Results for 'geometric conventionalism'

446 found
Order:
  1.  61
    Hypothesis and Convention in Poincaré’s Defense of Galilei Spacetime.Scott Walter - 2009 - In Michael Heidelberger & Gregor Schiemann (eds.), The Significance of the Hypothetical in Natural Science. De Gruyter. pp. 193-220.
    According to the conventionalist doctrine of space elaborated by the French philosopher-scientist Henri Poincaré in the 1890s, the geometry of physical space is a matter of definition, not of fact. Poincaré's Hertz-inspired view of the role of hypothesis in science guided his interpretation of the theory of relativity (1905), which he found to be in violation of the axiom of free mobility of invariable solids. In a quixotic effort to save the Euclidean geometry that relied on this axiom, Poincaré extended (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  2. A função e natureza das convenções e hipóteses segundo o convencionalismo francês da virada do século XIX para o XX: relações entre ciência e metafísica nas obras de Henri Poincaré, Pierre Durem e Édouard Le Roy.Andre Philot - 2015 - Dissertation, Rio de Janeiro State University
    In this work we present the function and we determine the nature of conventions and hypotheses for the scientific foundations according with the conventionalist doctrine that arose in France during the turning of the XIX century to the XX. The doctrine was composed by Henri Poincaré, Pierre Duhem and Édouard Le Roy. Moreover, we analyze the relation that conventions and hypotheses can establish with metaphysical thesis through criteria used by scientists in order to determine the preference for certain theories. Thereunto, (...)
    Download  
     
    Export citation  
     
    Bookmark  
  3. Grassmann’s epistemology: multiplication and constructivism.Paola Cantu - 2010 - In Hans-Joachim Petsche (ed.), From Past to Future: Graßmann's Work in Context. Springer.
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  4. Conventionalism about time direction.Matt Farr - 2022 - Synthese 200 (1):1-21.
    In what sense is the direction of time a matter of convention? In 'The Direction of Time', Hans Reichenbach makes brief reference to parallels between his views about the status of time’s direction and his conventionalism about geometry. In this article, I: (1) provide a conventionalist account of time direction motivated by a number of Reichenbach’s claims in the book; (2) show how forwards and backwards time can give equivalent descriptions of the world despite the former being the ‘natural’ (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  5. A Conventionalist Account of Distinctively Mathematical Explanation.Mark Povich - 2023 - Philosophical Problems in Science 74:171–223.
    Distinctively mathematical explanations (DMEs) explain natural phenomena primarily by appeal to mathematical facts. One important question is whether there can be an ontic account of DME. An ontic account of DME would treat the explananda and explanantia of DMEs as ontic structures and the explanatory relation between them as an ontic relation (e.g., Pincock 2015, Povich 2021). Here I present a conventionalist account of DME, defend it against objections, and argue that it should be considered ontic. Notably, if indeed it (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  6. Conventionalism about Persons and the Nonidentity Problem.Michael Tze-Sung Longenecker - 2023 - Australasian Journal of Philosophy 101 (4):954-967.
    ABSTRACT I motivate ‘Origin Conventionalism’—the view that which facts about one’s origins are essential to one’s existence depends partly on our person-directed attitudes. One important upshot is that the view offers a novel and attractive solution to the Nonidentity Problem. That problem typically assumes that the sperm-egg pair from which a person originates is essential to that person’s existence; in which case, for many future persons that come into existence under adverse conditions, had those conditions not been realized, the (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  7. Logical Conventionalism.Jared Warren - unknown - In Filippo Ferrari, Elke Brendel, Massimiliano Carrara, Ole Hjortland, Gil Sagi, Gila Sher & Florian Steinberger (eds.), Oxford Handbook of Philosophy of Logic. Oxford, UK: Oxford University Press.
    Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific picture of reality. For (...)
    Download  
     
    Export citation  
     
    Bookmark  
  8.  71
    Conventionalism about Persons and Reflexive Reference: A Contextualized Approach.Michael Tze-Sung Longenecker - forthcoming - Erkenntnis.
    Many Perdurantists have been drawn to the “Conventionalist” idea that our person-directed attitudes can determine whether or not we survive events such as teletransportation. In this paper, I suggest a novel “Contextualist Conventionalism” according to which Conventionalism is true with respect to some, but not all, contexts in which we ask “will I survive?”—instead in “reflexive” contexts, “I” reflexively refers to a thinker whose persistence conditions are mind-independent. Unlike one form of Conventionalism which implies that the reference (...)
    Download  
     
    Export citation  
     
    Bookmark  
  9. Was Wittgenstein a radical conventionalist?Ásgeir Berg - 2024 - Synthese 203 (2):1-31.
    This paper defends a reading of Wittgenstein’s philosophy of mathematics in the Lectures on the Foundation of Mathematics as a radical conventionalist one, whereby our agreement about the particular case is constitutive of our mathematical practice and ‘the logical necessity of any statement is a direct expression of a convention’ (Dummett 1959, p. 329). -/- On this view, mathematical truths are conceptual truths and our practices determine directly for each mathematical proposition individually whether it is true or false. Mathematical truths (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  10. Conventionalism: Poincaré, Duhem, Reichenbach.Torsten Wilholt - 2012 - In James Robert Brown (ed.), Philosophy of Science: The Key Thinkers. New York: Continuum Books. pp. 32.
    A recurrent theme in philosophy of science since the early twentieth century is the idea that at least some basic tenets within scientific theories ought to be understood as conventions. Various versions of this idea have come to be grouped together under the label ‘conventionalism’. This chapter presents and discusses some important historical stages in the development of conventionalism. Particular attention is paid to the contributions made by Henri Poincaré, Pierre Duhem and Hans Reichenbach.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  11. Geometric Averaging in Consequentialist Ethics.Alfred Harwood - manuscript
    When faced with uncertainty, consequentialists often advocate choosing the option with the largest expected utility, as calculated using the arithmetic average. I provide some arguments to suggest that instead, one should consider choosing the option with the largest geometric average of utility. I explore the difference between these two approaches in a variety of ethical dilemmas and argue that geometric averaging has some appealing properties as a normative decision-making tool.
    Download  
     
    Export citation  
     
    Bookmark  
  12. On the development of geometric cognition: Beyond nature vs. nurture.Markus Pantsar - 2022 - Philosophical Psychology 35 (4):595-616.
    How is knowledge of geometry developed and acquired? This central question in the philosophy of mathematics has received very different answers. Spelke and colleagues argue for a “core cognitivist”, nativist, view according to which geometric cognition is in an important way shaped by genetically determined abilities for shape recognition and orientation. Against the nativist position, Ferreirós and García-Pérez have argued for a “culturalist” account that takes geometric cognition to be fundamentally a culturally developed phenomenon. In this paper, I (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  13. Plato on conventionalism.Rachel Barney - 1997 - Phronesis 42 (2):143 - 162.
    A new reading of Plato's account of conventionalism about names in the Cratylus. It argues that Hermogenes' position, according to which a name is whatever anybody 'sets down' as one, does not have the counterintuitive consequences usually claimed. At the same time, Plato's treatment of conventionalism needs to be related to his treatment of formally similar positions in ethics and politics. Plato is committed to standards of objective natural correctness in all such areas, despite the problematic consequences which, (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  14.  63
    Are geometrical trinity of gravity underdetermined?Yitong Zhou - manuscript
    General relativity (GR) describes gravity through the curvature of spacetime. However, there are two equivalents of GR that describe flat spacetimes with gravitational effects attributed to torison or non-metricity. These theories, together with GR, are known as the geometrical trinity of gravity and are said to present a case of underdetermination by Wolf et al. (2024). In this article, I argue against this stance by examining the empirical equivalence and possible interpretations of the trinity. I propose a unifying framework where (...)
    Download  
     
    Export citation  
     
    Bookmark  
  15. Support for Geometric Pooling.Jean Baccelli & Rush T. Stewart - 2023 - Review of Symbolic Logic 16 (1):298-337.
    Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be nontrivially Bayes-compatible. We show by contrast that geometric pooling can be nontrivially Bayes-compatible. Indeed, we show that, under certain assumptions, (...) and Bayes-compatible pooling are equivalent. Granting supra-Bayesianism its usual normative status, one upshot of our study is thus that, in a certain class of epistemic contexts, geometric pooling enjoys a normative advantage over linear pooling as a social learning mechanism. We discuss the philosophical ramifications of this advantage, which we show to be robust to variations in our statement of the Bayes-compatibility problem. (shrink)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  16. Geometrical premisses in Aristotle’s Incessu animalium and kind-crossing.Lucas Angioni - 2018 - Anais de Filosofia Clássica 24 (12):53-71.
    At some point in the Incessu Animalium, Aristotle appeals to some geometrical claims in order to explain why animal progression necessarily involves the bending (of the limbs), and this appeal to geometrical claims might be taking as violating the recommendation to avoid “kind-crossing” (as found in the Posterior Analytic). But a very unclear notion of kind-crossing has been assumed in most debates. I will argue that kind-crossing in the Posterior Analytics does not mean any employment of premises from a discipline (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  17. Geometric Pooling: A User's Guide.Richard Pettigrew & Jonathan Weisberg - forthcoming - British Journal for the Philosophy of Science.
    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.
    Download  
     
    Export citation  
     
    Bookmark  
  18. Ordinary Language, Conventionalism and a priori Knowledge.Henry Jackman - 2001 - Dialectica 55 (4):315-325.
    This paper examines popular‘conventionalist’explanations of why philosophers need not back up their claims about how‘we’use our words with empirical studies of actual usage. It argues that such explanations are incompatible with a number of currently popular and plausible assumptions about language's ‘social’character. Alternate explanations of the philosopher's purported entitlement to make a priori claims about‘our’usage are then suggested. While these alternate explanations would, unlike the conventionalist ones, be compatible with the more social picture of language, they are each shown to (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  19. Geometrical objects and figures in practical, pure, and applied geometry.Mario Bacelar Valente - 2020 - Disputatio. Philosophical Research Bulletin 9 (15):33-51.
    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.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  20. Realism, Antirealism, and Conventionalism about Race.Jonathan Michael Kaplan & Rasmus Grønfeldt Winther - 2014 - Philosophy of Science 81 (5):1039-1052.
    This paper distinguishes three concepts of "race": bio-genomic cluster/race, biological race, and social race. We map out realism, antirealism, and conventionalism about each of these, in three important historical episodes: Frank Livingstone and Theodosius Dobzhansky in 1962, A.W.F. Edwards' 2003 response to Lewontin (1972), and contemporary discourse. Semantics is especially crucial to the first episode, while normativity is central to the second. Upon inspection, each episode also reveals a variety of commitments to the metaphysics of race. We conclude by (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  21. What Is Conventionalism about Moral Rights and Duties?Katharina Nieswandt - 2019 - Australasian Journal of Philosophy 97 (1):15-28.
    A powerful objection against moral conventionalism says that it gives the wrong reasons for individual rights and duties. The reason why I must not break my promise to you, for example, should lie in the damage to you—rather than to the practice of promising or to all other participants in that practice. Common targets of this objection include the theories of Hobbes, Gauthier, Hooker, Binmore, and Rawls. I argue that the conventionalism of these theories is superficial; genuinely conventionalist (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  22. Geometric model of gravity, counterfactual solar mass, and the Pioneer anomalies.Andrew Holster - manuscript
    This study analyses the predictions of the General Theory of Relativity (GTR) against a slightly modified version of the standard central mass solution (Schwarzschild solution). It is applied to central gravity in the solar system, the Pioneer spacecraft anomalies (which GTR fails to predict correctly), and planetary orbit distances and times, etc (where GTR is thought consistent.) -/- The modified gravity equation was motivated by a theory originally called ‘TFP’ (Time Flow Physics, 2004). This is now replaced by the ‘ (...) Model’, 2014 [20], which retains the same theory of gravity. This analysis is offered partially as supporting detail for the claim in [20] that the theory is realistic in the solar system and explains the Pioneer anomalies. The overall conclusion is that the model can claim to explain the Pioneer anomalies, contingent on the analysis being independently verified and duplicated of course. -/- However the interest lies beyond testing this theory. To start with, it gives us a realistic scale on which gravity might vary from the accepted theory, remain consistent with most solar-scale astronomical observations. It is found here that the modified gravity equation would appear consistent with GTR for most phenomena, but it would retard the Pioneer spacecraft by about the observed amount (15 seconds or so at time). Hence it is a possible explanation of this anomaly, which as far as I know remains unexplained now for 20 years. -/- It also shows what many philosophers of science have emphasized: the pivotal role of counterfactual reasoning. By putting forward an exact alternative solution, and working through the full explanation, we discover a surprising ‘counterfactual paradox’: the modified theory slightly weakens GTR gravity – and yet the effect is to slow down the Pioneer trajectory, making it appear as if gravity is stronger than GTR. The inference that “there must be some tiny extra force…” (Musser, 1998 [1]) is wrong: there is a second option: “…or there may be a slightly weaker form of gravity than GTR.” . (shrink)
    Download  
     
    Export citation  
     
    Bookmark  
  23. Carnap’s conventionalism in geometry.Stefan Lukits - 2013 - Grazer Philosophische Studien 88 (1):123-138.
    Against Thomas Mormann's argument that differential topology does not support Carnap's conventionalism in geometry we show their compatibility. However, Mormann's emphasis on the entanglement that characterizes topology and its associated metrics is not misplaced. It poses questions about limits of empirical inquiry. For Carnap, to pose a question is to give a statement with the task of deciding its truth. Mormann's point forces us to introduce more clarity to what it means to specify the task that decides between competing (...)
    Download  
     
    Export citation  
     
    Bookmark  
  24. Geometrical Leitmotifs in Carnap’s Early Philosophy.Thomas Mormann - 2007 - In Richard Creath & Michael Friedman (eds.), Cambridge Companion to Rudolf Carnap. Cambridge University Press.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  25. A Survey of Geometric Algebra and Geometric Calculus.Alan Macdonald - 2017 - Advances in Applied Clifford Algebras 27:853-891.
    The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  26. Conventionalism and the Impoverishment of the Space of Reasons: Carnap, Quine and Sellars.Kenneth R. Westphal - 2015 - Journal for the History of Analytical Philosophy 3 (8).
    This article examines how Quine and Sellars develop informatively contrasting responses to a fundamental tension in Carnap’s semantics ca. 1950. Quine’s philosophy could well be styled ‘Essays in Radical Empiricism’; his assay of radical empiricism is invaluable for what it reveals about the inherent limits of empiricism. Careful examination shows that Quine’s criticism of Carnap’s semantics in ‘Two Dogmas of Empiricism’ fails, that at its core Quine’s semantics is for two key reasons incoherent and that his hallmark Thesis of Extensionalism (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  27. A Geometric Model of the Universe with Time Flow.Andrew Holster - manuscript
    This study presents a new type of foundational model unifying quantum theory, relativity theory and gravitational physics, with a novel cosmology. It proposes a six-dimensional geometric manifold as the foundational ontology for our universe. The theoretical unification is simple and powerful, and there are a number of novel empirical predictions and theoretical reductions that are strikingly accurate. It subsequently addresses a variety of current anomalies in physics. It shows how incomplete modern physics is by giving an example of a (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  28. Spinoza’s Ontology Geometrically Illustrated: A Reading of Ethics IIP8S.Valtteri Viljanen - 2018 - In Beth Lord (ed.), Spinoza’s Philosophy of Ratio. Edinburgh: Edinburgh University Press. pp. 5-18.
    This essay offers an in-depth reading of the geometrical illustration of Ethics IIP8S and shows how it can be used to explicate the whole architecture of Spinoza’s system by specifying the way in which all the key structural features of his basic ontology find their analogies in the example. The illustration can also throw light on Spinoza’s ontology of finite things and inform us about what is at stake when we form universal ideas. In general, my reading of IIP8S thus (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  29. A Geometrical Perspective of The Four Colour Theorem.Bhupinder Singh Anand - manuscript
    All acknowledged proofs of the Four Colour Theorem (4CT) are computerdependent. They appeal to the existence, and manual identification, of an ‘unavoidable’ set containing a sufficient number of explicitly defined configurations—each evidenced only by a computer as ‘reducible’—such that at least one of the configurations must occur in any chromatically distinguished, putatively minimal, planar map. For instance, Appel and Haken ‘identified’ 1,482 such configurations in their 1977, computer-dependent, proof of 4CT; whilst Neil Robertson et al ‘identified’ 633 configurations as sufficient (...)
    Download  
     
    Export citation  
     
    Bookmark  
  30. Against Depictive Conventionalism.Catharine Abell - 2005 - American Philosophical Quarterly 42 (3):185 - 197.
    In this paper, I discuss the influential view that depiction, like language, depends on arbitrary conventions. I argue that this view, however it is elaborated, is false. Any adequate account of depiction must be consistent with the distinctive features of depiction. One such feature is depictive generativity. I argue that, to be consistent with depictive generativity, conventionalism must hold that depiction depends on conventions for the depiction of basic properties of a picture’s object. I then argue that two considerations (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  31. On the relationship between geometric objects and figures in Euclidean geometry.Mario Bacelar Valente - 2021 - In Diagrammatic Representation and Inference. 12th International Conference, Diagrams 2021. pp. 71-78.
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  32. (1 other version)Carnap's metrical conventionalism versus differential topology.Thomas Mormann - 2004 - Proc. 2004 Biennial Meeting of the PSA, vol. I, Contributed Papers 72 (5):814 - 825.
    Geometry was a main source of inspiration for Carnap’s conventionalism. Taking Poincaré as his witness Carnap asserted in his dissertation Der Raum (Carnap 1922) that the metrical structure of space is conventional while the underlying topological structure describes "objective" facts. With only minor modifications he stuck to this account throughout his life. The aim of this paper is to disprove Carnap's contention by invoking some classical theorems of differential topology. By this means his metrical conventionalism turns out to (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  33. Attentional processing of geometric figures.Ronald A. Rensink - 1999 - Perception 28 (suppl.).
    Focused attention is needed to perceive change (Rensink et al., 1997; Psychological Science, 8: 368-373) . But how much attentional processing is given to an item? And does this depend on the nature of the task? To answer these questions, "flicker" displays were created, where an original and a modified image continually alternated, with brief blanks between them. Each image was an array of simple figures, half being horizontal and the other half vertical. In half the trials, one of the (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  34. Interaction of color and geometric cues in depth perception: When does red mean "near"?Christophe Guibal & Birgitta Dresp - 2004 - Psychological Research 69:30-40.
    Luminance and color are strong and self-sufficient cues to pictorial depth in visual scenes and images. The present study investigates the conditions Under which luminance or color either strengthens or overrides geometric depth cues. We investigated how luminance contrasts associated with color contrast interact with relative height in the visual field, partial occlusion, and interposition in determining the probability that a given figure is perceived as ‘‘nearer’’ than another. Latencies of ‘‘near’’ responses were analyzed to test for effects of (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  35. Plato on Geometrical Hypothesis in the Meno.Naoya Iwata - 2015 - Apeiron 48 (1):1-20.
    This paper examines the second geometrical problem in the Meno. Its purpose is to explore the implication of Cook Wilson’s interpretation, which has been most widely accepted by scholars, in relation to the nature of hypothesis. I argue that (a) the geometrical hypothesis in question is a tentative answer to a more basic problem, which could not be solved by available methods at that time, and that (b) despite the temporary nature of a hypothesis, there is a rational process for (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  36. What is the Value of Geometric Models to Understand Matter?Francoise Monnoyeur (ed.) - 2015 - palermo italy: review of Ontology.
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  37. Scotus geometres: The longevity of Duns Scotus’s geometric arguments against indivisibilism.Jean-Luc Solere - 2013 - In M. Dreyer, E. Mehl & M. Vollet (eds.), La posterité de Duns Scot / Die Rezeption des Duns Scotus / Scotism through the Centuries. pp. 139-154.
    Download  
     
    Export citation  
     
    Bookmark  
  38. The limits of conventional justification: inductive risk and industry bias beyond conventionalism.Miguel Ohnesorge - 2020 - Frontiers in Research Metric and Analytics 14.
    This article develops a constructive criticism of methodological conventionalism. Methodological conventionalism asserts that standards of inductive risk ought to be justified in virtue of their ability to facilitate coordination in a research community. On that view, industry bias occurs when conventional methodological standards are violated to foster industry preferences. The underlying account of scientific conventionality, however, is problematically incomplete. Conventions may be justified in virtue of their coordinative functions, but often qualify for posterior empirical criticism as research advances. (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  39. A hub-and-spoke model of geometric concepts.Mario Bacelar Valente - 2023 - Theoria : An International Journal for Theory, History and Fundations of Science 38 (1):25-44.
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  40. On geometric nature of numbers and the non-empirical scientific method.Elias Smith - manuscript
    We give a brief overview of the evolution of mathematics, starting from antiquity, through Renaissance, to the 19th century, and the culmination of the train of thought of history’s greatest thinkers that lead to the grand unification of geometry and algebra. The goal of this paper is not a complete formal description of any particular theoretical framework, but to show how extremisation of mathematical rigor in requiring everything be drivable directly from first principles without any arbitrary assumptions actually leads to (...)
    Download  
     
    Export citation  
     
    Bookmark  
  41. On Becoming a Rooster: Zhuangzian Conventionalism and the Survival of Death.Michael Tze-Sung Longenecker - 2022 - Dao: A Journal of Comparative Philosophy 21 (1):61-79.
    The Zhuangzi 莊子 depicts persons as surviving their deaths through the natural transformations of the world into very different forms—such as roosters, cart-wheels, rat livers, and so on. It is common to interpret these passages metaphorically. In this essay, however, I suggest employing a “Conventionalist” view of persons that says whether a person survives some event is not merely determined by the world, but is partly determined by our own attitudes. On this reading, Zhuangzi’s many teachings urging us to embrace (...)
    Download  
     
    Export citation  
     
    Bookmark  
  42. An Empirical Route to Logical 'Conventionalism'.Eugene Chua - 2017 - In Baltag Alexandru, Seligman Jeremy & Yamada Tomoyuki (eds.), Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science, vol 10455. Springer. pp. 631-636.
    The laws of classical logic are taken to be logical truths, which in turn are taken to hold objectively. However, we might question our faith in these truths: why are they true? One general approach, proposed by Putnam [8] and more recently Dickson [3] or Maddy [5], is to adopt empiricism about logic. On this view, logical truths are true because they are true of the world alone – this gives logical truths an air of objectivity. Putnam and Dickson both (...)
    Download  
     
    Export citation  
     
    Bookmark  
  43. The Geometrical Solution of The Problem of Snell’s Law of Reflection Without Using the Concepts of Time or Motion.Radhakrishnamurty Padyala - manuscript
    During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. We demonstrate in (...)
    Download  
     
    Export citation  
     
    Bookmark  
  44. Why the Perceived Flaw in Kempe's 1879 Graphical `Proof' of the Four Colour Theorem is Not Fatal When Expressed Geometrically.Bhupinder Singh Anand - manuscript
    All accepted proofs of the Four Colour Theorem (4CT) are computer-dependent; and appeal to the existence, and manual identification, of an ‘unavoidable’ set containing a sufficient number of explicitly defined configurations—each evidenced only by a computer as ‘reducible’—such that at least one of the configurations must occur in any chromatically distinguished, minimal, planar map. For instance, Appel and Haken ‘identified’ 1,482 such configurations in their 1977, computer-dependent, proof of 4CT; whilst Neil Robertson et al ‘identified’ 633 configurations as sufficient in (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  45. Kant’s analytic-geometric revolution.Scott Heftler - 2011 - Dissertation, University of Texas at Austin
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  46. A discussion of a geometric shape that became a symbol known as mandorla or vesica piscis, starting from a Pythagorean point of view.Amelia Carolina Sparavigna - manuscript
    Here we propose a discussion about the "mandorla" or "vesica piscis". It is a type of 2-dimensional lens, that is, a geometric shape formed by the intersection of two circles with the same radius, intersecting in such a way that the centre of each circle lies on the perimeter of the other. The aim of the discussion is that of understanding when such a geometric shape became a symbol and when this symbol received a specific name. We will (...)
    Download  
     
    Export citation  
     
    Bookmark  
  47. Review of Geometric Possibility. [REVIEW]Chris Smeenk - 2013 - Philosophia Mathematica 21 (3):416-421.
    Review of Geometric Possibility (2011), by Gordon Belot. Oxford and New York: Oxford University Press. x + 219 pp.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  48.  74
    Philosophical geometers and geometrical philosophers.Christopher Smeenk - 2016 - In Geoffrey Gorham (ed.), The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century. Minneapolis: University of Minnesota Press.
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  49. On the Cartesian Ontology of General Relativity: Or, Conventionalism in the History of the Substantival‐Relational Debate.Edward Slowik - 2005 - Philosophy of Science 72 (5):1312-1323.
    Utilizing Einstein’s comparison of General Relativity and Descartes’ physics, this investigation explores the alleged conventionalism that pervades the ontology of substantival and relationist conceptions of spacetime. Although previously discussed, namely by Rynasiewicz and Hoefer, it will be argued that the close similarities between General Relativity and Cartesian physics have not been adequately treated in the literature—and that the disclosure of these similarities bolsters the case for a conventionalist interpretation of spacetime ontology.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  50. All Together Now: Conventionalism and Everyday Moral Life.Erin Taylor - manuscript
    Download  
     
    Export citation  
     
    Bookmark  
1 — 50 / 446