Skip to main content
Log in

Know-how, action, and luck

  • S.I.: Knowledge and Justification, New Perspectives
  • Published:
Synthese Aims and scope Submit manuscript

Abstract

A good surgeon knows how to perform a surgery; a good architect knows how to design a house. We value their know-how. We ordinarily look for it. What makes it so valuable? A natural response is that know-how is valuable because it explains success. A surgeon’s know-how explains their success at performing a surgery. And an architect’s know-how explains their success at designing houses that stand up. We value know-how because of its special explanatory link to success. But in virtue of what is know-how explanatorily linked to success? This essay provides a novel argument for the thesis that know-how’s special link to success is to be explained at least in part in terms of its being, or involving, a doxastic attitude that is epistemically alike propositional knowledge. It is argued that the role played by know-how in explaining intentional success shows that the epistemic differences between know-how and knowledge, if any, are less than usually thought; and that “revisionary intellectualism”, the view that know-how is true belief that might well fall short of knowledge, is not really a stable position. If its explanatory link to success is what makes know-how valuable, an upshot of my argument is that the value of know-how is due, to a considerable extent, to its being, or involving, a kind of propositional knowledge.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Notes

  1. Although I also believe the claim that know-how is identical to a propositional knowledge state, in this essay I will only defend the weaker claim that know-how requires, or involves, a propositional knowledge state. Many people object to the sufficiency of propositional knowledge for know-how. (For more recent criticism, see Audi 2017; Levy 2017). I agree with them that the sufficiency claim is implausible unless a clear and worked-out picture of practical modes of presentation is provided. Although in this essay I do not talk about practical modes of presentation, I have been developing a theory of practical modes of presentation in a series of papers (Pavese 2015b, 2017c, forthcoming) and in some work in progress.

  2. Hawley (2003: p. 19) also emphasizes the similarity between know-how and knowledge, when she says: “Just as propositional knowledge can be understood in terms of true belief plus warrant, knowledge-how can be understood in terms of successful action plus warrant”. There are important differences, however Hawley (2003) leaves open that know-how and knowledge might be different kinds of states and that warrant applies to belief in one case and to action in the other. In contrast, my claim is the anti-luck condition is the same for both know-how and knowledge and that in both cases it is a condition on a belief state.

  3. I will be assuming that beliefs, rather than credences or levels of confidence, is the relevant doxastic attitude. But this assumption is not essential to my argument. My argument can be reframed in terms of credences, for they are arguably also the candidates for knowledge (Moss 2013). I am also not taking a stance on whether or not belief reduces to credence above a threshold.

  4. Note that my claim that intentionally φ requires a belief about how to φ is independent of the claim that intentions themselves are beliefs. (See criticisms of this claim in Thompson 2008; Holton 2009. For a recent defense instead, see Marusic and Schwenkler, forthcoming). Intentions might not be beliefs and yet might require beliefs in order for the action that they cause to be intentional. Goldman (1970) himself does not present his view as a theory of intentions but rather as an analysis of intentional action. The same consideration also makes my proposal immune to Hornsby’s (2016) criticism against intellectualism about know-how—criticism that relies on equating propositionalist treatments of know-how and propositionalist treatments of intentions.

  5. Even if one thinks that “psychological” explanations must only be restricted to trying or attempts (Alston 1974: p. 95; Stich 1978), one might grant that intentional successes are also susceptible of an explanation, though one that will not be purely psychological.

  6. In Goldman’s (1970) sense of “generation”.

  7. On this view, were one not to believe that one is sufficiently likely to φ by ψ-ing, for some way ψ, one could only try to φ but not intentionally succeed at φ-ing.

  8. Similarly, the following Belief requirement on know-how is compatible with subintentional actions being guided by a state, different from human know-how, that does not require belief. We might call that state know-how (cfr. Audi 2017) if we want, but calling it the same does not entail that it is the same sort of state.

  9. Here, I am grateful to Bob Beddor for discussion.

  10. Brownstein and Michaelson (2016) challenge a belief requirement on know-how but their challenge is unsuccessful (Cfr. Pavese 2016 for discussion of their criticism). Brownstein and Michaelson (2016) discuss studies showing that when catching a ball, ball players make anticipatory saccades to shift their gaze ahead their gaze ahead of the ball one or more time during the course of its fight toward them. These players know how to catch the ball, and they can intentionally do it, but they do not believe that making anticipatory saccades is part of how they catch the ball. Rather they believe they are tracking the ball all the time. Brownstein and Michaelson (2016) conclude that know-how does not require a belief. Not so fast! Note that from the fact that the players have possibly multiple false beliefs about how to catch the ball, it does not follow that they do not also possess true beliefs about how they do it. One way of motivating this idea is to appeal to a picture of our belief box as “fragmented” or “compartmentalized” (Lewis 1982, 1988; Stalnaker 1984)—a model of our doxastic life that is independently motivated. Indeed, all has been said so far suggests that that additional true belief has to be there, if they can intentionally catch the ball—i.e., if, in other words, there is a belief requirement on intentional action as standard action theory has it (Intentionality/Belief).

  11. Although weaker than the standard intellectualist thesis, the conclusion (4) is compatible with the claim that, in many and maybe even the majority of cases, knowing how to perform that action does involve a true belief, and not just the ability to have one. Cfr. Dickie (2012), Lowenstein (2017) for views allowing know-how to be a disposition to form a belief and Stanley and Williamson (2017) for a view according to which skill is a disposition to know. See also Audi (2017: p. 288) for the idea that a disposition to form beliefs is necessary (although he claims not sufficient) for know-how. Pavese (2013, 2017a, b, c) also discusses this sort of view. As Stanley and Williamson (2017) observe, the claim that skill is an ability to know is a form of intellectualism, in that it preserves the distinctively intellectualist claim that skillful actions characteristically manifest propositional knowledge. Although Stanley and Williamson (2017) argue for the claim that skills are abilities to know, they fail to provide arguments for thinking that knowledge, rather than true beliefs, is the sort of state that skills are abilities to be in. I undertake this task in the next sections.

  12. On the concept of basic action, see Danto (1965).

  13. It is true that some intellectualists (cfr. Snowdon 2004) deny Basic Knowledge. However, as noted by Setiya (2012), denying Basic Knowledge amounts to accepting the hardly believable consequence that we may not know how to perform some of our basic actions.

  14. Here, I am grateful to Setiya for personal communication.

  15. Wouldn’t it be more correct to say that, in a circumstance such as Clenching, one can only genuinely intend to try to clench but cannot possibly intend to clench? Cfr. Mele (1989). The view that intending to φ requires believing that one will φ (cfr. Harman 1976) has been discredited by Davidson’s (1971: p. 50) example of somebody heavily writing on a page in order to produce ten legible carbon copies, without having any confidence that they will succeed. Yet, other versions of the view are more tenable. For example, the relevant belief might be that ψ-ing is a way for one to φ, where ψ-ing is a way for one to φ only if it is sufficiently likely that, in suitably favourable conditions, one can φ by ψ-ing (Harman 1976; Ginet 1990: pp. 77–78; Audi 1973: p. 388, 1986).

  16. Cfr. Cath (2015) for criticisms of Setiya (2012).

  17. Setiya (pc) pointed out to me that Clenching satisfies Anscombe’s (1957) criterion for intentional action: it would make sense to ask Marie why she clenched. By this criterion, Marie’s clenching counts as intentional. However, one might object that although necessary for intentional action, Anscombe’s criterion is not sufficient. More argument is needed for the sufficiency of Anscombe’s criterion for intentional action, which is far from obvious.

  18. Cfr. Marley-Payne (2016).

  19. As Marley-Payne (2016) observes, an intellectualist friendly explanation of both sets of intuitions might require a subtle form of contextualism for both knowledge ascriptions and know-how ascriptions, one that would have to explain at once why knowledge ascriptions come out false when taken in isolation in standard Gettier scenarios but true when taken together with know-how ascriptions. Finally, the relevant context-sensitivity would also have to allow for sensitivity to stakes. In addition, as noted by Cath (2015: p. 12), in view of Know-how/intentionality, the relevant analysis would have to explain away our intuitions according to which Gettiered subjects such as Charlie and Bob may act intentionally on their Gettiered beliefs.

  20. For an error theory of Cath’s and Poston’s intuitions, see Stanley (2011, chapter 8), in part based on Hawthorne (2002).

  21. My argument follows closely a recent argument by Daniel Greco (2016) for a safety condition on knowledge. However, my argument diverges from Greco in some important respects, the most notable being that it does not need to make a crucial assumption needed for Greco’s argument—i.e., that propositional knowledge plays an essential role in explaining success.

  22. Both a strong and weak safety requirement on knowledge have advocates in the current literature. Sosa (1999), Williamson (2000), Pritchard (2005), Manley (2007), and Daniel Greco (2016) defend a version of a strong safety requirement. By contrast, Pritchard (2012), Sosa (2015), and John Greco (2016) discuss a weaker version of safety. Pritchard (2012) talks of safe beliefs as ones formed according to a method that “would reliably yield correct answers,” underwriting something like the definition of safety of a belief in terms of sufficiently many of the close worlds where it is true. Cfr. Sosa (2015: pp. 117–121). John Greco (2016: p. 53) formulates it in terms of “most or almost most” close worlds where it is true.

  23. As Daniel Greco (2016: p. 189) notes, if the explanandum is a fluke, a non-modally robust explanation might be all that is available. Consider winning a fair lottery. The best one can do to explain the victory is to show that the winning was possible. In cases such as these, showing the possibility of an event is all that can be done.

  24. Daniel Greco (2016) concludes from this that, if knowledge plays an ineliminable role in explaining success (Williamson 2000; Nagel 2013), because explanations must be modal robust, there must be a modal condition on knowledge.

  25. It is notoriously difficult to spell out what conditions count as relevant. But this problem is not specific to the explanatory role of beliefs vis a vis success: arguably, it is a problem that is inherited by the context-sensitivity of explanation.

  26. Thanks to Daniel Greco for discussion here.

  27. Anne Bonny was an exceptionally skilled Irish pirate, operating in the Caribbean.

  28. Does the relevant belief itself need to be safe, or is it sufficient, in order to ensure the modal robustness of the explanation, that the way to perform the relevant action be reliable? Thanks to Bob Beddor for raising this issue. Suppose my belief about how to hijack ships is about a way to hijack ships that is reliable. Then by following that way I will succeed at hijacking ships in sufficiently many of the relevantly close worlds, where what counts as sufficiently many worlds depends on the relevant degree of reliability of that way. But a way w may count as reliable, and so may lead to success in sufficiently many of the closest worlds, without the range of close worlds being the same as the range of close worlds that counts for the explanation being modally robust. After all, part of the explanation of the intentionality of the success in the close worlds will have to encompass the fact that the subject has acted on a true belief. Moreover, if the belief b, or a counterpart of that belief, is false in some close world, that world might count among the worlds that witness the reliability of w and yet be one where by acting on b, or by acting on its counterpart, the subject fails. So a world’s being the witness for the reliability of w does not entail that that world will be also the witness to one’s success on the basis of a given belief. Because of this, it seems to me that for it to figure in satisfactory explanations of success, the modal robustness of the relevant belief is needed in addition to the reliability of the relevant way.

  29. Here I am indebted to Tim Williamson for helpful discussion.

  30. Some find a safety condition on knowledge controversial (cfr. Neta and Rohrbaugh 2004; Comesaña 2005; Bogardus 2014; Kelp 2016). But see Lasonen-Aarnio (2010) for a defense of a throughout modal account of knowledge.

  31. Cath (2015) only discusses one of Gibbons’ cases, the one involving Harry’s trying to kill his uncle. But the same consideration discussed in the text applies to Harry’s case too.

  32. For a more theoretical argument for thinking that intentional action is action based on knowledge, cfr. Hawthorne and Stanley (2008) and Williamson (2015).

References

  • Alston, W. (1974). Conceptual prolegomena to a psychological theory of intentional action. In S. Brown (Ed.), Philosophy of psychology (Vol. 7, pp. 1–101). New York: Harper & Row.

    Google Scholar 

  • Anscombe, G. E. M. (1957). Intention. Cambridge: Harvard University Press.

    Google Scholar 

  • Audi, R. (1973). Intending. The Journal of Philosophy, 70, 387–402.

    Google Scholar 

  • Audi, R. (1986). Intending, intentional action, and desire. In Joel Marks (Ed.), The ways of desire (pp. 17–38). Chicago: Precedent.

    Google Scholar 

  • Audi, R. (2017). On intellectualism in the theory of action. Journal of the American Philosophical Association, 3(3), 284–300.

    Google Scholar 

  • Bengson, J., & Moffett, M. (2011). Non-propositional intellectualism. In J. Bengson & M. Moffett (Eds.), Knowing how: Essays on knowledge, mind, and action. Oxford: Oxford University Press.

    Google Scholar 

  • Bengson, J., Moffett, M., & Wright, J. (2009). The folk on knowing how. Philosophical Studies, 142, 24–50.

    Google Scholar 

  • Bogardus, T. (2014). Knowledge under threat. Philosophy and Phenomenological Research, 88(2), 289–313.

    Google Scholar 

  • Brand, M. (1984). Intending and acting. Cambridge, MA: MIT Press.

    Google Scholar 

  • Bratman, M. (1987). Intention, plans, and practical reason. Stanford: Center for the Study of Language and Information.

    Google Scholar 

  • Brownstein, M., & Michaelson, E. (2016). Doing without believing: intellectualism, knowledge-how, and belief-attribution. Synthese, 193(9), 2815–2836.

    Google Scholar 

  • Burge, T. (2010). Origins of objectivity. Oxford: Oxford University Press.

    Google Scholar 

  • Carter, A., & Pritchard, D. (2015). Knowledge-how and epistemic luck. Noûs, 49(3), 440–453.

    Google Scholar 

  • Cath, Y. (2011). Knowing how without knowing that. In J. Bengson & M. Moffett (Eds.), Knowing how: Essays on knowledge, mind, and action. Oxford: Oxford University Press.

    Google Scholar 

  • Cath, Y. (2015). Revisionary intellectualism and gettier. Philosophical Studies, 172(1), 7–27.

    Google Scholar 

  • Chisholm, R. M. (1964). The descriptive element in the concept of action. The Journal of Philosophy, 61(20), 613–625.

    Google Scholar 

  • Comesaña, J. (2005). Unsafe knowledge. Synthese, 146(3), 395–404.

    Google Scholar 

  • Danto, A. C. (1965). Basic actions. American Philosophical Quarterly, 2(2), 141–148.

    Google Scholar 

  • Davidson, D. (1971). Agency. Reprinted in Davidson (1980) (pp. 43–61).

  • Davidson, D. (1973). Freedom to act. In T. Honderich (Ed.), Essays on freedom of action. London: Routledge.

    Google Scholar 

  • Davidson, D. (1980). Essays on actions and events. Oxford: Clarendon Press.

    Google Scholar 

  • Dennett, D. (1981). Intentional systems. In John Haugeland (Ed.), Mind design. Cambridge: Bradford Books.

    Google Scholar 

  • Dickie, I. (2012). Skill before knowledge. Philosophy and Phenomenological Research, 85(3), 737–745.

    Google Scholar 

  • Dretske, F. (1988). Explaining behavior. Cambridge: MIT Press.

    Google Scholar 

  • Gibbons, J. (2001). Knowledge in action. Philosophy and Phenomenological Research, 62(3), 579–600.

    Google Scholar 

  • Ginet, C. (1975). Knowledge, perception and memory. Boston: Reidel.

    Google Scholar 

  • Ginet, C. (1990). On action. Cambridge: Cambridge University Press.

    Google Scholar 

  • Glick, E. (2012). Abilities and know-how attributions. In J. Brown, & M. Gerken (Eds.), Knowledge Ascriptions (pp. 120–138). Oxford: Oxford University Press.

    Google Scholar 

  • Goldman, A. (1970). A theory of human action. Englewood Cliffs, NJ: Prentice Hall Inc.

    Google Scholar 

  • Goldman, A. (1976). Discrimination and perceptual knowledge. The Journal of Philosophy, 73(20), 771–791.

    Google Scholar 

  • Greco, J. (2016). Knowledge, virtue, and safety. In M. A. Fernández (Ed.), Performance epistemology. Oxford: Oxford University Press.

    Google Scholar 

  • Greco, D. (2016). Safety, explanation, iteration. Philosophical Issues, 26(1), 187–208.

    Google Scholar 

  • Harman, B. (1976). Practical reasoning. The Review of Metaphysics, 79, 431–463.

    Google Scholar 

  • Hawley, K. (2003). Success and knowledge how. American Philosophical Quarterly, 40(1), 19–31.

    Google Scholar 

  • Hawthorne, J. (2002). Deeply contingent a priori knowledge. Philosophy and Phenomenological Research, 65(2), 247–269.

    Google Scholar 

  • Hawthorne, J., & Stanley, J. (2008). Knowledge and action. Journal of Philosophy, 105(10), 571–590.

    Google Scholar 

  • Holton, R. (2009). Willing, wanting, waiting. Oxford: Oxford University Press.

    Google Scholar 

  • Hornsby, J. (2016). Intending, knowing how, infinitives. Canadian Journal of Philosophy, 46(1), 1–17.

    Google Scholar 

  • Hunter, D. (2012). Guidance and belief. In D. Hunter (Ed.), Belief and agency. Calgary: Calgary University Press.

    Google Scholar 

  • Kelp, C. (2016). Epistemic Frankfurt cases revisited. American Philosophical Quarterly, 53, 27–37.

    Google Scholar 

  • Lasonen-Aarnio, M. (2010). Unreasonable knowledge. Philosophical Perspectives, 24, 1–21.

    Google Scholar 

  • Levy, N. (2017). Embodied savoir-faire: Knowledge-how requires motor representations. Synthese, 194(2), 511–530.

    Google Scholar 

  • Lewis, D. (1974). Radical interpretation. Synthese, 27, 331–344.

    Google Scholar 

  • Lewis, D. (1982). Logic for equivocators. Noûs, 16(3), 431–441.

    Google Scholar 

  • Lewis, D. (Ed.) (1987). Causal explanation. In Philosophical papers (Vol. II). Oxford: Oxford University Press.

    Google Scholar 

  • Lewis, D. (1988). Relevant implication. Theoria, 54(3), 161–174.

    Google Scholar 

  • Lowenstein, D. (2017). Know-how as competence. A Rylean responsibilist account. Frankfurt am Main: Vittorio Klostermann.

    Google Scholar 

  • Manley, D. (2007). Safety, content, apriority, self-knowledge. The Journal of Philosophy, 104(8), 403–423.

    Google Scholar 

  • Marley-Payne, J. (2016). Action-first attitudes. Doctoral dissertation, MIT.

  • Marusic, B., & Schwenkler, J. (forthcoming). Intending is believing: A defense of strong cognitivism. Analytic Philosophy.

  • Mele, A. (1989). Intention, belief, and intentional action. American Philosophical Quarterly, 26(1), 19–30.

    Google Scholar 

  • Mele, A. (1992). Springs of action. New York: Oxford University Press.

    Google Scholar 

  • Mele, A., & Moser, P. (1994). Intentional action. Noûs, 28, 39–48.

    Google Scholar 

  • Moss, S. (2013). Epistemology formalized. Philosophical Review, 122(1), 1–43.

    Google Scholar 

  • Nagel, J. (2013). Knowledge as a mental state. Oxford Studies in Epistemology, 4, 275–310.

    Google Scholar 

  • Nanay, B. (2013). Between perception and action. Oxford: Oxford University Press.

    Google Scholar 

  • Neta, R., & Rohrbaugh, G. (2004). Luminosity and the safety of knowledge. Pacific Philosophical Quarterly, 85(4), 396–406.

    Google Scholar 

  • Noë, A. (2005). Against intellectualism. Analysis, 65(288), 278–290.

    Google Scholar 

  • Pavese, C. (2013). The unity and the scope of knowledge. Ph.D. dissertation, Rutgers University.

  • Pavese, C. (2015a). Knowing a rule. Philosophical Issues, 25(1), 165–188.

    Google Scholar 

  • Pavese, C. (2015b). Practical senses. Philosophers’ Imprint, 15(29), 1–25.

    Google Scholar 

  • Pavese, C. (2016). Skill in epistemology II. Philosophy Compass, 11(11), 650–660.

    Google Scholar 

  • Pavese, C. (2017a). Know-how and gradability. Philosophical Review, 126(3), 345–383.

    Google Scholar 

  • Pavese, C. (2017b). Appendix to ‘know-how and gradability’. Philosophical Review.

  • Pavese, C. (2017c). A theory of practical meaning. Philosophical Topics, 45(2), 85–116.

    Google Scholar 

  • Pavese, C. (forthcoming). The psychological reality of practical representation. Philosophical Psychology.

  • Peacocke, C. (1985). Intention and akrasia. In Bruce Vermazen & Merrill B. Hintikka (Eds.), Essays on Davidson. Oxford: Oxford University Press.

    Google Scholar 

  • Poston, T. (2009). Know how to be gettiered? Philosophy and Phenomenological Research, 79(3), 743–747.

    Google Scholar 

  • Pritchard, D. (2005). Epistemic luck. Oxford: Oxford University Press.

    Google Scholar 

  • Pritchard, D. (2012). Anti-luck virtue epistemology. Journal of Philosophy, 109(3), 247–279.

    Google Scholar 

  • Railton, P. (1981). Probability, explanation, and information. Synthese, 48(2), 233–256.

    Google Scholar 

  • Ryle, G. (1949). The concept of mind. London: Hutchinson.

    Google Scholar 

  • Setiya, K. (2012). Know-how. Proceedings of the Aristotelian Society, 112(3), 285–307.

    Google Scholar 

  • Snowdon, P. (2004). Knowing how and knowing that: A distinction reconsidered. In Proceedings of the aristotelian society (Vol. 104, No. 1). Oxford: Oxford University Press.

  • Sosa, E. (1999). How to defeat opposition to Moore. Philosophical Perspectives, 13, 141–153.

    Google Scholar 

  • Sosa, E. (2007). A virtue epistemology. Oxford: Clarendon Press.

    Google Scholar 

  • Sosa, E. (2015). Judgment and agency. Oxford: Oxford University Press.

    Google Scholar 

  • Stalnaker, R. (1984). Inquiry. Cambridge: The MIT Press.

    Google Scholar 

  • Stanley, J. (2011). Know how. Oxford: Oxford University Press.

    Google Scholar 

  • Stanley, J., & Krakauer, J. (2013). Motor skill depends on knowledge of facts. Frontiers in Human Neuroscience. https://doi.org/10.3389/fnhum.2013.00503.

    Article  Google Scholar 

  • Stanley, J., & Williamson, T. (2001). Knowing how. The Journal of Philosophy, 98(8), 411–444.

    Google Scholar 

  • Stanley, J., & Williamson, T. (2017). Skill. Noûs, 51(4), 713–726.

    Google Scholar 

  • Stich, S. (1978). Autonomous psychology and the belief-desire thesis. The Monist, 61(4), 573–591.

    Google Scholar 

  • Strevens, M. (2008). Depth: An account of scientific explanation. Cambridge: Harvard University Press.

    Google Scholar 

  • Thalberg, I. (1984). Do our intentions cause our intentional actions? American Philosophical Quarterly, 21(3), 249–260.

    Google Scholar 

  • Thompson, M. (2008). Life and action: Elementary structures of practice and practical thought. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.

    Google Scholar 

  • Williamson, T. (2015). Acting on knowledge. In J. A. Carter, E. C. Gordon, & B. Jarvis (Eds.), Knowledge first: Approaches in epistemology and mind (pp. 163–183). Oxford: Oxford University Press.

    Google Scholar 

  • Woodward, J. (2000). Explanation and invariance in the special sciences. The British Journal for the Philosophy of Science, 51(2), 197–254.

    Google Scholar 

Download references

Acknowledgements

I am grateful to Bob Beddor and Dan Greco for helpful discussions on topics related to this essay. This project also benefited from comments at the Copenhagen Epistemology Workshop and the Knowledge First Workshop at Cardiff. I am particularly grateful to Tim Williamson and Clayton Littlejohn for their comments in that occasion. The critical remarks of two anonymous referees have led to substantial improvements.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carlotta Pavese.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pavese, C. Know-how, action, and luck. Synthese 198 (Suppl 7), 1595–1617 (2021). https://doi.org/10.1007/s11229-018-1823-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-018-1823-7

Keywords

Navigation