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- Richard Gaskin (2008). The Unity of the Proposition. Oxford University Press.Truth, falsity, and unity -- Sentences, lists, and collections -- Declarative and other kinds of sentence -- Declarative sentences and propositions -- Sentences, propositions, and truth-values -- Sentences, propositions, and unity -- Unity and complexity -- Reference and supposition -- Reference and signification -- Linguistic idealism and empirical realism -- Russell on truth, falsity, and unity (I) : 1903 -- Russell on truth, falsity, and unity (II) : 1910-13 -- Russell on truth, falsity, and unity (III) : 1918 -- Sense, reference, and propositions -- Russellian propositions, Fregean thoughts, and facts -- The location of propositions -- Proper names, concept-expressions, and definite descriptions -- Concept-expressions and Carnapian intensions -- Carnapian intensions and understanding -- Carnapian intensions and Russellian propositions -- Russellian propositions and functionality -- A revised semantic map -- Sentences as referring expressions -- False propositions at the level of reference -- The world's own language -- Signification and supposition revisited -- Frege and Russell on unity -- Saturatedness and unsaturatedness -- The copula as secundum adiacens and as tertium adiacens -- Frege and the Copula -- The paradox of the concept horse -- Russell on unity and the paradox -- An unsuccessful attempt to avoid the paradox -- The paradox and the level of language -- Reforming Frege's treatment of concept-expressions -- Concepts and functions -- The reformed Frege : refinements and objections -- Frege, Russell, and the anti-fregean strategy -- The anti-fregean strategy : the case of names -- Disquotation and propositional form -- The context principle -- Prabhakara semantics and the related designation theory -- For that is not a word which is not the name of a thing -- The impartial strategy -- Secundum and tertium adiacens, matter and form -- The hierarchy of levels and the syntactic priority thesis -- Fregean and anti-fregean strategies -- The anti-fregean strategy and relations (I) -- Interlude: The subject--predicate distinction -- The anti-fregean strategy and relations (II) -- The reality of relations -- Polyadicity, monadicity, and identity -- The anti-fregean strategy and Montague grammar -- Fregean and anti-fregean strategies : further comparison -- Ramsey on the subject : predicate distinction -- Dummett's attack on the anti-fregean strategy -- Linguistic idealism revisited -- Alternative hierarchies and the context principle -- The linguistic hierarchy and categorial nonsense -- Logical syntax and the context principle -- Proper names, singular terms, and the identity test -- Proper names, Leibniz's law, and the identity of indiscernibles -- The negation asymmetry test -- Dummett's tests for singular termhood -- Discarding the syntactic priority thesis -- Logical predication, logical form, and Bradley's regress -- Names, verbs, and the replacement test -- AnalyReading list | Discuss | Edit | Categorize |My bibliography
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In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein.
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| | Other links: informaworld.com scholarworks.umass.edu tandfonline.com dx.doi.org | Scholar | At my library | More options ... The idea that an utterance of a basic (nondeviant) declarative sentence expresses a single true-or-false proposition has dominated philosophical discussions of meaning in this century. Refinements aside, this idea is less of a substantive theses than it is a background assumption against which particular theories of meaning are evaluated. But there are phenomena (noted by Frege, Strawson, and Grice) that threaten at least the completeness of classical theories of meaning, which associate with an utterance of a simple sentence a truth-condition, a Russellian proposition, or a Fregean thought. And it may well be the case that a framework within which utterances express sequences of propositions provides much of what is needed to account for the relevant phenomena, a better overall picture of the way language works, and an enticingly uniform perspective on a variety of semantic problems. I do not myself take to theories that multiply propositions by appealing to propositions “presupposed” or to pairs of Fregean and Russellian propositions, or theories that show no respect for a distinction between semantics and pragmatics— where the former is the study of propositions whose general form and character is determined by word meaning and syntax—or for theories that blithely abandon general principles of composition and semantic innocence. I would like to sketch a package based on four interconnected ideas: (i) the meaning of an individual word is a sequence of instructions for generating a sequence of propositions (in conjunction with compositional instructions (syntax) and elements of context); (ii) utterances themselves are not bearers of truth or falsity; (iii) judgements of truth, falsity, commitment, and conflict are shaped, in part, by the weights attached to individual 1 propositions that occur in sequences expressed by utterances, weights that may be set (and reset) by contextual considerations; (iv) Fregean senses are superfluous; propositions might as well be Russellian (Mont Blanc and all its snow fields will do as well as any mode of presentation)..
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| | Scholar | At my library | More options ... Originally motivated by a sophism, Pardo's discussion about the unity of mental propositions allows him to elaborate on his ideas about the nature of propositions. His option for a non-composite character of mental propositions is grounded in an original view about syncategorems: propositions have a syncategorematic signification, which allows them to signify aliquid aliqualiter, just by virtue of the mental copula, without the need of any added categorematic element. Pardo's general claim about the simplicity of mental propositions is developed into several specific thesis about mental propositions: a) it is not judgement which gives its unity to mental propositions, but judicative acts always follow some previous apprehensive act that is simple in its own right; b) this simplicity is compatible with a certain kind of complexity, that can be explained in terms of the "causal history" of the acts of knowing; c) traditional conceptions about subject and predicate must be recast, while keeping their usual explicative power concerning logical properties; d) of course, the traditional conception about the copula has been modified, giving rise to a fully innovative conception of the nature of mental propositions. Nevertheless, this innovative conception of mental language seems still infected by certain "common sense" prejudices, which lead Pardo to propose also a provocative conception of vocal language, which I consider unnecessary.
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| | Scholar | At my library | More options ... It is not immediately clear from Wittgenstein’s Tractatus how to connect his idea there of an object with the logical ontologies of Frege and Russell. Toward clarification on this matter, this paper compares Russell’s and Wittgenstein’s versions of the thesis of an atomic fact that it is a complex composition. The claim arrived at is that whilst Russell (at times at least) has one particular of the elements of a fact – the relation – responsible for the unity of the whole, for Wittgenstein the unity of a fact is the product of copulative powers inherent in all its elements. All kinds of constituents of Tractarian facts – all kinds (forms) of object – are, to use Fregean terminology, unsaturated.
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| | Other links: hdl.handle.net jstor.org | Scholar | At my library | More options ... ‘The Unity of the Proposition’ is a label for a problem which has intermittently intrigued philosophers but which for much of the last century lay neglected in the sad, lightless room under the stairs of philosophical progress, along with other casualties and bugaboos of early analytic philosophy such as the doctrine of internal relations, the identity theory of truth, and Harold Joachim. Yet it was while struggling with this problem (among others), that Bertrand Russell built one of the first steps on the staircase by creating what came later to be called the theory of descriptions.1 According to that theory, statements containing definite descriptions are true only if there exists a unique thing satisfying the description. So nothing one says about ‘The Problem of the Unity of the Proposition’, for example, can be true unless there is one and only one such problem. Yet, as we shall explain below (§1), on the one hand it is unclear that there is any such problem at all, while, on the other, if there is a problem, there seem to be several. One might conclude, then, that everything we say in this paper is likely to be false. But perhaps the paper could be, in the context, appropriately treated as a ladder, to be kicked away after climbing. For Wittgenstein, too, was concerned with the problem: ‘At the centre of Wittgenstein’s project was the task of explaining the unity of the proposition’, says Michael Potter, for example.2 Wittgenstein had inherited the task from two of his philosophical mentors, Russell and Frege. Yet while Russell’s series of failed accounts of propositions, and then judgments, each of which was meant to resolve the problem, seemed ultimately to serve only as a sort of negative inspiration for him,3 Frege’s response to the problem proved a deep influence. We will outline Frege’s position as a backdrop to Wittgenstein’s below (§§2 and 3). As we will argue, one of the most important ways in which Wittgenstein’s position resembles Frege’s is precisely that his (Wittgenstein’s) solution to the problem of unity required treating his own book as an attempt to say the unsayable..
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| | Scholar | More options ... Gaskin's book The Unity of the Proposition is very rich in material. I will focus only on its central thesis: Gaskin holds that Bradley's regress (more precisely, one particular version of it) is not only innocent, but in fact philosophically significant because it plays a crucial role in solving what Gaskin calls the problem of the unity of the proposition . In what follows, I first explain what that problem is meant to be ( section 1 ), then I present and criticise Gaskin's proposal about how Bradley's regress bears on the problem ( section 2 ), and finally I sketch an alternative approach to the problem ( section 3 ).
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| | Other links: dx.doi.org | Scholar | At my library | More options ... The Russell-Myhill Antinomy, also known as the Principles of Mathematics Appendix B Paradox, is a contradiction that arises in the logical treatment of classes and "propositions", where "propositions" are understood as mind-independent and language-independent logical objects. If propositions are treated as objectively existing objects, then they can be members of classes. But propositions can also be about classes, including classes of propositions. Indeed, for each class of propositions, there is a proposition stating that all propositions in that class are true. Propositions of this form are said to "assert the logical product" of their associated classes. Some such propositions are themselves in the class whose logical product they assert. For example, the proposition asserting that all-propositions-in-the- class-of-all-propositions-are-true is itself a proposition, and therefore it itself is in the class whose logical product it asserts. However, the proposition stating that all-propositions-in-the-null-class-are-true is not itself in the null class. Now consider the class w, consisting of all propositions that state the logical product of some class m in which they are not included. This w is itself a class of propositions, and so there is a proposition r, stating its logical product. The contradiction arises from asking the question of whether r is in the class w. It seems that r is in w just in case it is not. This antinomy was discovered by Bertrand Russell in 1902, a year after discovering a simpler paradox usually called Russell's paradox ". It was discussed informally in Appendix B of his 1903 Principles of Mathematics . In 1958, the antinomy was independently rediscovered by John Myhill, who found it to plague the "Logic of Sense and Denotation" developed by Alonzo Church.
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| | Scholar | At my library | More options ... In Bertrand Russell’s The Principles of Mathematics and related works, the notion of a proposition plays an important role; it is by analyzing propositions, showing what kinds of constituents they have, that Russell arrives at his core logical concepts. At this time, his conception of proposition contains both a conventional and an unconventional part. The former is the view that propositions are the ultimate truth-bearers; the latter is the view that the constituents of propositions are “worldly” entities. In the latter respect, Russellian propositions are akin to states-of-affairs on some robust understanding of these entities. The idea of Russellian propositions is well known, at least in outline. Not so well known is his treatment of truth, which nevertheless grows directly out of this notion of proposition. For the early Russell, the import of truth is primarily metaphysical, rather than semantic; reversing the usual direction of explanation, he holds that truth is explanatory of what is the case rather than vice versa. That is, what properties a thing has and what relations it bears to other things is determined, metaphysically speaking, by there being a suitable array of true and false propositions. In the present paper, this doctrine is examined for its content and motivation. To show that it plays a genuine role in Russell’s early metaphysics and logic, I examine its consequences for (1) the possibility of truth-definitions and (2) the problem of the unity of the proposition. I shall draw a few somewhat tentative conclusions about where Russell stood vis-à-vis his metaphysics of propositions, suggesting a possible source of dissatisfaction that may have played a role in his eventual rejection of his early notion of proposition.
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| | Scholar | At my library | More options ... The problem of the ‘Unity of the Proposition’ is the problem of explaining the difference between a content-expressing declarative sentence and a ‘mere list’ of referents. The prevailing view is that such a problem is to be solved metaphysically, either by reducing our ontology to exclude propositions or universals, or by explaining how it is possible for a certain kind of complex entity – the ‘proposition’– to ‘unify’ its constituents. I argue that these metaphysical approaches cannot succeed; instead the only viable approach is linguistic, identifying features of the (type–) sentence itself that enable it to express a content. Thus the problem of the ‘Unity of the Proposition’ (distinguishing sentences from lists) is distinct from the problem of ‘propositional unity’ (explaining how the constituents of propositions form a unified content). I suggest that, while the latter problem is not pressing, the former does not permit of an answer which applies in generality in all languages; we can only fully explain the Unity of the Proposition for single languages or groups of similar languages.
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| | Other links: dx.doi.org | Scholar | At my library | More options ... It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition.
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| | Other links: tandfonline.com dx.doi.org | Scholar | At my library | More options ... Discussion of Richard Gaskin, The Unity of the Proposition
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