Point-Free Geometry and Verisimilitude of Theories

@article{Gerla2007PointFreeGA,
  title={Point-Free Geometry and Verisimilitude of Theories},
  author={Giangiacomo Gerla},
  journal={Journal of Philosophical Logic},
  year={2007},
  volume={36},
  pages={707-733}
}
  • Giangiacomo Gerla
  • Published 2007
  • Mathematics, Computer Science
  • Journal of Philosophical Logic
A metric approach to Popper’s verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth… Expand
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References

SHOWING 1-10 OF 22 REFERENCES
Distances, diameters and verisimilitude of theories
TLDR
An approach to the verisimilitude of a theory T should be defined as a decreasing function of 6(T, V and ]T], which avoids the well known Miller-Tichy's results about the incomparability of false theories. Expand
Pointless Metric Spaces
TLDR
This paper proposes and examines a system of axioms for the pointless space theory in which “regions”, “inclusion”. Expand
Chapter 18 – Pointless Geometries
Publisher Summary The focus of this chapter is on pointless geometries. The concept of point is assumed as the main primitive term for an axiomatic foundation of geometry. In pointless geometry,Expand
On Distance from the Truth as a True Distance
False scientific theories, we imagine, can differ in their closeness to the truth. Popper’s qualitative theory of verisimilitude ([1963], pp. 228–237) sought to explain this difference as a variationExpand
Handbook of incidence geometry : buildings and foundations
An introduction to incidence geometry, F. Buekenhout projective and affine geometry over division rings, F. Buekenhout and P. Cameron foundations of incidence geometry, F. Buekenhout projectiveExpand
POPPER'S DEFINITIONS OF ‘VERISIMILITUDE’1
  • John H. Harris
  • Philosophy
  • The British Journal for the Philosophy of Science
  • 1974
Things, of course, get vastly more complicated when we turn to the more typical kind of theories, i.e., theories formulated in a first-order language. But the idea underlying the above definition ofExpand
POPPER'S QUALITATIVE THEORY OF VERISIMILITUDE
  • David W. Miller
  • Philosophy
  • The British Journal for the Philosophy of Science
  • 1974
MILLER, D. [1974]: 'Popper's Qualitative Theory of Verisimilitude' British fournalfor the Philosophy of Science, 25, pp. 166-177. POPPER, K. R. [1963]: Conjectures and Refutations. POPPER, K. R.Expand
An enquiry concerning the principles of natural knowledge
Part I. The Traditions of Science: 1. Meaning 2. The foundations of dynamical physics 3. Scientific relativity 4. Congruence Part II. The Data of Science: 5. The natural elements 6. Events 7. ObjectsExpand
Approximate Truth and Truthlikeness
Our standard logic is two-valued: every meaningful statement is regarded as being either true or false. Thus it may seem pointless or misleading to speak of degrees of truth or of partial truth.Expand
ON POPPER'S DEFINITIONS OF VERISIMILITUDE1
  • P. Tichý
  • Mathematics
  • The British Journal for the Philosophy of Science
  • 1974
Introduction. 1 Preliminaries. 2 Popper's Logical Definition of Verisimilitude. 3 Popper's Probabilistic Definition of Verisimilitude. 4 Conclusion.
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2
3
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