Mathematics and language

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping us understand the general principles by which it serves its purposes well

A Paradox of Inferentialism

John McDowell articulated a radical criticism of normative inferentialism against Robert Brandom’s expressivist account of conceptual contents. One of his main concerns consists in vindicating a notion of intentionality that could not be reduced to the deontic relations that are established by discursive practitioners. Noticeably, large part of this discussion is focused on empirical knowledge and observational judgments. McDowell argues that there is no role for inference in the application of observational concepts, except the paradoxical one of justifying the content of an observational judgment in terms of itself. This paper examines the semantical consequences of the analysis of the content of empirical judgments in terms of their inferential role. These, it is suggested, are distinct from the epistemological paradoxes that McDowell charges the inferentialist approach with

Some views on information fusion and logic based approaches in decision making under uncertainty

Decision making under uncertainty is a key issue in information fusion and logic based reasoning approaches. The aim of this paper is to show noteworthy theoretical and applicational issues in the area of decision making under uncertainty that have been already done and raise new open research related to these topics pointing out promising and challenging research gaps that should be addressed in the coming future in order to improve the resolution of decision making problems under uncertainty