Home Philosophy Advances in Proof-Theoretic Semantics

## Equality of SensesOne of the fundamental challenges for every theory of senses is the notion of equality of senses. In our setting the notion of sense is naturally relativized to (the knowledge of) an agent if the senses of two terms denoting the same object in cases where the proof of the corresponding equality at hand. But it would compromise Frege's original idea, as the senses of “morning star” and “evening star” should clearly stay different even if somebody knows that both denote Venus. Still, we may obtain an interesting notion of equality of senses if we allow for the closure of the mode of presentation under It is not our aim to specify concrete criteria concerning which (type of) equations should be taken into account for the equality of senses. In contrast, we think that equality of senses should not only be relativized to an agent (or an agent's knowledge) but that it could also be graduated and that it depends on the chosen axiomatic context. The rôle of the axiomatic context can be exemplified by the natural numbers: if they are introduced as a commutative semigroup, commutativity is, of course, “build in” and numbers are introduced by use of the Peano Axioms, the commutativity of addition requires a rather non-trivial proof by induction, and, in this context, one might say that the sense of (only) one of the summands to calculate the value may lead to substantially different computations. This last example shows that, for our notion of mode of presentation, the underlying axiomatic setting forms an integral part of the sense of a term.15 |

< Prev | CONTENTS | Next > |
---|

Related topics |

Academic library - free online college e textbooks - info{at}ebrary.net - © 2014 - 2019