This paper is a reaction to G. Küng's and J. T. Canty's Substitutional Quantification and Leniewskian quantifiers'Theoria 36 (1970), 165–182. I reject their arguments that quantifiers in Ontology cannot be referentially interpreted but I grant that there is what can be called objectual — referential interpretation of quantifiers and that because of the unrestricted quantification in Ontology the quantifiers in Ontology should not be given a so-called objectual-referential interpretation. I explain why I am in agreement with Küng and Canty's recommendation (...) that Ontology's quantifiers not be substitutionally interpreted even if Leniewski intended them to be so interpreted. A notion of an interpretation which is referential but yet which does not interpret as an assertor of existence of objects in a domain is developed. It is then shown that a first order version of Ontology is satisfied by those special kind of referential interpretations which read as Something as epposed to Something existing. (shrink)

No detailed description available for "Strict finitism".

The purpose of this paper is to mark a significant difference between classical and several non-classical prepositional calculi. The argument presupposes familiarity with Kripke/Hintikka semantics for modal logic. The non-classical systems are Hintikka's logic of belief and alethic modal systems which have Kripke/Hintikka semantics. The difference is marked by showing that the semantic validity operator in classical logic behaves as a normal alethic necessity-operator while the non-classical semantic validity operators behave as normal deontic ought-operators. The crucial step is showing that (...) a formula, valid by non-classical semantics, can be falsified. I show that the negation of a non-classical thesis can be added to a consistent set of formulae without making the set inconsistent or any other set inconsistent. This is shown by observing that consistent sets of formulae do not need to be related to other consistent sets by any of the alternativeness relations of Kripke/Hintikka model structures for non-classical systems. The deontic behavior of non-classical semantical validity operators is interpreted as showing that being a thesis of a non-classical system means, not that the thesis is a logical truth, but that the thesis is the content of a norm on how we ought to use, crucial terms such as ‘believe’ and ‘necessity’. (shrink)

There is a review of how Mark Addis has made a case that it would require great effort for scant philosophical profit to formalize a notion of surveyability as a metamathematical predicate demarcating strict finitistic mathematics. It is then suggested how the notion of surveyability is useful in informal philosophizing about mathematics.