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Frege's introduction of the new logical notion of an object considered in the previous chapter is concomitant with a rejection of both empiricist and psychologistic approaches to the philosophy of arithmetic. This rejection accordingly suggests an alternative construal of the status of mathematical objects as non spatio-temporal, yet objective. In the first section of the current chapter I engage in a detailed consideration of Husserl's early philosophy of arithmetic in an attempt to disentangle some important strands in Frege's critique of late nineteenth century psychologistic theories of abstraction. My argument is that the early Husserl's tendency to conflate the subjective presentation of content with objective content should be clearly distinguished from his project to uncover the role played by meaning-constitution in the mathematical sciences. This account sets the scene for a critical analysis of Frege's notion of objectivity in the second section of the chapter – an analysis which culminates in the claim that Dummett's critique of Frege's third realm itself suggests the need for an account of meaning-constitution along the lines of that provided by Husserl.

DOI: 10.1057/9780230378438_3

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