Topics in Philosophical Logic

Dissertation, Harvard (2012)
  Copy   BIBTEX

Abstract

In “Proof-Theoretic Justification of Logic”, building on work by Dummett and Prawitz, I show how to construct use-based meaning-theories for the logical constants. The assertability-conditional meaning-theory takes the meaning of the logical constants to be given by their introduction rules; the consequence-conditional meaning-theory takes the meaning of the logical constants to be given by their elimination rules. I then consider the question: given a set of introduction rules \, what are the strongest elimination rules that are validated by an assertability conditional meaning-theory based on \? I prove that the intuitionistic introduction rules are the strongest rules that are validated by the intuitionistic elimination rules. I then prove that intuitionistic logic is the strongest logic that can be given either an assertability-conditional or consequence-conditional meaning-theory. In “Grounding Grounding” I discuss the notion of grounding. My discussion revolves around the problem of iterated grounding-claims. Suppose that \ grounds \; what grounds that \ grounds that \? I argue that unless we can get a satisfactory answer to this question the notion of grounding will be useless. I discuss and reject some proposed accounts of iterated grounding claims. I then develop a new way of expressing grounding, propose an account of iterated grounding-claims and show how we can develop logics for grounding. In “Is the Vagueness Argument Valid?” I argue that the Vagueness Argument in favor of unrestricted composition isn’t valid. However, if the premisses of the argument are true and the conclusion false, mereological facts fail to supervene on non-mereological facts. I argue that this failure of supervenience is an artifact of the interplay between the necessity and determinacy operators and that it does not mean that mereological facts fail to depend on non-mereological facts. I sketch a deflationary view of ontology to establish this

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Grounding Grounding.Jon Litland - 2017 - Oxford Studies in Metaphysics 10.
Harmony and autonomy in classical logic.Stephen Read - 2000 - Journal of Philosophical Logic 29 (2):123-154.
General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.
Pure logic of iterated full ground.Jon Erling Litland - 2018 - Review of Symbolic Logic 11 (3):411-435.
O fundamentach dla metafizycznego fundowania.Karol Lenart - 2019 - Analiza I Egzystencja 45 (2019):5-24.
What Grounds What Grounds What.Michael J. Clark - 2018 - Philosophical Quarterly 68 (270):38-59.
Harmonic inferentialism and the logic of identity.Stephen Read - 2016 - Review of Symbolic Logic 9 (2):408-420.
Grounding rules and (hyper-)isomorphic formulas.Francesca Poggiolesi - 2020 - Australasian Journal of Logic 17 (1):70-80.

Analytics

Added to PP
2012-09-08

Downloads
440 (#46,817)

6 months
79 (#67,028)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Jon Litland
University of Texas at Austin

Citations of this work

Axiomatic Theories of Partial Ground I: The Base Theory.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):161-191.

Add more citations

References found in this work

Metaphysical Dependence: Grounding and Reduction.Gideon Rosen - 2010 - In Bob Hale & Aviv Hoffmann (eds.), Modality: metaphysics, logic, and epistemology. Oxford University Press. pp. 109-135.
Four Dimensionalism.Theodore Sider - 1997 - Philosophical Review 106 (2):197-231.
Is there a fundamental level?Jonathan Schaffer - 2003 - Noûs 37 (3):498–517.
Grounding Explanations.Louis deRosset - 2013 - Philosophers' Imprint 13.

View all 29 references / Add more references