Joao Schmidt

Even though it is obvious that mathematics involves social activities, this rather trivial fact is rarely considered as important for its subject matter, mostly due to its undesired ontological consequences. An attempted solution for this tension was developed by Julian Cole’s institutional account of mathematics, named Practice- Dependent Realism. In the present paper, Cole’s account is evaluated, and its lights and shadows assessed concerning the ontological problem that he seeks to solve. I argue that his institutional account, although failing in delivering a sufficient ontological account of mathematics, still opens an important linguistic route for explaining its practice.

Following logicism, Frege famously held that logic is a science on its own. Particularly, he held the informativity thesis, viz., that logic is a science because it is deductively informative. This paper aims to understand Frege’s informativity thesis and its connection with the conception of logic as science. For such, it focuses on some features of Frege’s philosophy that are key for understanding this connection, particularly his conception of analyticity, the role of judgments in inferential reasoning, and the use of decomposition of functions as a means for concept-formation, which Frege names as fruitful definitions. Keywords: Gottlob Frege; Informativity of Logic; Judgements; Fruitful Definitions.