Who Cares About the Fallacies?

  • John Woods
Part of the Applied Logic Series book series (APLS, volume 32)


The main business of this chapter is to motivate the systematic study of fallacious reasoning and argument. In its most usual meaning, a fallacy is a common misconception; that is, a false statement that is widely believed. Examples of such statements are, “Handling frogs causes warts” , “You’ll catch a cold if you sit in a draft” , and at a more academic level “John Stuart Mill thought that every valid argument begs the question”. (Recall the Prologue!)


Probability Calculus Conjunctive Probability Fallacious Reasoning Boundary Question Fallacy Theory 
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  1. 1.
    See, for example, [Massey, 1975a]. Shades of DeMorgan: “There is no such thing as a classification of the ways in which men arrive at an error: it is much to be doubted whether there ever can be” , [DeMorgan, 1926, p. 2761.Google Scholar
  2. 2.
    “We should retain the historical nucleus of the idea of a fallacy as a logically bad argument” [Johnson, 1987a, p. 245].Google Scholar
  3. 3.
    Johnson “we shall introduce the notion of frequency; because a fallacy is not just any mistake in an argument, but one that occurs with some frequency” [Johnson, 1987a, p. 245]. Cf. Scriven “Fallacies are the attractive nuisances of argumentation, the ideal types of improper inference. They acquire labels because they are thought to be common enough or important enough or to make the cost of labels worthwhile” [Scriven, 1987a, p. 333].Google Scholar
  4. 4.
    Treating fallacies as inference-mistakes is “a colossal mistake, a super-fallacy...” [Hintikka, 1987, p. 211].Google Scholar
  5. 5.
    See Govier, “By definition, a fallacy is a mistake in reasoning, a mistake that occurs with some frequency in real arguments and which is characteristically deceptive” [Govier, 1987, p. 177], emphasis added. Cf. Woods and Walton, “a fallacy is an argument that is a tricky deception, because it is incorrect even while it has a tendency to seem correct” [Woods and Walton, 1982, p. 2]. And, more carefully, Fogelin and Duggan, “the term ‘fallacy’ is our most general term for criticizing any general procedure used for the fixation of beliefs that has an unacceptably high tendency to generate false or unfounded beliefs” [Fogelin and Duggan, 1987, p. 262].Google Scholar
  6. 6.
    See Harper in reaction to the Woods-Walton treatment of the petitio in Kripke-structures [Harper, 1980].Google Scholar
  7. 7.
    I am grateful to Scott Jacobs for discussion of these matters.Google Scholar
  8. 8.
    See, for example, Cohen. Pascalian probability (also called aleatory) is the sort of probability embedded in games of chance, such as roulette. One of the founders of the mathematical theory of this concept was Blaise Pascal (1623–1662), hence the name. “Baconian” probability is named after Francis Bacon (1561–1626), one of the earliest, and staunchest, inductivists of modern science. Baconian probability is the degree of likelihood conferred on general propositions by their true positive instances. Cohen’s submission is that these are different concepts of probability, and that each has (a contextually qualified) place in our cognitive lives [Cohen, 1989]. I also note that among the alternative formalisms for representing uncertainty is what some AI theorists call possibility theory (and which makes essential use of fuzzy set theory) as well as Dempster–Shafer theory (which permits the probabilities of disjoint sets to sum to more than 1.)Google Scholar
  9. 9.
    Those familiar with the basic AI literature will be aware that von Neumann has a celebrated argument about the complexity of functions, an impediment to information-processing by humans which computers manage to overcome. Nested functions are the problem. The problem extends to existential quantifiers by way of Skolem functions with which they can be replaced [von Neumann, 1958].Google Scholar
  10. 10.
    See the references herein to [Fogelin and Duggan, 1987; Cohen, 1989; Stich, 1985; Garcia et al., 1972]. See also [Nisbett et al., 1983; Nisbett and Ross, 1980; Tversky and Kahneman, 1983; Cohen, 1981; Holland et al., 1986].Google Scholar
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    Similarly, the statistical fallacies came to light with the emergence of probability theory. We find the gambler’s fallacy, for example, in [Laplace, 1951, p. 163].Google Scholar
  12. 12.
    See also [Cartwright, 1983, 87 ff] and [Hintikka, 1989, p. 4]. See [Gabbay and Woods, 2004] for further discussion.Google Scholar
  13. 13.
    The modern locus classicus of this view is [Toulmin, 1969]. McPeck may have taken Toulmin’s insight somewhat further than originally intended [McPeck, 1981]. An excellent response to McPeck is [Ennis, 1996].Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • John Woods
    • 1
    • 2
    • 3
  1. 1.The Abductive Systems GroupUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Computer ScienceKing’s CollegeLondonEngland
  3. 3.Department of PhilosophyUniversity of LethbridgeCanada

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