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Prof. Andrew Bacon (USC) will give a masterclass on Higher-Order Metaphysics at King’s College London on May 8th-10th, 2019. The masterclass will include guest talks by Nick Jones (Birmingham), Jessica Leech (KCL), and Timothy Williamson (Oxford).

The event is open to graduate students and researchers from any institution. Attendance is free but registration is required. To register fill in the form below.

You can download a pdf version of the programme.


Some central questions of metaphysics revolve around propositions, properties and relations and around how they interact with modality: What does it mean for a necessity to be broader than another? Is there such a thing as a broadest necessity? what does it mean for a property or relation to be fundamental? Are fundamental properties and relations `freely recombinable’ in the sense that they can instantiate any logically consistent pattern? Are propositions structured entities constructed out of fundamental properties and relations?   More generally, to what extent can we make good on the metaphor of reality as a language, and the corresponding metaphor of the fundamental as the primitive constants of that language? 

Unfortunately, debates on such questions are often formulated in ways that are prone to lead to paradoxes. Higher-order logic is a precise framework for regimenting such debates. It is a generalization of first-order logic that allows one to quantify not just into singular position but into any given grammatical position. It allows one to replace quantification over propositions, properties and modalities by quantification into sentence, predicate or operator position. Higher-order logic is often studied in a broadly Fregean setting  which in effect assumes that there are only two propositions. Once this assumption is lifted there are a surprising number of choice points regarding the logic and model theory of higher-order logic, corresponding to a number of different metaphysical pictures of the granularity of properties and propositions. Many of the technical tools in this area have been developed by computer scientists and category theorists but aren’t widely known to philosophers. 

This masterclass will present these ideas in a way that is accessible to philosophers, and tailored to their concerns. The first half of the series will cover general technical machinery needed for modelling higher-order logic. The second half we will apply these tools to the metaphysical questions raised above.

The event is organized by the Formal Methods research group of KCL’s philosophy department.


Please register to be included in the participants list and to get access to the building.

Note that you will not receive a confirmation email. You are registered if after clicking “submit” below the page displays “message sent”. If you need a further confirmation please write to Julien Dutant..


All talks take place in room BH(SE)2.09, that is Bush House South East wing, level 2, room 09. See this pdf map of the campus or the location on google maps.


You can download a pdf version of the programme.

Wednesday, May 8th

  • 11:00-12:30, Andrew Bacon, masterclass lecture 1. Introduction to functions and higher-order functions.
  • 14:00-15:30, Andrew Bacon, masterclass lecture 2. Type theory and Higher-order logic.
  • 16:00-17:30, Jessica Leech, Relative Necessity Extended.

Thursday, May 9th

  • 11:00-12:30, Andrew Bacon, masterclass lecture 3. Propositional Granularity.
  • 14:00-15:30, Andrew Bacon, masterclass lecture 4. Modality.
  • 16:00-17:30, Timothy Williamson, Are Counterfactuals Hyperintensional?

Friday, May 10th

  • 11:00-12:30, Andrew Bacon, masterclass lecture 5. Logical Necessity and Fundamentality.
  • 14:00-15:30, Andrew Bacon, masterclass lecture 6. Substitution Structures.
  • 16:00-17:30, Nick Jones, Type-Neutrality and Pattern Recognition.

Masterclass lectures programme

Lecture 1: Introduction to functions and higher-order functions. Introduction to higher-order functions, Curried functions, combinators and applicative structures.

Lecture 2: Type theory and Higher-order logic. The lambda calculus and higher-order logic. 

Lecture 3: Propositional Granularity. Theories of propositional granularity in higher-order logic. We will formulate the structural theory of propositions in higher-order logic and outline the Russell-Myhill paradox. We will then formulate and discuss a more coarse grained theory of granularity, Adjunctive Booleanism. 

Lecture 4: Modality. Given the background of Adjunctive Booleanism, we will formalise what it means for (i) an operator to be a modality, (ii) one modality to be as broad as another. We will then show that there is a broadest necessity, and that it can be defined in logical (indeed extensional terms). A general model theory for Adjunctive Booleanism is outlined.

Lecture 5: Logical Necessity and Fundamentality. In this lecture I will present a theory of fundamentality, in higher-order logic, which substantiates the following ideas: (i) the fundamental properties an relations are freely recombinable, (ii) arbitrary properties and relations can be decomposed uniquely into the fundamental by logical operations. Both ideas will be seen to be closely connected, and surprisingly the second is consistent with Adjunctive Booleanism.

Lecture 6: Substitution Structures. In this lecture I will outline a class of applicative structures that are well-suited for theorizing about propositional granularity. I will indicate how the technology can be used to create models of the theory in lecture 5.

Further information

For further information contact Julien Dutant.