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.
Language, Truth, and Logic be true or false. Ethical or aesthetic judgments express feelings, not propositions, and have no objective validity. Value-judgments are not analytic, and are not verifiable as 'matters of fact.' According to Ayer when we argue about whether a value-judgment is right or wrong, we are really arguing about the empirical facts on which a value-judgment is based, or about the logical interpretation of empirical facts. We cannot argue about something that cannot be expressed as a proposition. We can only argue about something that can be analytically or empirically verified. For Ayer, metaphysical statements, such as statements about transcendent reality,