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- Esther Ramharter (2006). Making Sense of Questions in Logic and Mathematics: Mill Vs. Carnap. Prolegomena 5 (2):209-218.Whether mathematical truths are syntactical (as Rudolf Carnap claimed) or empirical (as Mill actually never claimed, though Carnap claimed that he did) might seem merely an academic topic. However, it becomes a practical concern as soon as we consider the role of questions. For if we inquire as to the truth of a mathematical statement, this question must be (in a certain respect) meaningless for Carnap, as its truth or falsity is certain in advance due to its purely syntactical (or formal-semantical) nature. In contrast, for Mill such a question is as valid as any other. These differing views have their consequences for contemporary erotetic logic.
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In earlier publicationss of the first author it was shown that intentional explanation of actions, functional explanation of biological traits and causal explanation of abnormal events share a common structure. They are called explanation by specification (of a goal, a biological function, an abnormal causal factor, respectively) as opposed to explanation by specification under a law. Explanation by specification is guided by a schematic train of thought, of which the argumentative steps not concerning questions were already shown to be logically valid (elementary) arguments. Independently, the second author developed a new, inferential approach to erotetic logic, the logic of questions. In this approach arguments resulting in questions, with declarative sentences and/or other questions as premises, are analyzed, and validity of such arguments is defined. In the prcsent paper it is shown that all four kinds of erotetic argumentative steps occurring in the train of thought of explanation by specification are valid arguments in the sense of inferential erotetic logic. Hence, in view of the fact thal tl~eo ther argumentative steps were already shown to be valid, it may be concluded that the logical structure of explanation by specification can be as well-established as that of explanation by nomological subsumption. Moreover, explanation by specification provides some illustrations of the applicability of erotetic logic in everyday life and some empirical sciences.
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For Rudolf Carnap the question ‘Do numbers exist?’ does not have just one sense. Asked from within mathematics, it has a trivial answer that could not possibly divide philosophers of mathematics. Asked from outside of mathematics, it lacks meaning. This paper discusses Carnap’s distinction and defends much of what he has to say.
"Homage to Rudolph Carnap."--Hempel, C. G. Rudolf Carnap, logical empiricist.--Wedberg, A. How Carnap built the world in 1928.--Eberle, R. A construction of quality classes improved upon the Aufbau.--Carnap, R. Observation language and theoretical language.--Kaplan, D. Significance and analyticity: a comment of some recent proposals of Carnap.--Wójcicki, R. The factual content of empirical theories.--Williams, P. M. On the conservative extensions of semantical systems: a contribution to the problem of analyticity.--Winnie, J. A. Theoretical analyticity.--Wedberg, A. Decision and belief in science.--Bohnert, H. G. Carnap's logicism.--Hintikka, J. Carnap's heritage in logical semantics.--Partee, B. H. The semantics of belief-sentences.--Kasher, A. Pragmatic representations and language-games.--Carnap, R. Notes on probability and induction.--Jeffrey, R. C. Carnap's inductive logic.--Hilpinen, R. Carnap's new system of inductive logic.--Kuipers, T. A. F. A generalization of Carnap's inductive logic. Essler, W. K. Hintikka versus Carnap.--Hintikka, J. Carnap and Essler versus inductive generalization.--Shimony, A. Carnap on entropy, introduction to "Two essays on entropy" by Rudolf Carnap.
The concept of search scenario is explicated in terms of erotetic logic, i.e., the logic of questions. Different kinds of erotetic search scenarios are characterized. The basic logical properties of erotetic search scenarios are analyzed.
This paper tries to show that although Carnap's distinction between internal and external questions in terms of a linguistic framework is philosophically important, and that although metaphysical questions are, as Carnap claims, external questions, Carnap's conclusion that all meaningful metaphysical questions are practical questions about language is not justified. This is done in three steps. First, it is argued that it is plausible to suppose that there is for languages a kind of external question other than the one kind Carnap specifies, because “language games” are like the game of chess in important ways and there seems to be such a kind of question for chess. Second, it is shown that at least some metaphysical questions can quite reasonably be interpreted as being of this kind. Third, reasons are given for rejecting Carnap's grounds for claiming that there is only one kind of external question.
According to the standard story (a) W. V. Quine’s criticisms of the idea that logic is true by convention are directed against, and completely undermine, Rudolf Carnap’s idea that the logical truths of a language L are the sentences of L that are true-in- L solely in virtue of the linguistic conventions for L , and (b) Quine himself had no interest in or use for any notion of truth by convention. This paper argues that (a) and (b) are both false. Carnap did not endorse any truth-by-convention theses that are undermined by Quine’s technical observations. Quine knew this. Quine’s criticisms of the thesis that logic is true by convention are not directed against a truth-by-convention thesis that Carnap actually held, but are part of Quine’s own project of articulating the consequences of his scientific naturalism. Quine found that logic is not true by convention in any naturalistically acceptable sense. But he also observed that in set theory and other highly abstract parts of science we sometimes deliberately adopt postulates with no justification other than that they are elegant and convenient. For Quine such postulations constitute a naturalistically acceptable and fallible sort of truth by convention. It is only when an act of adopting a postulate is not indispensible to natural science that Quine sees it as affording truth by convention ‘unalloyed’. A naturalist who accepts Quine’s notion of truth by convention is therefore not limited (as naturalists are often thought to be) to accepting only those postulates that she regards as indispensible to natural science.
This paper will deal with three questions regarding Carnap's transition from the position he held at the time of writing Syntax to the doctrines he held during his semantic phase: (1) What was Carnap's attitude towards truth at the time of writing Syntax? (2) What was Carnap's position regarding questions of reference and ontology at the time of writing Syntax? (3) Was Carnap's acceptance of Tarski's analysis of truth and reference detrimental to his philosophical project? Section 1 of this paper will deal with the first of these questions. Special attention will be paid to identifying what it was that prevented Carnap from defining a truth predicate for descriptive languages in Syntax. Section 2 of this paper will deal with the question of Carnap's attitude towards reference and ontology in Syntax. It will be shown that the attempt in Syntax to address ontological questions is seriously defective. Section 3 of this paper addresses the last of the questions posed above. It is argued that in the light of what is established in Sections 1 and 2, Carnap could not have retained the position of Syntax with respect to truth and reference.
A relativized concept of a possiblecorrect answer to a why-question is introduced. Acertain procedure of looking for acceptable answers towhy-questions is analyzed in terms of erotetic logic,i.e., the logic of questions.
Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic. CiteULike Connotea Del.icio.us What's this?
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