Description, Construction and Representation. From Russell and Carnap to Stone

The first aim of this paper is to elucidate Russell’s construction of spatial points, which is to be considered as a paradigmatic case of the "logical constructions" that played a central role in his epistemology and theory of science. Comparing it with parallel endeavours carried out by Carnap and Stone it is argued that Russell’s construction is best understood as a structural representation. It is shown that Russell’s and Carnap’s representational constructions may be considered as incomplete and sketchy harbingers of Stone’s representation theorems. The representational program inaugurated by Stone’s theorems was one of the success stories of 20th century’s mathematics. This suggests that representational constructions à la Stone could also be important for epistemology and philosophy of science. More specifically it is argued that the issues proposed by Russellian definite descriptions, logical constructions, and structural representations still have a place on the agenda of contemporary epistemology and philosophy of science. Finally, the representational interpretation of Russell’s logical constructivism is used to shed some new light on the recently vigorously discussed topic of his structural realism.