The Realm of Sense

The "Sense" section consists of the following essays:

1.0 Introduction to the Theory of Sense

1.1 Mathematics as the Science of Sense

1.2 Expressive and Algorithmic Power

1.3 Against Sets

1.4 The Problem of Quantity

At present, only one of these essays, namely 1.1, is in place.

Summary of Contents

In developing his theory of Sense and Reference, Frege did more than simply divide the notion of meaning into two components. He developed the idea that the possible senses of expressions are objective, and together make up a realm which we can explore and talk about using language. These essays argue in favour of this view, and develop ideas about what it is to study the realm of sense and what we might find there.

The first essay in this section, Introduction to the Theory of Sense, will be made up of an exposition of the notion of sense and a defence of the claim that senses are objective items which constitute a subject matter to be studies in their own right.

In the essay The Science of Sense, I argue that we all ready have in place an enterprise dedicated to the systematic exploration of the realm of sense, namely pure mathematics. In doing pure mathematics we are not concerned whether the expressions refer to anything in the world, but rather we use them to express senses, and then study the logical connections between these senses. In applied mathematics we use the fund of senses thus built up and explored to articulate more precisely facts about the world and understand their logical implications.

In a short essay entitled Expressive and Algorithmic Power I will look at two distinct but inter-related functions of mathematics. The first, expressive power, is the function of mathematics to develop a vocabulary which allows us to express things which were simply inexpressible before. The second, which follows on from this is algorithmic power, the ability to mechanise thought. The shocking discovery of 20th century mathematics has been the limitations on algorithmic power, and in particular the trade-off that has to be made between expressive and algorithmic power.

In physics it is taken for granted that empirical facts about the world should be expressed in terms of real-numbered values of various quantities. In the essay The Problem of Quantity, I will ask the question why that should be so, and what are the consequences for our (Fregean) ontology of the physical world.