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Fundamental weight systems are quantum states
Weight systems on chord diagrams play a central role in knot theory and Chern–Simons theory; and more recently in stringy quantum gravity. We highlight that the noncommutative algebra of horizontal chord diagr...
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Article
Correction to: Expressing ‘the structure of’ in homotopy type theory
The original article has been corrected. The article is published with Open Access but was missing Open Access information. This has been added.
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Article
Open AccessExpressing ‘the structure of’ in homotopy type theory
As a new foundational language for mathematics with its very different idea as to the status of logic, we should expect homotopy type theory to shed new light on some of the problems of philosophy which have b...
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Article
Varieties of Justification in Machine Learning
Forms of justification for inductive machine learning techniques are discussed and classified into four types. This is done with a view to introduce some of these techniques and their justificatory guarantees ...
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Open AccessFalsificationism and Statistical Learning Theory: Comparing the Popper and Vapnik-Chervonenkis Dimensions
We compare Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory. Popper’s notion of the dimension of a theory is contr...
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Article
Complementarity and Convergence in the Philosophies of Mathematics and Physics
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Chapter
Argumentation and the Mathematical Process
We have reached a position today from which to evaluate judiciously Lakatos’ contribution to the philosophy of mathematics. We should applaud unreservedly his decision to take the development of mathematics as...
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Book
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Chapter
Introduction: Bayesianism into the 21st Century
Bayesian theory now incorporates a vast body of mathematical, statistical and computational techniques that are widely applied in a panoply of disciplines, from artificial intelligence to zoology. Yet Bayesian...
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Chapter
Bayesianism in Mathematics
I shall begin by giving an overview of the research programme named in the title of this paper. The term ‘research programme’ suggests perhaps a concerted effort by a group of researchers, so I should admit st...
