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Inferential Constants

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Abstract

A metainference is usually understood as a pair consisting of a collection of inferences, called premises, and a single inference, called conclusion. In the last few years, much attention has been paid to the study of metainferences—and, in particular, to the question of what are the valid metainferences of a given logic. So far, however, this study has been done in quite a poor language. Our usual sequent calculi have no way to represent, e.g. negations, disjunctions or conjunctions of inferences. In this paper we tackle this expressive issue. We assume some background sentential language as given and define what we call an inferential language, that is, a language whose atomic formulas are inferences. We provide a model-theoretic characterization of validity for this language—relative to some given characterization of validity for the background sentential language—and provide a proof-theoretic analysis of validity. We argue that our novel language has fruitful philosophical applications. Lastly, we generalize some of our definitions and results to arbitrary metainferential levels.

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Acknowledgements

The ideas included in this article were presented to the audiences of the X Workshop on Philosophical Logic (Buenos Aires, 2021), the Oberseminar Logik und Sprachtheorie (Tuebingen, 2021) and the Buenos Aires Logic Group WIP Seminar (Buenos Aires, 2021), to which we are grateful for their feedback. We are specially thankful to Eduardo Barrio, Bruno Da Ré, Bodgan Dicher, Thomas Ferguson, Andreas Fjellstad, Rea Golan, Elio La Rosa, Isabella McAllister, Dave Ripley, Ariel Roffé, Lucas Rosenblatt, Peter Schroeder-Heister, Damián Szmuc, Paula Teijeiro, Joaquín Toranzo Calderón, Luca Tranchini and the members of the Buenos Aires Logic Group. Also, we would like to thank an anonymous reviewer of this journal for their valuable comments. While writing this paper, Federico Pailos enjoyed a Humboldt Research Fellowship for experienced researchers (March 2020 to July 2021)

Funding

During the preparation of this paper, Federico Pailos enjoyed a Humboldt Research Fellowship for Experienced Researchers (March 2020 to July 2021); also, Federico Pailos, Mariela Rubin and Camillo Fiore were supported by CONICET and the University of Buenos Aires.

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  1. UBA / IIF-SADAF-CONICET, Bulnes 642, Buenos Aires, Argentina

    Camillo Fiore, Federico Pailos & Mariela Rubin

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  1. Camillo Fiore
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  2. Federico Pailos
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  3. Mariela Rubin
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The author report the work was divided as follows: 33% Camillo Fiore, 33% Federico Pailos 33% Mariela Rubin. Availability of data and materials: Not applicable.

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Correspondence to Camillo Fiore.

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Fiore, C., Pailos, F. & Rubin, M. Inferential Constants. J Philos Logic 52, 767–796 (2023). https://doi.org/10.1007/s10992-022-09687-z

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