Abstract
In this paper I focus on two contrasting concepts of deduction and induction that have appeared in introductory (formal) logic texts over the past 75 years or so. According to the one, deductive and inductive arguments are defined solely by reference to what arguers claim about the relation between the premises and the conclusions. According to the other, they are defined solely by reference to that relation itself. Arguing that these definitions have defects that are due to their simplicity, I develop definitions that remove these defects by assigning a combination of roles to both arguers’ claims concerning the premises/conclusion relation and the relation itself. Along the way I also present and briefly defend definitions of both deductive and inductive validity that are significantly different from the norm.
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Notes
For example, see Baum (1996).
However, see my final addendum in Sect. 6 for a brief discussion of the views of an author who has developed a version of these definitions that, he believes, avoids these difficulties—and a theory of validity to go with it.
For example, see Runes (2009), Flew (1979) and Blackburn (1994). Also see relevant sections of PhilosophyPages.com; PhilosophyClass.com; philosophy.lander.edu; plato/Stanford.edu/.
For example, see Baum’s acceptance of the notion of invalid syllogisms and invalid arguments in propositional logic. He treats syllogisms and arguments of propositional logic as parts of deductive logic. See Baum, op. cit., Chapters 4 and 6.
It should be noted that these corollaries hold if and only if a deductive argument is understood as an argument in which the conclusion follows necessarily from the premises.
Engel, op. cit., p. 7. Italicized words are italicized in the text.
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Wilbanks, J.J. Defining Deduction, Induction, and Validity. Argumentation 24, 107–124 (2010). https://doi.org/10.1007/s10503-009-9131-5
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DOI: https://doi.org/10.1007/s10503-009-9131-5