Sammendrag: The objective of the thesis is to give one account of Dummett’s philosophical approach in the justification for intuitionistic logic. Dummett’s argumentation is worth being considered not merely in its attempt to repudiate the Platonist understanding of mathematics in favor for Intuitionism, but it also provides one perspective of the nature of disagreement between Platonism and Intuitionism in the philosophy of mathematics.
In the course of the exposition, we will learn that Dummett’s justification for intuitionistic logic takes the form of a challenge known as the Semantic Anti-Realist Challenge (ARC). The central theme of the thesis is an enquiry of the argumentative strength of the Semantic Anti-Realist Challenge.
The first chapter serves as an introduction giving a general background of ARC, and the content of ARC. Here are we concerned with the underlying principles of ARC.
The second chapter is a hermeneutic exposition, in an analytic tradition, of the arguments supporting the principles of ARC. In the exposition, we try to find interpretations which would render the arguments as strong as possible.
The third chapter is an evaluation of the arguments and their role in the formulation of ARC is being examined.
In the fourth chapter, we are examining the Platonist reply to the Challenge of ARC. Our examination is based on Alexander George’s paper "How not to refute realism." His paper is worth to take into account, in that it considers a Platonist reply, which accepts the underlying principles of ARC. The dispute between a Platonist and an Intuitionist has the character of a dispute between realism versus anti-realism (R/AR dispute) concerning mathematical objects.
In the fifth chapter, we will deal with one Holistic Realist reply to ARC. It differs from the first reply in that it is not concerned with the particular R/AR dispute between Platonists and Intuitionists in the philosophy of mathematics, but rather with the general meaning theoretic considerations. Although we are most concerned with the R/AR dispute in the philosophy of mathematics, we cannot ignore the Holistic Realist reply, since the force of the Semantic Anti-Realist Challenge is heavily based upon general meaning theoretic considerations and has, thus, prima facie a global anti-realist character not limited within the R/AR disputes in the philosophy of mathematics. The holistic realist reply in question is Brian Loar’s reply, and our examination of his reply will be based upon his paper "Truth Beyond All Verification."
In the exposition, we are concerned with two central questions:
1) The validity of the underlying principles of ARC
2) The force of ARC
The first question is concerned about the cogency of the arguments for the underlying principles of ARC. The second question is concerned whether the Challenge of ARC can be met by a realist, given that the principles of ARC are accepted.