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pro vyhledávání: '"Ellerman, David P."'
Autor:
Ellerman, David
This is an essay in what might be called ``mathematical metaphysics.'' There is a fundamental duality that run through mathematics and the natural sciences. The duality starts as the logical level; it is represented by the Boolean logic of subsets an
Externí odkaz:
http://arxiv.org/abs/2409.18134
Autor:
Ellerman, David
The Born Rule plays a critical role in quantum mechanics (QM) since it supplies the link between the mathematical formalism and experimental results in terms of probabilities. The Born Rule does not occur in ordinary probability theory. Where then do
Externí odkaz:
http://arxiv.org/abs/2310.04188
Autor:
Ellerman, David
This paper presents a new `partitional' approach to understanding or interpreting standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, convers
Externí odkaz:
http://arxiv.org/abs/2304.09644
Autor:
Ellerman, David
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is, the math of
Externí odkaz:
http://arxiv.org/abs/2208.00384
Autor:
Ellerman, David
We live in the information age. Claude Shannon, as the father of the information age, gave us a theory of communications that quantified an "amount of information," but, as he pointed out, "no concept of information itself was defined." Logical entro
Externí odkaz:
http://arxiv.org/abs/2112.01966
Autor:
Ellerman, David
The purpose of this paper is to abstractly describe the notion of a generative mechanism that implements a code and to provide a number of examples including the DNA-RNA machinery that implements the genetic code, Chomsky's Principles & Parameters mo
Externí odkaz:
http://arxiv.org/abs/2105.03907
Autor:
Ellerman, David
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinction
Externí odkaz:
http://arxiv.org/abs/2104.08583
Autor:
Ellerman, David
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The
Externí odkaz:
http://arxiv.org/abs/2007.05733
Autor:
Ellerman, David
The Boolean logic of subsets, usually presented as `propositional logic,' is considered as being "classical" while intuitionistic logic and the many sublogics and off-shoots are "non-classical." But there is another mathematical logic, the logic of p
Externí odkaz:
http://arxiv.org/abs/2007.05192