 The distinction made here between analysis and construction deliberately side-steps and important discussion among scholars of Frege and Russell about the nature of analysis. Frege held, in his Foundations of Arithmetic (1884, §64), that a proposition about identity of numbers could be also analyzed as one about the similarity of classes. He describes this as “recarving ” one and the same content in different ways. Later Frege asserted that the same thought could be viewed as the result of the application of a function to an argument in different ways. As the logical form of a thought is the result of the application of concepts to arguments, this means that distinct logical forms are assigned to the same thought. To resolve the apparent conflict with Frege’s famous thesis of  compositionality , that a thought is built up from its constituents in a fashion that by and large follows its syntactic form, Michael Dummett (1981, chapter 15) distinguishes two notions of analysis in Frege, one as “analysis” proper, the other as “decomposition”. Peter Hylton (2005, 43) argues that there is a problematic notion of analysis in Russell, with it being very difficult to say that sentences containing definite descriptions have the complicated quantificational structures assigned to them in “On Denoting” (1905) as their “real structure”. Michael Beaney, in his introduction to (2007, 8) gives the names “decompositional” and “transformative” to two kinds of analysis in his introduction to papers that discuss the significance of this distinction for Russell. James Levine claims that in fact the first form of analysis, by which the project is to find the ultimate constituents of propositions, belongs to an early project of “Moorean Analysis” that Russell abandoned early. Indeed, by the time of the account of numbers as classes of equinumerous classes, Russell had already adopted what Levine calls “Russell’s Post-Peano Analysis ”. 