Petrus Hispanus Lectures 2022 – Cian Dorr
LanCog is pleased to announce that the 2022 Petrus Hispanus Lectures will be delivered at FLUL by Cian Dorr, Professor of Philosophy at New York University, on April 19th and 22nd.
Higher-Order Quantification and the Elimination of Objects
Higher-Order Quantification and the Elimination of Abstract Objects
April 19th (Tuesday), 2022, 16h00, Anfiteatro III, FLUL
Higher-Order Quantification and the Elimination of Concrete Objects
April 22nd (Friday), 2022, 16h00, Anfiteatro III, FLUL
In higher-order formal languages, one can have variables that take the place of expressions of arbitrary syntactic categories, and these variables can be bound by quantifiers just like the more familiar first-order variables. For example, from the simple subject-predicate sentence ‘Wise(Socrates)’, one can derive not just the existentially quantified sentence ‘∃x(Wise(x))′, but also ‘∃X(X(Socrates))’ (where X is a variable in the syntactic category of predicates) and ‘∃p(p)′ (where p is a variable in the syntactic category of sentences). English contains some phenomena that work like this—consider ‘He is something she thinks it’s important for a philosopher to be, namely wise’—but there is no straightforward or uncontroversial scheme for systematically translating from a higher-order language into any natural language. Nevertheless, many philosophers, including Frege, Russell, Prior, and Williamson, have taken the natural higher-order generalization of classical quantification theory to provide an adequate basis for understanding higher-order quantification.
In the first lecture, I will assume the correctness of this perspective, and consider what it means for questions in natural language such as ‘Are there abstract objects?’, or more specifically, ‘Are there properties?’, ‘Are there relations?’, ‘Are there numbers?’, etc. I will try to occupy the perspective of a native speaker of “higher-orderese” trying to make sense, as a field linguist, of the rather mysterious behaviour of words like ‘property’. On the one hand, syntactic similarities suggest that they are semantically analogous to other common nouns like ‘horse’ and ‘unicorn’, putatively standing for objects of some rather special sort which our field linguist would see little reason to believe in. On the other hand, at least when used by non-metaphysicians, sentences involving such words often play a communicative role quite similar to that of sentences involving higher-order quantification: for example, ‘Socrates has some property’ looks like a natural language analogue of ‘∃X(X(Socrates))’, and ‘Socrates has at least one property that Aristotle claims Plato has’ looks like an analogue of ‘∃X(X(Socrates) ∧ Claims(Aristotle, X(Plato)))’. I will develop the second of these perspectives, by providing a systematic semantic account on which the relevant ‘property’-sentences in fact express the same thing as their higher-order analogues. The key idea is that many expressions of natural language, including all nouns, verbs, and adjectives, are highly type-ambiguous. I’ll show how the apparatus of producttype and sum-types, which can be introduced as a harmless shorthand, lets us provide an account of tricky sentences like ‘Athens and the property of being Athenian were both mentioned by Socrates’. And I’ll show how by adding the finite Tarskian hierarchy of truth-predicates to our higher-order language, we can even provide “type-neutral” readings of quantified sentences like ‘Everything mentioned by Socrates was mentioned by Plato’. I’ll finally sketch how this technique of “eliminating” properties (considered as objects) can be extended to various other supposed “abstract objects”, such as numbers.
In the second lecture of the series, I will consider the extent to which the same techniques of “elimination” can be applied to concret objects. I will begin with ordinary objects like tables, chairs, planets, plants, and people, arguing that these should be identified with certain properties, and thus not taken to be genuine objects at all. In other words: quantification over such objects is really of some predicate type, rather than of a type at the base of the type-hierarchy. I’ll argue that this approach provides a natural explanation of the distinctive modal profiles of such objects, and opens the way for attractively simple ontologies such as the view that the only genuine objects are elementary particles and the view that the only genuine objects are points (of space,spacetime, or some less familiar manifold). Finally, I will take up the even more radical proposal that all objects—even particles and points—can be “eliminated” in the same way. I will develop one version of this, on which ordinary objects like chairs and microphysical objects like electrons are properties of points of space, and points of space in turn are just certain special propositions—i.e., quantification over points is really just a misleading way of conveying something that could be expressed in a higher-order formalism by a restricted quantification into sentence position. I’ll conclude that such “eliminativism about objects” is a coherent and respectable option, although the theoretical case for it is much weaker than the case for “eliminativism” about ordinary objects.
Registration: in-person attendance
All are welcome. For safety and organizational reasons, those willing to attend are asked to register in advance. Please register by filling out the following form:
Registration: online attendance
For those who are interested but cannot be in Lisbon, there will be an option for online attendance, via zoom. Please sign up by writing to firstname.lastname@example.org (subject: “PH Lectures”) and you will receive the invitation for the meeting at least one day before.