Logical constants as punctuation marks
type: Item
instance of: scholarly article
title: Logical constants as punctuation marks
zbMATH Open document ID: 0692.03003
author: Kosta Došen
published in: Notre Dame Journal of Formal Logic
publication date: 1989-01-01T00:00:00Z
review text: One of the most important questions of the philosophy of logic is the question ``What is a logical constant?'' Starting from the assumptions that logic is the science of formal deductions and that basic formal deductions are structural deductions, i.e. deductions which can be described independently of the constants belonging to the object language, the author presents a proof-theoretical attempt (I would say a fairly successful one) to answer the question above. Assuming further that any constant of the object language on whose presence the description of a nonstructural formal deduction depends can be ultimately analyzed in structural terms, the author reaches the following thesis, characterizing the nature of the logical constant: a constant is logical iff it can be ultimately analyzed in structural terms. Some other assumptions concerning logic are considered as well as some other philosophical approaches, treating the problem of logical constants, including the grammatical, the model-theoretical and the proof- theoretical. It should be emphasized that the thesis above has already been corroborated in a certain way by the same author by means of formulations of various families of different logical systems [J. Symb. Logic 50, 149-168 (1985; Zbl 0562.03009); Publ. Inst. Math., Nouv. Sér. 39(53), 3-12 (1986; Zbl 0586.03014); Stud. Logica 47, 353-385 (1988; Zbl 0671.03018)]. It is a real pleasure to read such a quite interesting and inspiring paper.
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03F07
zbMATH DE Number: 4132119
zbMATH Keywords: proof theory
zbMATH Keywords: philosophy of logic
zbMATH Keywords: logical constants
reviewed by: Branislav Boričić
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093635154
OpenAlex ID: W2067172985
DOI: 10.1305/NDJFL/1093635154
description: scientific article; zbMATH DE number 4132119