Theoria: An International Journal for Theory, History and Foundations of Science

Jorgensen’s dilemma has been analysed from various theoretical angles. However, it is not the aim of this essay to “theorize” but to “experiment” on the above mentioned dilemma; particularly to carry out attempts of deontic reproduction of a logical paradox substituting the value “truth” for the value “validity”. The relevance of the obtained results will be appraised from the point of view of Conte’s paradigm“syntactic (deontic) validity” vs. “dianoetic validity”.

Taking into account that no subordering of a scattered partial ordering is dense, we are going to define one idea of rank of a partial ordering which will make possible an equivalent but more operative definition of a scattered partial ordering. Using this notion of rank and the Scott’s sentence associated with the ordering, we are going to characterise in the infinitary language Lw1.w each element of a subclass of the partial orderings, this of the strongly scattered countable partial orderings.

The notion of hyperrandomness is introduced and it is proved that the set of the hyperrandom numbers is effectively inmune but not hyperinmune.