The main conclusion of the thesis is that, rather than deciding disputes over the validity of logical laws between classical and intuitionist logicians, Dummett’s and Prawitz’ proof-theoretic justification of deduction entails a pluralism in which both logics have their place. I begin by isolating the essential parts of Dummett’s and Prawitz theory. This allows me to modify it at various places so as to free it from verificationist presuppositions which permeate the original theory. Dummett and Prawitz think that the decision which logic is the justified one goes in favour of intuitionist logic. I show them to be mistaken at two points. First, I show that the meaning of negation cannot be defined proof-theoretically. It follows that the prooftheoretic justification of deduction cannot decide whether negation should be governed by classical or by intuitionist rules. As a consequence, Dummett and Prawitz are left with no good argument against classical logic. I argue that there is also no acceptable amendment of the theory to remedy this. Secondly, Dummett and Prawitz only consider deductions made from sets of hypotheses, but there is at least one other reasonable way of collecting them, which is used in relevance logic. I conclude that the proof-theoretic justification of deduction commits us to accepting at least classical, intuitionist and relevance logic. Because this logical pluralism is a consequence of the proof-theoretic justification of deduction, I argue that it is a wellmotivated position and outline how to defend it against objections that it is incoherent. In a formal chapter I specify the general forms of rules of inference and general methods for determining elimination/introduction rules for logical constants from their introduction/elimination rules. On this basis I re-define Dummett’s and Prawitz’ notions of harmony and stability in a formally precise way and provide generalised procedures for removing maximal formulas from deductions. The result is a general framework for proving normalisation theorems for a large class of logics. The thesis ends with some reflections on the consequences of pluralism for the relation between logic and metaphysics. I argue that what has to be given up is the thought that the proof-theoretic justification of deduction can decide the metaphysical issues between realists and anti-realists.

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The main purpose of the thesis is the establishment of an improved system of logical types. The absolutist view, according to which there exists only one hierarchy of types which has to be found out by consideration of empirical facts and by logical analysis, has been abandoned, and the attempt has been made to raise the whole problem from the material into the formal, the syntactical, sphere. Thereby such pseudo-problems disappear as usually arise when the borderline between cognoscence and stipulation is not strictly respected. From the two alternatives of treating the various branches of science either within one and the same linguistic system (Carnap's "Logischer Aufbau der Welt"; the "Unity of Science"-thesis of Physicalism), or separately in the form of axiomatic systems, I have chosen the latter; and accordingly, instead of erecting one system of types, conventions have been suggested for the erection of a special type-hierarchy for every given axiomatic system. In the course of the investigation, it has been necessary to discuss more or less independently a number of special logical problems in greater detail. Thus one chapter of the thesis has been devoted to the syntax of axiomatic systems, another to the introduction of parameters as a counterpart to constants and variables. Further, I have studied the concept of a cardinal number closely, and I have tried to make a small contribution to the theory of identity.

Orientador: Newton C. A. da Costa / Tese (doutorado)-Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-07-13T21:22:19Z (GMT). No. of bitstreams: 1 SanchezBotero_ClaraHelena_D.pdf: 10846766 bytes, checksum: b8527f7f03ce7c31c311fae84e1dfc9d (MD5) Previous issue date: 1988 / Resumo: Na presente tese apresenta-se uma descrição do sistema formal Lww(Ql, ee), sendo Lww a lógica de primeira ordem, Ql o quantificador generalizado de KEISLER e e o símbolo de HILBERT. Demonstra-se que o sistema é correto e completo e preserva a maioria das propriedades de teoria da prova e teoria de modelos da lógica de primeira ordem. Demonstra-se igualmente que o símbolo e é eliminável em Lww(e) em certos tipos de fórmulas a que chamaremos de e-invariantes e que, para este mesmo tipo de fórmulas, o símbolo e não é eliminável em Lww (Ql ,e ). Demonstra-se assim, o poder expressivo de e quando se acrescenta à lógica de primeira ordem, além do e, o quantificador generalizado Ql. Esses resultados podem ser estendidos tanto a outros operadores nominais (vbto's) quanto a outros quantificadores generalizados. Além disso, inclui-se neste trabalho, um resumo histórico dos operadores nominais, que procura mostrar a relevância da teoria geral de tais operadores e, em particular, dos teoremas de eliminação, para a lógica, a filosofia, a matemática e a lingüística / Abstract: Not informed. / Doutorado / Doutor em Lógica e Filosofia da Ciência

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In my thesis, I address the question ʽWhat normative status does logic have?', to argue that logical normativity is of a weak sort, and that its constraining power is similar to that of recommendations. The thesis first discusses the notion of logical validity and logical formality, then asks whether logic is a priori and whether it can provide a priori norms for thinking. Subsequently, the issue of the bridge principles linking formal logic to informal reasoning is addressed, jointly with a brief discussion of the deontic operators included in the bridge principles. Then, the thesis addresses three criticisms of the normative role of logic with respect to rational reasoning. The first criticism is discussed in the fourth chapter; it starts from the consideration of the cognitive limitations of human agents and discusses a model of rationality that takes those limitations into account. The second criticism is analyzed in the fifth chapter; it is motivated by the empirical studies in the psychology of reasoning, and discusses human reasoning from a descriptive point of view, lending support to the model of rationality presented in the fourth chapter. The third criticism, presented in the sixth and final chapter, addresses the normative role of logic from an a priori point of view, showing how the epistemic paradoxes are crucial for determining what normative import logic has on rational reasoning. The final chapter defends the main thesis that logic has a weak import on our reasoning, which resembles a recommendation rather than an obligation.

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