Nino Cocchiarella Collection

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Professor Emeritus
Department of Philosophy
Indiana University Bloomington

Nino Cocchiarella (born 1933), Professor Emeritus of Philosophy at Indiana University, is best known for his work in formal logic and ontology.

He received his B.S. in Philosophy from Columbia University in 1958, and then went on to complete a Ph.D. and M.A. in Philosophy from the University of California, Los Angeles in 1966. His areas of special interest are logic and formal semantics; philosophy of mathematics, language, and science; artificial intelligence and cognitive science; metaphysics and comparative formal ontology; Montague grammar and philosophical linguistics; and Indian philosophy.

He is a member of the editorial board of Journal of Philosophical Logic, Metalogicon, and Axiomathes. He has been both an National Endowment for the Humanities and National Science Foundation fellow. Dr. Cocchiarella received the "Gladiatore dí Oro" award (Golden Gladiator) in 2004, the "Diploma di Benemerenza" in November 2002 for excellence in scholarship, and was awarded a "Cittadinanza Onoraria" (honorary citizenship) and given the keys to the city in November 2003 by Fragneto L'Abate, Benevento Province, Italy.

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Recent Submissions

Now showing 1 - 20 of 41
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    A Logical Reconstruction of Medieval Terminist Logic in Conceptual Realism
    (2001) Cocchiarella, Nino B􏰀.
    The framework of conceptual realism provides a logically ideal lan􏰈guage within which to reconstruct the medieval terminist logic of the 􏰉􏰊14th century􏰀 The terminist notion of a concept􏰇 which shifted from Ockham􏰄s early view of a concept as an intentional object 􏰅the 􏰃fictum theory􏰆 to his later view of a concept as a mental act 􏰅the intellectio theory􏰆􏰇 is reconstructed in this framework in terms of the idea of con􏰈cepts as unsaturated cognitive structures.
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    A Modal-Ontological Argument and Leibniz's View of Possible Worlds
    (2018-04) Cocchiarella, Nino
    We critically discuss an ontological argument that purports to prove not only that God, or a God-like being, exists, but in addition that God's existence is necessary. This requires turning to a modal logic, $S5$ in particular, in which the argument is presented. We explain why the argument fails. We then attempt a second version in which one of its premises is strengthened. That attempt also fails because of its use of the Carnap-Barcan formula in a context in which that formula is not valid. A third is presented as well using the proper name 'God' as a singular term, but it too fails for the same reason, though in a later section we show how this last argument can be validated under a re-interpretation of the quantifiers of the background logic. In our later sections, we explain what is wrong with the original first premise as a representation of what Leibniz meant by the consistency of God's existence, specifically as God's existence in a possible world. Possible worlds exist only as ideas in God's mind, and the consistency of God's existence cannot be God's existence in a possible world. Realism regarding possible worlds must be rejected. Only our world is real, the result of an ontological act of creation. We also explain in a related matter why according to Leibniz, Boethius, Aquinas and other medieval philosophers, God s omniscience does not imply fatalism.
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    Russells Logical Atomism 1914-1918: Epistemological Ontology and Logical Form
    (2017-05) Cocchiarella, Nino
    Logical analysis, according to Bertrand Russell, leads to and ends with logical atomism, an ontology of atomic facts that is epistemologically founded on sense-data, which Russell claimed are mind-independent physical objects. We first explain how Russell's 1914-1918 epistemological version of logical atomism is to be understood, and then, because constructing logical forms is a fundamental part of the process of logical analysis, we briefly look at what has happened to Russell's type theory in this ontology. We then turn to the problem of explaining whether or not the logical forms of Russell's new logic can explain both the forms of atomic facts and yet also the sentences of natural language, especially those about beliefs. The main problem is to explain the logical forms for belief and desire sentences and how those forms do not correspond to the logical forms of the facts of logical atomism.
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    Review: "An Algebraic Study of Tense Logic with Linear Time," by R. A. Bull
    (Journal of Symbolic Logic, 1971-03) Cocchiarella, Nino
    In these papers (the second of which is principally a correction and adumbration of the first) Bull constructs algebraic semantics which provide completeness theorems for three prepositional tense logics for linear time, depending on whether the linear ordering of moments is rational, real, or integral. It is also shown that the systems for time rational or real have the finite model property, but that the system for discrete (integral) time lacks this property. The notion of formulahood is the same for each of these propositional tense logics—in addition to the operators of the classical propositional calculus there are P, H, F, and G, which read, respectively, as "It has been the case that," "It has always been the case that," "It will be the case that," and "It will always be the case that." G and H are taken primitively with F and P defined as their respective duals.
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    Richard Montague and the Logical Analysis of Language
    (Martinus Nijhoff Publishers, 1981) Cocchiarella, Nino
    Richard Montague was an exceptionally gifted logician who made important contributions in every field of inquiry upon which he wrote. His professional career was not only marked with brilliance and insight but it has become a classic example of the changing and developing philosophical views of logicians in general, especially during the 1960s and 70s, in regard to the form and content of natural language. We shall, in what follows, attempt to characterize the general pattern of that development, at least to the extent that it is exemplified in the articles Montague wrote during the period in question.
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    Quantification, Time and Necessity
    (Oxford University Press, 1991) Cocchiarella, Nino
    The fundamental assumption of a logic of actual and possible objects is that the concept of existence is not the same as the concept of being. Thus, even though necessarily whatever exists has being, it is not necessary in such a logic that whatever has being exists; that is, it can be the case that there be something that does not exist. No occult doctrine is needed to explain the distinction between existence and being, for an obvious explanation is already at hand in a framework of tense logic in which being encompasses past, present, and future objects (or even just past and present objects) while existence encompasses only those objects that presently exist. We can interpret modality in such a framework, in other words whereby it can be true to say that some things do not exist. Indeed, as indicated in Section 3, infinitely many different modal logics can be interpreted in the framework of tense logic. In this regard, we maintain, tense logic provides a paradigmatic framework in which possibilism (i.e., the view that existence is not the same as being, and that therefore there can be some things that do not exist) can be given a logically perspicuous representation.
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    Tense Logic: A Study of Temporal Reference
    (University of California, Los Angeles, 1966) Cocchiarella, Nino
    This work is concerned with the logical analysis of topological or non-metrical temporal reference. The specific problem with which it successfully deals is a precise formalization of (first-order) quantificational tense logic wherein both an appropriate formal semantics is developed and a meta-mathematically consistent and complete axiomatization for that semantics given.
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    Logical Studies in Early Analytic Philosophy
    (Ohio State University Press, 1987) Cocchiarella, Nino
    The essays collected here deal with the development of analytic philosophy in the first quarter of the twentieth century. In addition to providing a historical account of early analytic philosophy, these essays also contain logical reconstructions of Frege's, Russell's, Meinong's, and Wittgenstein's views during the period in question. Several of these reconstructions can and have been used in the new logicolinguistic developments in pragmatics and intensional logic that make up the vanguard of contemporary analytic philosophy. Others, such as the interpretation of the logical modalities in logical atomism, or the determination of the objects of fiction and dreams in Meinong's theory of objects or Russell's early logic, provide a useful introduction, if not also a solution, to a number of problems confronting analytic philosophy today. Indeed, for that matter, all of the essays collected here provide a useful propaedeutic to much of the research now going on in the study of logic and language.
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    Conceptualism, realism, and intensional logic
    (Topoi, 1989-03) Cocchiarella, Nino
    Linguists and philosophers are sometimes at odds in the semantical analysis of language. This is because linguists tend to assume that language must be semantically analyzed in terms of mental constructs, whereas philosophers tend to assume that only a platonic realm of intensional entities will suffice. The problem for the linguist in this conflict is how to explain the apparent realist posits we seem to be committed to in our use of language, and in particular in our use of infinitives, gerunds and other forms of nominalized predicates. The problem for the philosopher is the old and familiar one of how we can have knowledge of independently real abstract entities if all knowledge must ultimately be grounded in psychological states and processes. In the case of numbers, for example, this is the problem of how mathematical knowledge is possible. In the case of the intensional entities assumed in the semantical analysis of language, it is the problem of how knowledge of even our own native language is possible, and in particular of how we can think and talk to one another in all the ways that language makes possible.
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    Conceptualism, Ramified Logic, and Nominalized Predicates
    (Topoi, 1986-03) Cocchiarella, Nino
    Conceptualism differs from intuitionism in being a theory about the construction of concepts and not about the construction of proofs. Constructive conceptualism is similar to nominalism in excluding an impredicative comprehension principle, but differs from nominalism in the kind of ramified predicative logic each validates. Ramified constructive conceptualism leads in a natural way to holistic conceptualism, and, unlike nominalism, both can extended to a type of realism in which some nominalized predicates denote abstract objects. Intermediate positions of conceptual realism are distinguished regarding which concepts can be projected to have abstract objects corresponding to their nominalizations.
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    Reference in Conceptual Realism
    (Synthese, 1998-02) Cocchiarella, Nino
    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.
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    Whither Russell's Paradox of Predication?
    (N.Y.U. Press, 1973) Cocchiarella, Nino
    Russell's paradox has two forms or versions, one in regard to the class of all classes that are not members of themselves, the other in regard to "the predicate: to be a predicate that cannot be predicated of itself." The first version is formulable in the ideography of Frege's Grundgesetze der Arithmetik and shows this system to be inconsistent. The second version, however, is not formulable in this ideography, as Frege himself pointed out in his reply to Russell. Nevertheless, it is essentially the second version of his paradox that leads Russell to avoid it (and others of its ilk) through his theory of types.
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    Review: "The Logic of Significance and Context, Vol. 1," by L. Goddard and R. Routley
    (Journal of Symbolic Logic, 1984-12) Cocchiarella, Nino
    The rejection of certain philosophical theses as nonsense has been a standard ploy in twentieth century philosophy - witness the rejection of metaphysics by logical positivism's identification of significance with verifiability. The ploy has been applied to non-philosophical (but no less bothersome) sentences as well - witness Russell's resolution of the paradoxes in terms of the significance criteria of the ramified theory of types. What is needed in all these cases, according to the authors of this text, is "a general formal theory of significance in terms of which significance claims, and arguments by means of which they are made, can be assessed" (pp. 5-6).
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    Conceptual Realism Versus Quine on Classes and Higher-Order Logic
    (Synthese, 1992-03) Cocchiarella, Nino
    The problematic features of Quine's ‘set’ theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as singular terms. We argue against Quine's view that predicate quantifiers can be given a referential interpretation only if the entities predicates stand for on such an interpretation are the same as the classes (assuming extensionality) that nominalized predicates denote as singular terms. Quine's alternative of giving predicate quantifiers only a substitutional interpretation is compared with a constructive version of conceptual realism, which with a logic of nominalized predicates is compared with Quine's description of conceptualism as a ramified theory of classes. We argue against Quine's implicit assumption that conceptualism cannot account for impredicative concept-formation and compare holistic conceptual realism with Quine's class Platonism.
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    Sortals, Natural Kinds and Re-Identification
    (Logique et Analyse, 1977-12) Cocchiarella, Nino
    Investigations into the logical structure underlying ordinary language and our common sense framework have tended to support the hypothesis that there are different stages of conceptual involvement and that while the structures elaborated at a later stage are in general not explicitly definable or reducible to those at the earlier they nevertheless presuppose them as conceptually prior bases for their own construction and elaboration-even when these conceptually prior structures are somehow eliminated or completely reconstructed at the later stages. This applies, moreover, not just to the conceptual structures underlying our common sense framework but to those underlying the development of logic, mathematics and the different sciences as well.
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    A New Formulation of Predicative Second Order Logic
    (Logique et Analyse, 1974) Cocchiarella, Nino
    In what follows, a predicative second order logic is formulated and shown to be complete with respect to the proposed model theoretic semantics. The logic differs in certain fundamental ways from the system formulated by Church in [1], § 58. The more important differences are noted and discussed throughout the present paper. A more specialized motivation for the new formulation is outlined in § 2.
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    Predication Versus Membership in the Distinction Between Logic as Language and Logic as Calculus
    (Synthese, 1988-10) Cocchiarella, Nino
    Two types of framework are distinguished regarding the nature of logic and the logical analysis of natural language. In the first, logic is a calculus subject to varying set-theoretic interpretations over domains of varying cardinality, and in this sense is based on a theory of membership in a set. This type need not restrict its analyses of natural language to extensional discourse only; e.g., Richard Montague's sense-denotation intensional logic, which has been used to provide analyses of intensional discourse, is really a type-theoretical set theory supplemented with a theory of senses. The analyses this type of framework provides are not entirely satisfactory, however, for reasons related to the way that intensional entities are analyzed in terms of membership in a set. The second type of framework, where logical forms are semantic structures in their own right, is based on predication as described in a formal theory of universals. This type of framework: gives a more adequate analysis of natural language and can be developed in a type-free way without generating the logical antinomies. Also, because a set-theoretic semantics provides only an extrinsic characterization of validity for this type of framework, such a semantics cannot be used to show that the laws of logic of this type of framework must be essentially incomplete.
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    Two Views of the Logic of Plurals and a Reduction of One to the Other
    (Studia Logica, 2015-08) Cocchiarella, Nino
    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.
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    Review: "Foundations Without Foundationalism, A Case for Second-Order Logic," by S. Shapiro
    (Notre Dame Journal of Formal Logic, 1993) Cocchiarella, Nino
    Foundations Without Foundationalism, A Case for Second-Order Logic (Ox-ford University Press, Oxford, 1991), by Stewart Shapiro, is an excellent book, covering of all of the main results in second-order logic and its applications to mathematical theories. Its main theme is that first-order logic does not adequately "codify the descriptive and deductive components of actual mathematical practice", and that first-order languages and semantics are also inadequate models of mathematics" (43). Second-order logic (under its "standard" semantics), Shapiro maintains, "provides better models of important aspects of mathematics, both now and in recent history, than first-order logic does" (v); and in that regard it is second-order, and not only first-order, logic that "has an important role to play in foundational studies" (ibid.). Indeed, the restriction of logic to first-order logic (without Skolem relativism) in such studies is "the main target of this book" (196).
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    Denoting Concepts, Reference, and the Logic of Names, Classes as Many, Groups and Plurals
    (Linguistics and Philosophy, 2005-04) Cocchiarella, Nino
    Bertrand Russell introduced several novel ideas in his 1903 Principles of Mathematics that he later gave up and never went back to in his subsequent work. Two of these are the related notions of denoting concepts and classes as many. In this paper we reconstruct each of these notions in the framework of conceptual realism and connect them through a logic of names that encompasses both proper and common names, and among the latter, complex as well as simple common names. Names, proper or common, and simple or complex, occur as parts of quantifier phrases, which in conceptual realism stand for referential concepts, i.e., cognitive capacities that inform our speech and mental acts with a referential nature and account for the intentionality, or directedness, of those acts. In Russell’s theory, quantifier phrases express denoting concepts (which do not include proper names). In conceptual realism, names, as well as predicates, can be nominalized and allowed to occur as "singular terms", i.e., as arguments of predicates. Occurring as a singular term, a name denotes, if it denotes at all, a class as many, where, as in Russell’s theory, a class as many of one object is identical with that one object, and a class as many of more than one object is a plurality, i.e., a plural object that we call a group. Also, as in Russell’s theory, there is no empty class as many. When nominalized, proper names function as "singular terms" just the way they do in so-called free logic. Leśniewski’s ontology, which is also called a logic of names can be completely interpreted within this conceptualist framework, and the well-known oddities of Leśniewski’s system are shown not to be odd at all when his system is so interpreted. Finally, we show how the pluralities, or groups, of the logic of classes as many can be used as the semantic basis of plural reference and predication. We explain in this way Russell’s "fundamental doctrine upon which all rests", i.e., "the doctrine that the subject of a proposition may be plural, and that such plural subjects are what is meant by classes [as many] which have more than one term" (Russell 1938, p. 517).