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A Logical Analysis of Slippery Slope Arguments

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Abstract

This article offers a logical analysis of Slippery Slope Arguments. Such arguments claim that adopting a certain act or policy would take us down a slippery slope to an undesirable bottom and infer from this that we should refrain from this act or policy. Even though a logical assessment of such arguments has not received much careful attention, it is of vital importance to their overall assessment because if the premises fail to support the conclusion an argument is worthless. I partition slippery slope reasoning by means of two dichotomies (reasoning under certainty vs. uncertainty and one-step vs. multiple-step reasoning) into four general categories and evaluate these in turn. The analysis reveals that slippery slope arguments are logically fallacious.

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Notes

  1. More about the distinction between different types of SSAs can be found in Enoch [10], den Hartogh [9], Lillehammer [15], Lode [16, p. 1477], or Smith [23].

  2. For example, the definition given by Volokh [26] refers to probabilistic versions of SSAs only.

  3. See, for instance, the definitions of Schauer [19] or Schubert [20], which have an indeterminate logical structure. It is not clear whether their form is a conditional or a biconditional.

  4. Other metaphors that have been used to refer to this type of reasoning are "wedge argument", "thin edge of the wedge", camel's nose", and sometimes "domino" because an SSA resembles a row of falling dominoes, with each event causing the next one in line (see [16]).

  5. I am grateful to an anonymous referee at this journal for alerting me to this problem.

  6. For instance, Codd [8] discusses the argument against allowing prisoners access to conjugal visits by their partners. Further legal discussion can be found in Enoch [10], Lewis [14], Lode [16], Schauer [19], Smith [22], or Volokh [26].

  7. See, for example, the example given by Volokh [26] against opposing partial-birth abortion bans because this might lead to a broader abortion restriction (p. 1031).

  8. Singer [21] holds that the SSA is "undoubtedly the most widely invoked secular argument" against the legalization of voluntary euthanasia and physician-assisted suicide (p. 538). See also Clark [6], Lode [16], Nielsen [17], and Smith [23].

  9. For example the argument "that even if research on embryos is not wrong in itself, it will open the way to a slippery slope of dehumanising practices, such as embryo farms, cloned babies, the use of fetuses for spare parts, and the commodification of human life" [18]; compare to this also Camporesi [5].

  10. Compare this example, given by Bayertz et al. [1], "The application and development of somatic gene therapy will lead to an increase in willingness to intervene in the germ-line cells …" (p. 467).

  11. For instance, "In vitro fertilization is another step down the slippery slope towards the clear evil of eugenics". Christianity Today, 2007. Available at: http://www.christianitytoday.com/ct/2007/march/24.29.html (accessed 12 May 2008).

  12. "Cloning human embryos for research purposes will lead down a slippery slope to reproductive cloning and finally to "designer babies". Available at: http://news.bbc.co.uk/2/hi/science/nature/377046.stm (accessed 10 August 2007).

  13. Compare this example, reported by Bostrom [3], "To forestall a slide down a slippery slope towards an ultimately debased 'posthuman' state, human enhancement technologies should be banned globally" (see p. 202).

  14. One argument in this context is that prenatal diagnosis may open the door for "sexing for all disorders in which the mutation's penetrance and/or the expression is lower or milder in one sex" (see [4]).

  15. See, for instance, Enoch [10] who asks, "Why, though, should we believe that allowing voluntary euthanasia would result in allowing involuntary euthanasia?" (p. 630). Compare also Gay-Williams [11], Lewis [14], and Singer [21].

  16. Schauer [19] claims to "flesh out the logical structure" of SSAs (p. 363) but his study is not a logical investigation. In general, if writers claim to give a logical assessment, they tend to confuse logical and epistemic issues (see, for instance, [16, 22, 27]).

  17. See Spielthenner [24]. It should be noted that my logical assessment will be based on an intuitive understanding of when practical arguments are valid. The chief reason for this is that a formal account of practical validity is an issue that is too complex to pursue in any detail here. Moreover, I think that my arguments are intuitively plausible upon consideration.

  18. Lode [16] holds that one-step arguments are not SSAs because the imagery such arguments suggest "is more reminiscent of a cliff or wall than a slope" (p. 1477). I agree that one-step arguments are borderline cases but since they are often used we cannot ignore them here.

  19. Of course, I have been speaking somewhat loosely here because nothing follows logically from doing something. My explanation must therefore be understood as shorthand for 'From the propositions that we step on the slope and that we slide to the bottom if we step on the slope, it follows the proposition that we slide to the bottom'.

  20. For simplicity, it is here assumed that there are a finite number of alternatives and a finite number of possible outcomes.

  21. See my "Instrumental Reasoning Reconsidered" [forthcoming].

  22. Observe, that we can use any of a number of phrases to express such conclusions because ordinary language does not uphold a sharp distinction between different deontic modals. For example, I could have said just as effectively that we canot allow therapeutic cloning or that this is out of the question.

  23. In a more traditional terminology, these argument have been called prima facie valid or pro tanto valid, but it is now an established terminology to call them defeasible.

  24. A case in point is Nielsen's [17] claim that "when the risked harm of a course of action outweighs its expected benefits, it ought to be avoided" (p. 17).

  25. Obviously, there can be combinations of certainties and uncertainties in one SSA—e.g., when one step down the slope is regarded as certain but others only as likely. However, I think it is safe to set such cases aside because my arguments can easily be adapted for such mixed forms.

  26. I exclude here the case where this possibility is 1 because if P = 1 we have a reasoning under certainty.

  27. Critics of slippery slope reasoning sometimes call attention to the fact that the probability of sliding to the bottom is the smaller the longer the slope is (e.g., [5]). If we assume that we slide to the bottom only if we step on the slope, this probability P(b) is P(i 1) × P(i 2|i 1) × … × P(b|i n ). For instance, in the case of a three-step slope with P(i 1) = 0.4, P(i 2|i 1) = 0.6 and P(b|i 3) = 0.3, the probability of sliding to the bottom is only 0.072. It is worth noticing, however, that this is only indirectly relevant because it makes the value of stepping on the slope less negative. It is not directly relevant because we do not compare the bottom to the other possible outcomes of stepping on the slope, but stepping on the slope to its alternatives.

  28. The term “maximin” is derived from the Latin term “maximum minimorum” which means “the maximum of the minima”—and it is exactly this maximum that should be chosen, according to this principle.

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  1. Department of Philosophy and Applied Ethics, The University of Zambia, Canada Court B3, P.O. Box 32967, Lusaka, Zambia

    Georg Spielthenner

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Spielthenner, G. A Logical Analysis of Slippery Slope Arguments. Health Care Anal 18, 148–163 (2010). https://doi.org/10.1007/s10728-009-0117-0

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