Identity Criteria of Common Nouns and dot-types for Copredication

Copredication, especially when combined with quantification, provides interesting examples to support the idea that common nouns have their own identity criteria, as once argued for by Geach and subsequently studied by others. In this paper, revisiting the use of dot-types in modern type theories to model copredication, we show that, when both copredication and quantification are involved, CNs are not just types but should better be interpreted as types associated with their own identity criteria. In other words, formally, CNs are setoids – pairs whose first component is a type that interprets the domain of a CN and whose second component gives the identity criterion for that CN. For copredication with quantification, identity criteria play an essential role in giving a proper treatment of individuation and counting and hence constructing appropriate semantics to facilitate reasoning correctly. With CNs being setoids, the dot-type approach provides an adequate theory for copredication in general and for copredication with quantification in particular. It is further explained that the CNs-as-types approach is still the appropriate characterisation of our approach to interpreting CNs since, in phenomena that do not involve the interaction of copredication with quantification, the identity criteria of related CNs are essentially the same and can be safely ignored.

Realistic structuralism’s identity crisis: A hybrid solution.

Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include ‘irreflexive two-place relations’. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly the same relations to all objects (including themselves). I conclude that realistic structuralists must compromise and treat some structures eliminativistically.Published in Analysis 66.3: 216–22.

Considerações acerca dos critérios de Identidade Intensional e Extensional na Conceitografia de Frege/Considerations on extensional and intensional identity criteria in Frege’s Begriffsschrift

Neste artigo daremos principal atenção aos dois critérios de identidade de conteúdo conceitual que estão presentes nos §§ 3 e 8 da Conceitografia de Gottlob Frege. Nosso propósito é analisar as características destes critérios da notação conceitual de Frege porque pretendemos delimitar a discussão em torno dos problemas relacionados às noções de identidade intensional e extensional. Dessa forma, pretendemos: (i) analisar os critérios de identidade de conteúdo conceitual presentes nos §§ 3 e 8 da Conceitografia com o objetivo de mostrar que Frege apresentou uma caracterização híbrida da noção de conteúdo conceitual (valor semântico) e (ii) fazer considerações a respeito de relações que podemos estabelecer entre os critérios intensionais e extensionais de Frege e Richard Kirkham presentes no livro Teorias da Verdade: Uma Introdução Crítica. Com tais comparações pretendemos averiguar: (iii) se o critério de identidade do § 8 da Conceitografia é idêntico ao critério extensional de equivalência material de Kirkham e (iv) se o critério de identidade do § 3 da Conceitografia é mais forte, mais fraco ou idêntico aos critérios intensionais de equivalência essencial e de equivalência de sinonímia de Kirkham.Abstract: In this paper we will give primary attention to two identity criteria of conceptual content that are present in §§ 3 and 8 of Gottlob Frege's Begriffsschrift. Our purpose is to analyze the characteristics of these criteria of conceptual notation of Frege because we want to delimit the discussion around problems related to the notions of intensional and extensional identity. Thus, we intend to: (i) analyze the identity criteria of conceptual content present in §§ 3 and 8 of Begriffsschrift aiming to show that Frege introduced a hybrid characterization of the notion of conceptual content (semantic value) and (ii) make considerations about the relationships that we establish between intensional and extensional criteria of Frege and Richard Kirkham present in the book Theories of Truth: A Critical Introduction. With such comparisons we intend to investigate: (iii) if the identity criterion of § 8 of Begriffsschrift is identical to the extensional criterion of material equivalence in Kirkham and (iv) if the identity criterion of § 3 of Begriffsschrift is stronger, weaker or identical to intensional criteria of essential equivalence and of synonyms equivalence of Kirkham. Key words: Identity, Intensional Criterion, Extensional Criterion.

In Search of a Purely Noematic Phenomenology

Husserl’s transcendental reduction admits of two motivations: the general methodological ban on begging the question, and the principle that a typology of objects ought to be based on a typology of my ways of cognizing them. As Husserl’s ‘transcendental phenomenology’ agrees with the ‘linguistic phenomenology’ of many analytic philosophers in being at bottom an effort to understand what precisely we mean to say by asserting that there ‘exists’ a ‘consciousness-independent’ or ‘transcendent’ world, the ‘residue’ of transcendental reduction is my subjective consciousness (my being aware of the world). My cognitive approaches to the latter and to that of somebody else are not only entirely different but ‘complementary’ in the sense of Bohr’s. In the course of searching for an identity criterion for temporal entities lacking a spatial localisation in the world, we can show that the allegedly noetic phenomenon of, say, my now seeing a cat is a noema, to wit, the cat-as-now-beingseen-by-me-in-such-and-such-a-manner. There is no sound base for postulating, over and above the noematic nature of my consciousness, a second, noetic, aspect thereof.

Do Sentences Have Identity?

We study here equiformity, the standard identity criterion for sentences. This notion was put forward by Lesniewski, mentioned by Tarski and defined explicitly by Presburger. At the practical level this criterion seems workable but if the notion of sentence is taken as a fundamental basis for logic and mathematics, it seems that this principle cannot be maintained without vicious circle. It seems also that equiformity has some semantical features ; maybe this is not so clear for individual signs but sentences are often considered as meaningful combinations of signs. If meaning has to play a role, we are thus maybe in no better position than when dealing with identity criterion for propositions. In formal logic, one speaks rather about well-formed formulas, but closed formulas are called sentences because they are meaningful in the sense that they can be true or false. Formulas look better like mathematical objects than material inscriptions and equiformity does not seem to apply to them. Various congruencies can be considered as identities between formulas and in particular "to have the same logical form". One can say that the objects of study of logic are rather logical forms than sentences conceived as material inscriptions.