Suppose one has a system, the infinite set of positive integers, P, and one wants to study the characteristics of a subset (or subsystem) of that system, the infinite subset of odd positives, O, relative to the overall system. In mathematics, this is done by pairing off each odd with a positive, using a function such as O=2P+1. This puts the odds in a one-to-one correspondence with the positives, thereby, showing that the subset of odds and the original set of (...) positives are the same size, or have the same cardinality. This counter-intuitive result ignores the “natural” relationship of one odd for every two positives in the sequence of positive integers, which would suggest that O is one-half the size of P. However, in the set of axioms that constitute mathematics, it is considered valid. Fair enough. In the physical universe (i.e., the starting system), though, relationships between entities matter. In biochemistry, if you start with an organism, say a rat, and you want to study its heart, you can do this by removing some heart cells and studying them in isolation in a cell culture system. But, the results often differ compared to what occurs in the intact animal because studying the isolated cultured cells ignores the relationships in the intact body between the cells, the rest of the heart tissue and the rest of the rat. In chemistry, if a copper atom were studied in isolation, it would never be known that copper atoms in bulk can conduct electricity because the atoms share their electrons. In physics, the relationships between inertial reference frames in relativity, and observer and observed in quantum physics can't be ignored. Relationships matter in the physical world, but the mathematics of infinite sets is still used to describe it. Does this matter? It seems to, at least in physics. Infinities cause numerous problems in theoretical physics such as non-renormalizability and problems in unifying quantum mehanics and general relativity . This suggests that the pairing off method and the mathematics of infinite sets based on it are analogous to a cell culture system or studying a copper atom in isolation if they are used in studying the physical universe because they ignore the inherent relationships between entities. In the real, physical world, the natural, inherent, relationships between entities can't be ignored. Said another way, the set of axioms that constitute abstract mathematics may be similar but not identical to the set of physical axioms by which the real, physical universe runs. This suggests that the results from abstract mathematics about infinities may not apply to or should be modified for use in physics. (shrink)

The link between the high-order metaphysics and abstractions, on the one hand, and choice in the foundation of set theory, on the other hand, can distinguish unambiguously the “good” principles of abstraction from the “bad” ones and thus resolve the “bad company problem” as to set theory. Thus it implies correspondingly a more precise definition of the relation between the axiom of choice and “all company” of axioms in set theory concerning directly or indirectly abstraction: the principle of abstraction, axiom (...) of comprehension, axiom scheme of specification, axiom scheme of separation, subset axiom scheme, axiom scheme of replacement, axiom of unrestricted comprehension, axiom of extensionality, etc. (shrink)

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

Neo-Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non-reflexive abstraction relations to restricted abstraction principles.

Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and (...) Replies5.1 Yablo’s likely response5.2 Charity6 Conclusion. (shrink)

It is illegitimate to read any ontology about "race" off of biological theory or data. Indeed, the technical meaning of "genetic variation" is fluid, and there is no single theoretical agreed-upon criterion for defining and distinguishing populations (or groups or clusters) given a particular set of genetic variation data. Thus, by analyzing three formal senses of "genetic variation"—diversity, differentiation, and heterozygosity—we argue that the use of biological theory for making epistemic claims about "race" can only seem plausible when it relies (...) on the user’s own assumptions about race; the move from biological measures to claims about “race” inevitably amounts to a pernicious reification. We also excavate assumptions in the history of the technical discourse over the concept of "race" (e.g., Livingstone's and Dobzhansky's 1962 exchange, Edwards' 2003 response to Lewontin 1972, as well as contemporary discussions of cladistic "race", and "races" as clusters). We show that claims about the existence (or non-existence) of "race" are underdetermined by biological facts, methods, and theories. Biological theory does not force the concept of "race" upon us; our social discourse, social ontology, and social expectations do. We become prisoners of our abstractions at our own hands, and at our own expense. (shrink)

An important lesson that philosophy can learn from the Turing Test and computer science more generally concerns the careful use of the method of Levels of Abstraction (LoA). In this paper, the method is first briefly summarised. The constituents of the method are “observables”, collected together and moderated by predicates restraining their “behaviour”. The resulting collection of sets of observables is called a “gradient of abstractions” and it formalises the minimum consistency conditions that the chosen abstractions must satisfy. Two useful (...) kinds of gradient of abstraction – disjoint and nested – are identified. It is then argued that in any discrete (as distinct from analogue) domain of discourse, a complex phenomenon may be explicated in terms of simple approximations organised together in a gradient of abstractions. Thus, the method replaces, for discrete disciplines, the differential and integral calculus, which form the basis for understanding the complex analogue phenomena of science and engineering. The result formalises an approach that is rather common in computer science but has hitherto found little application in philosophy. So the philosophical value of the method is demonstrated by showing how making the LoA of discourse explicit can be fruitful for phenomenological and conceptual analysis. To this end, the method is applied to the Turing Test, the concept of agenthood, the definition of emergence, the notion of artificial life, quantum observation and decidable observation. It is hoped that this treatment will promote the use of the method in certain areas of the humanities and especially in philosophy. (shrink)

I reconcile the spatiotemporal location of repeatable artworks and impure sets with the non-location of natural numbers despite all three being varieties of abstract objects. This is possible because, while the identity conditions for all three can be given by abstraction principles, in the former two cases spatiotemporal location is a congruence for the equivalence relation featuring in the relevant principle, whereas in the latter it is not. I then generalize this to other ‘physical’ properties like shape, mass, and causal (...) powers. (shrink)

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...) Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. This paper considers how the doctrine of symbolism and the philosophers' different commitments to the laws of logic, especially the Law of Non-Contradiction (LNC), enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

A paradox about sets of properties is presented. The paradox, which invokes an impredicatively defined property, is formalized in a free third-order logic with lambda-abstraction, through a classically proof-theoretically valid deduction of a contradiction from a single premise to the effect that every property has a unit set. Something like a model is offered to establish that the premise is, although classically inconsistent, nevertheless consistent, so that the paradox discredits the logic employed. A resolution through the ramified theory of types (...) is considered. Finally, a general scheme that generates a family of analogous paradoxes and a generally applicable resolution are proposed. (shrink)

(...) However, whether we chose a weak or strong approximation, the set would not make any sense at all, if (once more) this choice would not be justified in either temporal or spatial sense or given the context of possible applicability of the set in different circumstances. This would obviously represent a dualism in itself as we would (for instance) posit and apply a full identity-equality-equivalence of x and y when applying Newtonian physics to certain observations we make (it would (...) be the case of neural correlates), and we would posit and apply a non - identity-equality-equivalence of x and y when applying Quantum mechanics to other observations. Following this dualism in and of theories, the same sate would need to be slightly modified: U2:(x~y)∪(x≈y); U3:(x~y)∩(x≈y); U4a:(x~y)⊆(x≈y) vs. U4b:(x~y)⊇(x≈y). (shrink)

The first year of design education is essential for students as it is their initial interaction with the design process. Awareness of the body through dance has the potential to reveal bodily experience in space. Abstraction of embodied experience contributes to realising the significance of the body and its analytical dimension for spatial and structural design. This study investigates the impact of embodied experience and abstraction on the architectural design process and the outcome through correlation and regression analysis. We observed (...) that increasing awareness of the space through bodily movement and its drawn representation positively impacted students’ success in architectural design. Also, the measures related to space and structure mainly advanced students’ success in the final design. However, the association of the abstraction process with the final design remained limited. The study’s contribution is the systematic and statistical evaluation of the relationship between body, movement, abstraction and architectural design by constructing a set of measures from various stages of the design studio. We hope our research will provide a basis for the upcoming discourse. (shrink)

ABSTRACT Theories of sets such as Zermelo Fraenkel set theory are usually presented as the combination of two distinct kinds of principles: logical and set-theoretic principles. The set-theoretic principles are imposed ‘on top’ of first-order logic. This is in agreement with a traditional view of logic as universally applicable and topic neutral. Such a view of logic has been rejected by the intuitionists, on the ground that quantification over infinite domains requires the use of intuitionistic rather than classical logic. In (...) the following, I consider constructive set theories, which use intuitionistic rather than classical logic, and argue that they manifest a distinctive interdependence or an entanglement between sets and logic. In fact, Martin-Löf type theory identifies fundamental logical and set-theoretic notions. Remarkably, one of the motivations for this identification is the thought that classical quantification over infinite domains is problematic, while intuitionistic quantification is not. The approach to quantification adopted in Martin-Löf’s type theory is subtly interconnected with its predicativity. I conclude by recalling key aspects of an approach to predicativity inspired by Poincaré, which focuses on the issue of correct quantification over infinite domains and relate it back to Martin-Löf type theory. (shrink)

Abstract: Theories of rough sets and fuzzy sets are related and complementary methodologies to handle uncertainty of vagueness and coarseness, respectively. They are generalizations of classical set theory for modeling vagueness and uncertainty. A fundamental question concerning both theories is their connections and differences. There have been many studies on this topic. Topology is a branch of mathematics, whose ideas exist not only in almost all branches of mathematics but also in many real life applications. The topological structure on an (...) abstract set is used as the base, which used to extract knowledge from data. In this paper: topological structure is used to study the relation between rough sets and fuzzy sets. Membership function is used to convert from rough set to fuzzy set and vice versa. This conversion will achieve the advantages of two theories. Some examples and theories are introduced to indicate the importance of using general binary relations in the construction of rough set concepts, and indicate the relation between rough sets and fuzzy sets according to the topological spaces. (shrink)

Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. (...) I argue that mathematicians introduce genuine models and I offer a rough classification of these models. (shrink)

We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction on which the (...) purported proof of inconsistency relies is analogous to naïve unrestricted set-theoretic comprehension. We conclude that logic imposes a restriction on property comprehension, a restriction that is satisfied by the ramified theory of types. By extension, our observations constitute defenses of theories that are structurally similar to SH+, such as the theory of singular propositions, against similar purported disproofs. (shrink)

Answer Set Programming is a new paradigm based on logic programming. The main component of answer set programming is a system that finds the answer sets of logic programs. During the computation of an answer set, systems are faced with choice points where they have to select a literal and assign it a truth value. Generally, systems utilize some heuristics to choose new literals at the choice points. The heuristic used is one of the key factors for the performance of (...) the system. A new heuristic for answer set programming has been developed. This heuristic is inspired by hierarchical planning. The notion of criticality, which was introduced for generating abstraction hierarchies in hierarchical planning, is used in this heuristic. The resulting system (CSMODELS) uses this new heuristic in a static way. CSMODELS is based on the system SMODELS. The experimental results show that this new heuristic is promising for answer set programming. A comparison of search times with SMODELS demonstrate CSMODELS’ usefulness. (shrink)

In Book I, Part I, Section VII of the Treatise, Hume sets out to settle, once and for all, the early modern controversy over abstract ideas. In order to do so, he tries to accomplish two tasks: (1) he attempts to defend an exemplar-based theory of general language and thought, and (2) he sets out to refute the rival abstraction-based account. This paper examines the successes and failures of these two projects. I argue that Hume manages to articulate a plausible (...) theory of general ideas; indeed, a version of his account has defenders in contemporary cognitive science. But Hume fails to refute the abstraction-based account, and as a result, the early modern controversy ends in a stalemate, with both sides able to explain how we manage to speak and think in general terms. Although Hume fails to settle the controversy, he nevertheless advances it to a point from which we have yet to progress: the contemporary debate over abstract ideas in cognitive science has stalled on precisely this point. (shrink)

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) It is hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). Nine predictions are derived (three semantic, two pragmatic, and four mixed) regarding people's assessment of how well each of the five diagrams expresses the meaning of each of the quantified sentences. The results from three experiments, using Gergonne's circles or an adaptation of Leibniz lines as external representations, are reported and shown to support the predictions. (shrink)

This thesis is concerned with the ways in which meaning is generically mediated in the novel. In particular it addresses the productive diversity of meanings generated by critical interpretation and asks how, given this diversity, comprehension and consensus might be possible. I argue that the construction of subject, object, space and time is achieved in the novel through different manifestations of four key metaphors: voice, view, setting and event. These metaphors supply meanings that rely on a common experience of embodiment. (...) Embodiment supplies the basis for an intersubjectively established consensus which identifies subjects and objects in terms that correspond to the semiotic, syntagmatic and semantic uses of metaphor. I begin by surveying and reviewing certain constructionist accounts of language and meaning in order to establish the importance of metaphor in conveying meaning in rhetorical, rather than linguistic, terms. I then discuss two examples of continental philosophy on speech: Derrida on voice and Foucault on discourse. I demonstrate how meaning is rhetorically constructed according to the use to which metaphors are put—whether they denote formal, semantic, or functional aspects of meaning—through an explication of Foucault’s theory, reserving Derrida’s grammatology for my analysis of the stabilisation of meaning in the theory of certain narratologists (Gérard Genette and Marie-Laure Ryan). Voice and view are key terms in literary theory, and I examine refinements to these metaphors in Genette and Ryan. The insistence of these narratologists on restricting the rhetorical dimension of meaning undermines the value of the literary work, prompting me to argue for a relaxing of such constraints. I read Peter Carey’s True History of the Kelly Gang for its uses of voice and point of view, many of which expose the limitations of the narratological approach. This is a theoretical thesis, which engages a wide range of perspectives—constructionist, deconstructionist, sociological and structuralist—together with their various accounts of language, metaphor, speech and meaning. In terms of sociological approaches to genre and discourse, I employ the chronotope as a critical tool, examining it in the context of the theme of the country house to demonstrate the role of two of my key metaphors, setting and event, which are important for the construction of space and time in abstract terms. Focusing on novels by Jane Austen, Virginia Woolf, and Kazuo Ishiguro, in which the country house defines the space and the temporality through which thematic and “material” elements are mediated, I reveal how the chronotope supplies an overarching coherence that unites thought and event in narrative. My readings of these novels describe a theory that is concerned with the rhetorical capacities of genre rather than with taxonomic constructions of form. To this end I argue that the metaphorical dimensions of narrative—voice, view, setting and event—be loosely drawn, according to the acknowledged mutability of genre. I also emphasise the constructive effect of metaphor whilst according it a rhetorical versatility consistent with the mutability and instability of genre as a semiotic tool, concluding that consensus is achieved in our readings of novels through the form’s reliance on these four key metaphors of embodiment. These metaphors have ordinary, everyday, widespread usage beyond narrative theory; in appreciating their rhetorical value, it must be noted nonetheless that any confusion that ensues is productive, for it results in the diversities of meaning and form celebrated in the literary work. (shrink)

Abstract: Nanka is in Orumba North Local Government Area in Anambra State of Nigeria. This work centred on the function of Nwadunu in Nanka administrative set up. This work is meant to make people understand administrative set up in Nanka clearer. Thus removing doubts that often arise as regards to the function of Nwadunu institution in Nanka. The work is also meant to draw the attention of researchers and educationist to the existence of this unique institution in Nanka. The researcher’s (...) paper being a stepping stone from where other researchers can take off. In carrying out this research, the researcher prepared questionnaires for oral interviews which the researcher administered on Nwadunu himself, the clan head of Umudunu quarter, Nanka and some selected elders from the seven villages that make up Nanka. From analysis of the responses, the researcher was able to arrive at conclusion of what Nwadunu’s position in administration set up in Nanka is. (shrink)

Plato’s philosophy is important to Badiou for a number of reasons, chief among which is that Badiou considered Plato to have recognised that mathematics provides the only sound or adequate basis for ontology. The mathematical basis of ontology is central to Badiou’s philosophy, and his engagement with Plato is instrumental in determining how he positions his philosophy in relation to those approaches to the philosophy of mathematics that endorse an orthodox Platonic realism, i.e. the independent existence of a realm of (...) mathematical objects. The Platonism that Badiou makes claim to bears little resemblance to this orthodoxy. Like Plato, Badiou insists on the primacy of the eternal and immu- table abstraction of the mathematico-ontological Idea; however, Badiou’s reconstructed Platonism champions the mathematics of post-Cantorian set theory, which itself af rms the irreducible multiplicity of being. Badiou in this way recon gures the Platonic notion of the relation between the one and the multiple in terms of the multiple-without-one as represented in the axiom of the void or empty set. Rather than engage with the Plato that is gured in the ontological realism of the orthodox Platonic approach to the philosophy of mathematics, Badiou is intent on characterising the Plato that responds to the demands of a post-Cantorian set theory, and he considers Plato’s philosophy to provide a response to such a challenge. In effect, Badiou reorients mathematical Platonism from an epistemological to an ontological problematic, a move that relies on the plausibility of rejecting the empiricist ontology underlying orthodox mathematical Platonism. To draw a connec- tion between these two approaches to Platonism and to determine what sets them radically apart, this paper focuses on the use that they each make of model theory to further their respective arguments. (shrink)

What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock of (...) higher set theory the jewel of mathematical Continuum -- this genuine, even if mostly forgotten today raison d'etre of all set-theoretical enterprises to Infinity and beyond, from Georg Cantor to W. Hugh Woodin to Buzz Lightyear, by simultaneously exhibiting the limits and pitfalls of all old and new reductionist foundational approaches to mathematical truth: be it Cantor's or post-Cantorian Idealism, Brouwer's or post-Brouwerian Constructivism, Hilbert's or post-Hilbertian Formalism, Goedel's or post-Goedelian Platonism. -/- In the spirit of Zeno's paradoxes, but with the enormous historical advantage of hindsight, we claim that Cantor's set-theoretical methodology, powerful and reach in proof-theoretic and similar applications as it might be, is inherently limited by its epistemological framework of transfinite local causality, and neither can be held accountable for the properties of the Continuum already acquired through geometrical, analytical, and arithmetical studies, nor can it be used for an adequate, conceptually sensible, operationally workable, and axiomatically sustainable re-creation of the Continuum. -/- From a strictly mathematical point of view, this intrinsic limitation of the constative and explicative power of higher set theory finds its explanation in the identified in this study ultimate phenomenological obstacle to Cantor's transfinite construction, similar to topological obstacles in homotopy theory and theoretical physics: the entanglement capacity of the mathematical Continuum. (shrink)

-/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a (...) correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. -/- The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis of (...) Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

In this thesis I argue against unrestricted mereological hybridism, the view that there are absolutely no constraints on wholes having parts from many different logical or ontological categories, an exemplar of which I take to be ‘mixed fusions’. These are composite entities which have parts from at least two different categories – the membered (as in classes) and the non-membered (as in individuals). As a result, mixed fusions can also be understood to represent a variety of cross-category summation such as (...) the abstract with the concrete, the physical with the non-physical, and the possible with the impossible, just to name a few. -/- Proposed by David Lewis (1991) alongside his defence of classical mereology (the major theory of parthood which permits such transcategorial composites through its principle of unrestricted composition) it is my contention that mixed fusions are an under-examined consequence of indiscriminate mereological fusion which harbour a multitude of complications. In my attempt to discern their substantive character, throughout this thesis I make a case study of mixed fusions and uncover several problematic consequences which I think follow from their most plausible assessment. -/- These include: (1) that mixed fusions’ probable membership relations may lead to dubious foundational loops in the mereological Universe, or (2) otherwise that mixed fusions oblige an implausible ontological priority of the mereological Universe as a whole; (3) that mixed fusions contradict the reductive account of set theory they are proposed within, by plausibly being seen to have the same members as their class parts, and (4) that mixed fusions therefore confound a mereological thesis of Composition as Identity, which some (including Lewis) use to support classical mereology – a consequence which is potentially self-defeating; (5) that mixed fusions as sums of abstract and concrete entities both subvert Lewis’s (1986) system of modal realism, while (6) also undermining less expansive theories of possible worlds; and finally, (7) that even where some of the foregoing is resisted, it remains implausible that mixed fusions are ontologically innocent, because their supposed distinction from their parts in this case ensures that they need to be counted as additional entities in one’s ontology. -/- To be clear, I do not advance a theory of mereological hybrid nihilism in the sense of denying all cases of transcategorial composition. (I only cover a few select instances of mereological hybridism via mixed fusions after all.) Rather, I deny that mereological hybridism is plausible in full generality, by demonstrating that any cases of it are at least limited by the constraints that I identify. This in turn vindicates a call for a restriction on parthood theories and composition principles which allow certain types of categorially mixed entities – including restricting classical mereology with its principle of unrestricted composition. -/- Although theories of parthood like the standard classical mereology are not ordinarily developed for the sake of mereological hybrids like mixed fusions, these and other transcategorial composites are still among the logical consequences of such parthood systems operating with sufficient generality. The significance of my thesis, then, comes from showcasing how some of these kinds of entities do not conform to the systems in which they are included as required, and hence I argue for the rejection of unrestricted mereological hybridism as well as any mereological principles which support it. (shrink)

ABSTRACT: This paper serves two purposes: (i) it can be used by students as an introduction to chapters 1-5 of book iii of the NE; (ii) it suggests an answer to the unresolved question what overall objective this section of the NE has. The paper focuses primarily on Aristotle’s theory of what makes us responsible for our actions and character. After some preliminary observations about praise, blame and responsibility (Section 2), it sets out in detail how all the key notions (...) of NE iii 1-5 are interrelated (Sections 3-9). The setting-out of these interconnections makes it then possible to provide a comprehensive interpretation of the purpose of the passage. Its primary purpose is to explain how agents are responsible for their actions not just insofar as they are actions of this kind or that, but also insofar as they are noble or base: agents are responsible for their actions qua noble or base, because, typically via choice, their character dispositions are a causal factor of those actions (Section 10). The paper illustrates the different ways in which agents can be causes of their actions by means of Aristotle’s four basic types of agents (Section 11). A secondary purpose of NE iii 1-5 is to explain how agents can be held responsible for consequences of their actions (Section 12), in particular for their character dispositions insofar as these are noble or base, i.e. virtues or vices (Section 13). These two goals are not the only ones Aristotle pursues in the passage. But they are the ones Aristotle himself indicates in its first sentence and summarizes in its last paragraph; and the ones that give the passage a systematic unity. The paper also briefly consider the issues of freedom-to-do-otherwise, free choice and free-will in the contexts in which they occur (i.e. in the final paragraphs of Sections 6, 7, 12, 13). (shrink)

Abstract Do the central aims of epistemology, like those of moral philosophy, require that we designate some important place for those concepts located between the thin-normative and the non-normative? Put another way, does epistemology need "thick" evaluative concepts and with what do they contrast? There are inveterate traditions in analytic epistemology which, having legitimized a certain way of viewing the nature and scope of epistemology's subject matter, give this question a negative verdict; further, they have carried with them a tacit (...) commitment to what we argue to be an epistemic analogue of the reductionistic centralist thesis which Bernard Williams, in our view, successfully repudiates in ethics. In this essay, we challenge the epistemic analogue of the traditional but mistaken thesis. In offering an alternative to it which provides a comfortable home for the epistemic normativity which attends thick evaluative concepts, we align ourselves with what has been recently called the Value Turn in epistemology. From this perspective, we defend that, contrary to tradition, as influenced by centralist assumptions, epistemology does need thick evaluative concepts. Further, the sort of theories that will be able to give thick evaluative concepts an irreducible role in both belief and agent evaluation are adequately social epistemologies. What loosely refer to as second-wave of virtue epistemology is the widespread interest to provide a comfortable home for the role of thick normativity, as it is connected both with epistemic evaluation, and guidance. We recognize that, in breaking from centralism, there is a worry that a resulting anti-centralist theory will be reductionistic in the other direction, making the thick primary. We contend however that second-wave virtue epistemologies take different sources of social and epistemic value into account; they seek the 'right thickness' to ride with conception of epistemology and a field which due in part to virtue theory's resurgence, is today normative, diverse and expansive than was the traditional set of problems from which it emerged. (shrink)

Abstract The paper explicates a set of criteria the joint satisfaction of which is taken to qualify moral judgements as cognitive. The paper examines evidence that some moral judgements meet these criteria, and relates the resulting conception of moral judgements to ongoing controversies about cognitivism in ethics.

The paper is the final, fifth part of a series of studies introducing the new conceptions of “Hilbert mathematics” and “ontomathematics”. The specific subject of the present investigation is the proper philosophical sense of both, including philosophy of mathematics and philosophy of physics not less than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization of ontology as well as of Heidegger’s “fundamental ontology” though in a sense) and history of philosophy (deepening Heidegger’s destruction of it from (...) the pre-Socratics to the Pythagoreans). Husserl’s phenomenology and Heidegger’s derivative “fundamental ontology” as well as his later doctrine after the “turn” are the starting point of the research as established and well known approaches relative to the newly introduced conception of ontomathematics, even more so that Husserl himself started criticizing his “Philosophy of arithmetic” as too naturalistic and psychological turning to “Logical investigations” and the foundations of phenomenology. Heidegger’s “Aletheia” is also interpreted ontomathematically: as a relation of locality and nonlocality, respectively as a motion from nonlocality to locality if both are physically considered. Aristotle’s ontological revision of Plato’s doctrine is “destructed” further from the pre-Socratics' “Logos” or Heideger’s “Language” (after the “turn”) to the Pythagoreans “Numbers” or “Arithmetics” as an inherent and fundamental philosophical doctrine. Then, a leap to contemporary physics elucidates the essence of ontomathematics overcoming the Cartesian abyss inherited from Plato’s opposition of “ideas” versus “things”, and now unifying physics and mathematics, particularly allowing for the “creation from nothing” instead of the quasi-scientific myth of the “Big Bang”. Furthermore, ontomathematics needs another interpretation of arithmetic, propositional logic and set theory in the foundations of mathematics, where the latter two ones are both identified with Boolean algebra, and the former is considered to be a “half of Boolean algebra” in the exact meaning to be equated to it after doubling by a dual anti-isometric counterpart of Peano arithmetic. That unified algebraic realization of the foundations of mathematics is related to Hilbert mathematics in both “narrow and wide senses” where the latter is isomorphic to the qubit Hilbert space, thus underlying all the physical world by the newly introduced substance of quantum information being physically dimensionless and generalizing classical information measured in bits. The substance of information, whether classical or quantum, visualizes the way of the unification of physics and mathematics by merging their foundations in Hilbert arithmetic and Hilbert mathematics: thus how ontomathetics is a “first philosophy”. The relation of ontomathematics to the Socratic “human problematics”, furthermore being fundamental for Western philosophy in Modernity, is discussed. Ontomathematics implies its “substitution” by abstract information (or by “subjectless choice” relevant to it), thus “obliterating the human outline on the ocean beach sand” (by Michel Foucault’s metaphor). A reflection back from the viewpoint of mathematic to Western philosophy as the philosophy of locality ends the study. (shrink)

Abstract David Sobel (2001) objects to Bernard Williams's internalism, the view that an agent has a reason to perform an action only if she has some motive that will be served by performing that action. Sobel is an unusual challenger in that he endorses neo-Humean subjectivism, ?the view that it is the agent's subjective motivational set that makes it the case that an agent does or does not have a reason to φ? (219). Sobel's objection in fact arises from this (...) very commitment. Internalism, he says, is incompatible with the best subjectivist accounts of reasons for action?accounts that suggest that there are what he calls fragile reasons and perhaps also superfragile ones, both of which allegedly provide for counterexamples to internalism. I argue that such reasons do not in fact threaten internalism. I then briefly explore whether internalism is vulnerable to a related charge?that it commits the conditional fallacy. (shrink)

Abstract: Potatoes are edible tubers, available worldwide and all year long. They are relatively cheap to grow, rich in nutrients, and they can make a delicious treat. The humble potato has fallen in popularity in recent years, due to the interest in low-carb foods. However, the fiber, vitamins, minerals, and phytochemicals it provides can help ward off disease and benefit human health. They are an important staple food in many countries around the world. There are an estimated 200 varieties of (...) potatoes, which can be classified into a number of categories based on the cooked texture and ingredient functionality. Using a public dataset of 2400 images of potatoes, we trained a deep convolutional neural network to identify 4 types (Red, Red Washed, Sweet, and White).The trained model achieved an accuracy of 99.5% of test set, demonstrating the feasibility of this approach. (shrink)

Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities. This paper considers two interpretations of second-order logic—as being either extensional or intensional—and whether either is (...) more appropriate for this approach to the foundations of set theory. Although there seems to be a case for the extensional interpretation resulting from modal considerations, I show how there is no obstacle to starting with an intensional second-order logic. I do so by showing how the $\varepsilon$ operator can have the effect of “extensionalizing” intensional second-order entities. (shrink)

Abstract. Intelligent Tutoring System Builder (ITSB) is an authoring tool designed and developed to aid teachers in constructing intelligent tutoring systems in a multidisciplinary fields. The teacher is needed to create a set of pedagogical fundamentals, which, in line, are inured to automatically build up a broad tutor framework and construct an intelligent tutoring system. In this paper an explanation of the theory and the architecture of the tool is outlined. A presentation of several system components, the requirements of the (...) different components, integration of these components in ITSB tool are shown. Furthermore, implanting of requirements, cognitive principle, and common design fundamentals in the tool to ease the use of teachers. A variety of design matters, an example of building an intelligent tutoring system for teaching Java language using ITSB tool and an evaluation are presented. (shrink)

Abstract: Fruits are a rich source of energy, minerals and vitamins. They also contain fiber. There are many fruits types such as: Apple and pears, Citrus, Stone fruit, Tropical and exotic, Berries, Melons, Tomatoes and avocado. Classification of fruits can be used in many applications, whether industrial or in agriculture or services, for example, it can help the cashier in the hyper mall to determine the price and type of fruit and also may help some people to determining whether a (...) certain type of fruit meets their nutritional requirement. In this paper, machine learning based approach is presented for classifying and identifying 10 different fruit with a dataset that contains 6847 images use 4793 images for training, 1027 images for validation and 1027 images for testing. A deep learning technique that extensively applied to image recognition was used. We used 70% from image for training and 15% from image for validation 15% for testing. Our trained model achieved an accuracy of 100% on a held-out test set, demonstrating the feasibility of this approach. (shrink)

Artificial agents (AAs), particularly but not only those in Cyberspace, extend the class of entities that can be involved in moral situations. For they can be conceived of as moral patients (as entities that can be acted upon for good or evil) and also as moral agents (as entities that can perform actions, again for good or evil). In this paper, we clarify the concept of agent and go on to separate the concerns of morality and responsibility of agents (most (...) interestingly for us, of AAs). We conclude that there is substantial and important scope, particularly in Computer Ethics, for the concept of moral agent not necessarily exhibiting free will, mental states or responsibility. This complements the more traditional approach, common at least since Montaigne and Descartes, which considers whether or not (artificial) agents have mental states, feelings, emotions and so on. By focussing directly on mind-less morality we are able to avoid that question and also many of the concerns of Artificial Intelligence. A vital component in our approach is the Method of Abstraction for analysing the level of abstraction (LoA) at which an agent is considered to act. The LoA is determined by the way in which one chooses to describe, analyse and discuss a system and its context. The Method of Abstraction is explained in terms of an interface or set of features or observables at a given LoA. Agenthood, and in particular moral agenthood, depends on a LoA. Our guidelines for agenthood are: interactivity (response to stimulus by change of state), autonomy (ability to change state without stimulus) and adaptability (ability to change the transition rules by which state is changed) at a given LoA. Morality may be thought of as a threshold defined on the observables in the interface determining the LoA under consideration. An agent is morally good if its actions all respect that threshold; and it is morally evil if some action violates it. That view is particularly informative when the agent constitutes a software or digital system, and the observables are numerical. Finally we review the consequences for Computer Ethics of our approach. In conclusion, this approach facilitates the discussion of the morality of agents not only in Cyberspace but also in the biosphere, where animals can be considered moral agents without their having to display free will, emotions or mental states, and in social contexts, where systems like organizations can play the role of moral agents. The primary cost of this facility is the extension of the class of agents and moral agents to embrace AAs. (shrink)

Abstract Heart Attack is the Cardiovascular Disease (CVD) which causes the most deaths among CVDs. We collected a dataset from Kaggle website. In this paper, we propose an ANN model for the predicting whether a patient has a heart attack or not that. The dataset set consists of 9 features with 1000 samples. We split the dataset into training, validation, and testing. After training and validating the proposed model, we tested it with testing dataset. The proposed model reached an accuracy (...) of 98.01% on the Heart Disease Dataset. (shrink)

Abstract: The aim behind analyzing Google Stock Prices dataset is to get a fair idea about the relationships between the multiple attributes a day might have, such as: the opening price for each day, the volume of trading for each day. With over a hundred thousand days of trading data, there are some patterns that can help in predicting the future prices. We proposed an Artificial Neural Network (ANN) model for predicting the closing prices for future days. The prediction is (...) based on these features (date, opening price, highest price, lowest price, volume), which were used as input variables and (closing price) as output variable for our ANN model. Our model was created, trained, and validated using data set in JNN environment, which its title is “Google-Stock-Prices”. The model evaluation showed that the ANN model is able to predict correctly 99.48% of the validation samples. (shrink)

Abstract: Tomatoes are part of the major crops in food security. Tomatoes are plants grown in temperate and hot regions of South American origin from Peru, and then spread to most countries of the world. Tomatoes contain a lot of vitamin C and mineral salts, and are recommended for people with constipation, diabetes and patients with heart and body diseases. Studies and scientific studies have proven the importance of eating tomato juice in reducing the activity of platelets in diabetics, which (...) helps in protecting them from developing deadly blood clots. A tomato classification approach is presented with a data set containing approximately 5,266 images with 7 species belonging to tomatoes. The Neural Network Algorithms (CNN), a deep learning technique applied widely in image recognition, is used for this task. (shrink)

Abstract : Background: Vegetable agriculture is very important to human continued existence and remains a key driver of many economies worldwide, especially in underdeveloped and developing economies. Objectives: There is an increasing demand for food and cash crops, due to the increasing in world population and the challenges enforced by climate modifications, there is an urgent need to increase plant production while reducing costs. Methods: In this paper, Lemon classification approach is presented with a dataset that contains approximately 2,000 images (...) belong to 3 species at a few developing phases. Convolutional Neural Network (CNN) algorithms, a deep learning technique extensively applied to image recognition was used, for this task. The results: found that CNN-driven lemon classification applications when used in farming automation have the latent to enhance crop harvest and improve output and productivity when designed properly. The trained model achieved an accuracy of 99.48% on a held-out test set, demonstrating the feasibility of this approach. (shrink)

Abstract: This paper defends a constraint that any satisfactory decision theory must satisfy. I show how this constraint is violated by all of the decision theories that have been endorsed in the literature that are designed to deal with cases in which opinions or values are represented by a set of functions rather than a single one. Such a decision theory is necessary to account for the existence of what Ruth Chang has called “parity” (as well as for cases in (...) which agents have incomplete preferences or imprecise credences). The problem with the all of the decision theories that have been defended to account for parity is that they are committed to a claim I call unanimity: when all of the functions in the set agree that an agent ought to do A, then an agent ought to do A. A decision theory committed to unanimity violates the constraint I defend in this paper. Thus, if parity exists, a new approach to decision theory is necessary. (shrink)

ABSTRACT:Many companies engage in dialogue with nongovernmental organizations about societal issues. The question is what a regulative ideal for such dialogues should be. In the literature on corporate social responsibility, the Habermasian notion of communicative action is often presented as a regulative ideal for stakeholder dialogue, implying that actors should aim at consensus and set strategic considerations aside. In this article, we argue that in many cases, communicative action is not a suitable regulative ideal for dialogue between companies and NGOs. (...) We contend that there is often an adversarial element in the relation between companies and NGOs, and that an orientation towards consensus can be in tension with this adversarial relation. We develop an alternative approach to stakeholder dialogue called ‘agonistic deliberation.’ In this approach, conflict and strategic considerations play a legitimate and, up to a certain point, desirable role. (shrink)

Abstract: Smoke detectors are critical devices for early fire detection and life-saving interventions. This research paper explores the application of Artificial Neural Networks (ANNs) in smoke detection systems. The study aims to develop a robust and accurate smoke detection model using ANNs. Surprisingly, the results indicate a 100% accuracy rate, suggesting promising potential for ANNs in enhancing smoke detection technology. However, this paper acknowledges the need for a comprehensive evaluation beyond accuracy. It discusses potential challenges, such as overfitting, dataset size, (...) and class imbalance, and presents strategies employed to address these issues. Additionally, the paper emphasizes the importance of alternative evaluation metrics, including precision, recall, and F1-score, to assess the model's performance comprehensively. Detailed information regarding the model architecture, data preprocessing, and hyperparameter tuning is provided to enhance the reproducibility of the research. The study also discusses ethical considerations and the implications of false positives and false negatives in smoke detection applications. While achieving 100% accuracy is a notable accomplishment, this paper calls for cautious interpretation and further validation in real-world settings. It concludes by highlighting areas for future research and improvement in smoke detection technology, emphasizing the need for practical deployment and the reduction of false alarms. (shrink)

Abstract. Richard Feldman’s Uniqueness Thesis holds that “a body of evidence justifies at most one proposition out of a competing set of proposi- tions”. The opposing position, permissivism, allows distinct rational agents to adopt differing attitudes towards a proposition given the same body of evidence. We assess various motivations that have been offered for Uniqueness, including: concerns about achieving consensus, a strong form of evidentialism, worries about epistemically arbitrary influences on belief, a focus on truth-conduciveness, and consequences for peer disagreement. (...) We argue that each of these motivations either misunderstands the commitments of permissivism or is question-begging. Better understanding permissivism makes it a much more plausible position. (shrink)

Abstract. On the Direct Reference thesis, proper names are what I call ‘genuine terms’, terms whose sole semantic contributions to the propositions expressed by their use are the terms’ semantic referents. But unless qualified, this thesis implies the false consequence that sentences containing names that fail to refer can never express true or false propositions. (Consider ‘The ancient Greeks worshipped Zeus’, for instance.) I suggest that while names are typically and fundamentally used as genuine terms, there is a small class (...) of names, which I call ‘descriptive names’, whose reference is fixed by commonly associated definite descriptions, and I also suggest that there is an idiom of natural language on which such names can be used as abbreviated definite descriptions in a limited set of sentential contexts, including (1) positive and negative existentials, (2) cognitive ascriptions, and (3) uses of names to talk about myth. Uses of empty descriptive names in such contexts can then be either true or false. Relying on Gregory Currie’s theory of truth in fiction, I also propose an idiom on which fictional names can be used as short for a certain type of description in talk about fiction. Along the way, I provide arguments that names are used as short for descriptions in substantive existential statements as well as in both metamythic and metafictive contexts. I also discuss and criticize alternative views of these matters, including the views of David Braun, Saul Kripke, Peter van Inwagen, and others. (shrink)

Opinionated state of the art paper on mathematical explanation. After a general introduction to the subject, the paper is divided into two parts. The first part is dedicated to intra-mathematical explanation and the second is dedicated to extra-mathematical explanation. Each of these parts begins to present a set of diverse problems regarding each type of explanation and, afterwards, it analyses relevant models of the literature. Regarding the intra-mathematical explanation, the models of deformable proofs, mathematical saliences and the demonstrative structure of (...) mathematical induction are addressed. Regarding the extra-mathematical explanation, modal, abstract and deductive models are addressed. (shrink)

In this article I offer an explicating interpretation of the procedure of content recarving as described by Frege in §64 of the Foundations of Arithmetic. I argue that the procedure of content recarving may be interpreted as an operation that while restricting the subject matter of a sentence, performs a generalization on what the sentence says about its subject matter. The characterization of the recarving operation is given in the setting of Yablo’s theory of subject matter and it is based (...) on the relation of determination between properties. The main advantage of the proposal is its generality, for it is applicable not just to the case of abstraction principles. (shrink)

Abstract cantaloupe and honeydew melons are part of the muskmelon family, which originated in the Middle East. When picking either cantaloupe or honeydew melons to eat, you should choose a firm fruit that is heavy for its size, with no obvious signs of bruising. They can be stored at room temperature until you cut them, after which they should be kept in the refrigerator in an airtight container for up to five days. You should always wash and scrub the rind (...) of your melon before you cut it to remove any dirt or bacteria on the outside. In this paper, cantaloupe classification approach is presented with a dataset that contains approximately 1,312 of Cantaloupes and honeydews. Convolutional Neural Network (CNN) algorithms, a deep learning technique extensively applied to image recognition was used, for this task. The results found that CNN-driven classification applications when used in farming automation have the latent to enhance crop harvest and improve output and productivity when designed properly. The trained model achieved an accuracy of 99.74% on a held-out test set, demonstrating the feasibility of this approach. (shrink)

ABSTRACT Truth-conditions are systematically determined when they are the output of an algorithmic procedure that takes as input a set of semantic and contextual features. Truth-conditional sceptics have cast doubts on the thesis that truth-conditions are systematic in this sense. Against this form of scepticism, Schoubye and Stokke : 759–793) and Dobler : 451–474.) have provided systematic analyses of utterance truth-conditions. My aim is to argue that these theories are not immune to the kind of objections raised by truth-conditional sceptics. (...) In particular, I argue that the use of Questions Under Discussion and ways of being is problematic. (shrink)

ABSTRACT In this article, I indicate how the naturalized and individualized conception of disability that prevails in philosophy informs the indifference of philosophers to the predictable COVID-19 tragedy that has unfolded in nursing homes, supported living centers, psychiatric institutions, and other institutions in which elders and younger disabled people are placed. I maintain that, insofar as feminist and other discourses represent these institutions as sites of care and love, they enact structural gaslighting. I argue, therefore, that philosophers must engage in (...) conceptual engineering with respect to how disability and these institutions are understood and represented. To substantiate my argument, I trace the sequence of catastrophic events that have occurred in nursing homes in Canada and in the Canadian province of Ontario in particular during the pandemic, tying these events to other past and current eugenic practices produced in the Canadian context. The crux of the article is that the COVID-19 pandemic has thrown into vivid relief the carceral character of nursing homes and other congregate settings in which elders and younger disabled people are confined. -/- KEYWORDS carceral, conceptual engineering, nursing home-industrial-complex, philosophy of disability, structural gaslighting. (shrink)