David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 141 (1):45 - 76 (2004)
A form (or pattern) of inference, let us say, explicitlysubsumes just such particular inferences as are instances of the form, and implicitly subsumes thoseinferences with a premiss and conclusion logically equivalent to the premiss and conclusion of an instanceof the form in question. (For simplicity we restrict attention to one-premiss inferences.) A form ofinference is archetypal if it implicitly subsumes every correct inference. A precise definition (Section 1)of these concepts relativizes them to logics, since different logics classify different inferences ascorrect, as well as ruling differently on the matter of logical equivalence which entered into the definitionof implicit subsumption. When relativized to classical propositional logic, we find (Section 2) thatall but a handful of `degenerate' inference forms turn out to be archetypal, whereas matters are verydifferent in this respect for the case of intuitionistic propositional logic (Sections 3 and 4), and an interestingstructure emerges in this case (the poset of equivalence classes of inference forms, with respect tothe equivalence relation of implicitly subsuming the same inferences). Thus a more accurate, if excessivelylong-winded title would be 'Archetypal and Non-Archetypal Forms of Inference in Classical andIntuitionistic Propositional Logic'. Some left-overs are postponed for a final discussion (Section 5).The overall intention is to introduce a new subject matter rather than to have the last word on thequestions it raises; indeed several significant questions are left as open problems.
|Keywords||No keywords specified (fix it)|
No categories specified
(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
David Sherry (1991). The Inconspicuous Role of Paraphrase. History and Philosophy of Logic 12 (2):151-166.
Ken Akiba (1996). Logic as Instrument: The Millian View on the Role of Logic. History and Philosophy of Logic 17 (1-2):73-83.
P. D. Magnus (2008). Demonstrative Induction and the Skeleton of Inference. International Studies in the Philosophy of Science 22 (3):303 – 315.
Lloyd Humberstone (2013). Replacement in Logic. Journal of Philosophical Logic 42 (1):49-89.
M. V. Dougherty (2004). The Comparative Set Fallacy. Argumentation 18 (2):213-222.
Fernando Raymundo Velázquez-Quesada (2009). Inference and Update. Synthese 169 (2):283 - 300.
Gennaro Auletta (2005). Semiosis, Logic, and Language. Croatian Journal of Philosophy 5 (1):51-69.
Vladimir V. Rybakov (1992). Rules of Inference with Parameters for Intuitionistic Logic. Journal of Symbolic Logic 57 (3):912-923.
Ronald Fagin, Joseph Y. Halpern & Moshe Y. Vardi (1992). What is an Inference Rule? Journal of Symbolic Logic 57 (3):1018-1045.
Added to index2009-01-28
Total downloads12 ( #137,564 of 1,139,956 )
Recent downloads (6 months)1 ( #165,020 of 1,139,956 )
How can I increase my downloads?