1,310 research outputs found
The Paraconsistent Approach to Quantum Superpositions Reloaded: Formalizing Contradictory Powers in the Potential Realm
In [7] the authors of this paper argued in favor of the possibility to
consider a Paraconsistent Approach to Quantum Superpositions (PAQS). We claimed
that, even though most interpretations of quantum mechanics (QM) attempt to
escape contradictions, there are many hints -coming from present technical and
experimental developments in QM- that indicate it could be worth while to
engage in a research of this kind. Recently, Arenhart and Krause have raised
several arguments against the PAQS [1, 2, 3]. In [11, 12] it was argued that
their reasoning presupposes a metaphysical stance according to which the
physical representation of reality must be exclusively considered in terms of
the equation: Actuality = Reality. However, from a different metaphysical
standpoint their problems disappear. It was also argued that, if we accept the
idea that quantum superpositions exist in a (contradictory) potential realm, it
makes perfect sense to develop QM in terms of a paraconsistent approach and
claim that quantum superpositions are contradictory, contextual existents.
Following these ideas, and taking as a standpoint an interpretation in terms of
the physical notions of power and potentia put forward in [10, 12, 15], we
present a paraconsistent formalization of quantum superpositions that attempts
to capture the main features of QM.Comment: 26 pages, no figures. arXiv admin note: substantial text overlap with
arXiv:1502.05081, arXiv:1404.5186, arXiv:1506.0737
The Epistemology of Modality
This article surveys recent developments in the epistemology of modality
Epistemicism and modality
What kind of semantics should someone who accepts the epistemicist theory of vagueness defended in Timothy Williamson’s Vagueness (1994) give a definiteness operator? To impose some interesting constraints on acceptable answers to this question, I will assume that the object language also contains a metaphysical necessity operator and a metaphysical actuality operator. I will suggest that the answer is to be found by working within a three-dimensional model theory. I will provide sketches of two ways of extracting an epistemicist semantics from that model theory, one of which I will find to be more plausible than the other
Platonism in Lotze and Frege Between Psyschologism and Hypostasis
In the section “Validity and Existence in Logik, Book III,” I explain
Lotze’s famous distinction between existence and validity in Book III of
Logik. In the following section, “Lotze’s Platonism,” I put this famous
distinction in the context of Lotze’s attempt to distinguish his own position
from hypostatic Platonism and consider one way of drawing the
distinction: the hypostatic Platonist accepts that there are propositions,
whereas Lotze rejects this. In the section “Two Perspectives on Frege’s
Platonism,” I argue that this is an unsatisfactory way of reading Lotze’s
Platonism and that the Ricketts-Reck reading of Frege is in fact the correct
way of thinking about Lotze’s Platonism
Two-Dimensional Tableaux
We present two-dimensional tableau systems for the actuality, fixedly, and up-arrow operators. All systems are proved sound and complete with respect to a two-dimensional semantics. In addition, a decision procedure for the actuality logics is discussed
Fredkin Gates for Finite-valued Reversible and Conservative Logics
The basic principles and results of Conservative Logic introduced by Fredkin
and Toffoli on the basis of a seminal paper of Landauer are extended to
d-valued logics, with a special attention to three-valued logics. Different
approaches to d-valued logics are examined in order to determine some possible
universal sets of logic primitives. In particular, we consider the typical
connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As
a result, some possible three-valued and d-valued universal gates are described
which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram
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