Clearly explain the ‘falsifiability test' and the ‘relational theory of identity.' How does Empiricism B (Logical Positivism) employ each of these theories in effort to establish its position?. Philosophy

Empiricism B disagrees with both of the options. The falsifiability test is a test that can be used to determine if a statement is synthetic or analytic. The test states that if true, it can never be conceived as false or vice versa. Analytic statements are either true or false. If something is possible, it is conceivable. Empiricism B proves that math is analytical and that all synthetic statements are falsifiable. This means that synthetic statements can be true, but also conceived as false, and vice versa. Mathematical statements are not falsifiable because they cannot be conceived as their incorrect counterpart. Secondly, he uses the relational theory of identity to explain how numbers can't possess meaning without other numbers and proves that mathematical truths are analytic. One can't understand 2 without understanding 1 and 3, meaning that statements like 7+5=12 imply one another. For example, 2 + 3 = 5 must be true, not falsifiable, not synthetic, analytic.