The Institute for Logic, Language and Computation
(ILLC) currently has two vacant Postdoc researcher positions as part of the ERC Starting Grant project GENERALISE, led by main researcher Dr. Thomas Schindler (Assistant Professor). The ILLC is one of the five Research Schools within the Amsterdam Institute for Humanities Research
(AIHR). What are you going to do?
The most basic and best understood form of generalisation is generalisation over objects. In formal logic, this form of generalisation is achieved via first-order quantifiers, i.e. operators that bind variables in the syntactic position of singular terms. However, many theoretical contexts require generalisation into sentence and predicate positions. Very roughly, generalisation into sentence and predicate positions is a high-level form of generalisation in which we make a general statement about a class of statements (e.g. the principle of mathematical induction, the laws of logic). We can distinguish two competing methods for achieving generalisation into sentence and predicate positions: (A) The direct method: by adding variables that can stand in the syntactic position of sentences and predicates, and quantifiers for them.
This method is exemplified in the use of second- and higher-order logic (type theory). (B) The indirect method: by adding singular terms that are obtained from sentences and predicates by nominalising transformations, or by ascending to a metalanguage and attributing semantic properties to linguistic expressions or their contents. This method is exemplified in the use of formal theories of reified properties, sets, and classes, and formal theories of truth and satisfaction.
As both methods come with their own ideological and ontological commitments, it makes a substantial difference which one is chosen as the framework for formulating our mathematical, scientific and philosophical theories. Some research has been done in this direction but it is still very much in its early stages. This research project will provide a sustained systematic investigation of the two methods from a unified perspective and develop novel formal tools to articulate deductively strong theories.
Both postdocs are expected to contribute to the research objectives of the project, in agreement with Thomas Schindler. The first postdoc will contribute to investigating and overcoming expressive limitations of higher-order logic / type theory. We are especially interested in the problem of cross-type generalisation and paradoxes such as the Russell-Myhill and the Prior-Kaplan paradox. The second postdoc will contribute to developing expressive type-free theories. We are especially interested in theories that feature a universal set or universal property so that they can model absolute generality. Your tasks and responsibilities:
- conducting research, presenting intermediate research results at workshops and conferences and publishing articles in top tier journals;
- participating in meetings of the project research group;
- co-organising knowledge dissemination activities.