Where are we on relations of form, on improper classes and indeterminates? Negative numbers?
Possibly we should be investigating the Baby PARP solution algorithm. Demonstration of concept knowledge and a modicum of focus will get us through to a desired outcome.
"From Baby PARP to Rockets ABC"
Curiously the Baby PARP solution algorithm angles in to a teaching about relations, about the logical universe and improper class theory. The logical universe is an improper class, because transitivity of logical implication is held up by a reference to sort in the same way as the transitivity of inclusion for improper classes (see debriefing checkpoint one). A proposition lacking in meaning because one or more of the 'names' in it have yet to earn their badges in meaningful naming must be taken as a different sort to an ordinary proposition in which the variables have their badges in meaningful naming. A mathematical puzzle like the Baby PARP is a way of showing, among other things, how a variable can get a badge in meaningful naming.
The logical universe was originally an artifact of modal logic, relating to the propositional form It is logically necessary that p. In this study, variables like p represent propositions. Among compound propositions created through logical connectives, some are true irrespective of the truth values of their component propositions and they are classed as logically necessary. The logical universe is exhausted by the space in which all such logically necessary are indeed true.
Modal logic as taught by the Philosophy Department may not extend to a definition of the mathematical symbol for implication but a suitable definition can be given with forms of modal logic. However it is not sufficient simply to take the antecedent and consequent in a simple generalisation of boolean material implication. Implicit in the sign for mathematical implication is an assertion about the possibility of the antecedent being true. Implication is not admitted from any antecedent that is false throughout the logical universe.
"What are we allowed to teach the children?" - one could be thinking thus with a cotton-wool helmet on. Possibly one dares not take off such helmet, especially if it was fitted at Teachers' College. However morally speaking one should not reward an annexure with a vassal's performance.