The object of the present discussion is to show that the analysis of indirect discourse obtained when the concept of assertion is construed as a relationship that obtains between the asserting person and the asserted proposition—along the familiar lines proposed by Church [3, 4]—is entirely adequate of itself to circumvent the semantical paradoxes in which indirect discourse is involved.

In his Foundations of Arithmetic, Frege aims to extend our a priori arithmetical knowledge by answering the question what a natural number is. He rejects conceptual analysis as a method to acquire a priori knowledge . Later he unsuccessfully tried to solve the problems that beset conceptual analysis . If these problems remain unsolved, which rational method can he use to extend our a priori knowledge about numbers? I will argue that his fundamental arithmetical insight that numbers belong (...) to concepts is based on the recognition that different sentences express the same thought. In Frege's philosophy of arithmetic, propositional analysis does the main work. How it can do this work will be discussed in sections 3, 4 and 5. Sections 6 and 7 explore this approach further. (shrink)

The work of Bertrand Russell had a decisive influence on the emergence of analytic philosophy, and on its subsequent development. The prize-winning Russell scholar Peter Hylton presents here some of his most celebrated essays from the last two decades, all of which strive to recapture and articulate Russell's monumental vision. Relating his work to that of other philosophers, particularly Frege and Wittgenstein, and featuring a previously unpublished essay and a helpful new introduction, the volume will be essential for anyone engaged (...) with the history of twentieth-century ideas. (shrink)

In the paper, we apply Kooi and Tamminga’s correspondence analysis to some conventional and functionally incomplete fragments of classical propositional logic. In particular, the paper deals with the implication, disjunction, and negation fragments. Additionally, we consider an application of correspondence analysis to some connectiveless fragment with certain basic properties of the logical consequence relation only. As a result of the application, one obtains a sound and complete natural deduction system for any binary extension of each fragment in (...) question. With the focus on exclusive disjunction we comparatively study the proposed systems. Finally, we discuss Segerberg’s systems for connectiveless and negation fragments and compare them with our systems. (shrink)

We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to give a (...) partial solution to the paradox of analysis. (shrink)

An important question in epistemology concerns how the two species of justification, propositional and doxastic justification, are related to one another. According to the received view, basing one’s belief p on the grounds that provide propositional justification to believe p is sufficient for the belief to be doxastically justified. In a recent paper, however, John Turri has suggested that we should reverse the direction of explanation. In this paper, I propose to see the debate in a new light (...) by suggesting that the best way to understand the relationship between these species of justification is by viewing propositional justification as an dispositional property that a subject can have with doxastic justification as its manifestation. I show how the debate in metaphysics over the question of how disposition statements should be analyzed runs parallel to the epistemological debate, and bring some of the results in the dispositions debate to bear on the epistemological question. I end by offering some tentative remarks regarding the order of priority of these two species of justification. (shrink)

On Zermelo's view, any mathematical theory presupposes a non-empty domain, the elements of which enjoy equal status; furthermore, mathematical axioms must be chosen from among those propositions that reflect the equal status of domain elements. As for which propositions manage to do this, Zermelo's answer is, those that are ?symmetric?, meaning ?invariant under domain permutations?. We argue that symmetry constitutes Zermelo's conceptual analysis of ?general proposition?. Further, although others are commonly associated with the extension of Klein's Erlanger Programme to (...) logic, Zermelo's name has a place in that story. (shrink)

Employing Constructive Type Theory Constructive Type Theory, we provide a logical analysis of[aut]Ibn SīnāIbn Sīnā’sIbn Sīnā descriptional propositions. Compared to its rivals, our analysis is more faithful to the grammatical subject-predicate structure of propositions and can better reflect the morphological features of the verbs that extend time to intervals. We also study briefly the logical structure of some fallacious inferences that are discussed by Ibn Sīnā. The CTT-framework makes the fallacious nature of these inferences apparent.

Normal 0 21 false false false ES-CO X-NONE X-NONE Procura-se com este artigo a posição da ética em relação com a análise lógica, no âmbito do “Circulo de Viena”, pelo pensamento de R. Carnap. Existem condições para determinar a aplicação do principio da verificabilidade, pela filosofia da linguagem, seguindo o pensamento de R. Carnap. Aqui serão apresentadas as lógicas deônticas, em orden á fundamentação lógica da Bioética, como forma de globalização lingüística da mesma.

In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have different underlying languages.

Having briefly sketched the aims of our paper, namely, to logically analyse the ascription of propositional attitudes to somebody else in terms, not of Fregean senses or of intensions-with-s, but of the intentional object of the person spoken about, say, the believer or intender (Section 1), we try to introduce the concept of an intentional object as simply as possible, to wit, as coming into view whenever two (or more) subjective belief-worlds strikingly diverge (Section 2). Then, we assess the (...) pros and cons of Frege’s view that the indirect reference of an expression is nothing but its customary sense (Sections 3–4), and call the reader’s attention to the fact that in belief ascriptions de re we take it for granted that the believer’s intentional object is at the same time a ‘citizen’ of the belief ascriber’s subjective world (or, for that matter, the real word), and that the idea of such a ‘dual citizenship’ is even more obviously presupposed in the cases of true belief and propositional knowledge (Section 5). Then, we try to argue that it is more fertile to take the belief ascriber’s intentional object to be, not the whole state of affairs the believer has in mind and thinks to exist, but the latter’s intentional object as such, that is, as being his intentional object (Section 6). Finally, we discuss the intricate and mostly neglected question of whether an intentional object’s inhabiting two or more subjective belief-worlds should be considered to be sort of a ‘transmundane identity’ in the numerical sense or rather in some deviant sense of the term, which can be specified as a momentous subcase of a ‘categorial difference’ (Section 7). (shrink)

// tl;dr A Proposition is a Way of Thinking // -/- This chapter is about type-theoretic approaches to propositional content. Type-theoretic approaches to propositional content originate with Hintikka, Stalnaker, and Lewis, and involve treating attitude environments (e.g. "Nate thinks") as universal quantifiers over domains of "doxastic possibilities" -- ways things could be, given what the subject thinks. -/- This chapter introduces and motivates a line of a type-theoretic theorizing about content that is an outgrowth of the recent literature (...) on epistemic modality, according to which contentful thought is broadly "informational" in its nature and import. The general idea here is that an object of thought is not a way *the world* could be, but rather a way *one's perspective* could be (with respect to a relevant representational question). I will spend the middle part of this chapter motivating and developing a version of this strategy that is, I’ll argue, well-suited to explaining clear phenomena concerning the attribution of perspectival attitudes -- in particular, attitudes towards loosely information-sensitive propositions -- with which extant approaches struggle. My overarching goal here will be to motivate a distinctive version of the "informational" approach -- the "Flexible Types" approach, which is based on the theory proposed in Charlow (2020). According to the Flexible Types approach, propositional attitude verbs are quantifiers over sets of possibilities, but a possibility is a type-flexible notion -- sometimes a possible world, sometimes a perspective, sometimes a set of possible worlds, sometimes a set of perspectives. -/- After introducing the Flexible Types approach, this chapter circles back to more traditional concerns for the analysis of propositions as types of possibilities -- Frege's Puzzle and the problem of Logical Omniscience. Here too the Flexible Types approach bears fruit. Although there are certainly significant differences -- I note some in the concluding section -- the gist of this theory is Hinitkkan or Lewisian in spirit (if not quite in letter). We can make progress on addressing the challenges for the analysis of propositional content in terms of types of possibilities, through empirically driven refinement of our notion of what kind of thing a "doxastic possibility" is. (shrink)

A Linguistic Analysis of Prior, Quine, and Searle on Propositional Attitudes, Martinich on Fictional Reference, Taglicht on the Active/Passive Mood Distinction in English, etc.

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal (...) class='Hi'>Analysis (SIA), as propounded by John Bell. Despite many parallels between SIA and Leibniz’s approach —the non-punctiform nature of infinitesimals, their acting as parts of the continuum, the dependence on variables (as opposed to the static quantities of both Standard and Non-standard Analysis), the resolution of curves into infinitesided polygons, and the finessing of a commitment to the existence of infinitesimals— I find some salient differences, especially with regard to higher-order infinitesimals. These differences are illustrated by a consideration of how each approach might be applied to Newton’s Proposition 6 of the Principia, and the derivation from it of the v2/r law for the centripetal force on a body orbiting around a centre of force. It is found that while Leibniz’s syncategorematic approach is adequate to ground a Leibnizian version of the v2/r law for the “solicitation” ddr experienced by the orbiting body, there is no corresponding possibility for a derivation of the law by nilsquare infinitesimals; and while SIA can allow for second order differentials if nilcube infinitesimals are assumed, difficulties remain concerning the compatibility of nilcube infinitesimals with the principles of SIA, and in any case render the type of infinitesimal analysis adopted dependent on its applicability to the problem at hand. (shrink)

Adversus Mathematicos x is the second book dedicated by Sextus to the discussion of the physical doctrines put forward by dogmatic philosophers. An extensive section deals with Diodorus Cronus' arguments concerning movement.

Adversus Mathematicos x is the second book dedicated by Sextus to the discussion of the physical doctrines put forward by dogmatic philosophers. An extensive section deals with Diodorus Cronus' arguments concerning movement.

It is a commonly held view that Frege's doctrine of senses and references is not compatible with the idea that there are de re beliefs. The present paper is meant to challenge that view. Moreover, it seeks to show that, instead of forcing Frege's semantic framework to answer questions raised by twentieth-century philosophy of language, we could try to find other questions to which it might be an answer. It is argued that the proper treatment of Frege's views requires the (...) acknowledgement of the central role of individualistic epistemology in his thought. Once this is recognized, Frege's doctrine of senses and references can be considered a theory, or at least a sketch of a theory, of cognition, which has interesting connections with Kant's and Husserl's views. (shrink)