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

*Grammar*: There are objects, which we call*grounds*, which can be grounds*for*propositions or grounds*against*propositions.*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 \(A\).*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.*Grasp*: Grounds are the kinds of things we can*possess*.*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 \(A\).*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.

This is a talk for the Melbourne Logic Seminar.

I’m *Greg Restall*, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is *in any way* endorsed by the University of Melbourne.

- School of Historical and Philosophical Studies, The University of Melbourne, Parkville 3010, Australia.
- greg@consequently.org
- keybase.io/consequently, to sign or encrypt a message to send to me privately.
- @consequently on Twitter.
- @consequently on Instagram.

To receive updates from this site, you can subscribe to the RSS feed of all updates to the site in an RSS feed reader, or follow me on Twitter at @consequently, where I’ll update you if anything is posted.