# Is there a neutral metalanguage?

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## Abstract

Logical pluralists are committed to the idea of a neutral metalanguage, which serves as a framework for debates in logic. Two versions of this neutrality can be found in the literature: an agreed upon collection of inferences, and a metalanguage that is neutral as such. I discuss both versions and show that they are not immune to Quinean criticism, which builds on the notion of meaning. In particular, I show that (i) the first version of neutrality is sub-optimal, and hard to reconcile with the theories of meaning for logical constants, and (ii) the second version collapses mathematically, if rival logics, as object languages, are treated with charity in the metalanguage. I substantiate (ii) by proving a collapse theorem that generalizes familiar results. Thus, the existence of a neutral metalanguage cannot be taken for granted, and meaning-invariant logical pluralism might turn out to be dubious.

## Keywords

Logical pluralism Meaning Quine Collapse## Notes

## References

- Beall, J. C., & Murzi, J. (2013). Two flavors of Curry’s paradox.
*The Journal of Philosophy*,*110*(3), 143–165.CrossRefGoogle Scholar - Beall, J. C., & Restall, G. (2006).
*Logical pluralism*. Oxford: Oxford University Press.Google Scholar - Blok, W. J., & Pigozzi, D. (2001). Abstract algebraic logic and the deduction theorem. Manuscript. http://orion.math.iastate.edu:80/dpigozzi/.
- Brandom, R. B. (2008).
*Between saying and doing: Towards ananalytic pragmatism*. Oxford, NY: Oxford University Press.CrossRefGoogle Scholar - Cerro, D., Farinas, L., & Herzig, A. (2013). Combining classical and intuitionistic logic, or Intuitionistic implication as a conditional. In F. Baader & K. U. Schulz (Eds.),
*Frontiers of combining systems: First international workshop, Munich, March 1996*(Vol. 3). Berlin: Springer Science & Business Media.Google Scholar - Davidson, D. (1984). On the very idea of a conceptual scheme. In D. Davidson (Ed.),
*Proceedings and addresses of the American philosophical association: 183–198*. Oxford: Oxford University Press.Google Scholar - Dicher, B. (2016a). Weak Disharmony: Some lessons for proof-theoretic semantics.
*The Review of Symbolic Logic*,*9*(3), 583–602.CrossRefGoogle Scholar - Dicher, B. (2016b). A proof-theoretic defence of meaning-invariant logical pluralism.
*Mind*,*125*(499), 727–757.CrossRefGoogle Scholar - Dicher, B (2018). Hopeful monsters: A note on multiple conclusions.
*Erkenntnis*. https://doi.org/10.1007/s10670-018-0019-3. - Dummett, M. A. E. (1978).
*Truth and other enigmas*. Cambridge, MA: Harvard University Press.Google Scholar - Dummett, M. A. E. (1991).
*The logical basis of metaphysics*. Cambridge: Harvard University Press.Google Scholar - Field, H. (2009). Pluralism in logic.
*The Review of Symbolic Logic*,*2*(02), 342–359.CrossRefGoogle Scholar - Font, J. M., Jansana, R., & Pigozzi, D. (2003). A survey of abstract algebraic logic.
*Studia Logica*,*74*(1), 13–97.CrossRefGoogle Scholar - Gabbay, D. M. (1996). An overview of fibred semantics and the combination of logics. In D. M. Gabbay & F. Guenthner (Eds.),
*Frontiers of combining systems*(pp. 1–55). Berlin: Springer.Google Scholar - Hewitt, C. (2008).
*Large-scale organizational computing requires unstratified reflection and strong paraconsistency*(pp. 110–124). Berlin: Springer.Google Scholar - Hjortland, O. T. (2012). Harmony and the context of deducibility. In C. D. Novaes & O. Hjortland (Eds.), Insolubles and consequences: Essays in honour of Stephen Read. New York: College Publications.Google Scholar
- Hjortland, O. T. (2013). Logical pluralism, meaning-variance, and verbal disputes.
*Australasian Journal of Philosophy*,*91*(2), 355–373.CrossRefGoogle Scholar - Humberstone, L. (2011).
*The Connectives*. Cambridge, MA: MIT Press.CrossRefGoogle Scholar - Kleene, S. C. (1938). On notation for ordinal numbers.
*The Journal of Symbolic Logic*,*3*(12), 150–155.CrossRefGoogle Scholar - Prawitz, D. (1979).
*Proofs and the Meaning and completeness of the logical constants*(pp. 25–40). Dordrecht: Springer.Google Scholar - Priest, G. (1979). The logic of paradox.
*Journal of Philosophical Logic*,*8*(1), 219–241.CrossRefGoogle Scholar - Priest, G. (2003). On alternative geometries, arithmetics, and logics: A tribute to Lukasiewicz.
*Studia Logica*,*74*(3), 441–468.CrossRefGoogle Scholar - Priest, G. (2006).
*Doubt truth to be a liar*. Oxford: Oxford University Press.Google Scholar - Quine, W. V. (1986).
*Philosophy of logic*. Harvard: Harvard University Press.Google Scholar - Rasiowa, H. (1974).
*An algebraic approach to non-classical logics. Studies in logic and the foundations of mathematics*(1st ed., Vol. 78). Amsterdam: North-Holland Publishing Company.Google Scholar - Read, S. (1994). Formal and material consequence.
*Journal of Philosophical Logic*,*23*(3), 247–265.CrossRefGoogle Scholar - Read, S. (2000). Harmony and autonomy in classical logic.
*Journal of Philosophical Logic*,*29*(2), 123–54.CrossRefGoogle Scholar - Read, S. (2006). Monism: The one true logic. In D. de Vidi & T. Kenyon (Eds.),
*A logical approach to philosophy*(pp. 193–209). Berlin: Springer.CrossRefGoogle Scholar - Read, S. (2010). General-elimination harmony and the meaning of the logical constants.
*Journal of Philosophical Logic*,*39*(5), 557–576.CrossRefGoogle Scholar - Ryle, G. (2009).
*Collected essays 1929–1968: Collected papers*(Vol. 2). Abingdon: Routledge.CrossRefGoogle Scholar - Shapiro, S. (2011).
*Varieties of pluralism and relativism for logic*(pp. 526–552). London: Wiley.Google Scholar - Shapiro, S. (2014).
*Varieties of logic*. Oxford: Oxford University Press.CrossRefGoogle Scholar - Sher, G. (1991).
*The bounds of logic: A generalized viewpoint*. Cambridge: MIT Press.Google Scholar - Tarski, A. (1946).
*Introduction to logic and to the methodology of deductive sciences*. Mineola: Dover Publications.Google Scholar - Weber, Z., Badia, G., & Girard, P. (2016). What is an inconsistent truth table?
*Australasian Journal of Philosophy*,*94*(3), 533–548.CrossRefGoogle Scholar - Williamson, T. (2014). Logic, metalogic and neutrality.
*Erkenntnis*,*79*(2), 211–231.CrossRefGoogle Scholar