Abstract
In this chapter, the calculus of effective (intuitionistic) quantum logic will be established. Starting from the observation that there are some material propositions which can be defended within the material dialog-game D* m irrespective of the elementary propositions contained in it, the concept of a formally true proposition will be defined in Section 4.1 by the respective argument rules. Eliminating elementary propositions but not commensurabilities in D m the semi-formal quantum dialog-game D (m) f is formulated in Section 4.2. Following this, the material availability propositions are also eliminated, thus achieving the formal quantum dialog-game D f (Section 4.3). The totality of propositions which can be defended in this formal dialog-game is comprehended in the calculus Q eff of effective quantum logic, which is established in Section 4.4. This calculus Q eff can be shown to be consistent and complete with respect to those propositions which can be defended in a formal dialog.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes and References
P. Lorenzen, Metamathematik, Bibliographisches Institut, Mannheim (1962).
W. Kamlah and P. Lorenzen, Logische Propadeutik, Bibliographisches Institut, Mannheim, (1973).
K. Lorenz, Arch. f. Math. Logik und Grundlagenforsch. 11, (1968).
P. Mittelstaedt, Philosophical Problems of Modern Physics, D. Reidel Publishing Co., Dordrecht, Holland (1976).
E.W. Stachow, J. Philos. Logic 5, 237 (1976).
E.W. Stachow, Dissertation, Köln, (1976).
H.M. Denecke, Dissertation, Köln, (1976).
P. Lorenzen, Formal logic, D. Reidel Publishing Co., Dordrecht, Holland (1965).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1978 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Mittelstaedt, P. (1978). The Calculus of Effective Quantum Logic. In: Quantum Logic. Synthese Library, vol 126. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9871-1_5
Download citation
DOI: https://doi.org/10.1007/978-94-009-9871-1_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-9873-5
Online ISBN: 978-94-009-9871-1
eBook Packages: Springer Book Archive