Truthmaker Semantics represents a new paradigm in mathematical and philosophical logic. At its core is a simple idea: truthmaker entailment is defined so that whatever possible entities make the premises true, also make the conclusion true. Understanding this notion in a precise logical way, however, represents a considerable philosophical and mathematical challenge.
Truthmaker Semantics aims to replace the currently dominant paradigm, Possible Worlds Semantics, in at least three important areas of philosophy of language and logic:
- The analysis of central semantic and linguistic notions, such as what proposition an utterance expresses, what that utterance is about, and its subject matter.
- The philosophical analysis of conditional statements, including counterfactuals.
- The philosophical interpretation of important non-classical logics.
At present, Truthmaker Semantics is in its infancy, and requires a good deal of mathematical development and clarification. This represents a considerable technical challenge. My aims in this project are (i) to develop the mathematics of Truthmaker Semantics; and (ii) to apply it as a semantics for relevant logic.
This project will be significant in providing a viable alternative to possible worlds semantics in philosophical logic. At present, possible worlds semantics is used extensively throughout philosophy, formal logic, and artificial intelligence, with applications in economics and computer science. Yet it has a number of unavoidable technical problems. In providing an improved theoretical tool in these areas, Truthmaker Semantics has the potential to be genuinely transformative. This project will be novel in that, at present, very little technical work has been done on Truthmaker Semantics (and what has been done is due almost entirely to Kit Fine), and little is known about its practical applications (eg, in computer science).