The puzzle of material constitution can be expressed in at least two ways. First, how can the constituting object and the constituted object, which are materially and spatially coincident, be regarded as different objects? Second, how can the constituting object and the constituted object, which are qualitatively distinct, be regarded as identical objects? Monists argue that the constituting and constituted objects are identical since they are materially and spatially coincident and the property differences between then are simply differences in description, perspective or context. In contrast, pluralists argue that the constituting and constituted objects are not identical even if they are materially and spatially coincident since they are qualitatively distinct. This paper proposes a solution to the puzzle of material constitution called ‘Fregean Monism’ (FM), and shows that it can better account for the property differences between the constituting and constituted objects without the need to regard them as two distinct objects. On the FM view, the puzzle of material constitution is partly a semantic puzzle and partly a metaphysical puzzle, and shows how a solution to the semantic part of the puzzle, based on the Fregean distinction between sense and reference, can yield a satisfactory solution to the metaphysical part of the puzzle. The key idea is that while the reference of a term picks out both the referent object and referent properties, the sense of the term determine which referent properties are picked out.