If the Kantian criterion that distinguishes synthetic from analytic propositions, whether they are axioms or postulates, is the non-inclusion of the synthetic ones versus the inclusion in the subject of the analytic propositions, an analytic proposition could not be reduced or transformed to a synthetic one, nor vice versa, since something is or is not included in something else. Well, the very concept of inclusion is not exactly clear, modern set theory has opted for an extensional definition, that is, giving a list of the things that are included in another given. Inclusion thus conceived is less problematic, although it is not without paradoxes. Let's skip this for a moment and focus on the Kantian distinction. Kant gives us his well-known example of a priori synthetic proposition, capable of giving us knowledge independently of experience: 7+5=12 But we can transform this equality into this other: 7=12-5 And then into: 7=7 That is an analytical proposition. And co...
On the symbolic constructions of human identity.