Corine Besson (University of Oxford) won an Arché Postgraduate competition for best paper on the
Basic Knowledge Project. In this weekend's Basic Knowledge Workshop she gave her talk, entitled 'Logical Knowledge and Gettier Cases', in front of an audience partly made up by the impressive list of invited speakers:
John Hawthorne 'Epistemic Modals'
Martin Davies '
Two Purposes of Arguing and Two Epistemic Projects'
Duncan Pritchard '
Knowledge and Value'
Timothy Williamson 'Knowing When You Probably Don't'
Jason Stanley 'Knowledge and Certainty'
Although there was certainly enough post-worthy talks (and responses) at the workshop, I've chosen to write about Besson's paper. Not only was the talk quite impressive, it also helped me find some crucial connections between my own work with proof-theoretic semantics and more or less free-floating epistemological considerations I've been entertaining about logic. One Quinean concession is called for immediately: I'm certainly no champion of epistemology, meaning that not only do I have many half-digested beliefs about epistemological problems, but hopefully I also still have some pre-theoretic intuitions left (although nothing rests on this). So, I cannot pretend to give full justice to the epistemological debate that Besson's paper touches on - I'll more or less confine myself to presenting the basics of her talk, and then relating it to some issues in the philosophy of logic. I also want to mention briefly that Elia Zardini gave a brilliant response to Besson, emphasizing several of the worries that I myself had with the argument. I hope to outline some of these thoughts as well, with appropriate acknowledgement of Elia's six page handout(!).
Here is the aim of Besson's paper as formulated in the handout: "Show that the possibility of constructing Gettier cases for the a priori knowledge of logical rules refutes what I call the 'Understanding Account' - according to which a priori knowledge of a basic rule of logic is grounded on semantic or conceptual understanding."
I'll just assume that my readers are familiar with Gettier cases, and focus on the speical case of Gettiered logical knowledge. First, however, let me briefly say something about the so-called Understanding Account (UA). UA appears in the talk as a rather broad position (as many of the commentators pointed out), and it is associated with philosophers such Boghossian, Peacocke, Wright and Hale. A good place to look up the details of their positions would be the following volume on the A Priori,
New Essays on the A Priori, eds. Boghossian & Peacocke. The central claim that Besson attaches to this position is from Boghossian: 'A statement is 'true by virtue of its meaning' provided that grasps of its meaning alone suffices for justified belief in its truth.' ('Analyticity Reconsidered',
Noûs 30, 1996: p. 363. An aside: Carrie Jenkins has a new paper on Boghossian
here.). This paper is a famous attempt at revitalizing the notion of analyticity after the Quinean onslaught. The above claim, however, attaches these considerations about meaning and analyticity directly to epistemic concepts, i.e., justified belief and understanding. When applied to logic, the idea is that grasping some logical
rules is sufficient for having a priori knowledge that they're valid. Unsurprisingly, the rules thought to display this epistemic property are the so-called
meaning-conferring rules, say, introduction-rules for classical connectives, e.g., implication-introduction. Besson's wants to show that by introducing an element of luck, also logical cases of this can be Gettiered so as to take apart knowledge (in this case apriori) from true, justified belief.
Here is the example reworked in my words. Say that two language users, Jean-Yves and Alfred, have a conversation about logic. It turns out that Alfred has no notion of material implication, so Jean-Yves sets out to help him with the concept. However, being something of a trickster, Jean-Yves wants to have some fun with Alfred: introducing the material implication by perverted rules, say rules that allow for affirming the consequent. But, as luck would have it, the proverbial "strange atmospheric conditions" interfere so that when Jean-Yves presents his perverse rules, what he actually gives Alfred is the correct rules for material implication. Now, on the Gettier analysis, the idea is that Alfred, going on to use material implication to everyone's satisfaction (well, perhaps not to Jean-Yves's, the trickster's, satisfaction) has a true, justified belief, but it still isn't knowledge. The intuition is, I gather, that just minor changes to the situation (i.e., in a close world with normal atmospheric conditions) would have led to Alfred applying the perverse rules, thus failing to grasp the concept.
What is the upshot if the Gettier example goes through? The UA is Gettiered in the sense that the example puts a wedge in between justification and knowledge: grasping the rule isn't sufficient for knowledge, it's only sufficient for justification. Let me couch this in langauge a bit closer to my own my own field of study. The idea advocated by for example Dummett and Prawitz was that the introduction-rules had a special status; not only did they confer meaning to the involved logical constant, since they had this definitorial feature they were also
self-justificatory. Although Dummett never wrote explicitly about these epistemological issues, it seems fair to assume that he would assent to expanding this talk into talk about
subjective justification, that is, if someone grasps the self-justificatory rule she/he has immediate justification. If anyone has references to passages where Dummett talks directly about knowledge of logic in this context, I would be glad to know. Because, undoubtedly, there is a temptation to go on to claim that the self-justificatory nature of the rule makes it a candidate for a priori
knowledge. It is this move, however, that is denied by Besson.
To evaluate precisely how Besson's point affects UA is not all that easy. In fact, as I myself suspected, and Elia pointed out in the response, it is not all clear that the proponents of UA are at talking about knowledge; most of the discussion turns around justification (Elia also adds, or entitlement). Granted, for all I know the discussion by Boghossian et al. might be confused on whether or not knowledge is involved, but perhaps they can recourse to just claiming that justification is what they want. The important point for me to make, at any rate, is that for proof-theoretic semantics, nothing obviously hinges on knowledge. For both inferentialism and the larger project of a proof-theoretic account of logical consequence, it suffices that our grasping of the rules is tied up with justification (what has been at stake has always been 'justification of deduction', not 'knowledge of deduction'). By attaching these logical concepts to justification (or entitlement), the prospect is that we end up with a semantics sensitive to the connection between epistemology and language - precisely what Dummett worried that the classical account lacked (I'm thinking about manifestation and aquisition here).
Furthermore, both Elia and John Hawthorne stressed that Besson's argument failed to make some important distinctions between knowing-that and knowing-how, or more precisely, belief in a logical statement and behaviour according to a logical practice. It is unclear that logical knowledge could consist in anything else than the type of competence that Alfred, in the above example, undeniably displays after grasping the rules. If such distinctions could be employed to refute Besson's argument, then perhaps UA propoenents and, thus, proof-theoretic semanticists could incorporate knowledge of logic into their theory after all.
As a final remark, I think it is decisive to appreciate that for proof-theoretic semantics, the notion of proof is first and foremost a justificatory notion, and only secondly related to knowledge.
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