Off-campus access
Using PhilPapers from home?
Click here to configure this browser for off-campus access.
- Vadim Batitsky (1998). From Inexactness to Certainty: The Change in Hume's Conception of Geometry. Journal for General Philosophy of Science 29 (1):1-20.Although Hume's analysis of geometry continues to serve as a reference point for many contemporary discussions in the philosophy of science, the fact that the first Enquiry presents a radical revision of Hume's conception of geometry in the Treatise has never been explained. The present essay closely examines Hume's early and late discussions of geometry and proposes a reconstruction of the reasons behind the change in his views on the subject. Hume's early conception of geometry as an inexact non-demonstrative science is argued to be a consequence of his attempt to discredit geometrical proofs of infinite divisibility of extension by anchoring the meaning of geometrical concepts in inherently inexact qualitative measurement procedures. This measurement-based attack on the exactness and certainty of geometry is analyzed and shown to be both self-refuting and inconsistent with the general epistemological framework of the Treatise. The revised conception of geometry as a demonstrative science in the first Enquiry is then interpreted as Hume's response to the failure of his earlier attempt to discredit geometrical proofs of infinite divisibility of extension.Reading list | Discuss | Edit | Categorize |My bibliography
| Export citation | Other links: springerlink.com dx.doi.org jstor.org | Scholar | At my library 
Similar books and articles
Throughout history, almost all mathematicians, physicists and philosophers have been of the opinion that space and time are infinitely divisible. That is, it is usually believed that space and time do not consist of atoms, but that any piece of space and time of non-zero size, however small, can itself be divided into still smaller parts. This assumption is included in geometry, as in Euclid, and also in the Euclidean and non- Euclidean geometries used in modern physics. Of the few who have denied that space and time are infinitely divisible, the most notable are the ancient atomists, and Berkeley and Hume. All of these assert not only that space and time might be atomic, but that they must be. Infinite divisibility is, they say, impossible on purely conceptual grounds.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | At my library | More options ...
| | Scholar | At my library | More options ... Abstract: In this paper I consider recent attempts to establish that the geometry of visual experience is a spherical geometry. These attempts, offered by Gideon Yaffe, James van Cleve and Gordon Belot, follow Thomas Reid in arguing for an equivalency of a geometry of ‘visibles’ and spherical geometry. I argue that although the proposed equivalency is successfully established by the strongest form of the argument, this does not warrant any conclusion about the geometry of visual experience. I argue, firstly, that the resistance of this contemporary argument to empirical considerations counts against its plausibility. Moreover, I argue that the contemporary approach provides no compelling reason for supposing that the geometry offered as the geometry of ‘visibles’ is the correct geometrical description of visual experience.
No categories
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: dx.doi.org blackwell-synergy.com | Scholar | At my library | More options ...
| | Other links: dx.doi.org blackwell-synergy.com | Scholar | At my library | More options ... This book provides the first comprehensive account of Hume’s conception of objects in Book I of the Treatise. What, according to Hume, are objects? Ideas? Impressions? Mind-independent objects? All three? None of the above? Through a close textual analysis, I show that Hume thought that objects are imagined ideas. However, I argue that he struggled with two accounts of how and when we imagine such ideas. On the one hand, Hume believed that we always and universally imagine that objects are the causes of our perceptions. On the other hand, he thought that we only imagine such causes when we reach a “philosophical” level of thought. This tension manifests itself in Hume’s account of personal identity; a tension that, I argue, Hume acknowledges in the Appendix to the Treatise. As a result of presenting a detailed account of Hume’s conception of objects, we are forced to accommodate new interpretations of, at least, Hume’s notions of belief, personal identity, justification and causality.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | At my library | More options ...
| | Scholar | At my library | More options ... The paper attempts to summarize the debate on Kant’s philosophy of geometry and to offer a restricted area of mathematical practice for which Kant’s philosophy would be a reasonable account. Geometrical theories can be characterized using Wittgenstein’s notion of pictorial form . Kant’s philosophy of geometry can be interpreted as a reconstruction of geometry based on one of these forms — the projective form . If this is correct, Kant’s philosophy is a reasonable reconstruction of such theories as projective geometry; and not only as they were practiced in Kant’s time, but also as architects use them today.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: philmat.oxfordjournals.org dx.doi.org | Scholar | At my library | More options ...
| | Other links: philmat.oxfordjournals.org dx.doi.org | Scholar | At my library | More options ... An explication is offered of Reid’s claim (discussed recently by Yaffe and others) that the geometry of the visual field is spherical geometry. It is shown that the sphere is the only surface whose geometry coincides, in a certain strong sense, with the geometry of visibles.
No categories
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: sitemaker.umich.edu blackwell-synergy.com jstor.org dx.doi.org | Scholar | At my library | More options ...
| | Other links: sitemaker.umich.edu blackwell-synergy.com jstor.org dx.doi.org | Scholar | At my library | More options ... Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts (and the views of his mentor, Isaac Barrow) shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity (which is what measurement makes known) is ultimately related to spatial extension. I use this conception of Newton’s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia (beginning in Sect. 2 of Book I). The placementof Kepler’s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry.
No categories
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: dx.doi.org | Scholar | At my library | More options ...
| | Other links: dx.doi.org | Scholar | At my library | More options ... Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | At my library | More options ...
| | Scholar | At my library | More options ... Hume's discussion of the idea of space in his Treatise on Human Nature is fundamental to an understanding of his treatment of such central issues as the existence of external objects, the unity of the self, the relation between certainty and belief, and abstract ideas. Marina Frasca-Spada's rich and original study examines this difficult part of Hume's philosophical writings and connects it to eighteenth-century works in natural philosophy, mathematics and literature. Focusing on Hume's discussions of the infinite divisibility of extension, the origin of the idea of space, geometry, and the notion of a vacuum, she shows that the central questions of Hume's 'science of human nature' - what does the 'science of human nature' reveal about the mind and its operations? what is experience? - underlie all of these discussions. Her analysis points the way to a reassessment of the central current interpretative problems in Hume studies.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | At my library | More options ...
| | Scholar | At my library | More options ... It has been argued that there is a genuine conflict between the views of geometry defended by Hume in the Treatise and in the Enquiry: while the former work attributes to geometry a different status from that of arithmetic and algebra, the latter attempts to restore its status as an exact and certain science. A closer reading of Hume shows that, in fact, there is no conflict between the two works with respect to geometry. The key to understanding Hume's view of geometry is the distinction he draws between two standards of equality in extension.
No categories
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: dx.doi.org doi.wiley.com | Scholar | At my library | More options ...
| | Other links: dx.doi.org doi.wiley.com | Scholar | At my library | More options ... In the Treatise, David Hume denies the thesis that extension is infinitely divisible, even though it can be derived as a theorem of Euclidean geometry. This clearly shows that he rejects some of the theorems of Euclidean geometry. What is less clear is the extent to which he thinks geometry needs to be revised. It has been argued that Hume's rejection of infinite divisibility entails that most of the familiar theorems of Euclidean geometry, including the Pythagorean theorem and the bisection theorem, are false, a view that is normally associated with Berkeley's earlier writings.I argue that Hume's denial of infinite divisibility is not incompatible with the Pythagorean theorem and other central theorems of ..
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: muse.jhu.edu dx.doi.org | Scholar | At my library | More options ...
| | Other links: muse.jhu.edu dx.doi.org | Scholar | At my library | More options ... Discussion of Vadim Batitsky, From inexactness to certainty: The change in Hume's conception of geometry
 Back
All discussions
Start a new thread
|
There are no threads in this forum |
Nothing in this forum yet.
