Physiological Optics and Physical Geometry

2001 ◽  
Vol 14 (3) ◽  
pp. 419-456 ◽  
Author(s):  
David Jalal Hyder
Keyword(s):  
A Priori ◽  
Color Space ◽  
Empirical Knowledge ◽  
Metrical Structure ◽  
James Clerk Maxwell ◽  
Essential Properties ◽  
Physical Apparatus ◽  
Physical Geometry ◽  
Hermann Graßmann ◽  
The Continuum

ArgumentHermann von Helmholtz’s distinction between “pure intuitive” and “physical” geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant’s claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz’s understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz’s development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz’s arguments concerning geometry.

scholarly journals Phenomenology as Radical Reflection

2021 ◽  
pp. 234-257
Author(s):  
Dave Ward
Keyword(s):  
Surface Properties ◽  
Perceptual Experience ◽  
A Priori ◽  
Phenomenological Approach ◽  
Husserlian Phenomenology ◽  
Empirical Knowledge ◽  
Philosophy Of Perception ◽  
Essential Properties ◽  
Intuitive Grasp

What does it mean to adopt a phenomenological approach when doing philosophy of perception? What form should such an approach take? This chapter addresses these questions by first distinguishing three different kinds of phenomenological approach: ‘Humean’ phenomenology, which attempts to discern the structure of perceptual experience via reflection on its surface properties; ‘Kantian’ phenomenology, which aims to provide a priori arguments about the structure perceptual experience must have if it is to possess manifest properties; and ‘Husserlian’ phenomenology, which aims to achieve an intuitive grasp of the essential properties of perceptual experience via imaginative variation. It then argues that the shortcomings of each of these approaches motivate a ‘Merleau-Pontian’ conception of phenomenology as ‘radical reflection’—a mode of reflection on perceptual experience that simultaneously attempts to understand the origins and authority of reflection itself. The methodology that results is thoroughly interdisciplinary, aiming to reconcile philosophical conclusions about the necessary structures of perceptual experience with our best empirical knowledge of the contingencies that shape both our experiences and our reflective capacities.

Advanced Math

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Riemann Hypothesis ◽  
Physical Theory ◽  
A Priori ◽  
Advanced Mathematics ◽  
Ancient Greek ◽  
Mathematical Objects ◽  
Inductive Methods ◽  
Modern Mathematics ◽  
The Continuum ◽  
Greek Geometry

This chapter proposes the idea that advanced mathematics is based on hypotheses—that far from being a priori, it is based on hypothetical assumptions. The concept of quasi-empiricism is often linked with the view that inductive methods are at play when the hypotheses are established. The presence of hypotheses at the very heart of mathematics establishes an important similitude with physical theory and undermines the simple distinction between “formal” and “empirical” sciences. The chapter first elaborates on a hypothetical conception of mathematics before discussing the ideas (and ideals) of certainty and objectivity in mathematics. It then considers the modern problems of the continuum that exist in ancient Greek geometry, along with the so-called methodological platonism of modern mathematics and its focus on mathematical objects. Finally, it describes the Axiom of Completeness and the Riemann Hypothesis.

A posteriori

2018 ◽  
Author(s):  
Paul K. Moser
Keyword(s):  
A Priori ◽  
Sensory Experience ◽  
A Priori Knowledge ◽  
Empirical Knowledge ◽  
A Posteriori ◽  
Critique Of Pure Reason ◽  
The Common ◽  
And Mathematics ◽  
Common Understanding ◽  
Priori Knowledge

A prominent term in theory of knowledge since the seventeenth century, ‘a posteriori’ signifies a kind of knowledge or justification that depends on evidence, or warrant, from sensory experience. A posteriori truth is truth that cannot be known or justified independently of evidence from sensory experience, and a posteriori concepts are concepts that cannot be understood independently of reference to sensory experience. A posteriori knowledge contrasts with a priori knowledge, knowledge that does not require evidence from sensory experience. A posteriori knowledge is empirical, experience-based knowledge, whereas a priori knowledge is non-empirical knowledge. Standard examples of a posteriori truths are the truths of ordinary perceptual experience and the natural sciences; standard examples of a priori truths are the truths of logic and mathematics. The common understanding of the distinction between a posteriori and a priori knowledge as the distinction between empirical and non-empirical knowledge comes from Kant’s Critique of Pure Reason (1781/1787).

Induction Justified (But Just Barely)

Philosophy ◽  
1983 ◽  
Vol 58 (226) ◽  
pp. 481-488
Author(s):  
Ralph W. Clark
Keyword(s):  
A Priori ◽  
Empirical Knowledge ◽  
The Past ◽  
Empirical World ◽  
Future Events

Hume's sceptical arguments regarding induction have not yet been successfully answered. However, I shall not in this paper discuss the important attempts to answer Hume since that would be too lengthy a task. On the supposition that Hume's sceptical arguments have not been met, the empirical world is a place where, as the popular metaphor goes, all the glue has been removed. For the Humean sceptic, the only empirical knowledge that we can have is given to us in immediate perception. We have no reason to believe that the patterns of future events will in any way resemble patterns of events in the present or past. We have no reason to believe even that present events not observed resemble present events that are observed, or that knowledge of past and present can be any guide in making new discoveries about what took place in the past. What we have is an ideal setting for the calculation of a priori probabilities. We have a field of distinct events having no logical or evidential ties to one another. The attempt to justify induction that I wish to present is an appeal to a priori probability.

Sublime Waste: Kant on the Destiny of the ‘Races’

1999 ◽  
Vol 25 ◽  
pp. 99-125 ◽  
Author(s):  
Mark Larrimore
Keyword(s):  
Immanuel Kant ◽  
A Priori ◽  
The Other ◽  
Moral Concern ◽  
Empirical Knowledge ◽  
Human Diversity ◽  
Specific Content ◽  
Other Hand ◽  
Human Difference

Wir dürfen aber den Untergang eines Weltgebäudes nicht als einen wahren Verlust der Natur bedauren. Sie beweiset ihren Reichthum in einer Art von Verschwendung … Der Mensch, der das Meisterstück der Schöpfung zu sein scheint, ist selbst von diesem Gesetze nicht ausgenommen.Immanuel Kant was an early and influential theorist on race. What place a theory of race could have within his system is, however, far from clear. Empirical knowledge about human diversity seems not to be the kind of thing that may find its way into morally acceptable maxims. Kant's understanding of the a priori nature of the moral seems to prevent any account or theory of human difference from leading to prejudice or discrimination. On the other hand, Kant defends race it-self as an a priori concept, and the specific content of his anthropology seems to justify the exclusion of non-whites from moral concern in a new and dangerous way.

Kripke, Saul Aaron (1940–)

2018 ◽  
Author(s):  
Michael Jubien
Keyword(s):  
Philosophy Of Mind ◽  
Philosophy Of Language ◽  
Possible Worlds ◽  
A Priori ◽  
Philosophical Significance ◽  
Essential Properties ◽  
Proper Name ◽  
Late Twentieth ◽  
Concept Of Truth ◽  
And Mathematics

Saul Kripke is one of the most important and influential philosophers of the late twentieth century. He is also one of the leading mathematical logicians, having done seminal work in areas including modal logic, intuitionistic logic and set theory. Although much of his work in logic has philosophical significance, it will not be discussed here. Kripke’s main contributions fall in the areas of metaphysics, philosophy of language, epistemology, philosophy of mind and philosophy of logic and mathematics. He is particularly well known for his views on and discussions of the following topics: the concepts of necessity, identity and ‘possible worlds’; ‘essentialism’ – the idea that things have significant essential properties; the question of what determines the referent of an ordinary proper name and the related question of whether such names have meanings; the relations among the concepts of necessity, analyticity, and the a priori; the concept of belief and its problems; the concept of truth and its problems; and scepticism, the idea of following a rule, and Ludwig Wittgenstein’s ‘private language argument’. This entry will be confined to the topics of identity, proper names, necessity and essentialism.

IS FOUNDATIONAL A PRIORI JUSTIFICATION INDISPENSABLE?

Episteme ◽  
2013 ◽  
Vol 10 (3) ◽  
pp. 317-331
Author(s):  
Ted Poston
Keyword(s):  
A Priori ◽  
Critical Discussion ◽  
Coherence Theory ◽  
Empirical Knowledge ◽  
A Priori Justification ◽  
Indispensability Arguments ◽  
Traditional Account

AbstractLaurence BonJour's (1985) coherence theory of empirical knowledge relies heavily on a traditional foundationalist theory of a priori knowledge. He argues that a foundationalist, rationalist theory of a priori justification is indispensable for a coherence theory. BonJour (1998) continues this theme, arguing that a traditional account of a priori justification is indispensable for the justification of putative a priori truths, the justification of any non-observational belief and the justification of reasoning itself. While BonJour's indispensability arguments have received some critical discussion (Gendler 2001; Harman 2001; Beebe 2008), no one has investigated the indispensability arguments from a coherentist perspective. This perspective offers a fruitful take on BonJour's arguments, because he does not appreciate the depth of the coherentist alternative to the traditional empiricist-rationalist debate. This is surprising on account of BonJour's previous defense of coherentism. Two significant conclusions emerge: first, BonJour's indispensability arguments beg central questions about an explanationist form of coherentism; second, BonJour's original defense of coherentism took on board certain assumptions that inevitably led to the demise of his form of coherentism. The positive conclusion of this article is that explanatory coherentism is more coherent than BonJour's indispensability arguments assume, and more coherent than BonJour's earlier coherentist epistemology.

An Efficient Static Analysis of Continuum Robots

2014 ◽  
Vol 6 (3) ◽  
Author(s):  
Shahir Hasanzadeh ◽  
Farrokh Janabi-Sharifi
Keyword(s):  
Real Time ◽  
Recursive Algorithm ◽  
A Priori ◽  
Real Time Control ◽  
Equilibrium Equations ◽  
Backbone Curve ◽  
Time Control ◽  
Continuum Robot ◽  
Main Component ◽  
The Continuum

An efficient yet accurate model of the continuum robot is the main component for its real-time control, simulation as well as localization. Previous models of the continuum robot, based on rod theory, suffer from high computational burden. The models also require a priori knowledge of the robot environment. This paper presents an efficient static model for the planar continuum robot that experiences external forces at the tip as a result of contact with its surroundings (measured by the built-in force sensors), thus no a priori information about the environment is required. The typical example of such robots is steerable catheters used in medical operations. The proposed approach involves discretizing the robot backbone curve to elastic arc elements. After deriving the equilibrium equations for the infinitesimal elements, a recursive algorithm with the time complexity of O(n) is proposed for realizing the shape of the robot as a result of the external force. Accuracy of the proposed method is evaluated both theoretically and experimentally for a case study, i.e., an intracardiac ablation catheter. Results validate the accuracy and time-efficiency of the proposed approach for real-time applications.

Logic: An Empirical Study of A Priori Truths

1998 ◽  
pp. 92-97
Author(s):  
John Kearns
Keyword(s):  
Empirical Study ◽  
Conceptual Framework ◽  
A Priori ◽  
A Priori Knowledge ◽  
Empirical Knowledge ◽  
Trial And Error ◽  
World Knowledge ◽  
The World ◽  
Correct Reasoning ◽  
Priori Knowledge

I distinguish a priori knowledge from a priori truths or statements. A priori knowledge either is evident or is derived from evident premisses by means of correct reasoning. An a priori statement is one that reflects features of the conceptual framework within which it is placed. The statement either describes semantic relations between concepts of the framework or it characterizes the application of the framework to experience and the world. An a priori statement is not necessarily part of anyone’s a priori knowledge. I also distinguish empirical knowledge from empirical statements. Both statements and theories are empirical if they are designed to characterize features of experience and the world. Knowledge is empirical if it fits experience; thus, one must check to see whether it fits. We do not obtain knowledge of logical systems by rational insight of evident truths and careful deductions from evident truths. Adequate logical systems are developed by trial and error. Logical knowledge is empirical knowledge that is not generally a priori. It is empirical knowledge of (some) a priori truths and principles of our conceptual systems. Logical systems are empirical theories of these truths and principles.

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