The Normative Autonomy of Logic
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The Normative Autonomy of Logic Diego Tajer1,2 Received: 29 December 2018 / Accepted: 3 September 2020 © Springer Nature B.V. 2020
Abstract Some authors have called into question the normativity of logic, using as an argument that the bridge principles for logical normativity (MacFarlane, In what sense (in any) is logic normative for thought, 2004)? are just by-products of general epistemic principles for belief. In this paper, I discuss that suggestion from a formal point of view. I show that some important bridge principles can be derived from usual norms for belief. I also describe some possible ways to block this derivation by modifying the epistemic norms or weakening the bridge principles. Finally, I discuss different philosophical interpretations of these results.
1 Introduction The problem of the normativity of logic has caught the attention of many philosophers of logic in the last decades. The problem itself is not easy to grasp, since the concept of normativity is also a matter of discussion. In general, I will take the main question on this debate to be ‘does logic impose specific norms over and above general epistemic norms (such as believing the truth or avoiding falsity)?’ Some authors are skeptical regarding this issue. In particular, Harman (1986) has famously argued that logic is not intrinsically related to our norms of reasoning. According to Harman, reasoning is dynamic, and based on principles of relevance, revision, and contraction; while logic is accumulative, with no place for revision or for practical considerations. In particular, asking people to believe the logical consequences of their beliefs is often incorrect. MacFarlane responded to Harman’s challenge by providing a more adequate theory about the normativity of logic. He developed a set of candidate ‘bridge principles’; i.e. principles which link logical facts to epistemic requirements. A bridge principle has the form ‘if φ1 , . . . , φn logically imply ψ, then [specific epistemic demand or
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Diego Tajer [email protected]
1
IIF-SADAF-CONICET, Bulnes 642, Buenos Aires, Argentina
2
University of Buenos Aires, Puan 480, Buenos Aires, Argentina
123
D. Tajer
permission]’, but its specific structure depends on many factors. For example, a bridge principle might say ‘If φ1 , . . . , φn imply ψ, and you believe φ1 , . . ., and φn , then you ought to believe ψ’. As we will see in the next section, MacFarlane believes that some bridge principles are not affected by Harman’s objections. The aim of this paper is to analyze a special topic in this debate. Kolodny (2007) observed that some apparent formal requirements of logical coherence can be explained by general epistemic principles about evidence. For example, suppose that you accept the general epistemic principle (E): ‘There is sufficient reason to believe that p only if the evidence indicates that p more strongly than it indicates that ¬ p’. Then there will be something wrong with believing p and ¬ p, for the evidence cannot indicate p more strongly than ¬ p and vice versa
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