Logical Studies

On the interdefinability of weak and strict full ground

Document Type : Research

Author

Davood Hosseini

Associate Professor, Department of Philosophy and Logic, Tarbiat Modares University, Tehran, Iran

10.30465/lsj.2023.45054.1433
Abstract
Abstract: Kit Fine developed a logic for different concepts of ground: weak full ground, weak partial ground, strict full ground, and strict partial ground. He claimed that one can define all other concepts of ground in terms of weak full or strict full ground. Particularly, he claimed that weak and strict full ground are inter-definable. He proposed the definitions as follows: strict full ground is irreversible weak full and weak full ground is nothing but preservation of strict full ground. Here, I argue that this interdefinability claim has problems. I first discriminate between two non-equivalent criteria for interdefinability: that some appropriate biconditionals are theorems of certain formal systems and that there are two formal systems for the two concepts in each of which the logical behavior of the other concept can be manifested. Then, I argue that based on these interdefinability criteria at least one of Fine’s proposed definitions fails. The conclusion is disjunctive: either there are other unknown definitions for these two concepts of ground in terms of each other or these two concepts are primitive.

Keywords

strict full ground
weak full ground
interdefinability
  1. Blanchette, P. (2018). The Frege-Hilbert Controversy, The Stanford Encyclopedia of Philosophy, (Fall 2018 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/fall2018/entries/frege-hilbert/
  2. deRosset, L. (2014). On weak ground. The Review of Symbolic Logic, 7(4), 713-744. https://doi.org/10.1017/S1755020314000306
  3. deRosset, L. (2015). Better Semantics for the Pure Logic of Ground. Analytic Philosophy, 56(3), 229-252. https://doi.org/10.1111/phib.12065
  4. Fine, K. (2012a). The pure logic of ground. The Review of Symbolic Logic, 5(1), 1–25. https://doi.org/10.1017/S1755020311000086
  5. Fine, K. (2012b). Guide to ground. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding: understanding the structure of reality (pp. 37–80). Cambridge: Cambridge University Press.
  6. Gentzen, G. (1969). Investigations Concerning Logical Deduction. In M. Szabo (Ed.), The Collected Papers of Gerhard Gentzen (pp.68–131). Amsterdam: North-Holland Publishing Company.
  7. Hosseini D. (2022). A Note on Fine’s Logic of Ground. Philosophical Thought, 2(1):1-8. (In Persian)

Poggiolesi, F. (2020). Logics. In M. J. Raven (Ed.), The Routledge Handbook of Metaphysical Grounding (pp. 213-227). London: Routledge.

Logical Studies
Volume 13, Issue 2 - Serial Number 2
February 2023
Pages 71-85

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