Common Knowledge and Hinge Epistemology

ABSTRACT

Common knowledge is ubiquitous in our lives and yet there remains considerable uncertainty about how to model or understand it. Standard analyses of common knowledge end up being challenged by either regress or circularity which then give rise to well-known paradoxes of practical reasoning, such as the Two Generals’ Paradox. This paper argues that the nature and utility of common knowledge can be illuminated by appeal to Wittgenstein’s Hinge Epistemology. It is argued that those things that we standardly think of as being common knowledge in our lives are the same as those that Wittgenstein identified as hinge certainties. This identification of common knowledge with hinge certainties allows us to resolve the regress problem for common knowledge and explain how the Two Generals’ Paradox arises.

KEYWORDS:

• Common Knowledge
• The Generals’ Paradox
• Hinge Epistemology
• Ludwig Wittgenstein
• Collective Intentionality

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Although see Williams (2021) for a recent attempt to provide a formal grounding for Common Knowledge.

2. So as to avoid prejudging the issue, I shall refer to what are sometimes called ‘hinge propositions’ as ‘Hinge Certainties’.

3. It might be argued, in response, that beliefs can be understood as implicit or tacit rather than explicit (see, e.g. Schiffer 1972). If so, then the empirical untenability argument might not have the teeth it initially seems to, since the infinite array of beliefs would not have to be explicitly entertained. It would take us too far afield to discuss in detail here, but it is worth noting that the constructivist and interpersonal nature of the iterations – of beliefs stacked upon beliefs – could not straightforwardly be understood as implicit (see Wilby 2010 for discussion). Thanks to anonymous referee for raising this question.

4. This is another way of saying that the iterative approach to CK presupposes the generation of a ‘supertask’ (Manchak and Roberts 2016; Thomson 1954).

5. This way of setting it out is adapted from Lederman (2018).

6. An alternative approach – consistent with the one pursued in this paper – would be to reject (1) if one reads ‘common knowledge’ in its formal, iterative sense. That is to say, if one regards common knowledge as iterative by definition, then the argument in this paper would be consistent with rejecting (1) and arguing that CK is not necessary for coordinated attack (since Hinge Certainties can play that role). The official position that I shall pursue here, however, is that CK is firstly an informal concept about publicity; as such the official argument is to reject (3). Thanks to an anonymous reviewer for pushing me on this point.

7. The sceptical paradox: 1) I don’t know that I am not a Brain in a Vat; 2) If I don’t know that I am not a Brain in a Vat, then I don’t know I have hands; 3) I know I have hands (see DeRose 1999).

8. See Schonbaumsfeld (2016) who argues that supposing that Hinges are just ‘groundless’ epistemic states misleads because it suggests a ‘lack or … epistemic shortcoming’ (Schonbaumsfeld 2016, 101) where, for Wittgenstein, the possibility of error is logically ruled out.

9. See, for instance, the dispute between Wright (2002, 2008) and John McDowell (2008).

10. Greco is notably ambivalent about the proposal however (‘Should we … endorse the [CK account of Hinges]? I don’t feel confident in judging either way’ (Greco 2016, 252), and he endorses a more individualistic understanding of entitlements elsewhere (Greco 2021), comparing them to the procedural rules discussed in cognitive science and AI.

11. See also Allan Hazlett (2020) who draws out the respect in which, because claims to knowledge mark out salient differences in epistemic status, Common Knowledge about p would tend to make claims to knowledge that p superfluous, and hence make them seem false. Hazlett put this observation to use in trying to explain away the Wittgensteinian intuition that Moorean propositions are not known. For Hazeltt, they are known, but their status as common knowledge makes it inappropriate to say so, and hence makes it seem that they are false, when they are not.

12. For comparison, see John Searle (1990) on collective intentions.

13. It is worth noting that there are other options that one could take in this area. For instance, Axel Seemann argues that the kind of regress that gives rise to the Two Generals’ Paradox can be resolved by appeal to an underlying enactivism that is more basic still than a personal-level perceptual state (see Seemann 2024). Nevertheless, such an approach – if understood along the lines of Moyal-Sharrock’s enactivism –

might still have difficulties accounting for the epistemic powers of what is commonly known (see Wilby 2020 for discussion). For overviews on the relation between individual cognition and collective cognition, see Jankovic and Ludwig (2016) or Schweikard and Schmid (2020). Thanks to an anonymous reviewer for asking me to address these points.

14. It might be more accurate to see individual (subjective) certainty as the narrow counterpart of the wide state of knowledge.

15. Moyal-Sharrock (2007a, 101–104) provides a four-way taxonomy of hinges as linguistic, personal, local, and universal. The above distinction maps broadly onto the local/universal distinction in Moyal-Sharrock’s taxonomy, with Linguistic Hinges having a place within the Background. Personal Hinges might need to be dealt with separately and are discussed below.

16. ‘Imagine a language game “When I call you, come in through the door”. In any ordinary case, a doubt whether there really is a door there would be impossible’ (OC 391).

17. On a Non-Epistemic view these certainties would be what Moyal-Sharrock calls ‘animal certainties’, part of our hard-wired neurological genetic inheritance, perhaps, and not a cognitive (or epistemic) achievement at all. However, this underplays, I think, Wittgenstein’s remark that the certainties that underpin our practices are held in place, and take the form that they do, because of the ‘activity that surrounds them’ (OC 152).

18. As indeed it doesn’t for Descartes’ Cogito.