Conceptual Philosophers believe that the goal of philosophy is to analyze the structure of concepts. A problem for this view is that concepts constitute only a small fraction of reality. Williamson considers that if Russellianism is true everything, by definition would be considered concepts. Williamson presents the following argument for the conclusion that one can oppose the conceptual turn even if one accepts Russellianism. If one can accept the conceptual turn, if one accepts Russellianism, then the conceptual turn analyzes everything philosophy should analyze.
1. If conceptualist accepts Russellianism then the conceptualist will analyze propositional conceptual structure and not other nonconceptual structure.
2. If the conceptual turn analyzes everything philosophy should analyze then philosophy should not analyze nonconceptual structure.
3. It is false that philosophy should not analyze nonconceptual structure.
4. Therefore it is false the conceptual turn analyzes everything philosophy should analyze.
5. Therefore it is false that one can accept the conceptual turn if one accepts Russellianism.
A criticism one could give to this argument is to deny the 3rd premise. However, mereological and chemical structure are nonconceptual structures, thus to deny that philosophy should analyze nonconceptual structure is to deny that philosophy should analyze mereological and chemical structures. Williamson argues “that philosophy can appropriately investigate general features of nonconceptual structure too, such as the mereological structure of physical objects.”
6. If philosophy should not analyze nonconceptual structure then philosophy should not analyze mereological or chemical structure.
7. It is false that philosophy should not analyze mereological or chemical structure.
8. Therefore it is false that philosophy should not analyze nonconceptual structure.