In this chapter I shall discuss Simone Weil's account of the natural world as an order of necessary relations. The main problem here is to see how the conception of an “order” in that sense is related to the “order” involved in human behaviour, and in particular to the ordered sequence of operations which constitutes a “method.” This will involve some consideration of what she says about the formation of mathematical concepts and their application.

In Chapter 5 I compared her conception of an operation, and of a sequence of operations, to Wittgenstein's in the Tractatus. Wittgenstein's concern there is with the nature of logic. He conceives logical relations between propositions as depending on, even consisting in, the relations between the various conditions that make propositions true (their “truth-conditions”). By virtue of these relations certain propositions can be seen as interlinked in systems of “truth-functions”: systems in which the truth of some propositions is displayed as depending on (as a function of) the truth or falsity of others. Such systems are generated through the application of certain operations on given propositions (which serve as the “bases” of the operations); in this way other propositions are formulated which are logically, truth-functionally, related to each other and to the original bases by virtue of the way they have been generated. In the Tractatus Wittgenstein held: (1) that there is only an apparent diversity between the operations that generate truthfunctional systems – that they can all be reduced to the single operation of iterated negation; (2) that all logical relations between propositions, and hence all logical necessity, can be understood in this way; (3) that all necessity is logical necessity.