Project description
Advancing the science of generalisation
Generalisation helps us turn specific facts into broad principles, such as ‘All cells have a membrane’. While we understand generalisation for objects, like cells or numbers, higher-level generalisation about statements themselves is more complex. This involves choosing between two methods: higher-order logic or self-applicable theories. The ERC-funded GENERALISE project tackles these challenges by investigating these two key methods. This pioneering research promises to refine how we develop deductively robust theories, impacting fields ranging from mathematics and logic to computer science and philosophy. By exploring these foundational methods, GENERALISE aims to advance our understanding of generalisation in science and beyond.
Objective
Generalisations are fundamental to every scientific discipline: Every cell has a plasma membrane, Every electron has a negative charge, Every natural number has a unique successor. By means of generalisation we turn a statement about a particular individual into a statement about a class of entities. Generalisations are essential to valid deductive reasoning. They are the building blocks of virtually every scientific theory, and therefore essential to understanding, explaining, and making predictions.
The most basic and best understood form of generalisation is generalisation over objects (e.g. cells, electrons, numbers). In formal logic, this form of generalisation is achieved via first-order quantifiers, i.e. operators that bind variables in argument position. But many theoretical contexts require generalisation into sentence and predicate positions, a high-level form of generalisation where we make a general statement about a class of statements (e.g. mathematical induction, laws of logic).
There are two competing methods for achieving this form of generality (i.e. higher-order logic and self-applicable theories of truth, properties, and sets respectively). 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 significantly advance this foundational project. It will provide the first sustained systematic investigation of the two methods from a unified perspective, and develop novel formal tools to articulate deductively strong theories. Due to its foundational character, it will have an impact on many disciplines, especially the foundations of mathematics, logic, formal semantics, metaphysics, philosophy of language, and theoretical computer science.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been validated by the project's team.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been validated by the project's team.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences computer and information sciences computational science
- humanities philosophy, ethics and religion philosophy metaphysics
- humanities philosophy, ethics and religion philosophy philosophy of language
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2022-STG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
1012WX Amsterdam
Netherlands
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.