalize a category's properties according to its base rate; however, for base-rate information acquired via direct observation, the inductive strength in generalizing properties would be greater for categories with high levels of coherence. Our results (Experiment 1 and Experiment 2) validated these two predictions. Finally, the interaction between category coherence and type of base-rate acquisition was discussed.

Leukemic Stem Cells Identities: A Philosophical Analysis

What are leukemic stem cells (LSCs)? This is a biological, a semantic, and a philosophical question. Leukemic stem cells raise a number of questions for onco-hematologists in particular when it comes to their clinical relevance. What are their functions in the initiation and in the progression of the disease? How to identify them? How to target them without damaging the non-malignant hematopoietic stem cells (HSCs)? Given that LSCs come from HSCs or progenitors, a semantic question arises: should we rather call them leukemic initiating cells? or leukemic propagating cells? As a philosopher, I approach all these biological and semantic issues with a slightly different perspective. Instead of asking what are LSCs, I will start by asking what kind of property is stemness.In previous work, I performed an analysis of the scientific literature on stem cells (including cancer stem cells) and framed a classification of their possible identities (Laplane, HUP 2016; reviewed in Clevers, Nature 2016):Categorical: stemness is a purely intrinsic property (e.g. of categorical property: the atomic number of chemical elements).Dispositional: stemness is an intrinsic property whose expression depends on extrinsic stimuli from the niche (e.g. of dispositional property: fragility).Relational: stemness is an extrinsic property that depends on a relationship between the cell and its environment; the microenvironment can induce stemness (e.g. of relational property: being the sister of someone).Systemic: stemness is an extrinsic property, maintained and controlled at the level of the system (e.g. of systemic properties: soccer positions that depend on the system of play)Here, I applied this framework to LSCs, in particular in acute myeloid leukemia. This analysis of the identity of stemness matters for onco-hematology because we cannot get rid of categorical, disposition, relational, and systemic properties in the same way. Thus, different therapeutic strategies will have different efficacy depending on the identity of LSCs. For example, targeting LSCs will be much more efficient if they are categorical or dispositional. Targeting the stem cell niche will be more efficient if they are dispositional or relational. But both strategies will lack efficiency if they are systemic. In such cases multi-drug treatments will predictably be more appropriate than targeted therapies.We think about properties as having fixed identities. This is how we study, learn, teach, and investigate biology, and more generally this is how we think. This typological thinking, inherited from Aristotle and Plato, applies well to normal hematopoiesis where most if not all reports describe stemness as a dispositional property. However, the progression of hematological malignancies, from clonal hematopoiesis and pre-malignant stages to chronic and acute leukemia, questions the relevance of this typological thinking in cancer. A first question is whether HSCs, pre-LSCs, and LSCs have the same identity. A second one is whether LSCs of different hematological malignancies and the LSCs in one patient all have the same identity. I will discuss cases of genetic and epigenetic alterations that suggest possible switches in stemness identity and their consequences for therapies.To conclude, I used a classical philosophical method developed in three steps: i- analysis of the scientific literature, ii- production of conceptual distinctions, iii- analysis of their consequences. I suggested the distinction between four stemness identities (categorical, dispositional, relational, systemic). HSCs fits the dispositional identity, suggesting that both LSCs-targeting and niche-targeting therapies could be efficient (provided that we can identity and target them properly). However, the identity of LSCs can differ from that of HSCs. Moreover, in contrast with HSCs that have one unique and stable identity, LSCs can be categorical, dispositional, relational, or systemic, and they can switch from one to another identity following particular genetic and epigenetic insults. This drastically complicates the therapeutic approaches and highlights the need to develop multiple therapies.ReferencesLaplane L, Cancer Stem Cells: Philosophy and Therapies. Harvard University Press, Cambridge (MA), 2016.Clevers H, Cancer Therapy: Defining Stemness. Nature 2016; 534(7606): 176-177. DisclosuresNo relevant conflicts of interest to declare.