David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
A new non-Aristotelian finitary logic (NAFL) is proposed in which it is postulated that the truth or falseness of an undecidable proposition in a theory T is meaningful only when asserted axiomatically; there is no truth other than axiomatic truth. It is shown that under this hypothesis, the law of the excluded middle and the law of non-contradiction for such undecidable propositions must fail to be theorems of T. The phenomenon of quantum superposition is thus explained in NAFL. It is also shown that infinite sets cannot exist in any consistent theory of NAFL, which makes it a very restrictive logic. Implications for some modern mathematical and physical theories are analyzed from the point of view of NAFL.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Bart D’Hooghe & Jaroslaw Pykacz (2004). Quantum Mechanics and Computation. Foundations of Science 9 (4):387-404.
J. L. Bell (1986). A New Approach to Quantum Logic. British Journal for the Philosophy of Science 37 (1):83-99.
Michael Dickson (1996). Logical Foundations for Modal Interpretations of Quantum Mechanics. Philosophy of Science 63 (3):329.
Peter Mittelstaedt (1978). The Metalogic of Quantum Logic. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:249 - 256.
Itamar Pitowsky (1982). Substitution and Truth in Quantum Logic. Philosophy of Science 49 (3):380-401.
Radhakrishnan Srinivasan, On the Logical Consistency of Special Relativity Theory and Non-Euclidean Geometries: Platonism Versus Formalism.
E. -W. Stachow (1976). Completeness of Quantum Logic. Journal of Philosophical Logic 5 (2):237 - 280.
Matthew J. Donald, Finitary and Infinitary Mathematics, the Possibility of Possibilities and the Definition of Probabilities.
Radhakrishnan Srinivasan, Platonism in Classical Logic Versus Formalism in the Proposed Non-Aristotelian Finitary Logic.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads2 ( #677,009 of 1,792,063 )
Recent downloads (6 months)2 ( #344,915 of 1,792,063 )
How can I increase my downloads?