X Workshop on Philosophical Logic:
August 5, 6 2021
Saul Kripke Center, CUNY
Online Conference via ZOOM Meetings
Natalia Buacar (University of Buenos Aires)
Melvin Fitting (The City University of New York)
Anandi Hattiagadi (Stockholm University)
Romina Padró (The City University of New York)
Jillian Rose Roberts (The City University of New York)
Olivia Sultanescu (University of Chicago)
Peter Susanszky (The City University of New York)
“What logic can (not) do for us”
The adoption problem (AP) arises from assuming (among other things) that the role of logical principles is to guide our inferential practices. AP is proposed as a reductio. What AP shows is, in Padró’s version, that if such a role is assumed for logical principles, then knowing and learning those principles is impossible. In Kripke’s version, what is impossible is the revision of logic. In this talk, I will offer additional reasons against adscribing such a guiding role to logical principles. Additionally, I will present an alternative view on the role of logical principles compatible with the possibility of learning, teaching and revising logic.
“A Logic Not Exactly Adopted”
The problems of adopting a logic have received significant recent attention. Less noted is the fact that, for almost all logicians, the logic they adopted and the formal system they take as representing it do not match. This is well-known, and largely ignored. The present work explores rather than ignores.
“Deductive Reasoning without Rule-Following”
According to a widely held view, deductive reasoning necessarily involves rule-following. In this paper, we present an objection to this view that is inspired by the ‘adoption problem’ that Kripke puts forward in ‘The Question of Logic’. Though Kripke’s official target in this paper is the anti-exceptionalism about logic associated with Putnam and Quine, we argue that this problem has a broader significance, and that one of the lessons that can be drawn from it is that it must be possible to reason deductively without following rules. Finally, we sketch a picture of how this is possible. This work is co-authored with Corine Besson, University of Sussex.
Logic: Unapologetically (Super) Special
Though there has been considerable discussion recently on the Adoption Problem itself, the issue of whether and how exactly it can be taken to challenge so-called ‘anti-exceptionalist’ views about logic remains unclear. I will propose a way of understanding this challenge that appeals to the self-supporting character of certain basic logical principles – central to the Adoption Problem – and argue that it not only sets logic apart from the natural sciences, but also from disciplines traditionally regarded as firm candidates for a priori knowledge, such as mathematics.
Jillian Rose Roberts:
“The Adoption Problem in Logic: Devitt’s Flawed Quinean Solution”
Can we adopt a new logic? If so, how? In unpublished talks, Saul Kripke has presented a certain message about this that Romina Padró has vigorously defended in What the Tortoise Said to Kripke—the Adoption Problem (2015). Padró contends certain basic logical principles cannot be adopted: “if a subject already infers in accordance with basic logical principles, no adoption is needed, and if the subject does not infer in accordance with them, no adoption is…possible.” Michael Devitt has taken up Kripke and Padró’s challenge in an unpublished paper, “The Adoption Problem in Logic: A Quinean Picture” (2016). Devitt argues for a Quinean solution to the adoption problem, concluding it is possible in principle for someone who does not reason by basic inferences to come to do so as a result of adopting the basic logical principles and training. I simply ask—does his solution work? I contend that Devitt’s attempted solution is critically flawed in a way that sheds new light on the problem.
“Inference without rules”
The ‘adoption problem’ purports to challenge the view according to which a thinker’s ability to reason is grounded in her previous acceptance of a basic inferential principle. It does this by revealing that it is not possible to adopt—and thus not possible to follow—basic inferential principles. In response to this challenge, it might seem that we have no choice but to think that inferential principles play no role in reasoning; if we don’t follow inferential principles, the best we can do is say that our reasoning happens to conform to such principles, or so the thought goes. In this paper, I offer a very rough sketch of an alternative view that respects the lesson that the ‘adoption problem’ conveys, namely, that inferential principles cannot intelligibly be viewed as rules that thinkers follow, but which does this without relinquishing the constitutive role they play in our thinking.
“Trying to Adjunct Without Knowing How: Adjunction and the Adoption Problem”
Adopting a logical rule is coming to infer in accordance with it in virtue of accepting it as correct. The adoption question asks whether it is always possible to adopt a logical rule if one does not already infer in accordance with it, and if not, which rules cannot be adopted this way. Picking up on previous work by Saul Kripke, Romina Padró argued that there are such unadoptable rules. Though the two rules which have taken center stage in the discussions of both Kripke and Padró are modus ponens (MP) and universal generalization (UI), they both hold that adjunction (AD) is also unadoptable. Pace Kripke and Padró, in a recent paper, Suki Finn argued that AD is not in the scope of the adoption problem. In the negative part of my talk, I will demonstrate how Finn’s arguments fail to show AD to be adoptable. In the positive part, I will elaborate on the reasons why AD is unadoptable, which will, in turn, shed light on the source of the adoption problem.
We are thankful for the support provided by CONICET and MINCYT