The scope of logic: deduction, abduction, analogy

Theoria 64 (2-3):217-242 (1998)
Abstract
The present form of mathematical logic originated in the twenties and early thirties from the partial merging of two different traditions, the algebra of logic and the logicist tradition (see [27], [41]). This resulted in a new form of logic in which several features of the two earlier traditions coexist. Clearly neither the algebra of logic nor the logicist’s logic is identical to the present form of mathematical logic, yet some of their basic ideas can be distinctly recognized within it. One of such ideas is Boole’s view that logic is the study of the laws of thought. This is not to be meant in a psychologistic way. Frege himself states that the task of logic can be represented “as the investigation of the mind; [though] of the mind, not of minds” [17, p. 369]. Moreover Frege never charges Boole with being psychologistic and in a letter to Peano even distinguishes between the followers of Boole and “the psychological logicians” [16, p. 108]. In fact for Boole the laws of thought which are the object of logic belong “to the domain of what is termed necessary truth” [2, p. 404]. For him logic does not depend on psychology, on the contrary psychology depends on logic insofar as it is only through an investigation of logical operations that we could obtain “some probable intimations concerning the nature and constitution of the human mind” [2, p. 1]. Logic is normative, not descriptive. For, the laws of thought do not “manifest their presence otherwise than by merely prescribing the conditions of formal inference” [2, p. 419]. They are, “properly speaking, the laws of right reasoning only” [2, p. 408]. So they “form but a part of the system of laws by which the actual processes of reasoning, whether right or wrong, are governed” [2, p. 409]. Boole’s idea that logic is the study of the laws of thought was taken over by Hilbert. According to him logic is “a discipline which expresses the structure of all our thought” [31, p..
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1111/j.1755-2567.1998.tb00188.x
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,694
External links

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
Logic in the Twenties: The Nature of the Quantifier.Warren D. Goldfarb - 1979 - Journal of Symbolic Logic 44 (3):351-368.
Self-Reference and Incompleteness in a Non-Monotonic Setting.Timothy G. Mccarthy - 1994 - Journal of Philosophical Logic 23 (4):423 - 449.
Analysis in Greek Geometry.Richard Robinson - 1936 - Mind 45 (180):464-473.

View all 6 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Boole's Abandoned Propositional Logic.Theodore Hailperin - 1984 - History and Philosophy of Logic 5 (1):39-48.
Aristotle's Prior Analytics and Boole's Laws of Thought.John Corcoran - 2003 - History and Philosophy of Logic. 24 (4):261-288.
Boole's Annotations on 'the Mathematical Analysis of Logic'.G. C. Smith - 1983 - History and Philosophy of Logic 4 (1-2):27-39.
What is “Formal Logic”?Jean-Yves Beziau - 2008 - Proceedings of the Xxii World Congress of Philosophy 13:9-22.
Boole and Mill: Differing Perspectives on Logical Psychologism.John Richards - 1980 - History and Philosophy of Logic 1 (1-2):19-36.
Broadened Logic.Avrum Stroll - 2003 - Topoi 22 (1):93-104.
Augustus De Morgan's Boolean Algebra.Daniel D. Merrill - 2005 - History and Philosophy of Logic 26 (2):75-91.
Semantic Descent.Joan Weiner - 2005 - Mind 114 (454):321-354.
19th Century Logic Between Philosophy and Mathematics.Volker Peckhaus - 1999 - Bulletin of Symbolic Logic 5 (4):433-450.
The Laws of Thought.George Boole - 1854 - Prometheus Books.
Added to PP index
2010-09-13

Total downloads
213 ( #19,341 of 2,197,230 )

Recent downloads (6 months)
1 ( #298,376 of 2,197,230 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature