The characterization of early token-based accounting using a concrete concept of number, later numerical notations an abstract one, has become well entrenched in the literature. After reviewing its history and assumptions, this article challenges the abstract–concrete distinction, presenting an alternative view of change in Ancient Near Eastern number concepts, wherein numbers are abstract from their inception and materially bound when most elaborated. The alternative draws on the chronological sequence of material counting technologies used in the Ancient (...) Near East—fingers, tallies, tokens, and numerical notations—as reconstructed through archaeological and textual evidence and as interpreted through Material Engagement Theory, an extended-mind framework in which materiality plays an active role (Malafouris 2013). (shrink)

Abstract creationism about fictional characters is the view that fictional characters are abstract objects that authors create. I defend this view against criticisms from Stuart Brock that hitherto have not been adequately countered. The discussion sheds light on how the number of fictional characters depends on authorial intention. I conclude also that we should change how we think intentions are connected to artifacts more generally, both abstract and concrete.

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, (...) propositions, and degrees is considerably more marginal than generally held. (shrink)

A number of philosophers have recently suggested that some abstract, plausibly non-causal and/or mathematical, explanations explain in a way that is radically dif- ferent from the way causal explanation explain. Namely, while causal explanations explain by providing information about causal dependence, allegedly some abstract explanations explain in a way tied to the independence of the explanandum from the microdetails, or causal laws, for example. We oppose this recent trend to regard abstractions as explanatory in some sui generis way, (...) and argue that a prominent ac- count of causal explanation can be naturally extended to capture explanations that radically abstract away from microphysical and causal-nomological details. To this end, we distinguish di erent senses in which an explanation can be more or less abstract, and analyse the connection between explanations’ abstractness and their explanatory power. According to our analysis abstract explanations have much in common with counterfactual causal explanations. (shrink)

A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers (...) are not primarily treated abstract objects, but rather 'aspects' of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. (shrink)

In this paper we describe and interpret the formal machinery of abstraction processes in which the domain of abstracta is a subset of the domain of objects from which is abstracted.

The question whether numbers are objects is a central question in the philosophy of mathematics. Frege made use of a syntactic criterion for objethood: numbers are objects because there are singular terms that stand for them, and not just singular terms in some formal language, but in natural language in particular. In particular, Frege (1884) thought that both noun phrases like the number of planets and simple numerals like eight as in (1) are singular terms referring to (...) class='Hi'>numbers as abstract objects. (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)

The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume's Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one‐to‐one:. The principal aim of this article is to use the notion of grounding to develop (...) this sort of abstractionism. The appeal to grounding enables a unified response to the two main challenges that confront abstractionism. First, we must explicate the metaphor of metaphysical “cheapness.” Second, we must rebut the “bad company” objection, which rejects abstraction principles like (HP) as tarnished by their similarity to inconsistent principles like Frege's Basic Law V. By enforcing a simple requirement that all abstraction be properly grounded, we propose a unified solution to these two hard, and prima facie unrelated, problems. On our view, grounded abstraction simultaneously ensures “cheap” abstracta and permissible abstraction. (shrink)

This is a book about numbers– what they are as concepts and how and why they originate–as viewed through the material devices used to represent and manipulate them. Fingers, tallies, tokens, and written notations, invented in both ancestral and contemporary societies, explain what numbers are, why they are the way they are, and how we get them. Cognitive archaeologist Karenleigh A. Overmann is the first to explore how material devices contribute to numerical thinking, initially by helping us to (...) visualize and manipulate the perceptual experience of quantity that we share with other species. She explores how and why numbers are conceptualized and then elaborated, as well as the central role that material objects play in both processes. Overmann’s volume thus offers a view of numerical cognition that is based on an alternative set of assumptions about numbers, their material component, and the nature of the human mind and thinking. Karim Zahidi (“Radicalizing numerical cognition,” Synthese, 2021, p. 530) called this reconstruction, as presented in journal articles, a “naturalistically plausible account of the emergence of the modern natural number concept," while César Dos Santos ("Review of: 'The Materiality of Numbers'," Qeios, 2023, p. 1) called it "a 'Copernican Revolution' in the way we understand the relationship between numbers and the material devices we use to record and manipulate them." . (shrink)

I respond to P. McLaughlin and O. Schlaudt’s critique of my analysis of the cross-cultural origins of numbers, noting that my work draws extensively upon number systems as ethnographically attested around the globe, and thus is based only in part on the important Mesopotamian case study. I place the work of Peter Damerow in its historical context, noting its genesis in Piaget’s genetic epistemology and the problems associated with applying Piaget’s developmental theory to societies. While Piaget assumed numeracy involves (...) invariant mental transformations, ongoing research in numerical cognition has been largely unsuccessful in identifying specific brain-bound mechanisms for numerical structure. Accordingly, I suggest the extended mind paradigm from the philosophy of mind may be a more fruitful approach, and detail such an approach using Material Engagement Theory. (shrink)

This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction (...) instead simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations. (shrink)

Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but (...) second, that if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

Philosophers frequently draw on natural language to motivate properties, numbers, and propositions as objects, and it is generally taken for granted that abstract objects of this sort are well-reflected in natural language and in fact that reference to them in natural language is pervasive In this paper, I will review and modify in a certain way the view I had advanced in Abstract Objects and the Semantics of Natural Language (Moltmann 2013a). This is the view that natural (...) language permits reference to abstract objects only in its periphery, not in its core. Even though reference to abstract objects of the sort of properties, propositions, and numbers is available only in the periphery of language, natural language permits reference to other sorts of abstract objects in its core, in particular abstract artifacts of various sorts. (shrink)

The existence of mereological sums can be derived from an abstraction principle in a way analogous to numbers. I draw lessons for the thesis that “composition is innocent” from neo-Fregeanism in the philosophy of mathematics.

What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but (...) currently, in the mainstream arena only definitions, descriptions of properties, and effects are presented as evidence. Enough historical description of numbers in history provides an empirical basis of number, although a case can be made that numbers do not exist by themselves empirically. Correspondingly, numbers exist as abstractions. All the while, though, these "descriptions" beg the question of what numbers are ontologically. Advocates for numbers being the ultimate reality have the problem of wrestling with the nature of reality. I start on the road to discovering the ontology of number by looking at where people have talked about numbers as already existing: history. Of course, we need to know not only what ontology is but the problems of identifying one, leading to the selection between metaphysics and provisional approaches. While we seem to be dimensionally limited, at least we can identify a more suitable bootstrapping ontology than mere definitions, leading us to the unity of opposites. The rest of the paper details how this is done and modifies Peano's Postulates. (shrink)

Abstract Tom Dougherty observes that challenges to counting the numbers often cite John Taurek’s 1977 article, “Should the Numbers Count.” Dougherty, though sympathetic to Taurek’s (and others) critique of consequentialism’s aggregating good across individuals, defends a non-consequentialist principle for addition he calls “the Ends Principle. Take the case (he labels “Drug”) when an agent, possessing a dose of a lifesaving drug, can save one person with the entire dose, or two people, each of whom only need half (...) the dose. Dougherty argues that a rational agent, summing her altruistic goals (three), but unable to save all three, will save two. I give two criticisms of Dougherty’s paper. (1) He hasn’t ruled out, though acknowledging, the equal chance principle as deontological grounds for deciding Drug. (2) An agent using the Ends Principle in Drug, as he formulates it, will not have the requisite aims to make use of the Principle. I also consider an issue, little discussed, the conditions for aggregation in general. (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)

In this paper, I defend traditional Platonic mathematical realism from its contemporary detractors, arguing that numbers, understood as abstract, non-physical objects of rational intuition, are indispensable for the act of counting.

According to Augustine, abstract objects are ideas in the mind of God. Because numbers are a type of abstract object, it would follow that numbers are ideas in the mind of God. Call such a view the “Augustinian View of Numbers” (AVN). In this paper, I present a formal theory for AVN. The theory stems from the symmetry conception of God as it appears in Studtmann (2021). I show that the theory in Studtmann’s paper can (...) interpret the axioms of Peano Arithmetic minus the induction schema. This fact allows for the development of arithmetic in a natural way. The development eventuates in a theory that can interpret second-order arithmetic. The conception of God that emerges by the end of the discussion is a conception of an infinite, ineffable, self-cause that contains objects that not only serve as numbers but also encode information about each other. (shrink)

The relationship between space and human occurs through the actions performed with the body. The abstraction study as an exploration of the body is one of the significant practices for first-year design students. However, there are not enough investigations for design students regarding body, space and basic design principles. This paper aims to explore the potentiality and limitations of the body-abstraction process by comparing the impact of two different educational models on students' perception and improvement. The applied methodology includes comparing (...) two design processes of the basic design course depending on parameters: Given example, source of the video, type of movement, the number of the selected-used scenes, mode of sketching, the method for production, requested outcome, the scale of the study, the material of models and critique of the video. The results present that the activation of the body through mental practice, drawing and modelling stages is critical to understand its abstract and spatial capabilities. The realisation of the potentials in the relationship between body and abstraction in spatial perception would enable us to create an advanced design process addressing more original concepts. (shrink)

Linnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter-argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided (...) in the account of arithmetic based on Hume's principle because we are specifying numbers in terms of the concept of equinumerosity, or its ordinal equivalent. But far from being only a matter for philosophy, this implies a distinct empirical prediction: in cognitive development, the principle of equinumerosity is primary to number concepts. However, by analysing and expanding on the bootstrapping theory of Carey in 2009, I argue in this paper that there are good reasons to think that the development could be the other way around: possessing numerosity concepts may precede grasping the principle of equinumerosity. I propose that this analysis of early numerical cognition can also help us understand what numbers as thin objects are like, moving away from Platonist interpretations. (shrink)

In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a (...) system treating apparent terms for numbers using these definitions. (shrink)

This study aimed to explore the rhetorical moves of article abstracts in Taiwanese Chinese philosophy journals. The most common theory for the discourse analysis of research abstracts is proposed by Hyland（2000）. Most of the research abstracts in the field of social sciences and natural sciences are composed of Hyland’s five rhetorical moves: introduction, purpose, method, results, and conclusion. Therefore, the question to be explored in this research is how to compose the rhetorical moves of abstracts of Chinese philosophy journal articles. (...) What is the frequency and order of each rhetorical move in the abstract of each paper? Do they reflect some particular type of distribution? Are there any rhetorical moves that occur exceptionally rarely? Does the abstract of research articles in Chinese philosophy journals apply the framework of the same five rhetorical moves? What are the conventions of the philosophy writing community reflected in the rhetorical moves of abstracts of academic journal articles in philosophy? -/- To answer the above questions, this research collected the abstracts of 18 papers from the representative Chinese philosophy journal "SOOCHOW JOURNAL OF PHILOSOPHICAL STUDIES " in Taiwan in the past five years (2017-2021) and used the five moves of Hyland（2000） one by one to answer the above questions. The rhetorical moves of each abstract were analyzed and presented in tables to show the frequency, order, and type of each rhetorical move. -/- The results of this study found that "method (M)" and "conclusion (C)" are not the rhetorical moves that constitute the abstract of articles in Taiwanese philosophy journals, but the rhetorical move "purpose (P)" is "necessary" to appear. In the Purpose move, the subject is usually "this article"; the verbs are "argue" or "inquire." Although "introduction (I)" is a "conventional" move, the total number of words in the introduction is the highest in the whole abstract. This study also shows rhetorical move variation of the abstracts of philosophy journal articles, reflecting the writing culture and conventions of the academic philosophy community. -/- Finally, this study proposes three teaching guidelines for abstract writing of academic papers in philosophy, which will be useful for philosophy scholars and graduate students to consult when writing and submitting abstracts of philosophy in conference or journal papers. -/- Keywords: philosophy, journal article, abstract, discourse analysis, rhetorical move . (shrink)

A Commonplace of recent philosophy of mind is that intentional states are relations between thinkers and propositions. This thesis-call it the 'Relational Thesis'-does not depend on any specific theory of propositions. One can hold it whether one believes that propositions are Fregean Thoughts, ordered n-tuples of objects and properties or sets of possible worlds. An assumption that all these theories of propositions share is that propositions are abstract objects, without location in space or time...

A growing body of evidence suggests that cognition is embodied and grounded. Abstract concepts, though, remain a significant theoretical chal- lenge. A number of researchers have proposed that language makes an important contribution to our capacity to acquire and employ concepts, particularly abstract ones. In this essay, I critically examine this suggestion and ultimately defend a version of it. I argue that a successful account of how language augments cognition should emphasize its symbolic properties and incorporate a view (...) of embodiment that recognizes the flexible, multi- modal and task-related nature of action, emotion and perception systems. On this view, language is an ontogenetically disruptive cognitive technology that expands our conceptual reach. (shrink)

What are numbers, and where do they come from? A novel answer to these timeless questions is proposed by cognitive archaeologist Karenleigh A. Overmann, based on her groundbreaking study of material devices used for counting in the Ancient Near East—fingers, tallies, tokens, and numerical notations—as interpreted through the latest neuropsychological insights into human numeracy and literacy. The result, a unique synthesis of interdisciplinary data, outlines how number concepts would have been realized in a pristine original condition to develop into (...) one of the ancient world’s greatest mathematical traditions, a foundation for mathematical thinking today. In this view, numbers are abstract from their inception and materially bound at their most elaborated. The research updates historical work on Neolithic tokens and interpretations of Mesopotamian numbers, challenging several longstanding assumptions about numbers in the process. The insights generated are also applied to the role of materiality in human cognition more generally, including how concepts become distributed across and independent of the material forms used for their representation and manipulation; how societies comprised of average individuals use material structures to create elaborated systems of numeracy and literacy; and the differences between thinking through and thinking about materiality. (shrink)

In this paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary (...) and sufficient for possession of mathematical concepts will always face counterexamples of the kind illustrated by Cardano. I close by suggesting that we should rely more heavily on resources of Anti-Individualism as a framework for understanding the acquisition and possession of concepts of abstract subject matters. (shrink)

Abstract: Heart attacks, or myocardial infarctions, are a leading cause of mortality worldwide. Early prediction and accurate analysis of potential risk factors play a crucial role in preventing heart attacks and improving patient outcomes. In this study, we conduct a comprehensive review of datasets related to heart attack analysis and prediction. We begin by examining the various types of datasets available for heart attack research, encompassing clinical, demographic, and physiological data. These datasets originate from diverse sources, including hospitals, research (...) institutions, and public health agencies. Our analysis aims to identify common features, data quality, and potential biases in these datasets. Next, we explore the predictive modeling techniques employed in heart attack prediction. Machine learning algorithms, such as decision trees, support vector machines, and deep neural networks, have gained prominence in predicting heart attacks. We discuss the strengths and limitations of these methods and highlight recent advancements in predictive modeling. Furthermore, we delve into the critical risk factors associated with heart attacks. Factors such as age, gender, hypertension, diabetes, and cholesterol levels are examined for their significance in predicting cardiac events. We also investigate the role of lifestyle factors, including smoking, diet, and physical activity, in heart attack risk assessment. Additionally, this review addresses the importance of data preprocessing and feature engineering in improving prediction accuracy. Feature selection methods, missing data handling, and data scaling techniques are discussed to enhance the robustness of heart attack prediction models. In conclusion, this comprehensive dataset review provides valuable insights into the state of heart attack analysis and prediction. It serves as a resource for researchers and healthcare professionals seeking to better understand the datasets available for heart attack research and the methods employed for accurate prediction. Ultimately, our efforts in dataset analysis and predictive modeling contribute to the advancement of preventive cardiology and the reduction of heart attack-related morbidity and mortality. (shrink)

Platonists affirm the existence of abstract mathematical objects, and Nominalists deny the existence of abstract mathematical objects. While there are standard arguments in favor of Nominalism, these arguments fail to account for the necessity of Nominalism. Furthermore, these arguments do nothing to explain why Nominalism is true. They only point to certain theoretical vices that might befall the Platonist. The goal of this paper is to formulate and defend a simple, valid argument for the necessity of Nominalism that (...) seeks to precisify the widespread intuition that mathematical objects are somehow ‘spooky’ or ‘mysterious’. (shrink)

In §57 of the Foundations of Arithmetic, Frege famously turns to natural language to support his claim that numbers are ‘self-subsistent objects’:I have already drawn attention above to the fact th...

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)

Abstract: The main purpose of this paper is to find Artin's characters table of the group (Q2n×D3)when n=p_1.p_2….p_n,and p_1,p_2,…,p_n are primes number, which is denoted by Ar(Q2n×D3) where Q2m is denoted to Quaternion group and D3 is the Dihedral group of order 6 .

This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...) independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance. (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)

Albert Einstein once made the following remark about "the world of our sense experiences": "the fact that it is comprehensible is a miracle." (1936, p. 351) A few decades later, another physicist, Eugene Wigner, wondered about the unreasonable effectiveness of mathematics in the natural sciences, concluding his classic article thus: "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve" (1960, p. 14). (...) At least three factors are involved in Einstein's and Wigner's miracles: the physical world, mathematics, and human cognition. One way to relate these factors is to ask how the universe could possibly be structured in such a way that mathematics would be applicable to it, and we would be able to understand that application. This is roughly Wigner's question. Alternatively, the way of the mathematical naturalist is to argue that we abstract certain properties from the world, perhaps using our bodies and physical tools, thereby articulating basic mathematical concepts, which we continue building into the complex formal structures of mathematics. John Stuart Mill, Penelope Maddy, and Rafael Nuñez teach this strategy of cognitive abstraction, in very different manners. But what if the very concepts and basic principles of mathematics were built into our cognitive structure itself? Given such a cognitive a priori mathematical endowment, would the miracles of the link between world and cognition (Einstein) and mathematics and world (Wigner) not vanish, or at least significantly diminish? This is the stance of Stanislas Deheane and Elizabeth Brannon's 2011 anthology, following a venerable rationalist tradition including Plato and Immanuel Kant. (shrink)

Kant and Descartes followed an extreme clever, secure way of reasoning. For them, there must be a world of differences, or of movement, before we can extract anything (ideas, laws, concepts, etc.) from the world. For Kant, these “changes” that secure the possibility of knowledge were the ones we can measure with the categories of space and time. While, for Descartes, since there exist two things: “me” and “the world”, we can say knowledge is possible. But I think we can (...) extract a more abstract, general principle from the similarities between both Descartes and Kant’s mobilist tendency. (shrink)

Language suggestive of natural law ethics, similar to the Catholic understanding of ethical foundations, is prevalent in a number of disciplines. But it does not always issue in a full-blooded commitment to objective ethics, being undermined by relativist ethical currents. In law and politics, there is a robust conception of "human rights", but it has become somewhat detached from both the worth of persons in themselves and from duties. In education, talk of "values" imports ethical considerations but hints at a (...) subjectivist view of them. In the psychology and sociology of drug use, ethically thin concepts of "harm minimisation" and "selfimage" dominate discussion and distract attention from the virtue of temperance and the training of character. A more forceful assertion of an ethics based on the worth of persons in these cases would be most desirable. Arguments against objectivity in the fundamentals may be replied to by examining the parallel between ethics and the discipline whose objectivity has been least challenged by relativist arguments, mathematics. (shrink)

SEMANTIC ARITHMETIC: A PREFACE John Corcoran Abstract Number theory, or pure arithmetic, concerns the natural numbers themselves, not the notation used, and in particular not the numerals. String theory, or pure syntax, concems the numerals as strings of «uninterpreted» characters without regard to the numbe~s they may be used to denote. Number theory is purely arithmetic; string theory is purely syntactical... in so far as the universe of discourse alone is considered. Semantic arithmetic is a broad subject which (...) begins when numerals are mentioned (not just used) and mentioned as names of numbers (not just as syntactic objects). Semantic arithmetic leads to many fascinating and surprising algorithms and decision procedures; it reveals in a vivid way the experiential import of mathematical propositions and the predictive power of mathematical knowledge; it provides an interesting perspective for philosophical, historical, and pedagogical studies of the growth of scientific knowledge and of the role metalinguistic discourse in scientific thought. (shrink)

This paper attempts to be a contribution to the epistemological project of explaining complex conceptual structures departing from more basic ones. The central thesis of the paper is that there are what I call “functionally structured concepts”, these are non-harmonic concepts in Dummett’s sense that might be legitimized if there is a function that justifies the tie between the inferential connection the concept allows us to trace. Proving this requires enhancing the russellian existential analysis of definite descriptions to apply to (...) functions and using this in proving the legitimacy of such concepts. The utility of the proposal is shown for the case of thick ethical terms and an attempt is made to use it in explaining the development of natural numbers. This last move could allow us to go one step lower in explaining the genesis of natural numbers while maintaining the notion of abstract numbers as higher order entities. (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)

ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is (...) why Hipparchus’ logic differed from Stoic logic, and consequently, whether Hipparchus actually refuted Chrysippus. This paper closes these explanatory gaps. (1) I reconstruct Hipparchus’ notions of conjunction and negation, and show how they differ from Stoic logic. (2) Based on evidence from Stoic logic, I reconstruct Chrysippus’ calculations, thereby (a) showing that Chrysippus’ claim of over a million conjunctions was correct; and (b) shedding new light on Stoic logic and – possibly – on 3rd century BCE combinatorics. (3) Using evidence about the developments in logic from the 3rd to the 2nd centuries, including the amalgamation of Peripatetic and Stoic theories, I explain why Hipparchus, in his calculations, used the logical notions he did, and why he may have thought they were Stoic. OPEN ACCESS LINK. (shrink)

Abstract: The study aimed to determine the strategic flexibility and its relationship to the level of quality of services provided, from the viewpoint of the internal beneficiary in non-governmental hospitals in Gaza Strip. The study relied on the descriptive and analytical approach, and the questionnaire was designed as a tool to collect data and consisted of (39) items, and the researchers used the comprehensive survey method, and the number of the study population was (536) individuals, where (434) questionnaires were (...) retrieved, and the recovery rate was (80.97%). The study revealed many results, the most important of which were: the existence of a moderate degree of approval by the study sample individuals on strategic flexibility, as it was evident through the area of strategic flexibility as a whole having a relative weight (60.44%). The study is on the quality of services, as it became clear through the field of service quality obtaining a relative weight (79.90%). The results of the study revealed a statistically significant relationship between strategic flexibility and the quality of services in non-governmental hospitals in Gaza Strip, with a correlation coefficient of 0.490. The study reached many recommendations, the most important of which were: the need to work on appointing young people and those with potentials, because jobs are vacant in the hospitals under study, and the need to seek the help of an administrative staff with scientific and practical qualifications, and to work on updating information systems, archiving and networks through which data and information are transferred between departments And the creation of mechanisms by which stored information can be used to enhance the decision-making process, and an effective system to receive patients' complaints in a manner that ensures rapid response and treatment, to achieve continuous communication between patients and the hospital management, and to notify patients of dealing with the complaints they submit, and work to provide all Medical and health specialties in the hospitals under study, by making use of the medical delegations that visit Gaza Strip, involving them in the treatment processes, bringing in doctors and specialists from abroad, updating the standards related to measuring the services provided to patients on an ongoing basis, based on the suggestions and complaints of patients, and developing facilities in hospitals As well as updating the medical devices and equipment used in hospitals periodically. (shrink)

Abstract: Sign language recognition is one of the most rapidly expanding fields of study today. Many new technologies have been developed in recent years in the fields of artificial intelligence the sign language-based communication is valuable to not only deaf and dumb community, but also beneficial for individuals suffering from Autism, downs Syndrome, Apraxia of Speech for correspondence. The biggest problem faced by people with hearing disabilities is the people's lack of understanding of their requirements. In this paper we (...) try to fill this gap. By trying to translate sign language using artificial intelligence algorithms, we focused in this paper using transfer learning technique based on deep learning by utilizing a MobileNet algorithm and compared it with the previous paper results[10a], where we get in the Mobilenet algorithm on the degree of Accuracy 93,48% but the VGG16 the accuracy was 100% For the same number of images (43500 in the dataset in size 64*64 pixel ) and the same data split training data into training dataset (70%) and validation dataset(15%) and testing dataset(15%) and 20 epoch . (shrink)

Abstract: This paper is a response to Park Seungbae’s article, “Defence of Cultural Relativism”. Some of the typical criticisms of moral relativism are the following: moral relativism is erroneously committed to the principle of tolerance, which is a universal principle; there are a number of objective moral rules; a moral relativist must admit that Hitler was right, which is absurd; a moral relativist must deny, in the face of evidence, that moral progress is possible; and, since every individual belongs (...) to multiple cultures at once, the concept of moral relativism is vague. Park argues that such contentions do not affect moral relativism and that the moral relativist may respond that the value of tolerance, Hitler’s actions, and the concept of culture are themselves relative. In what follows, I show that Park’s adroit strategy is unsuc-cessful. Consequently, moral relativism is incoherent. (shrink)

ABSTRACT A thriving project in contemporary epistemology concerns identifying and explicating the epistemic virtues. Although there is little sustained argument for this claim, a number of prominent sources suggest that curiosity is an epistemic virtue. In this paper, I provide an account of the virtue of curiosity. After arguing that virtuous curiosity must be appropriately discerning, timely and exacting, I then situate my account in relation to two broader questions for virtue responsibilists: What sort of motivations are required for (...) epistemic virtue? And do epistemic virtues need to be reliable? I will sketch an account on which curiosity is only virtuous when rooted in a non-instrumental appreciation of epistemic goods, before arguing that curiosity can exhibit intellectual virtue irrespective of whether one is reliable in satisfying it. (shrink)

ABSTRACT Contemporary relativists often see their view as contributing to a semantic/post-semantic account of linguistic data about disagreement and retraction. I offer an independently motivated metasemantic account of the same data, that also handles a number of cases and empirical results that are problematic for the relativist. The key idea is that the content of assertions and beliefs is determined in part by facts about other times, including times after the assertion is made or the belief is formed. On (...) this temporal externalist view, speaker behaviours such as retraction of previous assertions play a role in making it the case that a past utterance has a given meaning. (shrink)

Abstract: The study aimed to determine the quality of services and its role in enhancing strategic flexibility, from the point of view of the internal beneficiary in non-governmental hospitals in Gaza Strip. The study relied on the descriptive and analytical approach, and the questionnaire was designed as a tool to collect data and consisted of (39) items, and the researchers used the comprehensive survey method, and the number of the study population was (536) individuals, where (434) questionnaires were retrieved, (...) and the recovery rate was (80.97%). The study revealed many results, the most important of which were: the existence of a high degree of approval by the study sample regarding the quality of services, as it was evident through the field of service quality obtaining a relative weight (79.90%), and the results of the study indicated that there is a moderate degree of approval by the members of the study sample. On the strategic flexibility, as it was evident by obtaining the area of strategic flexibility as a whole on a relative weight (60.44%). The results of the study revealed a statistically significant relationship between the quality of services and the strategic flexibility in non-governmental hospitals in Gaza Strip, with a correlation coefficient of 0.490). The results of the study also revealed a statistically significant effect of the quality of services on the strategic flexibility in non-governmental hospitals in Gaza Strip. The study reached many recommendations, the most important of which were: Establishing an effective system to receive patients' complaints in a manner that ensures rapid response and treatment, to achieve continuous communication between patients and the hospital administration, to notify patients of dealing with the complaints they submit, and to work to provide all medical and health specialties in hospitals in place. The study, by making use of medical delegations visiting Gaza Strip, involving them in therapeutic operations, bringing in doctors and specialists from abroad, updating the criteria for measuring services provided to patients on an ongoing basis, based on patients' suggestions and complaints, developing facilities in hospitals, as well as updating medical devices and equipment Used in hospitals periodically and the need to work on appointing young people and people of energy, for vacancies in the hospitals under study, and the need to seek the help of an administrative staff that is distinguished by scientific and practical qualifications, and to work on updating information systems, archiving and networks through which data and information are transferred between departments, and finding mechanisms to be done from During which the information stored can be used to enhance the decision-making process. (shrink)

ABSTRACT This paper compares Spinoza with Daniel Dennett and uncovers a number of striking parallels. Genevieve Lloyd’s recent work on Spinoza reveals a picture of a philosopher that anticipated many of Dennett’s later ideas. Both share a fervent opposition to Descartes’ conception of mind and body and endorse a strikingly similar naturalist philosophy. It is the goal of this paper to tease out these connections and once again highlight the richness of a Spinozist lens of the world.

Abstract: Recently, the experimental philosopher Joshua Knobe has shown that the folk are more inclined to describe side effects as intentional actions when they bring about bad results. Edouard Machery has offered an intriguing new explanation of Knobe's work—the 'trade-off hypothesis'—which denies that moral considerations explain folk applications of the concept of intentional action. We critique Machery's hypothesis and offer empirical evidence against it. We also evaluate the current state of the debate concerning the concept of intentionality, and argue (...) that, given the number of variables at play, any parsimonious account of the relevant data is implausible. (shrink)