The Different Ways in which Logic is (said to be) Formal

History and Philosophy of Logic 32 (4):303 - 332 (2011)
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Abstract

What does it mean to say that logic is formal? The short answer is: it means (or can mean) several different things. In this paper, I argue that there are (at least) eight main variations of the notion of the formal that are relevant for current discussions in philosophy and logic, and that they are structured in two main clusters, namely the formal as pertaining to forms, and the formal as pertaining to rules. To the first cluster belong the formal as schematic; the formal as indifference to particulars; the formal as topic-neutrality; the formal as abstraction from intentional content; the formal as de-semantification. To the second cluster belong the formal as computable; the formal as pertaining to regulative rules; the formal as pertaining to constitutive rules. I analyze each of these eight variations, providing their historical background and raising related philosophical questions. The significance of this work of ?conceptual archeology? is that it may enhance clarity in debates where the notion of the formal plays a prominent role (such as debates where it is expected to play a demarcating role), but where it is oftentimes used equivocally and/or imprecisely

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Catarina Dutilh Novaes
VU University Amsterdam

Citations of this work

The Normativity of Kant's Logical Laws.Jessica Leech - 2017 - History of Philosophy Quarterly 34 (4).
The Foundational Problem of Logic.Gila Sher - 2013 - Bulletin of Symbolic Logic 19 (2):145-198.
Mathematical Inference and Logical Inference.Yacin Hamami - 2018 - Review of Symbolic Logic 11 (4):665-704.

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References found in this work

Introduction to Metamathematics.Stephen Cole Kleene - 1952 - Princeton, NJ, USA: North Holland.
Change in View: Principles of Reasoning.Gilbert Harman - 1986 - Cambridge, MA, USA: MIT Press.
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
What Are Logical Notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.

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