A brief review of the historicalrelation between logic and ontologyand of the opposition between the viewsof logic as language and logic as calculusis given. We argue that predication is morefundamental than membership and that differenttheories of predication are based on differenttheories of universals, the three most importantbeing nominalism, conceptualism, and realism.These theories can be formulated as formalontologies, each with its own logic, andcompared with one another in terms of theirrespective explanatory powers. After a briefsurvey of such a comparison, we argue (...) that anextended form of conceptual realism provides themost coherent formal ontology and, as such, canbe used to defend the view of logic as language. (shrink)

L'Existence de choses telles que des propositions, conc,ues comme distinctes des phrases qui les expriment et dont elles constituent comme le sens — cela que l'on comprend en entendant une phrase — a été mise en question, par Quine, en particulier, et aussi défendue. Ce débat fera l'objet de ce texte.La proposition, comme on l’entendra ici, se définit essentiellement comme une synthèse de concepts. Cette définition en a été donnée par G.E. Moore, un peu avant que Russell ne la reprenne (...) dans trois grands articles publiés dans Mind en 1904, sous le titre de « Meinong’s Theory of Complexes and Assumptions ». (shrink)

Truthmaker theorists often express their core commitment by saying that truth is grounded in being, and grounding theorists often take truthmaking to be a paradigm case of grounding. But I will argue that truthmaking is not a case of grounding. What is crucial for understanding truthmaking is not grounding but rather meaning (in a broad sense including reference). Truth is still constrained by how things are, so even if (so‐called) truthmakers don't play a role in grounding truths, the methodological program (...) of truthmaker theory survives. Here I lay out my understanding of truth and truthmaking, and distinguish two conceptions of grounding. I argue that truthmaking is not plausibly seen as a case of grounding on either conception. I argue further that treating truthmaking as grounding threatens to violate a plausible irreflexivity principle, and makes trouble for the view that grounding is transitive. I then suggest that there is no genuine relation of truthmaking (which there would have to be if it were a true case of grounding). Finally, I show how the core insights of truthmaker theory are preserved by the understanding of truthmaking that I favor. (shrink)

The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an agent to (...) enlarge his knowledge, and this significance can be accounted in model-theoretic terms. I will argue first that the paradox is based on an equivocation, namely, it arises because logical containment, i.e., logical implication, is identified with epistemological containment, i.e., the knowledge of the premises entails the knowledge of the conclusion. Second, I will argue that a truth-conditional theory of meaning has the necessary resources to explain the epistemic significance of valid inferences. I will explain this epistemic significance starting from Carnap’s semantic theory of meaning and Tarski’s notion of satisfaction. In this way I will counter (Prawitz 2012b)’s claim that a truth-conditional theory of meaning is not able to account the legitimacy of valid inferences, i.e., their epistemic significance. (shrink)

Os tópicos e problemas filosóficos discutidos no volume são de natureza bastante variada: a natureza da complexidade computacional no processamento de uma língua natural; a relação entre o significado linguístico e o sentido Fregeano; as conexões entre a a agência e o poder; o conteúdo semântico da ficção; a explicação dos impasses éticos; a natureza dos argumentos cépticos; as conexões entre as dissociações cognitivas e o carácter modular da mente; a relação entre a referência e o significado. Estes tópicos deixam-se (...) subsumir num tema mais geral, o tema das ligações múltiplas entre a cognição e o conteúdo, mental ou linguístico. O tópico do conteúdo, a questão de determinar como é que muitas das nossas elocuções e muitos dos nossos estados mentais são dotados de conteúdo, representam algo (correcta ou incorrectamente), e o tópico da cognição, a investigação da natureza e dos mecanismos envolvidos na cognição humana, no processamento de informação tipicamente proveniente do exterior, são inegavelmente tópicos centrais da investigação filosófica, presente ou passada.Dado o carácter inclusivo e pluridisciplinar dos tópicos cobertos, não é surpreendente que os ramos da Filosofia representados no presente volume sejam igualmente diversificados: a Filosofia Moral, a Filosofia da Linguagem, a Teoria do Conhecimento, a Filosofia da Mente, os Fundamentos da Ciência Cognitiva. E também não é surpreendente que nele também estejam representados outros ramos do conhecimento cuja relevância para o estudo do conteúdo e da cognição é conspícua: a Psicologia Cognitiva; a Linguística Computacional e a Inteligência Artificial. Os autores dos ensaios são de proveniências diversas. De um lado, há um conjunto de especialistas nacionais a trabalhar na tradição analítica em Filosofia, como João Branquinho, ou a trabalhar em algumas áreas filosoficamente importantes da Ciência Cognitiva, como António Branco (Processamento da Língua Natural), José Frederico Marques (Psicologia Cognitiva) e Helder Coelho (Inteligência Artificial). Do outro lado, há um conjunto de especialistas estrangeiros de elevada reputação internacional: Allan Gibbard, da Universidade de Michigan, autor de livros influentes na área da Ética e Filosofia Moral; Stephen Schiffer, da New York University, uma das principais figuras actuais da Filosofia da Linguagem e da Semântica Geral; Paolo Leonardi, da Universidade de Bolonha, um especialista nas áreas da Filosofia da Linguagem e Filosofia da Comunicação; e Manuel García-Carpintero, da Universidade de Barcelona, um dos grandes vultos da Filosofia Analítica praticada em Espanha e na Europa Continental. (shrink)

Sets are multitudes which are also unities. It is surprising that the fact that multitudes are also unities leads to no contradictions: this is the main fact of mathematics.Kurt Gödel (Hao Wang,A Logical Journey: From Gödel to Philosophy)In what sense can something be at the same time one and many? The problem is familiar since Plato (for example,Republic524e). In recent times, Whitehead and Russell, inPrincipia Mathematica,have been struck by the difficulty of the problem: ‘If there is such an object as (...) a class, it must be in some senseoneobject, yet it is only of classes that many can be predicated. Hence, if we admit classes as objects, we must suppose that the same object can be both one and many, which seems impossible.' It is, however, in Frege's great work,The Foundations of Arithmetic(henceforth,Grundlagen),that many see the final resolution of the old question: how can something be at the same time one and many? (shrink)

In this paper we introduce a theoretical framework and a logical application for analysing the semantics and pragmatics of contrastive conjunctions in natural language. It is shown how expressions like although, nevertheless, yet, and but are semantically definable as connectives using an operator for implication in natural language and how similar pragmatic principles affect the behaviour of both contrastive conjunctions and indicative conditionals. Following previous proposals, conditions on contrast in a conjunction are analysed as presuppositions of die conjunction. Further linguistic (...) evidence leads to a distinction between restrictive and non-restrictive connectives of contrast, and consequently between direct and indirect contrast, which are given a precise definition. A general interface for a theory of contrast using possible world semantics for implication is then presented. As a test case, we show how this interface is applicable to the semantics for conditionals that was introduced by Veltman in his article 'Data semantics and the pragmatics of indicative conditionals' (1986). This application yields an extension of Veltman's Data Logic, called Contrastive Data Logic Once appropriate modifications are added to Veltman's pragmatic considerations, we show that contrastive data logic provides an adequate tool for the analysis of substantial linguistic data concerning contrast and implication in natural language. (shrink)

SUMMARY1 The rational soul becomes the constant and dimensionless Euclidean point in all experience - defining the situations in which it finds itself, but itself undefined and undefinable in any situation. It is in nature but not of nature. Just as the dimensionless Euclidean point can occupy infinite positions on a line and yet remain unaltered, so the immortal, active intellect remains unaffected by the world in which it finds itself. It is not influenced by age, sense data, sickness or (...) death. It is the knower whose nature is pure knowing or reason. This is in great part the basic assumption that runs through the history of Aristotelean and modern symbolic logics24.The rational soul grasps identity, reasons consistently, and knows objectively for though it is in the world it is not of the world. Thus it is unnecessary and impossible to relate its truth to time or place or condition. As the source of understanding it need not be understood. It understands in that it knows. It is this which places the objective knower and observer outside of all systems of knowledge that it creates in philosophy, science and theology, and frees it from subjective interpretation. It is the absolute observer beyond self-observation.252 Language, values, and meanings reflect the absolute viewpoint of the dimensionless observer beyond the necessity of observation. The task of this observer is to know trie world just as the task of the animal and plant soul is motion and reproduction. The rational soul performs its task beyond nature as surely as animals and plants perform their tasks in nature. This is why it is possible to discuss the necessary evolution of living organisms in nature, but unnecessary to discuss the necessary or unnecessary nature of the evolution of this discussion. This is one of the reasons why determinism or predestination which seem so clearly applicable to nature, need not be applied to theories of determinism and predestination. These are principles grasped in reality beyond nature and totally inapplicable to the non-natural spirit that comprehends their essences. Thus self-reflexive questions about the questioner are as irrelevant as would be questions historically of “in what sense might the definition of dimensionless point itself be dimensioned or dimension-less?”26 Questions, on the other hand, that relate to the observed world are important for they can be truly answered (where questions as to the nature of the questioner cannot). In this view reality is not nature, but rather it is from reality that the objective observer, philosopher, scientist, and theologian understands and controls nature.3 Logic, the science of reason, is the science of all sciences. It reflects the pure and innate rational nature of the knowing intellect or soul. It is pure form beyond nature. Its realm is that of first principles or axioms. These too are in the world but not of it, as with Plato's eidos and Aristotle's universals. They are clear, true and self-evident. This explains the on going use of axiomatized revelations in studies in the natural and social sciences, the arts and the humanities. In symbolic logics, natural languages are in and of the world, but meta-languages are the constructs of pure intellectual activity and thus not natural. The abstract tends to become the more real, the less it can be found in nature. Rational souls, however, share a common reality that is as universal for Frege as it was for Aristotle.274 The occidental object tradition in general breaks out of the nature continuum by withdrawing into reality where the intellect knows and manipulates the world in philosophy, science, and theology from its position in and understanding of reality. Nature is a sub-set of reality and not vice versa. Axioms are the laws and determinants of nature and logic, but they are not nature.28 This means that at the basis of the occidental continuum of nature there is a qualitative and irreducible dichotomy of reality vs. nature. This has been most useful in the history of occidental science, but it produces a world view in which nature may lose the race with reality. SUMMARY IIIn the first portion of my paper, I discussed the implications of the Euclidean egg for philosophy and science as nature is understood and manipulated from reality. I shall now turn to what I see as the implications of the three-legged chicken view that the human intellect is in and of nature and that reality is a perspective in nature and is not simply the other of an irreducible qualitative dichotomy. Although there are an endless number of such implications that I could explore, the following, it seems to me are the most important:1 In the natural continuum there is no “dimensionless real” which can serve either as the locus of an external observer or a fixed position in nature. There is no perspective which is not an aspect of that upon which it is a perspective. The Chinese sage, for example, is one who sees himself/herself as one with or within natural process. This is expressed in a number of ways. Fung Yu-lan speaks of the difference between having no knowledge and having no-knowledge.34 Within such a continuum there can be no abstracting out of the absolute and unchanging. The nameless is the source of the named. First principles are the process itself and these principles are the alternation of opposites:“The Nameless is the origin of Heaven and Earth;The Named is the mother of all things.Therefore let there always be non-being so we may see their subtlety, And let there always be being so we may see their outcome. The two are the same.“352 An empty mind is not a blank mind. Where Aristotle viewed the mind as a blank tablet at birth to be filled by sense experience, Hsun Tzu speaks of its emptiness. It is the emptiness of the Tao itself:“The mind is constantly storing up things, and yet it is said to be empty. The mind is constantly marked by diversity, and yet it is said to be unified. The mind is constantly moving, and yet it is said to be still. Inevitably it will see things for itself. And although the objects it perceives may be many and diverse, if its acuity is of the highest level, it cannot become divided within itself.”36The nature in which and of which the mind is both perspective and aspect remains a totality. Being a totality, it is empty of itself just as any part of a whole, while a part of the whole, is empty of the whole. My ideas of myself are both of myself and empty of myself. This point can be illustrated with the simple example of knowing and speaking about two hands – one of which is mine, and the second of which belongs to someone else. 1 can objectify the second hand and fill my blank mind with information and observations about it, but I continue to remain outside of it –the arbiter in my statements of its nature and reality. However, in knowing my own hand, the hand known is also the knower and what I know represents a perspective upon an aspective of a totality of which “I–my–hand” are aspects. Being an aspect of the whole is being empty of the whole. If mind is in and of nature, any perspective on nature is an aspect of the whole. A blank mind is an unnatural mind outside of nature, filling up with impressions of nature. An empty mind is nature viewing nature as aspect and perspective. The occidental would be ashamed to reach old age and still have a blank mind. The Chinese sage would be ashamed to reach old age and still not recognize that the mind is empty.3 If mind is in nature and like nature, then language too reflects natural flow and change and process. It is one thing for me to talk about myself and another for me to talk about someone else. In the case of the latter, I may insist that objectively this other subject fits into this or that category and even administer tests to determine that it does do indeed so. But when I talk about myself, the speaker and the object of speech are one and the same. The terms I select do represent a dichotomy of sorts, but it is one of aspect and perspective and not subject and object. When I say “this is my hand” for example, the words create distinctions which are aspects of awareness but do not create an / that is or is not my hand. Language does not model or even represent reality as opposed to nature. It makes reality possible as something that nature says or thinks. Reality through language is an aspect of nature and thus a perspective upon itself as aspect. This is an important distinction that translators often miss.4 Logic in this natural continuum is concerned with distinctions in a very different sense. As a consequence of the unity of nature and mind, three kinds of distinction in experience are manifested: (a) Those distinctions which come into being as aspects of the changing world.The 10,000 things are in this sense aspects and not separate “identities” as some philosophers and scientists presuppose.37 (b) Those distinctions which come into being as aspects of the human mind. These are impressions of and thoughts about the infinite distinctions of which the restless mind is capable, (c) Those distinctions which come into being by way of the mind's use of symbols. These are the distinctions which permit us to stabilize and store our experiences, preserve the answers to our questions, and name the world into compartments and relationships.Implicit in these three assumptions which connect the distinguishing mind to the unity of a nature of'10,000‘ aspects, is an inferential process of aspect to perspective to knowledge to understanding to attitude to action/response. The reasoning mind synthesizes some aspect of experience in nature with a perspective upon this aspect. This synthesis, in turn, is an aspect of mind and the reasoning process proceeds from it to a perspective upon it which is knowledge and understanding. Knowledge and understanding in turn are aspects of thinking and the reasoning process proceeds from them to a perspective upon them which is an attitude. Attitude in turn is an aspect of thinking and the reasoning process proceeds from it to a perspective upon it which is reflected in the reasoning individual's actions and responses. This inferential process is a continuum which proceeds from aspects of experience to perspectives in thought to action and response. In this sequence an aspect is always connected by a perspective which becomes an aspect, until action/non-action, response occurs. This is as applicable to the details of life as it is to mastering life as a whole. When this inference process is incomplete many problems may result, ranging from action without understanding to the confusion of aspect and perspective with one another or to “obsession with distinctions.”38In practice this is a logic of paradox. The human being is aware that he or she is a living-dying aspect of nature, but an aspect which is also a perspective upon nature's aspects of living and dying. This paradox is the process around which a profound logic of aspect/perspective is developed by the sage. This view of logic within a continuum does not mean that there is no principle of identity, contradiction or excluded middle present – as some Chinese and European philosophers assume.These principles are also implicit in the knowing of my hand versus the knowing of the hand of another. However, the content, meaning, and application of these principles may vary just as when I say propriety, I mean propriety, and when the Chinese says li he means li but the context, meaning and application of the term may differ in each case.5 Aspect logic as it relates mind to nature in a cosmological totality is a series of syntheses in a cyclic continuum organizing thinking in phases. Each phase is an aspect/perspective synthesis which becomes an aspect of a further aspect/perspective synthesis. This progression might be described thusly: The synthesis of nature/human which is Tao (non-being) translates into the aspects of being (the 10,000 things), and as such is a synthesis of aspect and perspective. This synthesis of aspect and perspective translates into an aspect of ideas and as such is a synthesis of perception and conception. This synthesis of perception and conception translates into an aspect of knowledge, and as such is a synthesis of knowledge and understanding (understanding is a perspective upon knowledge) i.e., no-knowledge. This synthesis of knowledge and understanding translates into an aspect of purpose, and as such is a synthesis of purpose and action. The perspective here on action is aesthetic and/or moral. This synthesis of purpose and actions translates again into an aspect of nature and as such is a synthesis beyond individual aspects and perspective, i.e. Tao. Thus there is a cyclic dynamic in the system which remains open to further development.Tai Chen in his Inquiry Into Goodness connects this cycle of syntheses with wisdom and benevolence:Because there are mind and intelligence, the superior man knows that the perfection of the Way of Man depends completely upon nature. When he looks at the signs of the natural (Cheng), he knows the beginning of things; when he cherishes the virtue of supreme illumination, (Shen-ming), he knows the end of things. Proceeding from mind and intelligence to the attainment of the virtue of supreme intelligence, [the superior man] in his treatment of things in the world will cause the world to return to [the principles of] benevolence; and in his treatment of the capability inherent in things, he will cause the world to follow wisdom (Chih).39. (shrink)

The formal structure of Frege’s ‘concept script’ has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the (...) paper then goes on to indicate the lines on which formal logic—and also the lambda calculus and set theory—needs to be restructured, to remove the difficulties. Throughout the study of what have come to be known as first-, second-, and higher-order languages, what has been primarily overlooked is that these languages are abstractions. Many well known paradoxes, we shall see, arose because of the elementary level of simplification which has been involved in the abstract languages studied. Straightforward resolutions of the paradoxes immediately appear merely through attention to languages of greater sophistication, notably natural language, of course. The basic problem has been exclusive attention to a theory in place of what it is a theory of, leading to a focus on mathematical manipulation, which ‘brackets off’ any natural language reading. (shrink)

Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion of logically equivalent (...) formulas, and presenting the notation's close connection to syntax trees. In the second part, Frege's considerations regarding the design principles underlying the Begriffsschrift are presented. Frege was quite explicit about these in his replies to early criticisms and unfavorable comparisons with Boole's notation for propositional logic. This discussion reveals that the Begriffsschrift is in fact a well thought-out and carefully crafted notation that intentionally exploits the possibilities afforded by the two-dimensional medium of writing like none other. (shrink)

This paper discusses the philosophical and logical motivations for rejectivism, primarily by considering a dialogical approach to logic, which is formalized in a Question–Answer Semantics. We develop a generalized account of rejectivism through close consideration of Mark Textor's arguments against rejectivism that the negative expression ‘No’ is never used as an act of rejection and is equivalent with a negative sentence. In doing so, we also shed light upon well-known issues regarding the supposed non-embeddability and non-iterability of force indicators.

The paper argues that the view that the particular quantifier is ‘existentially loaded’ is a relatively new one historically and that it has become entrenched in modern philosophical logic for less than happy reasons.

This paper aims to develop the implications of logical expressivism for a theory of dialogue coherence. I proceed in three steps. Firstly, certain structural properties of cooperative dialogue are identified. Secondly, I describe a variant of the multi-agent natural deduction calculus that I introduced in Piwek (J Logic Lang Inf 16(4):403–421, 2007 ) and demonstrate how it accounts for the aforementioned structures. Thirdly, I examine how the aforementioned system can be used to formalise an expressivist account of logical vocabulary that (...) is inspired by Brandom (Making it explicit: reasoning, representing, and discursive commitment, 1994 ; Articulating reasons: an introduction to inferentialism, 2000 ). This account conceives of the logical vocabulary as a tool which allows speakers to describe the inferential practices which underlie their language use, i.e., it allows them to make those practices explicit. The rewards of this exercise are twofold: (1) We obtain a more precise account of logical expressivism which can be defended more effectively against the critique that such accounts lead to cultural relativism. (2) The formalised distinction between engaging in a practice and expressing it, opens the way for a revision of the theory of dialogue coherence. This revision eliminates the need for logically complex formulae to account for certain structural properties of cooperative dialogue. (shrink)

Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ (...) and ‘y’ are synonymous, since sentences differing by the total, proper substitution of ‘x’ for ‘y’ always agree in meaning. We offer a precise interpretation of the challenge posed by (i) and (ii). We then develop some neglected passages of Tarski to show that his semantics for variables has the resources to resolve the antinomy without abandoning standard compositional semantics. (shrink)

Formal semantics and pragmatics as they have developed since the late 1960's have been shaped by fruitful interdisciplinary collaboration among linguists, philosophers, and logicians, among others, and in turn have had noticeable effects on developments in syntax, philosophy of language, computational linguistics, and cognitive science.In this paper I describe the environment in which formal semantics was born and took root, highlighting the differences in ways of thinking about natural language semantics in linguistics and in philosophy and logic. With Montague as (...) a central but not solo player in the story, I reflect on crucial developments in the 1960's and 70's in linguistics and philosophy, and the growth of formal semantics and formal pragmatics from there. I discuss innovations, key players, and leading ideas that shaped the development of formal semantics and its relation to syntax, to pragmatics, and to the philosophy of language in its early years, and some central aspects of its early impact on those fields. (shrink)

Platonism, considered as a philosophy of mathematics, can be formulated in two interestingly different ways. Strong platonism holds that numerals, for example, refer to certain non-physical, non-mental entities. Weak platonism holds only that numerals uniquely apply to certain non-physical, non-mental entities. (Of course, there may even be weaker views that deserve to be called ‘platonistic.’The distinction between referring to an object and uniquely applying to an object may be illustrated as follows. If there is a tallest person and I say, (...) ‘the tallest person is over seven feet tall,’ without knowing who that person is, then my use of ‘the tallest person’ uniquely applies to someone, but it does not refer to anyone. The distinction is at least as old as Russell, for we might put his views in our terms by saying that for Russell only logically proper names refer to things, while ordinary proper names and definite descriptions at best uniquely apply to things. (shrink)

One of the central debates in the philosophy of language is that between defenders of the causal-historical and descriptivist theories of reference. Most philosophers involved in the debate support one or the other of the theories. Building on recent experimental work in semantics, we argue that there is a sense in which both theories are correct. In particular, we defend the view that natural kind terms can sometimes take on a causal-historical reading and at other times take on a descriptivist (...) reading. The meaning will shift depending on the conversational setting. The theoretical view has roots in work by Kitcher. We present some original experiments that support the thesis. (shrink)

This is the introductory essay to a collection commemorating the 100th anniversary of the publication in Mind of Bertrand Russell’s paper ‘On Denoting’.

In this essay, I argue for an account of property possession as strict, numerical identity. According to this account, for an entity to possess a property is for that entity to be numerically identical to that property.

Whether a predicate is a referential expression depends upon what reference is conceived to be. Even if it is granted that reference is a relation between words and worldly items, the referents of expressions being the items to which they are so related, this still leaves considerable scope for disagreement about whether predicates refer. One of Frege's great contributions to the philosophy of language was to introduce an especially liberal conception of reference relative to which it is unproblematic to suppose (...) that predicates are referring expressions. According to this liberal conception, each significant expression in a language has its own distinctive semantic role or power, a power to effect the truth-value of the sentences in which it occurs. (shrink)

This paper discerns two types of mathematization, a foundational and an explorative one. The foundational perspective is well-established, but we argue that the explorative type is essential when approaching the problem of applicability and how it influences our conception of mathematics. The first part of the paper argues that a philosophical transformation made explorative mathematization possible. This transformation took place in early modernity when sense acquired partial independence from reference. The second part of the paper discusses a series of examples (...) from the history of mathematics that highlight the complementary nature of the foundational and exploratory types of mathematization. (shrink)

Wittgenstein was unreliable as an historian of philosophy. When he criticised other philosophers he rarely gave chapter and verse for his criticism, and on the rare occasions on which he quoted verbatim he did not always do justice to the authors quoted. I will illustrate this first in the comparatively unimportant case of Augustine and then in the more serious case of Frege.

Part 1 sets out the logical/semantical background to ‘On Denoting’, including an exposition of Russell's views in Principles of Mathematics, the role and justification of Frege's notorious Axiom V, and speculation about how the search for a solution to the Contradiction might have motivated a new treatment of denoting. Part 2 consists primarily of an extended analysis of Russell's views on knowledge by acquaintance and knowledge by description, in which I try to show that the discomfiture between Russell's semantical and (...) epistemological commitments begins as far back as 1903. I close with a non-Russellian critique of Russell's views on how we are able to make use of linguistic representations in thought and with the suggestion that a theory of comprehension is needed to supplement semantic theory. (shrink)

§1 Analytic philosophers interested in depiction have focused for the most part on two problems: first, explaining how pictures represent; second, describing the distinctive kinds of artistic value pictures can possess, or the distinctive ways in which they can embody artistic values that extend more broadly across the arts. I shall discuss the first problem here. The main concepts I shall be concerned with are depiction, resemblance, sense and reference.

Frege begins his exposition of the symbol system employed in his Begriffsschrift by introducing the sign ⟝, whereby, he says, “[a] judgment is always to be expressed”.[The judgment sign] stands to the left of the sign or complex of signs in which the content of the judgment is given. If we omit the little stroke at the left of the horizontal stroke, then the judgment is to be transformed into a mere complex of ideas; the author is not expressing his (...) recognition or nonrecognition of the truth of this. (shrink)

The translation of both ‘bedeuten’ and ‘Bedeutung’ in Frege's works remains sufficiently problematic that some contemporary authors prefer to leave these words untranslated. Here a case is made for returning to Russell's initial choice of ‘to indicate’ and ‘indication’ as better alternatives than the more usual ‘meaning’, ‘reference’, or ‘denotation’. It is argued that this choice has the philosophical payoff that Frege's controversial doctrines concerning the semantic values of sentences and predicative expressions are rendered far more comprehensible by it, and (...) that this translational strategy fulfills the desiderata of offering a translation which is acceptable both before and after Frege introduced the distinction between sense and reference or, as this paper would have it, between the sense of an expression and what it indicates. (shrink)

Koopman’s book revolves around the notion of transition, which he proposes is one of the central ideas of the pragmatist tradition but one which had not previously been fully articulated yet nevertheless shapes the pragmatist attitude in philosophy. Transition, according to Koopman, denotes “those temporal structures and historical shapes in virtue of which we get from here to there”. One of the consequences of transitionalism is the understanding of critique and inquiry as historical pro...

Bertrand Russell, in the second of his 1914 Lowell lectures, Our Knowledge of the External World, asserted famously that ‘every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical’ (Russell 1993, p. 42). He went on to characterize that portion of logic that concerned the study of forms of propositions, or, as he (...) called them, ‘logical forms’. This portion of logic he called ‘philosophical logic’. Russell asserted that ... some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure. (p. 53) Perhaps no one still endorses quite this grand a view of the role of logic and the investigation of logical form in philosophy. But talk of logical form retains a central role in analytic philosophy. Given its widespread use in philosophy and linguistics, it is rather surprising that the concept of logical form has not received more attention by philosophers than it has. The concern of this paper is to say something about what talk of logical form comes to, in a tradition that stretches back to (and arguably beyond) Russell’s use of that expression. This will not be exactly Russell’s conception. For we do not endorse Russell’s view that propositions are the bearers of logical form, or that appeal to propositions adds anything to our understanding of what talk of logical form comes to. But we will be concerned to provide an account responsive to the interests expressed by Russell in the above quotations, though one clarified of extraneous elements, and expressed precisely. For this purpose, it is important to note that the concern expressed by Russell in the above passages, as the surrounding text makes clear, is a concern not just with logic conceived narrowly as the study of logical terms, but with propositional form more generally, which includes, e.g., such features as those that correspond to the number of argument places in a propositional function, and the categories of objects which propositional.... (shrink)

In this paper, we will discuss what is called the “Manifestation Challenge” to semantic realism, which was originally developed by Michael Dummett and has been further refined by Crispin Wright. According to this challenge, semantic realism has to meet the requirement that knowledge of meaning must be publically manifested in linguistic behaviour. In this regard, we will introduce and evaluate John McDowell’s response to this anti-realistic challenge, which was put forward to show that the challenge cannot undermine realism. According to (...) McDowell, knowledge of undecidable sentences’ truth-conditions can be properly manifested in our ordinary practice of asserting such sentences under certain circumstances, and any further requirement will be redundant. Wright’s further objection to McDowell’s response will be also discussed and it will be argued that this objection fails to raise any serious problem for McDowell’s response and that it is an implausible objection in general. (shrink)

This is a position paper concerning the role of empirical studies of human default reasoning in the formalization of AI theories of default reasoning. We note that AI motivates its theoretical enterprise by reference to human skill at default reasoning, but that the actual research does not make any use of this sort of information and instead relies on intuitions of individual investigators. We discuss two reasons theorists might not consider human performance relevant to formalizing default reasoning: (a) that intuitions (...) are sufficient to describe a model, and (b) that human performance in this arena is irrelevant to a competence model of the phenomenon. We provide arguments against both these reasons. We then bring forward three further considerations against the use of intuitions in this arena: (a) it leads to an unawareness of predicate ambiguity, (b) it presumes an understanding of ordinary language statements of typicality, and (c) it is similar to discredited views in other fields. We advocate empirical investigation of the range of human phenomena that intuitively embody default reasoning. Gathering such information would provide data with which to generate formal default theories and against which to test the claims of proposed theories. Our position is that such data are the very phenomena that default theories are supposed to explain. (shrink)

This paper makes a Fregean analysis of certain expressions which, according to the way they are constructed, can refer, firstly, to events and, secondly, to the results of these events. This paper intends to show that –if we take into account the above mentioned expressions and use Fregean notions such as meaning, reference, function, argument and concept– it is possible to consider events as objects. To do this we need to articulate developments made both from a linguistic perspective and a (...) philosophical one. In this particular case, we take into account the Fregean ontology; we try to analyze ontologically the linguistic phenomena called nominalization and arrive to interesting conclusions about the ontological and semantic behavior of the expressions that contain event and result nominalizations. (shrink)