## New Work for a (Formal) Theory of Grounds

#### December 14, 2018

Abstract: In this talk, I provide two different models for a theory of grounds meeting the following desiderata:$$\def\yright{\succ}$$

1. Grammar: There are objects, which we call grounds, which can be grounds for propositions or grounds against propositions.
2. Derivation: A derivation of a sequent $$X\yright A,Y$$ gives us a systematic way to construct a ground for $$A$$ out of grounds for each member of $$X$$ and grounds against each member of $$Y$$, and a derivation of a sequent $$X,A\yright Y$$ gives us a systematic way to construct a ground against $$A$$ out of grounds for each member of $$X$$ and grounds against each member of $$Y$$. So, a derivation of $$\yright A$$ gives us a way to construct a ground for $$A$$, and a derivation of $$A\yright$$ gives us a way to construct a ground against $$A$$.
3. Interpretation: This theory can be interpreted in an epistemic sense, where grounds are our means to access the truth or falsity of a proposition, or a metaphysical sense, where grounds show how a proposition is made true by the world.
4. Grasp: Grounds are the kinds of things we can possess.
5. Hyperintensionality: Not every ground is a ground for every tautology. A ground for $$A$$ need not also be a ground for each logical consequence of $$A$$.
6. Structure: A ground for $$A\to B$$ can be seen as a function from grounds for $$A$$ to grounds for $$B$$. A ground for $$A\land B$$ can be seen as consisting of a ground for $$A$$ and a ground for $$B$$. A ground against $$A\lor B$$ can be seen as consisting of a ground against $$A$$ and a ground against $$B$$. A ground for $$\neg A$$ can be obtained from a ground against $$A$$, and a ground against $$\neg A$$ can be obtained from a ground for $$A$$.

The result is a model of grounds with significant similarities to the BHK interpretation of constructive logic, but for the classical sequent calculus.