Overcoming Newman’s Objection

Bertrand Russell (The analysis of matter. Routledge, London, 1927) defended a form of structuralism according to which all we can know about the world is structure. In response, Max Newman (Mind 37:137–148, 1928) raised a formidable challenge that threatens to turn structuralism into something trivial: as long as there are enough objects in the relevant domain, one can always obtain a structure suitable for that domain. In this paper, I consider two responses to this objection. The first is provided by Rudolf Carnap (The logical structure of the world. Trans. Rolf A. George. University of California Press, Berkeley, 1928/1967) in terms of founded relations. I argue that it ultimately fails. Another alternative insists that the structures that have content about the world are ultimately finite, and it is a non-trivial matter to figure out what the appropriate structure for finite domains ultimately is. Russell (The autobiography of Bertrand Russell, vol 2. Allen & Unwin, London, 1968, 176) briefly considered this option in his response to Newman, but did not develop it further. I argue that, when coupled with a proper account of detectable relations, it is a far more promising route than it may initially seem.