The definition of a point in geometry is primordial in order to understand the different elements of this branch of mathematics ( line, surface, solids…). This paper aims at shedding fresh light on the concept to demonstrate that it is related to another one named, here, the Primary Geometric Object; both concepts concur to understand the multiplicity of geometries and to provide hints as concerns a new understanding of some concepts in physics such as time, energy, mass….

The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.

In this paper, we will make explicit the relationship that exists between geometric objects and geometric figures in planar Euclidean geometry. That will enable us to determine basic features regarding the role of geometric figures and diagrams when used in the context of pure and applied planar Euclidean geometry, arising due to this relationship. By taking into account pure geometry, as developed in Euclid’s Elements, and practical geometry, we will establish a relation between geometric objects and (...) figures. Geometric objects are defined in terms of idealizations of the corresponding figures of practical geometry. We name the relationship between them as a relation of idealization. This relation, existing between objects and figures, is what enables figures to have a role in pure and applied geometry. That is, we can use a figure or diagram as a representation of geometric objects or composite geometric objects because the relation of idealization corresponds to a resemblance-like relationship between objects and figures. Moving beyond pure geometry, we will defend that there are two other ‘layers’ of representation at play in applied geometry. To show that, we will consider Euclid’s Optics. (shrink)

On 6 January 1795, the twenty-year-old Schelling—still a student at the Tübinger Stift—wrote to his friend and former roommate, Hegel: “Now I am working on an Ethics à la Spinoza. It is designed to establish the highest principles of all philosophy, in which theoretical and practical reason are united”. A month later, he announced in another letter to Hegel: “I have become a Spinozist! Don’t be astonished. You will soon hear how”. At this period in his philosophical development, Schelling had (...) been deeply under the spell of Fichte’s new philosophy and the Wissenschaftslehre. The text Schelling was writing at the time was the early Vom Ich als Prinzip der Philosophie, though his characterization of this text would much better fit the somewhat later work which is the focus of the current paper: Schelling’s 1801 Darstellung meines System der Philosophie (hereafter: Presentation). The Presentation is a text written more geometrico, following the style of Spinoza’s Ethics. While Spinoza’s influence and inspiration is stated explicitly and unmistakably in Schelling’s preface, the content of this composition might seem quite foreign to Spinoza’s philosophy, so much so, in fact, that Michael Vater—the astute translator and editor of the recent English translation of the text—has contended that “despite the formal similarities between Spinoza’s geometrical method and Schelling’s numbered mathematical-geometrical constructions, Schelling’s direct debts to Spinoza are few”. The Presentation is an extremely dense and difficult text, and while I agree that at first glance Schelling’s engagement with the concept of reason (Vernunft) and the identity formula ‘A=A’ seems to have little if anything to do with Spinoza (especially since Spinoza’s key terminology of ‘God’, ‘causa sui’, ‘substance’, ‘attribute’, and ‘mode’ is barely mentioned in the Presentation), I suspect that at a deeper level Schelling is attempting to transform Spinoza’s system by replacing God, Spinoza’s ultimate reality, with reason. Though this might at first seem bizarre, I believe it can be profitably motivated and explained upon further reflection. It is this transformation of Spinoza’s God into (the early) Schelling’s reason that is the primary subject of this study. I develop this paper in the following order. In the first part I provide a very brief overview of Schelling’s lifelong engagement with Spinoza’s philosophy, which will prepare us for my study of the 1801 Presentation. In the second part, I consider the formal structure and rhetoric of the Presentation against the background of Spinoza’s Ethics, and show how Schelling regularly imitates Spinoza’s tiniest rhetorical gestures. In the third and final part I turn to the opening of the Presentation, and argue that Schelling attempts there to distance himself from Fichte by developing a conception of reason as the absolute, or the identity of the subject and object, just as the thinking substance and the extended substance are identified in Spinoza’s God. (shrink)

Much of our information comes to us indirectly, in the form of conclusions others have drawn from evidence they gathered. When we hear these conclusions, how can we modify our own opinions so as to gain the benefit of their evidence? In this paper we study the method known as geometric pooling. We consider two arguments in its favour, raising several objections to one, and proposing an amendment to the other.

The cognitive basis of geometry is still poorly understood, even the ‘simpler’ issue of what kind of representation of geometric objects we have. In this work, we set forward a tentative model of the neural representation of geometric objects for the case of the pure geometry of Euclid. To arrive at a coherent model, we found it necessary to consider earlier forms of geometry. We start by developing models of the neural representation of the geometric figures of (...) ancient Greek practical geometry. Then, we propose a related model for the earliest form of pure geometry – that of Hippocrates of Chios. Finally, we develop the model of the neural representation of the geometric objects of Euclidean geometry. The models are based on the hub-and-spoke theory. In our view, the existence of specific models opens the possibility of addressing the relationship between geometric figures and geometric objects, in a novel way, in terms of their neural representation. (shrink)

This article analyzes the value of geometric models to understand matter with the examples of the Platonic model for the primary four elements (fire, air, water, and earth) and the models of carbon atomic structures in the new science of crystallography. How the geometry of these models is built in order to discover the properties of matter is explained: movement and stability for the primary elements, and hardness, softness and elasticity for the carbon atoms. These geometric (...) models appear to have a double quality: firstly, they exhibit visually the scientific properties of matter, and secondly they give us the possibility to visualize its whole nature. Geometrical models appear to be the expression of the mind in the understanding of physical matter. (shrink)

In the Critique of Pure Reason, Kant defends the mathematically deterministic world of physics by arguing that its essential features arise necessarily from innate forms of intuition and rules of understanding through combinatory acts of imagination. Knowing is active: it constructs the unity of nature by combining appearances in certain mandatory ways. What is mandated is that sensible awareness provide objects that conform to the structure of ostensive judgment: “This (S) is P.” -/- Sensibility alone provides no such objects, so (...) the imagination compensates by combining passing point-data into “pure” referents for the subject-position, predicate-position, and copula. The result is a cognitive encounter with a generic physical object whose characteristics—magnitude, substance, property, quality, and causality—are abstracted as the Kantian categories. Each characteristic is a product of “sensible synthesis” that has been “determined” by a “function of unity” in judgment. -/- Understanding the possibility of such determination by judgment is the chief difficulty for any rehabilitative reconstruction of Kant’s theory. I will show that Kant conceives of figurative synthesis as an act of line-drawing, and of the functions of unity as rules for attending to this act. The subject-position refers to substance, identified as the objective time-continuum; the predicate-position, to quality, identified as the continuum of property values (constituting the second-order type named by the predicate concept). The upshot is that both positions refer to continuous magnitudes, related so that one (time-value) is the condition of the other (property-value). -/- Kant’s theory of physically constructive grammar is thus equivalent to the analytic-geometric formalism at work in the practice of mathematical physics, which schematizes time and state as lines related by an algebraic formula. Kant theorizes the subject–predicate relation in ostensive judgment as an algebraic time–state function. When aimed towards sensibility, “S is P” functions as the algebraic relation “t → ƒ(t).”. (shrink)

The aim of this paper is to bring the resources of virtue epistemology to bear on the issue of the epistemic objectivity of science. A distinction is made between theoretical virtues that may be possessed by scientific theories and epistemic virtues that may be exercised by individual scientists. A distinction is then made between ontological objectivity, objectivity of truth and epistemic objectivity, the latter being the principal focus of the paper. It is then noted that a role must be played (...) by deliberative judgement in determining how to apply the theoretical virtues. It is suggested that such judgement may be virtuous in light of the exercise of the epistemic virtues. It is argued that the primary location of epistemic objectivity is the theoretical virtues, whereas the epistemic virtues of scientists play a subordinate role. (shrink)

Some things look more complex than others. For example, a crenulate and richly organized leaf may seem more complex than a plain stone. What is the nature of this experience—and why do we have it in the first place? Here, we explore how object complexity serves as an efficiently extracted visual signal that the object merits further exploration. We algorithmically generated a library of geometric shapes and determined their complexity by computing the cumulative surprisal of their internal (...) skeletons—essentially quantifying the “amount of information” within each shape—and then used this approach to ask new questions about the perception of complexity. Experiments 1–3 asked what kind of mental process extracts visual complexity: a slow, deliberate, reflective process (as when we decide that an object is expensive or popular) or a fast, effortless, and automatic process (as when we see that an object is big or blue)? We placed simple and complex objects in visual search arrays and discovered that complex objects were easier to find among simple distractors than simple objects are among complex distractors—a classic search asymmetry indicating that complexity is prioritized in visual processing. Next, we explored the function of complexity: Why do we represent object complexity in the first place? Experiments 4–5 asked subjects to study serially presented objects in a self‐paced manner (for a later memory test); subjects dwelled longer on complex objects than simple objects—even when object shape was completely task‐irrelevant—suggesting a connection between visual complexity and exploratory engagement. Finally, Experiment 6 connected these implicit measures of complexity to explicit judgments. Collectively, these findings suggest that visual complexity is extracted efficiently and automatically, and even arouses a kind of “perceptual curiosity” about objects that encourages subsequent attentional engagement. (shrink)

Primary and secondary processes are the foundational axes of the Freudian mental apparatus: one horizontally as a tendency to associate, the primary process, and one vertically as the ability for perspective taking, the secondary process. Primary process mentation is not only supposed to be dominant in the unconscious but also, for example, in dreams. The present study tests the hypothesis that the mental activity during REM-sleep has more characteristics of the primary process, while during non-REM-sleep more (...) secondary process operations take place. Because the solving of a rebus requires the ability to non-contexually condensate the literal reading of single stimuli into a new one, rebus solving is a primary process operation by excellence. In a replication of the dream-rebus study of Shevrin and Fisher (1967), a rebus, which consisted of an image of a comb (German: “Kamm”) and an image of a raft (German: “Floß”), resulting in the German rebus word “kampflos” (Engl.: without a struggle), was flashed subliminally (at 1 ms) to 20 participants before going to sleep. Upon consecutive awakenings participants were asked for a dream report, free associations and an image description. Based on objective association norms, there were significantly more conceptual associations referring to Kamm and Floß indexing secondary process mentation when subjects were awakened from non-REM sleep as compared to REM-awakenings. There were not significantly more rebus associations referring to kampflos indexing primary process mentation when awakened from REM-sleep as compared to non-REM awakenings. However, when the associations were scored on the basis of each subject’s individual norms, there was a rebus effect with more idiosyncratic rebus associations in awakenings after REM than after non-REM-sleep. Our results support the general idea that REM-sleep is characterized by primary process thinking, while non-REM-sleep mentation follows the rules of the secondary process. (shrink)

Objectives -/- Surveys in various countries suggest 17% to 80% of doctors prescribe ‘placebos’ in routine practice, but prevalence of placebo use in UK primary care is unknown. Methods -/- We administered a web-based questionnaire to a representative sample of UK general practitioners. Following surveys conducted in other countries we divided placebos into ‘pure’ and ‘impure’. ‘Impure’ placebos are interventions with clear efficacy for certain conditions but are prescribed for ailments where their efficacy is unknown, such as antibiotics for (...) suspected viral infections. ‘Pure’ placebos are interventions such as sugar pills or saline injections without direct pharmacologically active ingredients for the condition being treated. We initiated the survey in April 2012. Two reminders were sent and electronic data collection closed after 4 weeks. Results -/- We surveyed 1715 general practitioners and 783 (46%) completed our questionnaire. Our respondents were similar to those of all registered UK doctors suggesting our results are generalizable. 12% (95% CI 10 to 15) of respondents used pure placebos while 97% (95% CI 96 to 98) used impure placebos at least once in their career. 1% of respondents used pure placebos, and 77% (95% CI 74 to 79) used impure placebos at least once per week. Most (66% for pure, 84% for impure) respondents stated placebos were ethical in some circumstances. Conclusion and implications -/- Placebo use is common in primary care but questions remain about their benefits, harms, costs, and whether they can be delivered ethically. Further research is required to investigate ethically acceptable and cost-effective placebo interventions. (shrink)

Newton frequently characterized his methodology as distinctive and capable of achieving greater evidential support than that of his contemporaries, due to its mathematical character. Newton's pronouncements reflect a striking position regarding the role of mathematics in natural philosophy. We can give an initial characterization of his position by considering two questions central to seventeenth century debates about the applicability of mathematics. First, how are we to understand the distinctive universality and necessity of mathematical reasoning? One common way to preserve the (...) demonstrative character of mathematics was to restrict its domain, as far as possible, to pure abstractions. The subject matter of mathematics is then taken to be abstracted from the changeable natural world, consisting of quantity and magnitude themselves rather than the objects bearing quantifiable properties. Yet restricting the domain in this way leaves it difficult to see how mathematics relates to natural phenomena. How could the book of nature be written in a language of pure abstractions? Second, what is the proper role of mathematical reasoning in natural philosophy? Many followed Aristotle in consigning mathematics to a subordinate role. Mathematics could not fulfill the main aim of natural philosophy, namely to provide demonstrations reflecting the essences of things and nature's causal order. A related concern was also pressing for the mechanical philosophers: a merely mathematical demonstration fails to provide an intelligible mechanical explanation. The very title of Newton's masterpiece, Philosophiae Naturalis Principia Mathematica, would have been extremely perplexing: how could natural philosophy be based on mathematical principles? My aim is to articulate Newton's position regarding the mathematization of nature in response to these two concerns. (shrink)

In De Anima II.6, Aristotle divides the objects of perception into three kinds: “special perceptibles" (idia aisthêta) such as colours, sounds and flavours, which can be perceived in their own right by only one sense; “common perceptibles" (koina aisthêta) such as shapes, sizes and movements, which can be perceived in their own right by multiple senses; and “incidental perceptibles,” such as the son of Diares, which can be perceived only “incidentally” (kata sumbebêkos). In this paper, I examine this division of (...) perceptibles and consider what it amounts to. First, I argue that Aristotle’s distinction between perceiving something in its own right (kath' hauto) and perceiving it incidentally marks a causal distinction: what is perceived in its own right causes perception as such, whereas what is perceived incidentally coincides with what is perceived in its own right. Second, I argue that for Aristotle special perceptibles, unlike common perceptibles, belong to homogeneous bodies on account of their chemical composition. Finally, I explain the primacy Aristotle assigns to special perceptibles and his claim that perception of them alone is free from error. I conclude with some brief remarks on Aristotle and the primary/secondary quality distinction. (shrink)

Objective: Primary care, which is often the first level of contact for patients with various communicable diseases (CDs) and noncommunicable diseases (NCDs), might exhibit patterns of injectable drug utilization different from hospitals. We aimed to examine injection prescribing to adults with CD or NCD in primary care. -/- Methods: In this retrospective study, single-diagnosis injectable drug-containing prescription data from Family Medicine Information System comprising 32 provinces of Turkey were analysed. The prescriptions were grouped by diagnosis as “CD” (n=3848) (...) and “NCD” (n=9338). Injectable drug utilization patterns in these groups were analysed by demographics, diagnoses, and drug subgroups. -/- Results: Out of 13186 prescriptions, 70.8% were issued for NCDs. NCD prescriptions were mostly generated for women and elderly (p<0.05 for both). About 63.3% (n=2948) of injectable drugs in CD prescriptions were antibiotics and 12.6% were analgesics. Cefazolin (15.2%) was the most commonly prescribed antibiotic for acute pharyngitis and acute sinusitis, and benzathine benzylpenicillin (12.8%) was the top-choice for acute tonsillitis and rheumatic fever. In NCD prescriptions, 34.0% (n=4214) of injectable agents were analgesics and 16.9% were muscle relaxants. The most frequently encountered drug in NCD prescriptions was thiocolchicoside (16.3%), which was the top-choice in all seven common musculoskeletal diagnoses. -/- Conclusion: Muscle relaxants and analgesics were the most commonly prescribed injectable drugs for NCDs, musculoskeletal diseases in particular. Antibiotics were frequently encountered in CD prescriptions, mostly as broad-spectrum for lower respiratory tract infections (RTIs) and narrow-spectrum for upper RTIs. These findings may elucidate the issues to especially focus on regarding excessive use of injections. (shrink)

A classic analytic approach to biological phenomena seeks to refine definitions until classes are sufficiently homogenous to support prediction and explanation, but this approach founders on cases where a single process produces objects with similar forms but heterogeneous behaviors. I introduce object spaces as a tool to tackle this challenging diversity of biological objects in terms of causal processes with well-defined formal properties. Object spaces have three primary components: (1) a combinatorial biological process such as protein synthesis (...) that generates objects with parts that are modular, independent, and organized according to an invariant syntax; (2) a notion of “distance” that relates the objects according to rules of change over time as found in nature or useful for algorithms; (3) mapping functions defined on the space that map its objects to other spaces or apply an evaluative criterion to measure an important quality, such as parsimony or biochemical function. Once defined, an object space can be used to represent and simulate the dynamics of phenomena on multiple scales; it can also be used as a tool for predicting higher-order properties of the objects, including stitching together series of causal processes. Object spaces are the basis for a strategy of theorizing, discovery, and analysis in biology: as heuristic idealizations of biology, they help us transform inchoate, intractable problems into articulated, well-structured ones. Developing an object space is a research strategy with a long, successful history under many other names, and it offers a unifying but not overreaching approach to biological theory. (shrink)

The subject’s perspective objection (SPO) is an objection against externalist theories of justification, warrant, and knowledge. In this article, I show that externalists can accommodate the SPO while remaining externalist. So, even if the SPO is successful, it does not motivate internalism, and the primary motivation for internalism has been lost. After this, I provide an explanation for why so many people find cases that motivate the SPO convincing.

This paper explicates the influential Confucian view that “people” and not “institutional rules” are the proper sources of good governance and social order, as well as some notable Confucian objections to this position. It takes Xunzi 荀子, Hu Hong 胡宏, and Zhu Xi 朱熹 as the primary representatives of the “virtue-centered” position, which holds that people’s good character and not institutional rules bear primary credit for successful governance. And it takes Huang Zongxi 黃宗羲 as a major advocate for (...) the “institutionalist” position, which holds that institutional rules have some power to effect success independently of improvements in character. Historians have often called attention to this debate but left the major arguments and positions relatively unspecified. As I show, the Confucian virtue-centered view is best captured in two theses: first, that reforming people is far more demanding than reforming institutional rules; second, that once the rules have reached a certain threshold of viability, further improvements in those rules are unlikely to be effective on their own. Once we specify the theses in this way, we can catalogue the different respects and degrees to which the more virtue-centered political thinkers endorse virtue-centrism in governance. Zhu Xi, for example, turns out to endorse a stronger version of virtue-centrism than Hu Hong. I also use this account of the major theses to show that Huang Zongxi, who is sometimes regarded as historical Confucianism’s foremost institutionalist, has more complicated and mixed views about the power of institutional reform than scholars usually assume. (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)

For Locke, an idea is ‘the immediate object of perception, thought, or understanding’ (§8).1 Perhaps this is something like a concept: he goes on to give examples of white, cold, and round, which look like they have some representational content. What do these ideas represent? Locke defines a quality: ‘the power to produce any idea in our mind, I call quality of the subject wherein that power is’ (§8). The natural thought is that these ideas represent some quality of (...) the object, which quality just is the power that the object has to produce that idea in us. Though the idea is in us, the power or quality is clearly in the object. Sometimes, it is true, we speak loosely and refer to the quality of the object by the same name that we use to refer to the idea in us, and talk of white being in the object, for example. Locke cautions that when we speak like this, we should ‘be understood to mean those qualities in the objects which produce them [the ideas] in us’ (§8). (shrink)

This article aims to provide a reassessment of the relationship between God and abstract objects. This reassessment will provide a new conceptualisation of this important relationship and will be formulated, first, within the theoretical framework of ‘Theistic Aspectivalism’, which is grounded on the notion of an aspect, proposed by Donald L.M. Baxter, which provides a means to ward off the ‘Bootstrapping Problem’. Second, within the theoretical framework of ‘Theistic Essentialism’, which is based on the notion of essence and essential dependence, (...) as proposed by Kit Fine, Jonathan Lowe, and Katherin Koslicki, which provides a metaphysical basis for the relationship between God and abstract objects to be further elucidated and for the position of 'Platonic Theism' to be free from the primary issues that are often raised against it. (shrink)

In a first investigation, a Lacan-motivated template of the Poe story is fitted to the data. A segmentation of the storyline is used in order to map out the diachrony. Based on this, it will be shown how synchronous aspects, potentially related to Lacanian registers, can be sought. This demonstrates the effectiveness of an approach based on a model template of the storyline narrative. In a second and more Comprehensive investigation, we develop an approach for revealing, that is, uncovering, Lacanian (...) register relationships. Objectives of this work include the wide and general application of our methodology. This methodology is strongly based on the “letting the data speak” Correspondence Analysis analytics Platform of Jean-Paul Benzécri, that is also the geometric data analysis, both qualitative and quantitative analytics, developed by Pierre Bourdieu. (shrink)

The main objective of this paper was to examine the relationship between management of educational support services and the attainment of Universal Basic Education goals in Cross River State. Three null hypotheses were formulated in this study. The study adopted correlational research design. Census technique was employed in selecting the entire population of 2,078 primary school administrators in the state. The instruments used for data collection were “Management of Educational Support Services Questionnaire (MESSQ); and Attainment of Universal Basic Education (...) Goals Questionnaire (AUBEGQ)” respectively. The data collected were analyzed using descriptive statistics, while the null hypotheses were all tested using Pearson Product Moment Correlation Analysis at .05 alpha levels. The results from the study revealed that; management of guidance/counselling services, staff development services, and ICT services are significantly related to the attainment of Universal Basic Education goals respectively. Based on these results, it was recommended among others that; the ministry of education should ensure that there is adequate provision of professional guidance counsellors to every primary school in Cross River State in order to help address the psychological and persona-social needs of the pupils. Contribution/Originality:. (shrink)

Are mathematical objects affected by their historicity? Do they simply lose their identity and their validity in the course of history? If not, how can they always be accessible in their ideality regardless of their transmission in the course of time? Husserl and Foucault have raised this question and offered accounts, both of which, albeit different in their originality, are equally provocative. Both acknowledge that a scientific object like a geometrical theorem or a chemical equation has a history because (...) it is only constituted in and transmitted through history. But they see that history as a part of its ideality, so that, although historical, a scientific object retains its identity as one and the same object. (shrink)

John Dewey's metaphysics of experience has been criticized by a number of philosophers-most notably, George Santayana and Richard Rorty. While mainstream Dewey scholars agree that these critical treatments fail to treat the American Pragmatist theory of what exists on its own terms, there has still been some difficulty reaching consensus on what the casual reader should take away from the pages of Experience and Nature, Deweys seminal work on naturalistic metaphysics. So, how do we unearth the significance of Dewey's misunderstood (...) metaphysics? One way is for philosophers to look to spatial and social-cultural geographers for help. To fully grasp the movement of experience, these geographers recommend that we start with an experiential activity, such as touring. The activity of sea kayak touring, I contend, discloses the general movement of experience in Dewey's metaphysics between its primary and secondary phases. With this illustration and a closely connected metaphor, I demonstrate that Dewey's naturalized metaphysics can not only withstand the objections of the likes of Santayana and Rorty it can also assist us in gaining a deeper appreciation of the qualitative richness of our own day-to-day practices. (shrink)

Michael Ayers’s Knowing and Seeing: Groundwork for a New Empiricism is a rich and detailed development of two ideas. The first is that perception presents reality to us directly in a perspicuous way. We thus acquire primary knowledge of the world: “knowledge gained by being evidently, self-consciously, in direct cognitive contact with the object of the knowledge.” (Ayers 2019, 63) The second idea is that concepts are not needed in perception. In this article, the author examines Ayers’s view. (...) The author proceeds as follows: In the first section, he identifies the target of Ayers’s attacks, conceptualism. He then describes why many philosophers have felt this conceptualist view to be attractive. In the next section, he discusses Ayers’s criticisms of conceptualism in an attempt to disentangle these criticisms from the statement of his positive view, which the author discusses in the following section. He ends by describing some problems for Ayers’s positive position that are, so he argues, the result of his vehement opposition to conceptualism. (shrink)

Two competing models of metaaxiological justification of politics are analyzed. Politics is understood broadly, as actions which aim at organizing social life. I will be, first of all, interested in law making activities. When I talk about metaaxiological justification I think not so much about determinations of what is good, but about determinations refering to the way the good is founded, in short: determinations which answer the question why something is good. In the first model, which is described here as (...) objectivistic, it is assumed that determining that which is good is a matter of cognition; in the second model, which could be described here as voluntaristic or excedingly liberal, it is assumed that determining good is not a matter of cognition but of will – something is good because it is wanted. In the latter model, the cognoscibility of good is rejected and therefore the objective criteria for evaluation of which ‘will’ is better and which is worse are rejected. As a consequence, negative freedom becomes the fundamental value of social order and the basic requirement is that of maximizing the sphere of individual’s free actions, the sphere which is free from interference of other individuals or institutions. I am going to argue that none of these models is acceptable as a basis of oragnizing social life, and at least because of one reason. Each of them leads to a certain version of totalitarianism. In the conclusion I am going to present a mixed model, which, in my opinion, reflexes well the practice of democratic states. Analysis of these three models allows, first of all, to identify more clearly some of the problems appearing in making law, including procedural questions. By pointing at the interdependence of the foundations of good and law making procedures it is argued that the choice of the concept of good (a metaaxiological choice) is primary to the choice of law making procedures. (shrink)

The influence that the meditations of Husserl's later years may have had on the younger generation is, as yet, difficult to assess. And it is, in fact, not important whether this question can or cannot be answered. Husserl, obviously, was not less sensitive to the problems arising from the intellectual and cultural situation as it developed around 1920, than were those who have emphatically made the Lebenswelt the primary object of their inquiries and the starting point for the (...) reconstruction of philosophy. (shrink)

Giovanni Mion defends the idea that knowledge is context relative, but, in contrast to current versions of epistemic contextualism, on his view, knowledge is relative to contexts that are objective. Following Christopher Gauker’s conception of what a context is, Mion argues that knowledge is relative to the speakers’ conversational goals; and since the best way to achieve the goals of a conversation depends upon the way the world really is, it follows that participants in a conversation might be unaware of (...) the content of the context that truly governs their conversation. Finally, Mion uses objective contexts to explain why practical interests have epistemic significance. According to him, if we assume that the primary function of language is not to share thoughts, but to achieve practical goals, and, accordingly, that knowledge attributions play primarily an action-guiding role (as opposed to a mind-revealing role), then we are in a better position to understand why knowledge is not just a matter of theoretical factors, but it is also a matter of how much is at stake. (shrink)

My concern in this paper is the role of subjectivity in the pursuit of the good. I propose that subjective thought as well as a subjective mental process underappreciated in philosophical psychology – contemplation – are instrumental for discovering and apprehending a whole range of value. In fact, I will argue that our primary contact with these values is through experience and that they could not be properly understood in any other way. This means that subjectivity is central to (...) our evaluative lives. (shrink)

For Aristotle, the shape of a physical body is perceptible per se (DA II.6, 418a8-9). As I read his position, shape is thus a causal power, as a physical body can affect our sense organs simply in virtue of possessing it. But this invites a challenge. If shape is an intrinsically powerful property, and indeed an intrinsically perceptible one, then why are the objects of geometrical reasoning, as such, inert and imperceptible? I here address Aristotle’s answer to that problem, focusing (...) on the version of it that he presents in De caelo III.8. I argue that if we grant that Aristotle conceived of the shape of a sensible body as some kind of causal power, then the satisfactory resolution of that challenge pushes us to interpret him as having conceived of it as being, more specifically, an impure power—that is, as a property that is not only intrinsically powerful but also, in some way, intrinsically non-powerful as well. This is a notable result not only insofar as it illuminates Aristotle’s conception of shape but also insofar as it contributes to our knowledge of Aristotle’s theory of dunameis and his ontology more broadly. (shrink)

This paper is about the question: what is it for a mental state to mean (or present) something as an intentional object? This issue is addressed from a broad perspective, against the background of Brentano’s philosophical programme in Psychology from an empirical standpoint, and the controversy between the proponents of a non-canonical interpretation of Brentano’s theory of intentionality, and the so-called orthodox interpretation advocated namely by R. Chisholm. My investigation is divided into six parts. In the first section, I (...) explain the meaning and function of the notion of phenomenon in light of Brentano’s philosophical programme, and I briefly elucidate the notion of physical phenomenon which, in Brentano’s Psychology, constitutes the primary object of consciousness. In the next two sections, I look at two aspects of Brentano’s criticism of the identity thesis that he attributes to British empiricism, namely the psychological aspect, which concerns the identification of the two classes of phenomena, and the metaphysical aspect relating to the relationship between physical phenomena and the reality of an extramental world. Once this double distinction will be established, I will turn to the relation of intentional objects to presentations and put forward the hypothesis that intentional objects are conceptually dependent upon presentations and that this dependence rests, in turn, upon the content of the mental phenomena. The next step concerns Brentano’s theory of primary and secondary objects, and one of the main non-orthodox arguments against the canonical interpretation, namely that the latter conflates primary and secondary objects. In this context, I examine a second hypothesis: that the secondary object, or intentional correlate of an act, is an intentional content, which is distinct both from the intentional object and from the reality to which it relates, and I maintain that the intentional content has the function of mediating the mental acts’ relation to their objects. Finally, I shall examine some objections against the hypothesis of intentional content in Brentano’s Psychology, and I will conclude with a brief commentary on the bearing of this investigation with regard to the interpretation of the genesis of Brentano’s theory of intentionality, before and after the reistic turn of his philosophy. (shrink)

Abstract: English language teaching is very important because of the global status of English. English language teaching is a process that requires great efforts on the part of all the participants. Classroom interactions, activities, textbooks are the most important elements of teaching process for the aims and objectives of a course. Main objective of this study is to discover English language teaching skills in primary schools of union council Kumb Taluka Kotdiji, District Khairpur Mir’s. The Questionnaire was prepared for (...) teachers to explore the different aspects of teaching English skills and teachers’ skills, (Training, teacher qualifications regarding English, English teaching methodologies). The questionnaire identifies teacher training and instructional materials. A sample of 20 teachers (both male and female) were selected from different schools of union council Kumb Taluka Kotdiji, District Khairpur Mir’s. The data obtained was tabulated and analyzed by the percentage. (shrink)

Like most, if not all, of his contemporaries, Spinoza never developed a full-fledged philosophy of mathematics. Still, his numerous remarks about mathematics attest not only to his deep interest in the subject (a point which is also confirmed by the significant presence of mathematical books in his library), but also to his quite elaborate and perhaps unique understanding of the nature of mathematics. At the very center of his thought about mathematics stands a paradox (or, at least, an apparent paradox): (...) mathematics provides Spinoza with an epistemic model. Mathematical knowledge is certain (II/138/9 and II/138/9), clear (IV/261/8), and free from teleological thinking (II/79/33), but the objects of mathematical knowledge – i.e., mathematical entities – are nothing but “auxila imaginationis [aids of the imagination],” (IV/57/16 and II/83/15), entities that are not real and merely assist the imagination in carving the world in manner that is suitable to our limited and distortive cognitive capacities. (shrink)

Presented at Philosophy Across Disciplines Conference 2021, Newcastle University. -/- As noted by philosopher Robert Pasnau, “our standard view of sound is incoherent” at best. A quick perusal of how we discuss and represent sound in our day-to-day language readily highlights a number of inconsistencies. Sound might be described roughly as emanating from the location of its material source (the ‘crack of the snare drum over there’ distal theory), as a disruption somewhere in the space in-between the sounding object (...) and the listener (the ‘longitudinal compression waves in the air’ medial theory), located with the hearer (the ‘inner sensations’ proximal theory), or perhaps as devoid of spatial characteristics at all (aspatial theory). Beyond these topographic ruminations on the location of sounds, even deeper disagreements arise around just what sorts of things sounds are. A broad array of theories treat sounds as events, as object-like particulars that travel through space, as properties of their sounding objects, etc.—with many subtle ontological variations springing up along the way. The philosophical plot further thickens as we expand from defining the ontology and spatial position of simple primary sounds through to the phenomenon of echoes, with certain theories arguably faring better than others. We’ll focus here on Casey O’Callaghan’s formulation of sounds as disturbance events which bind primary sounds and their echoes together as one. In short, the claim that echoes are identical to their associated primary sound and are not distinct sounds in their own right. Described as the ‘Primary Sound Account of Echoes’ (‘PSAE’) in Gregory Fowler’s “Against the Primary Sound Account of Echoes,” the intricacies of this particular aspect of O’Callaghan’s theory of a primary sound’s connection to its echo bears greatly upon the workability of distal theories of sound in general. What I seek to achieve in this presentation is to illustrate how O’Callaghan’s PSAE fails when subjected to increased scrutiny across a broader range of echo scenarios, which in turn presents a significant issue for proponents of distal theories of sound. (shrink)

This essay explores theories of place, or lived-space, as regards the role of objectivity and the problem of relativism. As will be argued, the neglect of mathematics and geometry by the lived-space theorists, which can be traced to the influence of the early phenomenologists, principally the later Husserl and Heidegger, has been a major contributing factor in the relativist dilemma that afflicts the lived-space movement. By incorporating various geometrical concepts within the analysis of place, it is demonstrated that the lived-space (...) theorists can gain a better insight into the objective spatial relationships among individuals and within groups—and, more importantly, this appeal to mathematical content need not be construed as undermining the basic tenants of the lived-space approach. (shrink)

This article presents the first annotated English translation and edition of the Tibetan text of the Madhyamakaratnapradīpa, chapter 5, whose original Sanskrit is to be considered lost. The Introduction contains a primary analysis of contents and aims of the chapter, together with general observations on the epoch and compositional style of the Madhyamakaratnapradīpa. It is suggested that the text is probably a 10 th century explanatory handbook of Bhāviveka’s Tarkajvālā for beginner students. Chapter 5, in particular, relying strongly upon (...) the “two truths” dialectics, focuses on how students can consistently respond to the main objections opponents used to raise against the Madhyamaka standpoint. (shrink)

Spinoza’s geometrical approach to his masterwork, the Ethics, can be represented by a digraph, a mathematical object whose properties have been extensively studied. The paper describes a project that developed a series of computer programs to analyze the Ethics as a digraph. The paper presents a statistical analysis of the distribution of the elements of the Ethics. It applies a network statistic, betweenness, to analyze the relative importance to Spinoza’s argument of the individual propositions. The paper finds that a (...) small percentage of the propositions greatly exceed the majority in this importance. The paper then describes two logical structures that appear respectively in the Ethics and argues that they result in redundancy in the sense that about ten percent of the propositions could have been eliminated. The appendices list these structures and describes how the resources of the study can be made available to readers. (shrink)

On the one hand, Scheler's critique of Kant's concept of a priori benefits from Husserl to a large extent, and it complements and deepens Husserl's. On the other hand, Scheler also critiques Husserl's definition of a priori. Husserl's material a priori as ideal object primarily thanks to his so-called "Bolzano- turn". In this connection, Scheler grabs hold of the relation of Husserl to Bolzano from the very beginning. For Scheler, Husserl thinks in a "platonic" way, and still falls in (...) a new type of "Platonism", or rather, logical Platonism, although he correctly refuses the ordinary Platonism. In Scheler's view, Husserl's phenomenological reduction is "not purely" executed, and therefore his phenomenological experience is problematic, or more precisely, the relation between categorial intuition and sensuous intuition is problematic. The final aim of Scheler's critique of Husserl's phenomenological understanding of "objective a priori" is to win the primary position of categorial intuition and its content , ethical insight and its correlate , and ultimately of phenomenological ethics of material value.Einerseits nimmt Schelers Kritik an Kant bezüglich des Begriffs des Apriori die Einsichten Husserls in großem Umfang auf. Schelers Kritik an Kant ergänzt und vertieft die Husserlsche Kant-Kritik. Andererseits kritisiert er aber auch Husserls Bestimmung des Apriori. Vor allem verdankt sich das materiale Apriori als idealer Gegenstand bei Husserl der sogenannten “Bolzano’schen Wendung”. Von Anfang an kritisiert Scheler Husserl in diesem Punkt, indem er dem Verhältnis zwischen Bolzano und Husserl immer präziser nachging. Für Scheler unterliegt Husserl mit Recht keinem platten Platonismus. Aber dennoch verfahre Husserl immerhin “platonistisch”, er unterliege einem “Neoplatonismus”, bzw. einem logischen Platonismus. Weil die phänomenologische Reduktion bei Husserl nach Schelers Meinung “nicht reinlich” durchgeführt wird, ist die phänomenologische Erfahrung bei Husserl problematisch, genauer gesagt ist das Verhältnis zwischen der kategorialen Anschauung und der sinnlichen Anschauung problematisch. Der Endzweck von Schelers Kritik an der phänomenologischen Auffassung des gegenständlichen Apriori bei Husserl besteht darin, die primäre Stelle der kategorialen Anschauung und ihrer Gehalte , sowie der sittlichen Einsicht und ihrer Korrelate und zuletzt der phänomenologisch materialen Wertethik zu gewinnen.S jedne strane, Schelerova kritika Kantova pojma a priori u velikoj mjeri duguje Husserlu, te dopunjuje i produbljuje Husserlovu. S druge strane, Scheler kritizira i Husserlovu definiciju apriorija. Husserlov materijalni a priori kao idealni predmet prvenstveno proizlazi iz njegova takozvanog bolzanovskog obrata. Prema Scheleru, Husserl razmišlja na "platonski" način te upada u novi tip "platonizma" ili, točnije, logičkog platonizma, iako s pravom odbacuje obični platonizam. Scheler smatra da Husserlova fenomenološka redukcija nije izvedena "čisto" te da je stoga njegovo fenomenološko iskustvo proble- matično ili, točnije, problematičan je odnos između kategorijalnog zora i osjetilnog zora. Krajnji cilj Schelerove kritike Husserlova fenomenološkog shvaćanja "objektivnog a priori" jest zadobivanje primarne pozicije kategorijalnog zora i njegova sadržaja , etičkog uvida i njegova korelata te, na koncu, fenomenološke etike materijalne vrijednosti. (shrink)

This dissertation examines the theory of perceptual cognition laid out by the 7th century Buddhist scholar, Dharmakīrti, in his magnum opus, the Pramāṇavārttika. Like most theories of perception, both ancient and modern, the sensory cognition of ordinary objects is a topic of primary concern. Unlike other theorists, however, Dharmakīrti advances a technical definition of “perception” as a cognition which is both nonconceptual and non-erroneous. Dharmakīrti’s definition of perception is thereby deliberately inclusive of three additional types of “perceptual” cognition, in (...) addition to veridical sensory awareness: the nonconceptual mental apprehension of an immediately-preceding cognition (“mental perception”), the vivid appearance of soteriologically efficacious objects of contemplative practice (“yogic perception”), and the sheer unmediated presence of the contents of cognition—whatever these might be—to the cognizing mind (“reflexive awareness”). Through the logical examination of what it means to be aware of an object, Dharmakīrti demonstrates that the awareness of an object is just the awareness of a phenomenal form or cognitive image produced by that object. Pursuing this analysis further, however, Dharmakīrti argues that the very notion of an object of cognition that exists “externally” or outside the mind is incoherent. Additionally, Dharmakīrti maintains that the phenomenological structure of subject and object—that is, the “first-personal” sense of one’s own cognitions as pertaining to oneself (“for-me-ness”), together with the inseparably concomitant sense that the objects of cognition exist “out there” in an extramental world—is strictly a form of cognitive error. Therefore, because ordinary sensory cognition is inherently structured by this subject-object duality, ordinary sensory cognition must in the final analysis be understood as erroneous. According to Dharmakīrti, in other words, ultimately only the nondual “luminosity” of reflexive awareness is genuinely perceptual, because only reflexive awareness is undistorted by nature. In this way, Dharmakīrti’s epistemology provides a theoretical foundation for the advanced nondual contemplative practices of Indian and Tibetan Buddhism, particularly Mahāmudrā and rDzogs chen. (shrink)

As soon as you believe an imagination to be nonfictional, this imagination becomes your ontological theory of the reality. Your ontological theory (of the reality) can describe a system as the reality. However, actually this system is only a theory/conceptual-space/imagination/visual-imagery of yours, not the actual reality (i.e., the thing-in-itself). An ontological theory (of the reality) actually only describes your (subjective/mental) imagination/visual-imagery/conceptual-space. An ontological theory of the reality, is being described as a situation model (SM). There is no way to prove/disprove (...) that there is only one reality, or there are two realities (i.e., “subjective reality” and “objective reality”). So, every ontology talk/theory/imagination about the two realities is only a talk/theory/imagination – we will never know whether it is true or not. The conventionally-called “physical/objective reality/world” around my conventionally-called “physical/objective body” is actually a geometric mathematical model (being generated/mathematically-modeled by my brain) – it's actually a subset/component/part/element of my brain’s mind/consciousness/manifest-image. Our cosmos is an autonomous objective parallel computing automaton (aka state machine) which evolves by itself automatically/unintentionally – wave-particle duality and Heisenberg’s uncertainty principle can be explained under this SM of my brain. Each elementary particle (as a building block of our cosmos) is an autonomous mathematical entity itself (i.e., a thing in itself). Our cosmos has the same nature as a Game of Life system – both are autonomous objective parallel-computing automata. Cosmos (as a state machine) is indistinguishable from a digital simulation – my consciousness (as something nonphysical) is not cosmos (as a state machine). If we are happy to accept randomness/stochasticity, then it is obviously possible that all other worlds in the many-worlds interpretation (MWI) actually do not exist (objectively). As one metaphysical option, we can treat all other worlds as subjective only (even if they are actually objective). Under the context of this metaphysical option, we are only living in one world (i.e., the world we are currently living in; this world) – we are not living in many worlds at the same time parallelly. Under the context of this metaphysical option, there is only one possible future. The relationship among any number of elementary particles, is governed/described by Schrodinger equation. If (in theory) Schrodinger equation can’t be used to reliably forecast whether I will go to McDonald for dinner in this world (based on the current state of all elementary particles of the cosmos), then what can Schrodinger equation do? The conventionally-called “space” does not exist objectively. “Time” and “matter” are not physical. Consciousness is the subjective-form (aka quale) of the mathematical models (of the objective cosmos) which are intracorporeally/subjectively used by the control logic of a Turing machine’s program fatedly. A Turing machine’s mind/consciousness/manifest-image or deliberate decisions/choices should not be able to actually/objectively change/control/drive the (autonomous or fated) worldline of any elementary particle within this world (i.e., the world we are currently living in, under the context of MWI). Besides the Schrodinger equation (or another mathematical equation/function which is yet to be discovered) which is a valid/correct/factual causality of our cosmos/state-machine, every other causality (of our cosmos/state-machine) is either invalid/incorrect/counterfactual or can be proved by deductive inference based on the Schrodinger equation (or the aforementioned yet-to-be-discovered mathematical equation/function) only. Closed causality entails no causality. Consciousness plays no causal role (“epiphenomenalism”), or in other words, any cognitive/behavioural activity can in principle be carried out without consciousness (“conscious inessentialism”). If the “loop quantum gravity” theory is correct, then time/space does not actually/objectively exist in the objective-evolution of the objective cosmos, or in other words, we should not use the subjective/mental concept of “time”, “state” or “space” to describe/imagine the objective-evolution of our cosmos. (shrink)

Throughout his works, St. Augustine offers at least nine distinct views on the nature of time, at least three of which have remained almost unnoticed in the secondary literature. I first examine each these nine descriptions of time and attempt to diffuse common misinterpretations, especially of the views which seek to identify Augustinian time as consisting of an un-extended point or a distentio animi . Second, I argue that Augustine's primary understanding of time, like that of later medieval scholastics, (...) is that of an accident connected to the changes of created substances. Finally, I show how this interpretation has the benefit of rendering intelligible Augustine's contention that, at the resurrection, motion will still be able to occur, but not time. (shrink)

This paper is about the question: what is it for a mental state to mean (or present) something as an intentional object? This issue is addressed from a broad perspective, against the background of Brentano’s philosophical programme in Psychology from an empirical standpoint, and the controversy between the proponents of a non-canonical interpretation of Brentano’s theory of intentionality, and the so-called orthodox interpretation advocated namely by R. Chisholm. My investigation is divided into six parts. In the first section, I (...) explain the meaning and function of the notion of phenomenon in light of Brentano’s philosophical programme, and I briefly elucidate the notion of physical phenomenon which, in Brentano’s Psychology, constitutes the primary object of consciousness. In the next two sections, I look at two aspects of Brentano’s criticism of the identity thesis that he attributes to British empiricism, namely the psychological aspect, which concerns the identification of the two classes of phenomena, and the metaphysical aspect relating to the relationship between physical phenomena and the reality of an extramental world. Once this double distinction will be established, I will turn to the relation of intentional objects to presentations and put forward the hypothesis that intentional objects are conceptually dependent upon presentations and that this dependence rests, in turn, upon the content of the mental phenomena. The next step concerns Brentano’s theory of primary and secondary objects, and one of the main non-orthodox arguments against the canonical interpretation, namely that the latter conflates primary and secondary objects. In this context, I examine a second hypothesis: that the secondary object, or intentional correlate of an act, is an intentional content, which is distinct both from the intentional object and from the reality to which it relates, and I maintain that the intentional content has the function of mediating the mental acts’ relation to their objects. Finally, I shall examine some objections against the hypothesis of intentional content in Brentano’s Psychology, and I will conclude with a brief commentary on the bearing of this investigation with regard to the interpretation of the genesis of Brentano’s theory of intentionality, before and after the reistic turn of his philosophy. (shrink)

The author considers that the Penal Sciences face a wide range of human pathogenic issues, ranging from terrorism and human trafficking to corruption and the use of substances and are, thus, the ideal discipline for investigating the various scientific issues and the implementation of the scientific findings arising from such investigations. He also believes that the Penal Sciences, being inextricably linked to human values and constitutional rights, are, by their nature, beneficial towards the promotion and consolidation of values, such as (...) freedom, solidarity and, especially, Social Justice. The latter concept is perceived by the author not only as a form of justice, which provides everyone with their due of proportion to their value, according to the famous saying of Ulpian “suum cuique tribuere”, but rather as a form of restitution from social injustices and as a treatment for social needs, particularly for our fellow human beings who are marginalized by society in conditions of poverty and degradation. It is interesting, at this point, to emphasize that the United Nations, in an important report from 2006 entitled “Social Justice in an Open World. The Role of the United Nations”, defines Social Justice as the fair and compassionate distribution of the fruits of economic growth (“Social Justice in an Open World. The Role of the United Nations”, edited by the International Forum for Social Development, New York: United Nations, 2006, p. 7, available online). The vision, therefore, of a society focused on goals such as combating socio-economic disparities and providing effective assistance for the weaker members of society signifies, especially in this period of Crisis, is a primary objective worthy, according to the author, of captivating us. Perhaps, indeed, the new target for Criminal Policy, following that of Restorative Justice, should now be that of Social Justice and, in fact, with a double project and aim: first for a fairer distribution of social goods and, also, for greater solidarity towards the weaker members of society. Indeed, it is a known fact to those involved with the Penal Sciences, that a dominant contemporaneous trend is that of Restorative Justice, in the sense that Criminal Law and Criminology finally have to address the needs of the victim of a criminal act and to advocate for relevant methods for extrajudicial settlements and for the conciliation of the offender and the victim. Restorative Justice is, hence, based on the triptych of the perpetrator assuming responsibilities for their actions, of restoring, as far as possible, the effects of the injurious actions against the victim and, also, of actively expressing the desire for conciliation with the victim. Certainly it would be greatly desirable if these ideas were to be consolidated within Greek legislation, albeit within the, always progressive, Greek Law for Minors there is a provision for the reformatory conciliation measure, pursuant to article 122 case e of the Greek Penal Code. However, the author believes that in this period of time, a time of profound crisis at all levels, there is need for more than simple offender-victim conciliation. There is a need for this spirit of reconciliation and solidarity to be extended to benefit all those who are experiencing hard times and may, therefore, in their deprivation and frustration, are led to committing crime. The author, at this point, refers to all the socially weak and often marginalized groups of people, who are scientifically characterized as "weak" or "vulnerable" and who try, with great courage, to survive without breaching the threshold of breaking the law. It is apparent here, according to the author, that if Criminal Policy actually aims to provide solutions to the problems of crime, it should not solely be limited to repairing the damage and conciliating the victim and perpetrator, but it should strike against the causative factors of crime and the primarily socio-economic inequalities and other forms of injustice which cause, according to Aristotle in his "Politics" (V. 1301b27, 1301a32 et seq., 1266b40), social reactions, attitudes and – Ι would add - a sequence of serious criminal acts. In other words, another kind of Justice is required in addition to Restorative, so that it may become the mission of our Criminal Policy to eliminate the injustices and inequalities that lead to crime. In view of this direction certain introductory thoughts are developed in this article. (shrink)

I investigate the role of geometric intuition in Frege’s early mathematical works and the significance of his view of the role of intuition in geometry to properly understanding the aims of his logicist project. I critically evaluate the interpretations of Mark Wilson, Jamie Tappenden, and Michael Dummett. The final analysis that I provide clarifies the relationship of Frege’s restricted logicist project to dominant trends in German mathematical research, in particular to Weierstrassian arithmetization and to the Riemannian conceptual/geometrical tradition at (...) Göttingen. Concurring with Tappenden, I hold that Frege’s logicism should not be understood as a continuing a project of reductionist arithmetization. However, Frege does not quite take up the Riemannian banner either. His logicism supports a hierarchical understanding of the structure of mathematical knowledge, according to which arithmetic is applicable to geometry but not vice versa because the former is more general, as revealed by the strictly logical nature of its objects in comparison to the intuitional nature of geometric objects. I suggest, in particular, that Frege intended that foundational work would show the use of geometric intuition in complex analysis, a source of error for Riemann that Weierstrass was proud to have uncovered, to be inessential. (shrink)

This work examines the unique way in which Benedict de Spinoza combines two significant philosophical principles: that real existence requires causal power and that geometrical objects display exceptionally clearly how things have properties in virtue of their essences. Valtteri Viljanen argues that underlying Spinoza's psychology and ethics is a compelling metaphysical theory according to which each and every genuine thing is an entity of power endowed with an internal structure akin to that of geometrical objects. This allows Spinoza to offer (...) a theory of existence and of action - human and non-human alike - as dynamic striving that takes place with the same kind of necessity and intelligibility that pertain to geometry. This fresh and original study will interest a wide range of readers in Spinoza studies and early modern philosophy more generally. (shrink)

The overreliance on verbal models and theories in psychology has been criticized for hindering the development of reliable research programs (Harris, 1976; Yarkoni, 2020). We demonstrate how the conceptual space framework can be used to formalize verbal theories and improve their precision and testability. In the framework, scientific concepts are represented by means of geometric objects. As a case study, we present a formalization of an existing three-dimensional theory of emotion which was developed with a spatial metaphor in mind. (...) Wundt posits that the range of human emotion can be represented along three axes of basic emotions (pleasure/displeasure, excitement/inhibition, tension/relaxation), just as color vision can be represented using three basic colors. We use dimensions to represent basic emotions, points to represent emotional states, and regions to represent broader emotional concepts. We then compare our formalization to an existing structuralist formalization of Wundt’s theory. Further, we discuss the empirical predictions that our formalization generates, such as comparisons of similarity and intensity. We conclude by demonstrating how the tools developed in the conceptual space framework can be used to formulate a theory of emotion based on empirical observation. (shrink)

The paper aims to establish if Grassmann’s notion of an extensive form involved an epistemological change in the understanding of geometry and of mathematical knowledge. Firstly, it will examine if an ontological shift in geometry is determined by the vectorial representation of extended magnitudes. Giving up homogeneity, and considering geometry as an application of extension theory, Grassmann developed a different notion of a geometrical object, based on abstract constraints concerning the construction of forms rather than on the homogeneity conditions (...) required by the modern version of the theory of proportions. Secondly, Grassmann’s conception of mathematical knowledge will be investigated. Parting from the traditional definition of mathematics as a science of magnitudes, Grassmann considered mathematical forms as particulars rather than universals: the classification of the branches of mathematics was thus based on different operational rules, rather than on empirical criteria of abstraction or on the distinction of different species belonging to a common genus. It will be argued that a different notion of generalization is thus involved, and that the knowledge of mathematical forms relies on the understanding of the rules of generation of the forms themselves. Finally, the paper will analyse if Grassmann’s approach in the first edition of the Ausdehnungslehre should be explained in terms of the notion of purity of method, and if it clashes with Grassmann’s later conventionalism. Although in the second edition the features of the operations are chosen by convention, as it is the case for the anti-commutative property of the multiplication, the choice is oriented by our understanding of the resulting forms: a simplification in the algebraic calculus need not correspond to a simplification in the ‘dimensional’ interpretation of the result of the multiplicative operation. (shrink)

At the turn of the seventeenth century, Bruno and Cavalieri independently developed two theories, central to which was the concept of the geometrical indivisible. The introduction of indivisibles had significant implications for geometry – especially in the case of Cavalieri, for whom indivisibles provided a forerunner of the calculus. But how did this event occur? What can we learn from the fact that two theories of indivisibles arose at about the same time? These are the questions addressed in this paper. (...) Relying on the methodology of “historical epistemology”, this paper asserts that the similarities and differences between the theories of Bruno and Cavalieri can be explained in terms of “shared knowledge”. The paper shows that the idea – on which both Bruno and Cavalieri build – that geometrical objects are generated by motion was part of the mathematical culture of the time. Tracing this idea back to its Pythagorean origins thus sheds light on the relationship between motion and continuum in mathematics. (shrink)

The purpose of this work is to address the relation existing between ancient Greek practical geometry and ancient Greek pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically (...) explicit in definitions, like that of segments in Euclid’s Elements. Then, we will address how in pure geometry we, so to speak, “refer back” to practical geometry. This occurs in two ways. One, in the propositions of pure geometry. The other, when applying pure geometry. In this case, geometrical objects can represent practical figures like, e.g., a practical segment. (shrink)