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Supported by the New York Institute of Philosophy, New York University will be hosting HOMeWork 8, the eighth iteration of the Higher-Order Metaphysics Workshop.
The workshop will take place in Room 202, 5 Washington Place, on November 15–16.
If you would like to attend, please fill in this registration form.

Sat Nov 15
Sun Nov 16
9:30AM–
10:00AM		 Coffee & breakfast
10:00AM–
11:30AM
11:40AM–
1:10PM
1:10PM–
2:30PM		 Lunch
2:30PM–
4:00PM
4:20PM–
5:50PM
Chair: Cian Dorr (NYU)
ROUNDTABLE
Open Questions in Higher-Order Metaphysics
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Organizers: Jeremy Goodman (JHU); Cian Dorr (NYU);
Ethan Russo (NYU); Christopher Sun (NYU)
If you have first-order questions, please email
higherordermetaphysicsworkshop[at]gmail[dot]com.
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ABSTRACTS

Logics of Metaphysical Definition

Andrew Bacon

The paper axiomatizes, in higher-order logic, the relation of one thing being metaphysically definable from some others. The logics are described model theoretically by adding to a general model of higher-order logic information about which functions between domains are logical forms, and propositional functions. The notion of metaphysical definition is that of one entity being a logical construction of some others.

Transparency Without Exportability

Lingzhi Shi

If we take Frege's puzzle as a motivation for revising classical logic of quantification and identity, then it is natural to hold that terms like ‘believe’ are not transparent and terms like ‘Hesperus’ are not exportable. Moreover, Bacon and Russell (2019) explore the idea of purity according to which purely logical (or pure) expressions—unlike ‘believe’ and ‘Hesperus’—are both transparent (Pure Transparency) and exportable (Pure Export). However, we take cases of identity confusions involving pure terms as straightforward counterexamples of Pure Export. Moreover, given that Pure Transparency and Pure Export are equivalent under a certain background logic, we are left to ask: how could pure terms be transparent without being generally exportable. This paper explores several approaches to this question and evaluates their respective strengths and weaknesses.

Horizontal Fregeanism

William Nava

Fregeanism is the view that distinct primitive expressive roles correspond to distinct and exclusive metaphysical kinds. By itself, this view leaves open what the space of roles (and corresponding kinds) is. I'll first argue, on expressive grounds, for narrowing the options to two candidates. One option, which I call hierarchical Fregeanism, has it that the expressive roles correspond to syntactic types of higher-orderese. The second, which I call horizontal Fregeanism, has it that the expressive roles are just reference and -place ascription (for each ). For the rest of the talk, I'll present and defend horizontal Fregeanism. I'll argue that the view calls for a novel syntax that allows direct self-application (i.e. sentences of the form ) while still respecting the distinction between reference and each -ascription. I will present this syntax, along with an attractive logic formulated in it. I'll also discuss how the issue of paradox bears on the choice between horizontal and hierarchical Fregeanism.

Why Sum Types, or Even Some Types at All?

Robert Trueman & Tim Button

In ‘Higher-order quantification and the elimination of abstract objects’, Dorr uses sum types to develop a novel higher-orderist account of nominalization in natural languages. Dorr's account is elegant and ingenious, but we argue that it faces some serious problems. Dorr could avoid these particular problems if he replaced sum types with (what we call) union types, but union types would then introduce new problems of their own. Fortunately, our own fictionalist approach to nominalization steers clear of all these difficulties.

Quantificationalism and the Intelligibility of Free Higher-Order Quantifiers

Antonio Maria Cleani

The meaning of classical quantifiers is uniquely determined, up to logical equivalence, by their inferential role. This result, known as the Harris result for classical quantifiers, is philosophically significant. It has been used to argue that primitive higher-order quantifiers are intelligible, and for the substantivity of ontological questions. It is well known that the Harris result does not extend to free quantifiers. For example, ‘all cats’ and ‘all dogs’ both satisfy the standard inferential role of a free universal quantifier, but are obviously inequivalent. Philosophers who take the logic of their primitive quantifiers to be free rather than classical (e.g., contingentists) thus face a problem of explaining which, among the many candidate meanings, their primitive quantifiers have.
I argue that philosophers with free logical sympathies can avoid this impasse if they are willing to embrace Quantificationalism—the view that propositions can be true or false at or relative to domains of quantification, in much the same sense they can be true or false at times or possible worlds. Quantificationalists have independent reasons to regard the inferential role of free quantifiers as richer than it is normally taken to be. This richer inferential role turns out to be strong enough to afford a generalization of the Harris result to (Quantificationalist) free quantifiers.

Logical Atomism

Verónica Gómez Sánchez & Ezra Rubenstein

Logical atomism is the view that fundamental reality is logically simple. We distinguish three ways of developing this view: Generative Atomism (roughly, all logically complex truths are generated by atomic truths); Structural Atomism (roughly, no logical notions carve reality at the joints); and Eliminative Atomism (roughly, there are no logical entities). We take Eliminative Atomism to be a natural consequence of Structural Atomism, and we argue that their combination fits the motivations for logical atomism much better than Generative Atomism does. We then develop the idea that a ‘metaphysical’ form of truthmaker semantics can be used to explain how logically complex sentences can be meaningful (and true) despite there being no logically complex propositions for them to express. Finally, we briefly discuss various ‘indispensability’ arguments against Eliminative Atomism.

Some Consistency Results for Contingent Mathematics

Zachary Goodsell & Neil Barton

In light of the development of forcing, philosophers and mathematicians have wondered whether the truths of mathematics might be contingent. This talk investigates that idea in the framework of higher-order logic. Our main result is that forcing-related contingency (e.g., contingency of the continuum hypothesis) is consistent in the higher-order logic Bacon and Dorr call Classicism + Rigid Comprehension, which permits quantification over both properties and modally rigid classes.


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