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 -- Analysis and paradox -- Simple, complex, and logical predicates -- The grammatical copula and the logical copula -- Predication in Frege -- Two exegetical problems in Frege -- Inference and the logical predicate -- Unity and the logical predicate -- Bradley's regress and the tradition -- Russell and the general form of the proposition -- Wittgenstein's criticism of Russell -- Logical form in theTractatus -- Bradley's regress and the unity of the proposition -- The logical copula and theories of meaning -- Reference and the logical copula -- Bradley's regress and the analysis of meaning -- Vicious practical regresses -- Bradley's regress and the solution to the unity problem -- Propositions, sets, sums, and the objects themselves -- Bradley's regress and the infinite -- Vallicella's onto-theology -- A comparison with other innocent regresses -- Truth, falsity, and unity revisited -- Bradley's regress, realism, and states of affairs -- Unity and use -- The unity of sentences and the unity of complex names (I) -- The unity of sentences and the unity of complex names (II) -- Congruence, functionality, and propositional unity -- Davidson on predication -- Epilogue: The limits of language. (shrink)
The paper contains a critical analysis of pluripropositionalism (or: multiple proposition approach), the view defended in recent years by authors such as Eros Corazza, Kepa Korta and John Perry.
Austin rejects the contention that every proposition has a contradictory. This paper finds problems with the case Austin makes for rejecting the contention in question.
I argue that the best way to solve Russell's problem of the relationship between propositions and their constituents is to think of propositions as properties of worlds. I argue that this view preserves the strengths and avoids some of the weaknesses of the view of the metaphysics of propositions defended by Jeff King in his _The Nature and Structure of Content_, and that it provides an explanation of the representational properties of propositions and the nature of indexical belief. I conclude (...) by discussing some problems about how to think about the semantics of propositional attitude ascriptions, if a view of this sort is correct. (shrink)
This monograph offers a reappraisal of the role of Bertrand Russell's philosophical works in establishing the analytical tradition in philosophy. It's main aims are to improve our understanding of the history of analytical philosophy, to engage in the important disputes surrounding the interpretation of Russell's philosophy, and to make a contribution to central issues in current analytical philosophy. Hence, this book will find a place on the bookshelf of many philosophers across the world.
In this article I present a summary of Bertrand Russell's protracted attempts to solve the problem of the unity of the proposition, and explain the significance of the problem for Russell's philosophy. Unlike many other accounts which take the problem to be confined to Russell's early theories of propositional content, I argue that the problem (or variants of it) is a recurring theme throughout the whole of Russell's career.
‘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.. (shrink)
Draft for Martinich and Hoekstra (ed.), Oxford Handbook of Hobbes. -/- Language was central to Hobbes's understanding of human beings and their mental abilities, and criticism of other philosophers' uses of language became a favorite critical tool for him. This paper connects Hobbes's theories about language to his criticisms of others' language, examining Hobbes's theories of propositions and truth, and how they relate to his claims that various sorts of proposition are absurd. It considers whether Hobbes in fact means (...) anything more by 'absurd' than 'false'. And it pays particular attention to Hobbes's categorization of causes of absurdity and of types of incoherent proposition, arguing that Hobbes's approach is only loosely related to later discussions of category mistakes. (shrink)
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 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)
According to Richard Gaskin, The Problem of the Unity of the Proposition is to explain 'what distinguishes propositions from mere aggregates, and enables them to be true or false' (18).1 This problem arises from the simpler problem of distinguishing a sentence from a 'mere list' of words (1). The unity of a sentence is due to its syntax, a level of structure which is not apparent in the string of words which are uttered or written, and which distinguishes a (...) sentence from a list. However, if one holds that sentences express propositions that are composed of objects which serve as semantic referents of its words, then the problem of unity becomes one about the metaphysics of propositions. What constitutes a .. (shrink)
The paper presents an interpretation of the thinking behind the early Wittgenstein's "general form of the proposition." It argues that a central role is played by the assumption that all domains of discourse are governed by the same laws of logic. The interpretation is presented partly through a comparison with ideas presented recently by Michael Potter and Peter Sullivan; the paper argues that the above assumption explains more of the key characteristics of the "general form of the proposition" (...) than Potter and Sullivan suppose, including, in particular, its claim that the bases from which all other propositions are derived must be elementary propositions. (shrink)
Fitch’s paradox of knowability is an apparently valid reasoning from the assumption (typical of semantic anti-realism) that every true proposition is knowable to the unacceptable conclusion that every true proposition is known. The paper develops a critical dialectic wrt one of the best motivated solutions to the paradox which have been proposed on behalf of semantic anti-realism—namely, the intuitionistic solution. The solution consists, on the one hand, in accepting the intuitionistically valid part of Fitch’s reasoning while, on the (...) other hand, exploiting the characteristic weakness of intuitionistic logic in order to preserve the consistency of such acceptance with the denial of omniscience. It is first remarked how the solution still commits one to acceptance of modal claims which are unwarranted even by the lights of standard intuitionistic semantics. A novel form of the paradox is then introduced, which focuses on infallibility rather than omniscience and derives, from semantic anti-realism and a highly plausible constraint on knowledge, that every believed proposition is not untrue. Because of the logical form of this conclusion, an analogue of the intuitionistic solution for the novel form of the paradox would require drawing the characteristic intuitionistic distinctions wrt decidable propositions, which cannot be done. Semantic anti-realism still intuitionistically entails the unacceptable conclusion that every believed (decidable) proposition is true. (shrink)
The medieval philosopher Jean Buridan says that at one time, he favored a solution to Liar−type paradoxes that relied on the claim that "every proposition, by its very form, signifies or asserts itself to be true."1 (I shall refer to this as Buridan's view, though he came to reject it when he wrote his Sophismata , in which he reports the view.) C.S. Peirce also suggested something like this in response to the Liar, and in a classic discussion of (...) Buridan, Arthur Prior evinces great sympathy for the view (in contrast to his rejection of Buridan's official solution).2 But what exactly does it mean for an arbitrary proposition to assert itself to be true? And is it really a plausible view to hold that every proposition does assert itself to be true? (shrink)
“To this day, partiality approaches to the paradox have been dogged by the so-called ‘Strengthened Liar’. .... The Strengthened Liar observes that if we follow a partiality theorist and declare the Liar sentence* neither true nor false (or failing to express a proposition,. or suffering from some sort of grave semantic defect), then the paradox is only pushed back. For we can go on to conclude that whatever this status may be, it implies that the Liar sentence is not (...) true. This claim is true, but it is just the Liar sentence again.* We are back in paradox.” (Glanzberg 2002, p. 468, bold emphasis added.) Cf.: “We are back in our contradiction,”(Glanzberg 2001, p. 222). *The Liar sentence intended is evidently the sentence ‘the Liar sentence is not true’, and, the Liar sentence = ‘the Liar sentence is not true’. Cf.: “Consider a Liar sentence: ...let us take a sentence l which says l is not true. We can, informally, reason as.. (shrink)
There are parallels between certain responses to local epistemological scepticism about religious belief and an influential reply to radical epistemological scepticism. What ties both accounts together is that they utilise, either implicitly or explicitly, a “hinge” proposition thesis which maintains that the pivotal beliefs in question are immune to sceptical attack even though they lack sufficient epistemic grounds. It is argued that just as this strategy lacks any anti-sceptical efficacy in the context of the radical sceptical debate, so it (...) offers no defence against a localised scepticism regarding religious belief either. What the defender of religious belief should do, it is claimed, is re-examine the manner in which a commitment to the doctrine of epistemological internalism underlies the sceptical attack. (shrink)
Bertrand Russell’s 1903 masterpiece The Principles of Mathematics places great emphasis on the need to separate propositions from psychological items such as thoughts. In 1919 (and until the end of his career) Russell explicitly retracts this view, however, and defines propositions as “psychological occurrences”. These psychological occurrences are held by Russell to be mental images. In this paper, I seek to explain this radical change of heart. I argue that Russell’s re-psychologising of the proposition in 1919 can only be (...) understood against the background of his struggle with the problem of the unity of the proposition in earlier work. Once this is recognized, and the solution to the problem offered by the 1919 theory is appreciated, new light is also shed on Russell’s naturalism. I go on to compare Russell’s psychological “picture theory” with the vehemently anti-psychological picture theory of Wittgenstein’s Tractatus Logico-Philosophicus and suggest that, once the background of the dispute is brought into clearer focus, Russell’s position can be seen to have many advantages over its more celebrated rival. (shrink)
In this paper we discuss the distinction between sentence and proposition from the perspective of identity. After criticizing Quine, we discuss how objects of logical languages are constructed, explaining what is Kleene’s congruence—used by Bourbaki with his square—and Paul Halmos’s view about the difference between formulas and objects of the factor structure, the corresponding boolean algebra, in case of classical logic. Finally we present Patrick Suppes’s congruence approach to the notion of proposition, according to which a whole hierarchy (...) of congruences leads to different kinds of objects. (shrink)
Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts (and the views of his mentor, Isaac Barrow) shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all (...) quantity (which is what measurement makes known) is ultimately related to spatial extension. I use this conception of Newton’s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia (beginning in Sect. 2 of Book I). The placementof Kepler’s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry. (shrink)
The Problem of Doxastic Shift may be stated as a dilemma: on the one hand, the distribution of nominal complements of the form `the that p strongly suggests that `that-clauses cannot be univocally assigned propositionaldenotations; on the other hand, facts about quantification strongly suggest that `that-clauses must be assigned univocal denotations. I argue that the Problem may be solved by defining the extension of a proposition to be a set of facts or, more generally, conditions. Given this, the logical (...) operation of descriptive predication can be introduced in a way that resolves the dilemma withoutsacrificing the singular term analysis of `that-clauses. (shrink)
There are two major semantic theories of proper names: Semantic Descriptivism and Direct Reference. According to Semantic Descriptivism, the semantic content of a proper name N for a speaker S is identical to the semantic content of a definite description “the F” that the speaker associates with the name. According to Direct Reference, the semantic content of a proper name is identical to its referent. Semantic Descriptivism suffers from a number of drawbacks first pointed out by Donnellan (1970) and Kripke (...) (1972). Direct Reference faces difficulties of its own, most importantly the problem of empty names. The most promising Directly Referential solution to this problem is the Unfilled Proposition view, according to which utterances of sentences containing empty names semantically express unfilled propositions. But this view faces the problem of accounting for the intuition that negative existentials involving empty names are true. The most promising way of dealing with this problem within Unfilled Proposition theory is to suppose (i) that utterances of sentences may be used to pragmatically convey propositions they do not semantically express, and (ii) that the proposition pragmatically conveyed by a speaker S's utterance of a sentence containing an empty name N (where “the F” is a definite description S associates with N) is identical to the proposition semantically expressed by an utterance of the sentence obtained by replacing N with “the F”. Call this view “Pragmatic Descriptivism”. With respect to the problem of negative existentials, Pragmatic Descriptivists can insist that, although an utterance of “Santa does not exist” is literally neither true nor false, our taking it to be true may be explained as the result of our having confused the unfilled proposition it semantically expresses with the clearly true descriptive proposition it pragmatically conveys. Despite its theoretical virtues, Pragmatic Descriptivism has recently come under fire. Everett (2003), in particular, has advanced four different lines of criticism, to which Adams and Dietrich (2004) have responded in some detail. In this article, I have two main aims. The first is to argue that Adams and Dietrich's replies to Everett's criticisms (with one exception) are ineffective. I conclude that there is no acceptable strategy for solving the problem of empty names within Direct Reference theory. The second is to argue that there is a promising alternative to Semantic Descriptivism and Direct Reference that requires us to fill unfilled propositions with names, thereby solving the problem of empty names. (shrink)
To understand pre-Fregean theories of judgment and proposition, such as those found in Locke and the Port-Royal logic, it is important to distinguish between propositions in the modern sense and propositions in the pre-Fregean sense. By making this distinction it becomes clear that these pre-Fregean theories cannot be meant to solve the propositional attitude problem. Notwithstanding this fact, Locke and Arnauld are able to make a distinction between asserted and unasserted propositions (in their sense). The way Locke makes this (...) distinction turns out to be very different from the way it is made by Arnauld. (shrink)
Within relevance theory the two local pragmatic processes of enrichment and loosening of linguistically encoded conceptual material have been given quite distinct treatments. Enrichments of various sorts, including those which involve a logical strengthening of a lexical concept, contribute to the proposition expressed by the utterance, hence to its truth-conditions. Loosenings, including metaphorical uses, do not enter into the proposition expressed by the utterance or affect its truth-conditions; they stand in a relation of 'interpretive resemblance' with the linguistically (...) encoded concept used to represent them. This asymmetric treatment is questioned here, arguments are given for an account which reflects the complementarity of these processes and several alternative symmetrical treatments are explored. (shrink)
Between 1903 and 1918 Russell made a number of attempts to understand the unity of the proposition, but his attempts all foundered on his failure clearly to distinguish between different senses in which the relation R might be said to relate a and b in the proposition aRb: he failed to distinguish between the relation as truth-maker and the relation as unifier, and consequently committed himself again and again to the unacceptable consequence that only true propositions are genuinely (...) unified. There is an anticipation of this confusion in the writings of the fourteenth-century philosopher Richard Brinkley. (shrink)
The notion of a proposition as a set of possible worlds or states occupies central stage in probability theory, semantics and epistemology, where it serves as the fundamental unit both of information and meaning. But this fact should not blind us to the existence of prospects with a different structure. In the paper I examine the use of random variables—in particular, proposition-valued random variables—in these fields and argue that we need a general account of rational attitude formation with (...) respect to them. (shrink)
This article argues in support of the proposition that “A Personality Disorder May Nullify Responsibility for a Criminal Act.” Building upon research in categorical and dimensional controversies in diagnosis, neurocognitive science and the behavioral genetics of mental disorders, and difficulties in differential diagnosis and co-morbidity with personality disorders, this article holds that a per se rule barring personality diagnosis as a basis for a defense of legal insanity is scientifically and conceptually indefensible. Rather, focus should be upon the severity (...) and impact in specific cases of any legally relevant functional deficits arising from a mental disorder (including personality disorders). Failure to do so risks potentially misleading “battles of the experts” about a defendant's diagnosis in criminal responsibility defenses and improper usurpation of the role of the legal finder of fact as mental health expert witnesses are inserted as gatekeepers indefensibly based upon diagnosis. Implications for practice and public policy are considered, including a “modest proposal” for post-trial management of defendants found not guilty by reason of insanity on the basis of functional deficits arising from personality disorder. (shrink)
This article attempts to explore ancient Chinese philosophical thought by analyzing how pioneering Chinese thinkers made judgments and inferences, and compares it to ancient Greek philosophy. It first addresses the starting-point and the object of cognition in Chinese ancient philosophy, then analyses how early thinkers construed definition and proposition, and finally discusses how they made inferences on the basis of definition and proposition. It points out that categorization is an important methodology in ancient Chinese philosophy, and that rectification (...) of names and the doctrine of the mean are key criteria in making judgments. (shrink)
In the first half of the 17th century the Aristotelian view that the same statement or belief may be true at one time and false at another and, on the other hand, the conception of a mental proposition as a fully explicit thought that lends a definite meaning to a declarative sentence originated a lively debate concerning the question whether a mental proposition can change its truth-value.In this article it is shown that the defenders of a negative answer (...) and the advocates of a positive answer argued on the basis of different notions of what a mental proposition is:one side taking it as more or less equivalent to a specific utterance?meaning and the other side as more or less equivalent to a generic sentence-meaning. (shrink)
Can we find propositions that cannot rationally be denied in any possible world without assuming the existence of that same proposition, and so involving ourselves in a contradiction? In other words, can we find transworld propositions needing no further foundation or justification? Basically, three differing positions can be imagined: firstly, a relativist position, according to which ultimately founded propositions are impossible; secondly, a meta-relativist position, according to which ultimately founded propositions are possible but unnecessary; and thirdly, an absolute position, (...) according to which such propositions are necessary. In this short essay I show that under the premise of modal logic S5 with constant domain there are ultimately founded propositions and that their existence is even necessary, and I will give some reasons for the superiority of S5 over other logics. (shrink)
Human embryonic stem cell research has generated considerable discussion and debate in bioethics. Bioethical discourse tends to focus on the moral status of the embryo as the central issue, however, and it is unclear how much this reflects broader community values and beliefs related to stem cell research. This paper presents the results of a study which aims to identify and classify the issues and arguments that have arisen in public discourse associated with one prominent policy episode in (...) the United States: the 2004 Californian Stem Cell Research and Cures Initiative (also known as Proposition 71). The findings show that public discourse about Proposition 71 is characterised by a broader range of issues than those usually addressed in scholarly publications and public policy documents. While attention to the moral status of the embryo is an important issue in stem cell research, making it the main focus of public discourse has a polarising effect. This also limits opportunities to identify shared values, understand how political alliances are forged, and develop social consensus. Implications for future research and policy are discussed. (shrink)
Two different uses of ‘proposition’ are distinguished: the meaning of an eternal sentence is distinguished from that which can be asserted, believed, conjectured, and so on. It is argued that, in the second sense of ‘proposition’, it is not the case that every proposition can be expressed by an eternal sentence.
Peter H. Hare (1935-2008) developed informed, original views about the proposition: some published (Hare 1969 and Hare-Madden 1975); some expressed in conversations at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse (1881-1969), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term.1Hare was already prominent in the University of Buffalo's Philosophy Department (...) in 1969 when I was appointed. Soon after, he became Chair. As his Associate Chair from 1971to 1975, I spent many hours with him in Buffalo and on professional trips .. (shrink)
A proposition is associated in classical mechanics with a subset of phase space, in quantum logic with a projection in Hilbert space, and in both cases with a 2-valued observable or test. A theoretical statement typically assigns a probability to such a pure test. However, since a pure test is an idealization not realizable experimentally, it is necessary — to give such a statement a practical meaning — to describe how it can be approximated by feasible tests. This gives (...) rise to a search for a formal representation of feasible tests, which leads via mixed tests (weighted means of pure tests) to vague tests (convex sets of mixed tests). A model is described in which the latter form a continuous lattice; the pure and mixed tests are the maximal elements and the feasible tests form a basis. Each type of test has its own logic; this is illustrated by the passage from mixed tests to pure tests, which corresponds to the transition from L to classical logic. (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)
The distinctions among facts, propositions, and events are supported by linguistic analyses segregating factive, propositional, and eventive predicates. The concepts of fact, proposition, and event may be basic categories of human understanding, as well as being ontologically significant. FPE theory was developed in part to reject the identification of facts with true propositions. The degree of ‘fineness’ of individuations within each category results from how closely event-, fact-, or proposition-individuation mirrors linguistic semantic structure. Event structure is not reflected (...) in many event phrases. Fact- and proposition-structure typically does reflect semantic structures of factive and propositional clauses. The relevant properties for event individuation are all expressible by eventive predicates. Fact and proposition individuation is not as straightforward, because so many factives and propositionals do not express properties relevant to the Leibnizian principle. The intractability of proposition individuation may be overcome through an explanation of fact cognition. (shrink)
After his refutation of the doubts concerning Proposition I.7 (in the Book of solving doubts), Ibn al-Haytham mentions three possible ways in which circles may intersect, submitting them to the following “intuitive” argument: one part of one of the two circles is situated inside of the other circle, and its other part is situated outside of it. One is therefore tempted to believe that the commentator accepts the principle of continuity in the case of circles, since his argument has (...) the following meaning: if a circle is divisible into two parts (or, again, passes through two points), one of which (or one of the two points) is situated inside the other circle, and the other outside of it, then the two circles cut one another. The author of this article proposes to establish the limits of this belief, on the basis of the following reflections: 1). It will be noted first of all that what could be called the ‘principle of the intersection of circles’ does not constitute ipso facto a principle in the mind of Ibn al-Haytham: no allusion is made to it in the commentary on Proposition I.1, among others. 2) It will be established later on that if one accepts (according to the explanation of Ibn al-Haytham in his Commentary on the premisses) that a line is the result of the movement of a point, the principle of continuity should be considered by him as something which is obvious by itself, without being stated. This conclusion will be based on an analysis of the notion of continuity in its classical meaning, and on Ibn al-Haytham’s commentary on Proposition X.1. 3) On the other hand, we should note the presence of a ‘sketch’ of topological language, which Ibn al-Haytham develops for the notion of a circle (particularly in the Commentary): one could say in this context that his reflection constitutes an important, if not principal, stage in the process which was to lead to the explicit formulation of the principle of continuity. Footnotes1 Je voudrais remercier chaleureusement Monsieur R. Rashed d'avoir bien voulu lire la première version de cet article, m'envoyer certaines de ses publications et me communiquer ses suggestions dont j'ai essayé de tirer le plus grand profit dans la révision que voici. Toutes les insuffisances qui s'y trouvent ne peuvent que m'être imputées. (shrink)
Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Moore-sentences is that not all propositions are known after their announcement, i.e., not every proposition is successful. Fitch's and Moore's results are related, as they equally apply to standard notions of knowledge and belief (S 5 and KD45, respectively). If we (...) interpret ‘successful’ as ‘known after its announcement’ and ‘knowable’ as ‘known after some announcement’, successful implies knowable. Knowable does not imply successful: there is a proposition ϕ that is not known after its announcement but there is another announcement after which ϕ is known. We show that all propositions are knowable in the more general sense that for each proposition, it can become known or its negation can become known. We can get to know whether it is true: ◊(Kϕ ∨ K¬ϕ). This result comes at a price. We cannot get to know whether the proposition was true. This restricts the philosophical relevance of interpreting ‘knowable’ as ‘known after an announcement’. (shrink)
Part of rethinking philosophy today, the author believes, is to rethink our logical concepts. The author questions the ontological existence of the proposition as the content of sentential utterances—written or spoken—as it was originally proposed by John Searle. While a performative is an utterance where the speaker not only utters a sentential or illocutionary content such as a statement, but also performs the illocutionary force such as the act of stating, the author reasserts John Austin’s constative as the general (...) label (genus) of specific utterances (species) that can be rendered true or false such as a statement, assertion, description, and prediction. In the remainder of the paper, the author tries to show that it is a category mistake for someone to assert a statement or to state an assertion. (shrink)
The interest of the field of Mathematical Knowledge Management is predicated on the assumption that by investing into markup or formalization of mathematical knowledge, we can reap benefits in managing (creating, classifying, reusing, verifying, and finding) mathematical theories, statements, and objects. This global value proposition has been used to motivate the pursuit of technologies that can add machine support to these knowledge management tasks. But this (rather naive) technology-centered motivation takes a view merely from the global (macro) perspective, and (...) almost totally disregards the user’s point of view and motivations for using it, the local (micro) perspective. In this paper we go a first step into a more principled analysis of the MKM value proposition by focusing on motivations for mathematical search engines from the micro perspective. We will use a table-based method called the “Added-Value Analysis” (AVA) developed by one of the authors. Even though we apply the AVA only to mathematical search engines, the method quickly leads to value considerations that are relevant for the whole field of MKM. (shrink)
The concept of a proposition is important in several areas of philosophy and central to the philosophy of language. This collection of readings investigates many different philosophical issues concerning the nature of propositions and the ways they have been regarded through the years. Reflecting both the history of the topic and the range of contemporary views, the book includes articles from Bertrand Russell, Gottlob Frege, the Russell-Frege Correspondence, Alonzo Church, David Kaplan, John Perry, Saul Kripke, Hilary Putnam, Mark Richard, (...) Scott Soames, and Nathan Salmon. (shrink)
The recent global financial crisis and worst recession since the Great Depression underscore the theoretical and practical importance of defining requirements for assessing alternative theories of capitalism. The expressed goal of Freeman and his co-authors is to replace value-allocating ‘shareholder capitalism’ with value-creating ‘stakeholder capitalism.’ Each theory combines a different value proposition and principal-agent conception. So interpreted, the value creation proposition suggests two requirements for assessing alternative theories. A proposed better theory of capitalism should demonstrate first practicality of (...) prescriptive guidance for managers and second superiority of its embedded value proposition for sustainable long-term performance. Shareholder and stakeholder conceptions are not the only approaches to developing a theory of capitalism embedding a different value proposition and agency model. Two other conceptions suggest organisational wealth and corporate social responsibility (CSR) theories of capitalism. All four alternatives meet the relatively minimal requirement of practicality. Freeman and his co-authors argue the value creation proposition will outperform the value allocation proposition. But organisational wealth and CSR theories may also outperform shareholder capitalism. Demonstrating that stakeholder capitalism will outperform organisational wealth and CSR theories depends on which principal and value proposition one judges most important in particular conditions. (shrink)
A História atesta diferentes abordagens da “proposição”. A proposição tem sido considerada como objeto de crença, descrença e de dúvida: geralmente como objeto de atitudes proposicionais , aquilo do qual pode se dizer ser acreditado, desacreditado, entendido, etc. Também tem sido tomada como sendo o objeto de apreensão, julgamento, suposição, afirmação, denegação, e de investigação: geralmente como o objeto das ações proposicionais , aquilo que pode ser dito ser apreendido, ser julgado verdadeiro ou falso, ser assumido para fins de raciocínio, (...) etc. A proposição tem sido tomada como sujeito da verdade e da falsidade: geralmente como o sujeito de propriedades proposicionais , aquilo que pode ser dito verdadeiro, falso, tautológico, informativo, inconsistente, etc. Ela também tem sido tomada como sujeito e objeto das relações lógicas , e.g., aquilo que pode ser dito implicar, ser implicado, contradizer, ser contradito, etc. Prima facie , tais propriedades e relações são não-mentais e objetivas. Também tem sido tomada como sendo a resultante ou o produto das operações proposicionais , usualmente mental ou linguística; e.g., julgar, afirmar, e denegar tem sido vistas como produtoras de proposições chamadas julgamentos, afirmações, e negações, respectivamente. As Proposições tem também sido tomadas como sendo certas sentenças declarativas . Finalmente, as proposições tem sido tomadas como sendo o significado de certas sentenças declarativas. Este ensaio é uma exame informal, seletivo, e incompleto de abordagens alternativas a “a proposição” com especial atenção aos pontos de vista do falecido filósofo americano Peter Hare (1935–2008) e daqueles que o influenciaram. DOI: 10.5007/1808-1711.2011v15n1p51. (shrink)
The paper argues that philosophers commonly misidentify the substitutivity principle involved in Russell’s puzzle about substitutivity in “On Denoting” (the so-called "George IV puzzle"). This matters because when that principle is properly identified the puzzle becomes considerably sharper and more interesting than it is often taken to be. This article describes both the puzzle itself and Russell's solution to it, which involves resources beyond the theory of descriptions. It then explores the epistemological and metaphysical consequences of that solution. One such (...) consequence, it argues, is that Russell must abandon his commitment to propositions. (shrink)
Recent work in philosophy of language has raised significant problems for the traditional theory of propositions, engendering serious skepticism about its general workability. These problems are, I believe, tied to fundamental misconceptions about how the theory should be developed. The goal of this paper is to show how to develop the traditional theory in a way which solves the problems and puts this skepticism to rest. The problems fall into two groups. The first has to do with reductionism, specifically attempts (...) to reduce propositions to extensional entities-either extensional functions or sets. The second group concerns problems of fine grained content-both traditional 'Cicero'/'Tully' puzzles and recent variations on them which confront scientific essentialism. After characterizing the problems, I outline a non-reductionist approach-the algebraic approach-which avoids the problems associated with reductionism. I then go on to show how the theory can incorporate non-Platonic (as well as Platonic) modes of presentation. When these are implemented nondescriptively, they yield the sort of fine-grained distinctions which have been eluding us. The paper closes by applying the theory to a cluster of remaining puzzles, including a pair of new puzzles facing scientific essentialism. (shrink)
The explanatory gap and theknowledge argument are rooted in the conflationof propositional and phenomenal knowledge. Thebasic knowledge argument is based on theconsideration that ``physical information'' aboutthe nervous system is unable to provide theknowledge of a ``color experience'' (Jackson,1982). The implication is that physicalism isincomplete or false because it leaves somethingunexplained. The problem with Jackson'sargument is that physical information has theform of highly symbolic propositional knowledgewhereas phenomenal knowledge consists in innateneurophysiological processes. In addition totheir fundamental epistemological differences,clinical, anatomical, pathological and brainimaging (...) studies demonstrate that phenomenal andpropositional knowledge are fundamentallydifferent neurobiological processes. Propositional knowledge is phylogeneticallynew, highly symbolic, culturally acquired,exclusively human and expressible in differentnatural and artificial languages. By contrast,phenomenal knowledge (i.e.: knowingwhat-it-is-like to see a color) consists inqualitative experiences and phenomenal conceptsthat provide an internal, language-independentreference to the properties of objects and theneeds of the organism. Language andpropositional knowledge are exclusively humanattributes implemented in specific regions ofthe dominant hemisphere. This contrastssharply with the phylogenicallysensory areas that are common to animals andhumans, which implement qualitativeexperiences. Experiences are hard-wiredneurobiological processes that can neither betransmitted nor re-created through thesymbolism of propositions. Thus, I concludethat the fallacy in the explanatory gap and inthe knowledge argument is a fallacy ofequivocation that results from ignoringfundamental neurobiological differences betweenphenomenal and propositional knowledge. (shrink)
This paper develops a novel version of anti-platonism, called semantic fictionalism. The view is a response to the platonist argument that we need to countenance propositions to account for the truth of sentences containing `that'-clause singular terms, e.g., sentences of the form `x believes that p' and `σ means that p'. Briefly, the view is that (a) platonists are right that `that'-clauses purport to refer to propositions, but (b) there are no such things as propositions, and hence, (c) `that'-clause-containing sentences (...) of the above sort are not true-they are useful fictions. Semantic fictionalism is an extension of Hartry Field's mathematical fictionalism, but my defense of the view is not analogous to his. One of the many virtues of my defense is its generality: it explains how we can adopt a fictionalist stance towards all abstract singular terms, e.g., mathematical singular terms and `that'-clauses. (shrink)
Parts I and II of 'Conflicting Appearances, Necessity and the Irreducibility of Propositions about Colours' review the argument from 'conflicting appearances' for the view that nothing has any one colour. I take further a well-known criticism of the argument made by Austin and Burnyeat. In Part III I undertake the task of positive construction, offering a theory of what it is that all things coloured a particular colour have in common. I end, in Part IV, by arguing that the resulting (...) 'colour phenomenalism', rather than physicalism, is required to give a satisfactory account of the necessity of Wittgenstein's 'puzzle propositions' about colour. (shrink)
Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts (...) of statements that are not themselves statements on their own, such as the subject and predicate of a statement. The most thoroughly researched branch of propositional logic is classical truth-functional propositional logic, which studies logical operators and connectives that are used to produce complex statements whose truth-value depends entirely on the truth-values of the simpler statements making them up, and in which it is assumed that every statement is either true or false and not both. However, there are other forms of propositional logic in which other truth-values are considered, or in which there is consideration of connectives that are used to produce statements whose truth-values depend not simply on the truth-values of the parts, but additional things such as their necessity, possibility or relatedness to one another. (shrink)
Habermas claims that the concept of ?communicative action? can be explained by illocutionary acts alone. It appears tó me that his explanation collapses into a sort of intentional theory (2[i]). Habermas maintains further that a speech act consists of three components which are ?correlated? to three worlds and to three validity claims. However, he also seems to mean that all worlds and validity claims are correlated to just one; the so?called propositional component. One consequence is that the propositional content, not (...) the illocutionary act, determines the main mode of at least some speech acts. Another is that the T as used in an expressive speech act will occur in the propositional part of the act and not, as claimed by Habermas, in the performative sentence (2[iii]). In 2(ii) two other problems concerning Habermas's view on the concept of ?I? ('the subject') are discussed. (shrink)
A number of philosophers are committed to the view that sense experiences, in so far as they have contents, have propositional contents, but this is more often tacitly accepted than argued for in the literature. This paper explains the propositional account and presents a basic case in support of it in a simple and straightforward way which does not involve commitment to any specific philosophical theory of perception.
I suggest that ubiquitous references made by Confucius to poetic songs in the Analects reveal an important aspect of his philosophy. This aspect involves the assumption that things in the world “resonate” with one another. Using elements of Alfred North Whitehead's thought, as well as metaphysical insights from the Han Dynasty text, Huainanzi, I first present an aesthetic theory along with a supporting cosmological vision that enhances our appreciation of this trait in the Confucian world. With these preliminaries in mind, (...) I approach the Analects itself. I will isolate the term xing, or “stimulation “, and demonstrate how this term allows us to understand the function of poetry for the early Confucians. I conclude that poetry was thought to behave much like what Whitehead called “propositions”, and that this function assumes a world with certain basic tendencies normally associated with Daoist cosmology. (shrink)
A study of the reception of Aristotle's Prior Analytics in the first half of the twelfth century. It is shown that Peter Abaelard was perhaps acquainted with as much as the first seven chapters of Book I of the Prior Analytics but with no more. The appearance at the beginning of the twelfth century of a short list of dialectical loci which has puzzled earlier commentators is explained by noting that this list formalises the classification of extensional relations between general (...) terms and that this classification had already be put forward by Boethius in his de Syllogismo Categorico and Introductio ad Syllogismos Categoricas . It is pointed out the kind of text referred to as an ` Introductio ' at the beginning of the twelfth-century follows very closely the structure of Boethius own Introductio and adds to it material drawn from his accounts of loci and the conditional propositions. It is argued that the reception of the Prior Analytics has to be understood against the background of this well developed tradition of treating together syllogisms, loci , and conditional propostions. Referring to a challenge to the formal validity of Darapti in the Ars Meliduna the paper concludes by illustrating that the theory of the syllogism presented in Prior Analytics was still controversial in the middle of the twelfth-century. (shrink)
In this paper I examine the analogical argument that the use that is made of propositions in folk psychology in the characterisation of propositional attitudes is no more puzzling than the use that is made of numbers in the physical sciences in the measurement of physical properties. It has been argued that the result of this analogy is that there is no need to postulate the existence of sentences in a language of thought which underpin the propositional characterisation of propositional (...) attitudes in order to provide a naturalistic account of their use. I argue that a closer examination of the analogy implies rather than avoids the existence of structured representations constituting a language of thought, and thus that it should be abandoned by those who wish to avoid the postulation of such internal representations. (shrink)
This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and (...) conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find this comprehensive treatment an excellent guide to this expanding interdisciplinary area. (shrink)
Support functions $s(h,e)=p(h\backslash e)-p(h)$ are widely used in discussion of explanation, causality and, recently, in connection with the possibility or otherwise of probabilistic induction. With this latter application in view, a rather complete analysis of the variety of support functions, their interrelationships and their "non-deductive" and "inductive" components is presented. With the restriction to two propositions, three variable probabilities are enough to discuss such problems. The analysis is illustrated by graphs, a Venn diagram and by using the Laplace Rule of (...) Succession as an illustrative example. It is concluded that within this framework one cannot prove or disprove the possibility of probabilistic induction. (shrink)
This paper discusses the meaning of expressed preference statements. A holistic explanation of preferences is proposed: preference relations between propositions are explained by preference relations over worlds. Only those world-preferences function as explanans which are maximally similar to the actual world, and which are maximally similar to each other. The concept of similarity as intuitive is rejected, and is interpreted instead with reference to causal structure: 'closest to the actual world' is interpreted as compatible with the causal structure of the (...) actual world, and 'most similar to each other' as sharing the same causal background conditions. (shrink)
The paradox of propositiOns, presented in Appenclix B of Russell's The Principies of Mathernatics (1903), is usually taken as Russell's principal motive, at the time, for moving from a simple to a ramified theory of types. I argue that this view is mistaken. A closer study of Russell's correspondence with Frege reveals that Russell carne to adopt a very different resolution of the paradox, calling into question not the simplicity of his early type theory but the simplicity of his early (...) theory of propositions. (shrink)
Can groups be rational agents over and above their individual members? We argue that group agents are distinguished by their capacity to mimic the way in which individual agents act and that this capacity must 'supervene' on the group members' contributions. But what is the nature of this supervenience relation? Focusing on group judgments, we argue that, for a group to be rational, its judgment on a particular proposition cannot generally be a function of the members' individual judgments on (...) that proposition. Rather, it must be a function of their individual sets of judgments across many propositions. So, knowing what the group members individually think about some proposition does not generally tell us how the group collectively adjudicates that proposition: the supervenience relation must be 'set-wise', not 'proposition-wise'. Our account preserves the individualistic view that group agency is nothing mysterious, but also suggests that a group agent may hold judgments that are not directly continuous with its members' corresponding individual judgments. (shrink)
In this paper, I defend a well-known theory of belief reports from an important objection. The theory is Russellianism, sometimes also called `neo-Russellianism', `Millianism', `the direct reference theory', `the "Fido"-Fido theory', or `the naive theory'. The objection concernssubstitution of co-referring names in belief sentences. Russellianism implies that any two belief sentences, that differ only in containing distinct co-referring names, express the same proposition (in any given context). Since `Hesperus' and `Phosphorus' both refer to the planet Venus, this view implies (...) that all utterances of (1) and.. (shrink)
We use names to talk about objects. We use predicates to talk about properties and relations. We use sentences to attribute properties and relations to objects. We say things when we utter sentences, often things we believe.
The paper argues that Wittgenstein's criticisms of Frege and Russell's assertion sign are, a bottom, criticisms of a common flaw in these philosophers' early conceptions of the proposition. Each philosopher offers an account of the proposition that *seems* to suggest that a sentence cannot get so far as to say something without the addition of the assertion sign. This leads to the mistaken idea that there is a coherent notion of "logical assertion.".
Belief in propositions has had a long and distinguished history in analytic philosophy. Three of the founding fathers of analytic philosophy, Gottlob Frege, Bertrand Russell, and G. E. Moore, believed in propositions. Many philosophers since then have shared this belief; and the belief is widely, though certainly not universally, accepted among philosophers today. Among contemporary philosophers who believe in propositions, many, and perhaps even most, take them to be structured entities with individuals, properties, and relations as constituents. For example, the (...)proposition that Glenn loves Tracy has Glenn, the loving relation, and Tracy as constituents. What is it, then, that binds these constituents together and imposes structure on them? And if the proposition that Glenn loves Tracy is distinct from the proposition that Tracy loves Glenn yet both have the same constituents, what is about the way these constituents are structured or bound together that makes them two different propositions? In The Nature and Structure of Content, Jeffrey C. King formulates a detailed account of the metaphysical nature of propositions, and provides fresh answers to the above questions. In addition to explaining what it is that binds together the constituents of structured propositions and imposes structure on them, King deals with some of the standard objections to accounts of propositions: he shows that there is no mystery about what propositions are; that given certain minimal assumptions, it follows that they exist; and that on his approach, we can see how and why propositions manage to have truth conditions and represent the world as being a certain way. The Nature and Structure of Content also contains a detailed account of the nature of tense and modality, and provides a solution to the paradox of analysis. Scholars and students working in the philosophy of mind and language will find this book rewarding reading. (shrink)
Recent developments in psychology and neuroscience suggest away to link the mental phenomenon of visual awareness with specific neural processes. Here, it is argued that the feed-forward activation of cells in any area of the brain is not sufficient to generate awareness, but that recurrent processing, mediated by horizontal and feedback connections is necessary. In linking awareness with its neural mechanisms it is furthermore important to dissociate phenomenal awareness from visual attention or decision processes.
Katz offers such a grammatical account, in which makes it possible for the first time to explain the illocutionary potential of sentences within grammar.
In establishing unexpected cross-connections between physics, the theory of perception, and logic, Hyder also makes a valuable contribution to the history of ...
Different perspectives on corporate social responsibility (CSR) exist, each with their own agenda. Some emphasise management responsibilities towards stakeholders, others argue that companies should actively contribute to social goals, and yet others reject a social responsibility of business beyond legal compliance. In addition, CSR initiatives relate to different issues, such as labour standards and corruption. This article analyses what types of CSR initiatives are supported by political and economic arguments. The distinction between different CSR perspectives and CSR issues on the (...) one hand and between political and economic arguments on the other could help to advance the debate on the justification and welfare impact of CSR. It is argued that ordinary boundary conditions for business behaviour in a market economy provide support for some, but not all, CSR initiatives. This has implications for policy priorities. Building on the analysis, it is proposed that more attention should be paid to the behaviour of large multinational enterprises in their normal business operations and to CSR issues with a potentially large impact on market functioning. (shrink)
It is argued that a second-order belief to the effect that I now have some particular propositional attitude is always true (Incorrigibility). This is not because we possess an infallible cognitive faculty of introspection, but because that x believes that he himself now has attitude A to proposition P entails that x has A to P. Incorrigibility applies only to second-order beliefs and not to mere linguistic avowals of attitudes. This view combines a necessary asymmetry between 1st and 3rd (...) person ascriptions with Objectivism about the propositional attitudes. The epistemic justification of second-order beliefs is shown to be a further question. (shrink)
I argue against the thesis that the thought expressed by the utterance of an indexical sentence can be re-expressed by means of a quasi-indicator in a belief-ascription. Constructivley, I propose that we describe throught by means of quasi-indicators.
I argue here that Frege’s eventual view on the relation between sentences and the thoughts they express is that, ideally, a sentence expresses exactly one thought, and a thought is expressed by exactly one (canonical) sentence. This may clash with some mainstream views of Frege, for it has the consequence of de-emphasizing the philosophical significance of the question of how it is possible for someone to regard one sentence as true yet regard another sentence that expresses the same thought as (...) false. This account of Frege was developed by taking a long-range look at his writings over the course of his life. (shrink)
