Archetypal forms of inference

Synthese 141 (1):45 - 76 (2004)
Abstract
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 Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
Categories No categories specified
(categorize this paper)
DOI 10.1023/B:SYNT.0000035850.89516.e1
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,220
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
The Inconspicuous Role of Paraphrase.David Sherry - 1991 - History and Philosophy of Logic 12 (2):151-166.
Semiosis, Logic, and Language.Gennaro Auletta - 2005 - Croatian Journal of Philosophy 5 (1):51-69.
The Comparative Set Fallacy.M. V. Dougherty - 2004 - Argumentation 18 (2):213-222.
Replacement in Logic.Lloyd Humberstone - 2013 - Journal of Philosophical Logic 42 (1):49-89.
Logic as Instrument: The Millian View on the Role of Logic.Ken Akiba - 1996 - History and Philosophy of Logic 17 (1-2):73-83.
What is an Inference Rule?Ronald Fagin, Joseph Y. Halpern & Moshe Y. Vardi - 1992 - Journal of Symbolic Logic 57 (3):1018-1045.

Monthly downloads

Added to index

2009-01-28

Total downloads

39 ( #131,707 of 2,164,599 )

Recent downloads (6 months)

6 ( #50,872 of 2,164,599 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums