The delicate point in the formalistic position is to explain how the non-intuitionistic classical mathematics is significant, after having initially agreed with the intuitionists that its theorems lack a real meaning in terms of which they are true (S. C. Kleene, 1952).

The idea that english has more than one declarative "mood" has been dismissed as superstitious by empirically-minded grammarians of english for centuries--with such spectacular unsuccess, however, that the indicative/subjunctive dichotomy stands today as a cornerstone for philosophical and logical speculation about "conditionals." let me be next into the breach. i shall urge that there is no grammatical basis for any such distinction. and as for the particular adjudications of mood logicians and philosophers actually propose, there is neither rhyme nor reason (...) to them. my bent, then, is basically destructive. but i shall also be outlining a better taxonomy. (shrink)

It has been widely accepted in the past and it remains accepted in many quarters even now, that an ontologically economical position is to be rejected if the corresponding Platonic or otherwise ontologically prodigal discourse cannot be translated, paraphrased or otherwise ‘reduced’ to discourse exhibiting a more economical ontology. Such an attitude is often accompanied by the claim that the prodigal ontology explains some important truthsandthe demand that the nominalist or fictionalist or economicalist provide an alternative explanation for those truths (...) — perhaps in terms of ontologically economical ersatz substitutes for the prodigal entities. (shrink)