Abstract
In 2011, Andrzej Grzegorczyk formulated Logic of Descriptions (LD), a new logical system in which the classical equivalence has been replaced with the descriptive equivalence. Two sentences are descriptively equivalent whenever they describe the same state of affairs. Grzegorczyk’s logic LD is built from the ground up by revising the axioms of classical propositional logic and rejecting those that do not correspond to the intended interpretation of the descriptive equivalence as the connective expressing equimeaning relations between sentences. Grzegorczyk’s last paper, which introduced in detail philosophical motivations of LD and its axiomatization, has become an inspiration for investigating the properties of LD and its various modifications. In this paper we present the basics of Grzegorczyk’s logic LD and then we survey the recent results on LD that have shed light on mysterious properties of the Grzegorczyk’s descriptive equivalence connective.
It is important to approach the deeds of previous generations with the right attitude, accepting the fact that their actions were an actual step of their development. Regardless of any alternative ways in which reality could have evolved, we must not belittle their thoughts and actions, but rather augment them, keeping in mind all that our ancestors could not have taken into account. So, let us not claim that we are building a new philosophy on new principles, as we are not essentially wiser than our predecessors, but let us utilize the whole record of the past, carefully considering their whole evolution (biological and cultural). Their experiences form the basis of our growth. Andrzej Grzegorczyk
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Recall that φ → ψ is short for ¬φ ∨ ψ.
References
Anderson, A.R., Belnap, N.D.: Entailment. The Logic of Relevance and Necessity, vol. I. Princeton University Press, Princeton (1975)
Golińska-Pilarek, J.: On the minimal non-Fregean Grzegorczyk’s logic. Stud. Logica. 104(2), 209–234 (2015)
Golińska-Pilarek, J., Huuskonen, T.: Logic of descriptions. A new approach to the foundations of mathematics and science. Stud. Log. Grammar Rhetor. 27(40), 63–94 (2012)
Grzegorczyk’s non-Fregean logics and their formal properties. In: Urbaniak, R., Payette, G. (eds.) Applications of Formal Philosophy: The Road Less Travalled, Logic, Argumentation & Reasoning, vol. 14. Springer (2017)
Grzegorczyk, A.: Filozofia logiki i formalna LOGIKA NIESYMPLIFIKACYJNA [Philosophy of Logic and Perceptive Equivalence]. Zagadnienia Naukoznawstwa 4(190), 445–450 (2011)
Grzegorczyk, A.: Errata to Grzegorczyk, A.: Filozofia logiki i formalna LOGIKA NIESYMPLIFIKACYJNA [Philosophy of Logic and Perceptive Equivalence]. Zagadnienia Naukoznawstwa 4(190), 445–450 (2011). Zagadnienia Naukoznawstwa 4(190) (2011)
Suszko, R.: Non-Fregean logic and theories. Analele Universitatii Bucuresti, Acta. Logica. 9, 105–125 (1968)
Suszko, R.: Semantics for the sentential calculus with identity. Stud. Logica. 28, 77–81 (1971)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Golińska-Pilarek, J., Huuskonen, T. (2018). A Mystery of Grzegorczyk’s Logic of Descriptions. In: Garrido, Á., Wybraniec-Skardowska, U. (eds) The Lvov-Warsaw School. Past and Present. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-65430-0_51
Download citation
DOI: https://doi.org/10.1007/978-3-319-65430-0_51
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-65429-4
Online ISBN: 978-3-319-65430-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)