Infinitary logic logical axiom, an element of T, or is deduced from previous statements using a rule of inference. As before, all rules of inference in finitary logic can be used, together with an additional one: The logical axiom schemata specific to infinitary logic are presented below. Global schemata variables: formula_3 and formula_18 such that formula_23. The last two axiom schemata require the axiom of choice because certain sets must be well orderable. The last axiom schema is strictly speaking unnecessary as Chang's distributivity laws imply it, however it is included as a natural way to allow natural weakenings to the logic.
Logical atomism then in Britain and exemplified in works of F. H. Bradley and J. M. E. McTaggart. Logical atomism is partly understood as a developed alternative to logical holism, or the "monistic logic" of Idealists, on which logical analysis is a kind of falsification. The theory holds that the world consists of ultimate logical "facts" (or "atoms") that cannot be broken down any further. Having originally propounded this stance in his "Tractatus Logico-Philosophicus", Wittgenstein rejected it in his later "Philosophical Investigations" (§§46–49, §81, §91). The term "logical atomism," partly because it was first introduced in a French paper that remained untranslated