Algorithms and the Mathematical Foundations of Computer Science
Walter Dean · Oxford University Press eBooks · 2016
The goal of this chapter is to bring to the attention of philosophers of mathematics the concept of algorithm as it is studied incontemporary theoretical computer science, and at the same time address several foundational questions about the role this notion plays in our practices. A view known as algorithmic realism will be described which maintains that individual algorithms are identical to mathematical objects. Upon considering several ways in which the details of algorithmic realism might be formulated, it will be argued (pace Moschovakis and Gurevich) that there are principled reasons to think that this view cannot be systematically developed in a manner which is compatible with the practice of computational complexity theory and algorithmic analysis.