Abstract
The goal of the current paper is to provide an introduction to and survey of the diverse landscape of relevant alternatives theories of knowledge. Emphasis is placed throughout both on the abstractness of the relevant alternatives approach and its amenability to formalization through logical techniques. We present some of the important motivations for adopting the relevant alternatives approach; briefly explore the connections and contrasts between the relevant alternatives approach and related developments in logic, epistemology and philosophy of science; provide a schema for classifying and studying relevant alternatives theories at different levels of abstraction; and present a sample of relevant alternatives theories (contrasting what we call question-first and topic-first theories) that tie our discussion to ongoing debates in the philosophical literature, as well as showcasing techniques for formalizing some of the important positions in these debates.
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- 1.
For this paper, we set aside the tricky question as to in what sense circumstances that are necessarily the case or not the case (such as Goldbach’s conjecture) can be thought to have alternatives – at least for the purposes of inquiry.
- 2.
Note that in Sect. 7.2.9 we discuss a tradition in the epistemology literature that focuses on a notion of “epistemic relevance” that arises from initial concerns quite distinct from those of the RA theorist. The overlapping terminology is no doubt a potential source for confusion, though hopefully not in the current paper.
- 3.
Throughout this section, the critical reader may well want to emphasize the use of the word appearance here in the absence of a proper empirical investigation of these purported linguistic facts.
- 4.
Our ordinary infallibilist tendencies have in fact been used as a weapon in internal debates among RA theorists, suggesting the possibility that some versions of RA theory are better suited to account for these tendencies than others. For instance, DeRose (1995) influentially criticizes Dretske’s version of RA theory as incorrectly predicting that so-called abominable conjunctions – notably “S knows that she has hands and S does not know that she is a handless brain-in-vat” – are felicitous in ordinary conversational contexts.
- 5.
Of course, this may be taken as further linguistic data, in the spirit of that from Sect. 7.2.1.
- 6.
Note that the barn case can be seen to teach a similar lesson to consideration of cartesian skepticism: that one can know something even though one has not ruled out all alternatives. However, the barn case potentially teaches us something more: that what counts as a relevant alternative can vary with the circumstances: the possibility of fake barns may be properly ignored, by knowledge ascribers, under one set of circumstances, but is not properly ignored in another.
- 7.
For a more careful defence of the ‘alternatives’ approach to capturing the relevant parameter that shifts across contexts, see Schaffer (2005b).
- 8.
The reader will note that we make no mention of a notion of ‘context’ anywhere in this semantics. We gloss over the role of context, as follows: context may be thought of as settling the valuation V and, potentially, the set of relevant alternatives R w . Thus, context may be thought of as settling the model in question. We do not explore this thought in any detail here.
- 9.
It also goes some way towards capturing Lewis’ notion of ruling out (Lewis 1996): for him, A is ruled out just in case it holds at no possible world in which the agent has the same memories and sensory experience.
- 10.
We may want to place Dretske and Nozick in this camp too.
- 11.
For recall that we self-consciously model the knowledge of an ideal agent that is always able to “put two and two together” and can therefore maximally extend her knowledge by way of reasoning. To deny of such an agent that closure under known implication is valid is to deny that we ordinary agents are always in principle able to extend our knowledge using self-conscious deductive reasoning by way of known implications.
- 12.
- 13.
We mention in footnotes some divergences from important details of Yablo’s theory as we proceed.
- 14.
Yablo in fact embraces a more general conception of a topic: for him, a topic can be associated with a reflexive, symmetric relation on the space of worlds, as opposed to an equivalence relation.
- 15.
Here we see another divergence from Yablo. For Yablo, the subject matter associated with \(\varphi\) is the set of ways that \(\varphi\) could be true and the ways it could be false. More precisely: it is the set of (what Yablo calls) the minimal partial models that succeed in either making \(\varphi\) true or \(\varphi\) false. The reader interested in a proper explication of these notions is directed to Yablo (2014).
- 16.
We depart from Yablo here as follows: for Yablo, elimination of alternatives is inspired by the “tracking” account of Nozick: A is eliminated just in case the agent believes \(\neg A\) and were A to be the case, the agent would not believe \(\neg A\). Despite this change in perspective, the technical details for Yablo’s account and our own are similar in many respects.
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Acknowledgements
I wish to thank Johan van Benthem and Krista Lawlor for much useful discussion during the development of material in this paper. Thanks for Chenwei Shi and an anonymous referee for many helpful comments based on a close reading of an earlier draft of this paper.
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Hawke, P. (2016). Relevant Alternatives in Epistemology and Logic. In: Redmond, J., Pombo Martins, O., Nepomuceno Fernández, Á. (eds) Epistemology, Knowledge and the Impact of Interaction. Logic, Epistemology, and the Unity of Science, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-26506-3_7
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