Nino Cocchiarella

Russell's involuted path in the development of his theory of logical types from 1903 to 1910-13 is examined and explained in terms of the development in his early philosophy of the notion of a logical subject vis-a-vis the problem of the one and many; i.e., the problem for russell, first, of a class-as-one as a logical subject as opposed to a class as many, and, secondly, of a propositional function as a single and separate logical subject as opposed to existing only in the many propositions that are its values

While operators for logical necessity and possibility represent "internal" conditions of propositions (or of their corresponding states of affairs), These conditions will be "formal", As is required by logical atomism, And not "material" in content if from the (pseudo) semantical point of view the modal operators range over "all the possible worlds" of a logical space rather than over arbitrary non-Empty sets of worlds (as is usually done in modal logic). Some of the implications of this requirement are noted and though several variants of realist logical atomism are distinguished and discussed, The theory of logical form developed is nominalist. Many of nominalism's difficulties and inadequacies become transparent in the context of logical atomism and are so noted

A minimal second order modal logic of natural kinds is formulated. Concepts are distinguished from properties and relations in the conceptual-logistic background of the logic through a distinction between free and bound predicate variables. Not all concepts (as indicated by free predicate variables) need have a property or relation corresponding to them (as values of bound predicate variables). Issues pertaining to identity and existence as impredicative concepts are examined and an analysis of mass terms as nominalized predicates for kinds of stuff is proposed. The minimal logic is extendible through a summum genus, an infima species or a partition principle for natural kinds

There are different views of the logic of plurals that are now in circulation, two of which we will compare in this paper. One of these is based on a two-place relation of being among, as in ‘Peter is among the juveniles arrested’. This approach seems to be the one that is discussed the most in philosophical journals today. The other is based on Bertrand Russell’s early notion of a class as many, by which is meant not a class as one, i.e., as a single entity, but merely a plurality of things. It was this notion that Russell used to explain plurals in his 1903 Principles of Mathematics; and it was this notion that I was able to develop as a consistent system that contains not only a logic of plurals but also a logic of mass nouns as well. We compare these two logics here and then show that the logic of the Among relation is reducible to the logic of classes as many

Some internal and philosophical remarks are made regarding a system of a second order logic of existence axiomatized by the author. Attributes are distinguished in the system according as their possession entails existence or not, The former being called e-Attributes. Some discussion of the special principles assumed for e-Attributes is given as well as of the two notions of identity resulting from such a distinction among attributes. Non-Existing objects are of course indiscernible in terms of e-Attributes. In addition, However, Existing objects indiscernible in terms of e-Attributes are indiscernible in terms of all attributes

Two fundamental categories of any ontology are the category of objects and the category of universals. We discuss the question whether either of these categories can be infinite or not. In the category of objects, the subcategory of physical objects is examined within the context of different cosmological theories regarding the different kinds of fundamental objects in the universe. Abstract objects are discussed in terms of sets and the intensional objects of conceptual realism. The category of universals is discussed in terms of the three major theories of universals: nominalism, realism, and conceptualism. The finitude of mind pertains only to conceptualism. We consider the question of whether or not this finitude precludes impredicative concept formation. An explication of potential infinity, especially as applied to concepts and expressions, is given. We also briefly discuss a logic of plural objects, or groups of single objects (individuals), which is based on Bertrand Russell’s (1903, The principles of mathematics, 2nd edn. (1938). Norton & Co, NY) notion of a class as many. The universal class as many does not exist in this logic if there are two or more single objects; but the issue is undecided if there is just one individual. We note that adding plural objects (groups) to an ontology with a countable infinity of individuals (single objects) does not generate an uncountable infinity of classes as many.

A conceptual theory of the referential and predicable concepts used in basic speech and mental acts is described in which singular and general, complex and simple, and pronominal and nonpronominal, referential concepts are given a uniform account. The theory includes an intensional realism in which the intensional contents of predicable and referential concepts are represented through nominalized forms of the predicate and quantifier phrases that stand for those concepts. A central part of the theory distinguishes between active and deactivated referential concepts, where the latter are represented by nominalized quantifier phrases that occur as parts of complex predicates. Peter Geach's arguments against theories of general reference in Reference and Generality are used as a foil to test the adequacy of the theory. Geach's arguments are shown to either beg the question of general as opposed to singular reference or to be inapplicable because of the distinction between active and deactivated referential concepts.

Conceptual realism begins with a conceptualist theory of the nexus of predication in our speech and mental acts, a theory that explains the unity of those acts in terms of their referential and predicable aspects. This theory also contains as an integral part an intensional realism based on predicate nominalization and a reflexive abstraction in which the intensional contents of our concepts are “object”-ified, and by which an analysis of predication with intensional verbs can be given. Through a second nominalization of the common names that are part of conceptual realism’s theory of reference (via quantifier phrases), the theory also accounts for both plural reference and predication and mass noun reference and predication. Finally, a separate nexus of predication based on natural kinds and the natural properties and relations nomologically related to those natural kinds, is also an integral part of the framework of conceptual realism