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<TitleType>01</TitleType>
<TitleText>Phylopraxis</TitleText>
<TitleType>01</TitleType>
<TitleText textcase="01">Mathematics in Philosophy</TitleText>
01
GCOI
28001100673510
1
A01
Katie Anderson
Anderson, Katie
Katie
Anderson
2
A01
François Beets
Beets, François
François
Beets
3
A01
Vesselin Petrov
Petrov, Vesselin
Vesselin
Petrov
01
eng
156
00
156
03
PHI000000
29
2012
3080
SCIENCES HUMAINES ET SOCIALES, LETTRES
01
06
03
<p>The authors we have gathered to do so —philosophers, mathematicians and logicians from across Europe— share a significant expertise in the history and the methodology of science and mathematics. Their complementary perspectives bring to light insights and tools that pave the way for new philosophical conceptualisations of the mathematical knowledge.<br />
Pr. Vesselin Petrov holds an M.A. in mathematics (1977), a Ph.D. in philosophy (1989) and a D.Sc. in philosophy (2011). He is Professor and Head of the Department of "Models, Methodologies, and Heuristics" of the Institute for the Study of Societies and Knowledge at the Bulgarian Academy of Sciences. His fields of research interest include process philosophy, metaphysics, ontology, applied ontology, philosophy of science and philosophy of mathematics. He is author of four books in Bulgarian and of more than 120 papers in Bulgarian, English, Russian and Chinese. He is also editor of twenty books in Bulgarian and English, among them Ontological Landscapes: Recent Thought on Conceptual Interfaces Between Science and Philosophy (Frankfurt: Ontos Verlag, 2011) and Dynamic Being:<br />
Essays in Process-Relational Ontology (Cambridge Scholars Publishing, 2015). Professor Petrov is Executive Director (2015 – 2017) of the International Process Network. Pr. François Beets holds an M.A. (1981) and a Ph.D. in philosophy (1991) from the Université de Liège. He teaches philosophy of logic, philosophy of language, philosophy of the Middle Ages and analytical philosophy. He has published on these subjects as well as the late Whitehead.<br />
Drs. Katie Anderson holds a B.A. in philosophy (2010) from Cambridge University andan M.Sc. in psychology (2013) from the University of East London. She is currently a Ph.D. candidate in psychology at London Southbank University and her thesis draws significantly on Whitehead's process philosophy.</p>
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The systematic mapping of the interplay of ontology and epistemology in the context of present day philosophy of mathematics constitutes an important heuristic goal. In order to achieve it, we must analyze and reinterpret the position of mathematics in philosophy.
04
<p>Introduction<br />
Vesselin Petrov<br />
Notes<br />
A favourable mathematical point of view<br />
on Aristotelian and Scholastic syllogisms<br />
Pascal Gribomont<br />
1. Introduction<br />
2. A concise introduction to Asyl with modern notation<br />
3. Asyl as a modern theory<br />
4. Conversion rules revisited<br />
5. Venn diagrams<br />
6. Conclusions<br />
Notes<br />
Are there synthetic a priori propositions? The paradigmatic case<br />
of mathematics, from Kant to Frege and Peirce<br />
Bruno Leclercq<br />
Abstract<br />
1. Kant's doctrine of pure intuition and schematism<br />
2. Objections to Kant's doctrine and the rise of the logicist program<br />
3. Ampliative reasoning<br />
4. Abstractive observation: seeing Ideas through Gestalten<br />
5. Taking a step aside in order to evolve what was involved<br />
Notes<br />
Caught in the ACT: Abstract Choice Theory<br />
and the Rationality of Cyclical Preferences<br />
Rosen Lutskanov<br />
Abstract<br />
Notes<br />
The Question of Intuition in Modern Epistemology of Mathematics<br />
and Logic<br />
Stany Mazurkiewicz<br />
Abstract<br />
1. Introduction<br />
2. History of mathematics<br />
3. Kant<br />
6 Contents<br />
4. Hegel<br />
5. Bolzano<br />
6. Conclusion<br />
Notes<br />
The Sense Perceived Continuum of Henri Poincaré<br />
Vesselin Petrov<br />
Abstract<br />
1. Introduction<br />
2. Poincaré’s philosophical views<br />
3. Poincaré and the continuum: Two types of continuum<br />
4. Conclusion<br />
Notes<br />
Sensible and Intellective Geometry.<br />
A Point-Free Geometry from the 10th Century<br />
François Beets<br />
Notes<br />
Mereotopological distributive lattices<br />
Georges Hansoul<br />
1. Introduction<br />
2. Multioperators on lattices<br />
3. Mereotopological lattices<br />
4. Final remarks<br />
Dominants and Limiters in Philosophy of Mathematics<br />
Engelsina Tasseva<br />
Abstract<br />
1. Disciplinary state of philosophy of mathematics<br />
2. Basic problems of philosophy of mathematics as a discipline<br />
3. Recent situation<br />
4. Structural stratification in the field of schools,<br />
trends and conceptions of mathematical philosophy<br />
5. Epistemic roots and their conceptual and instrumental derivatives:<br />
epistemological dominants and limiters<br />
6. Conclusion: Three key points<br />
Notes<br />
Bibliography</p>
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CHROMATIKA
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