¿Qué es la mente humana? ¿Es un aspecto de la naturaleza? ¿O acaso la trasciende? ¿Se puede explicar enteramente al hombre en un lenguaje científico-natural? Desde que Aristóteles definió al hombre como un "animal racional", el pensamiento occidental ha erigido una distinción ontológica entre hombre y naturaleza. Sin embargo, el darwinismo nos ha legado una verdad ineludible: que somos organismos animales, cuyas capacidades conceptuales no escapan a los procesos propios de la naturaleza. ¿Se puede, entonces, pensar al hombre como un (...) ser mental, y al mismo tiempo como un organismo natural? Para ello, sin duda, será necesario reformular los conceptos tradicionales de "mente" y de "naturaleza" en busca de una reconciliación conceptual. El siguiente volumen recorre campos como la fenomenología trascendental, la lógica, la biología, la semiótica, la lingüística y la psicología con el fin de superar este dualismo tan antiguo como la filosofía. (shrink)

This chapter focuses on picture theory, which is sometimes spoken of as a theory of the proposition. By a proposition, Wittgenstein like Frege means something that determines its sense by means of a correlation between the mode of combination of its constituent symbols and the structure of its sense. It has been an orthodoxy amongst Tractatus interpreters, and continues to be such in the wider philosophical community, that Wittgenstein follows the Russell in offering a correspondence theory of truth. The expression (...) of a Tractarian fact provides that fact's mode of combination, and from here there can be no further question as to the ontological types of its constituents. Tractarian facts, it is however added, are not truth conditions but items whose existence explains the obtaining of truth conditions: a Tractarian atomic fact is not a truth condition but a truthmaker. (shrink)

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

In his early essay, “Must We Mean What We Say”, Cavell argues that the claims of ordinary language philosophers regarding “what we say when” are not empirical generalizations about a given group of speakers but are rather to be understood as measuring the limits of what counts as a coherent act of thinking and speaking. Cavell’s charge against the skeptic about the external world is that he seeks to think and speak beyond these limits. In this paper I compare Cavell’s (...) response to the skeptic to Davidson’s. Both base their responses on a broadly Kantian approach that appeals to the conditions under which thinking or speaking about objects is possible. On this approach the skeptic isn’t giving a false answer to an intelligible question, but rather, the question to which the skeptic is giving an answer is shown to be in some way unintelligible. But while Davidson’s critique of the skeptic is based on the conditions of ascribing meaning to one’s words, and contents to one’s beliefs, Cavell’s critique is based on the failure of the skeptic to mean the words he uses in the way that he needs. This difference expresses an underlying disagreement about the meaning of “meaning”: for Davidson the world comes into view through the meaning of our words and concepts, through the contents of our beliefs; for Cavell, the world comes into view through the agreement in “criteria” that are a condition of applying words and concepts to the world. This difference illuminates what Cavell calls “the truth of skepticism”: the idea that “my relation to the world and to others in general is not one of knowing”. (shrink)

I explore the possibility of a structuralist interpretation of homotopy type theory (HoTT) as a foundation for mathematics. There are two main aspects to HoTT's structuralist credentials. First, it builds on categorical set theory (CST), of which the best-known variant is Lawvere's ETCS. I argue that CST has merit as a structuralist foundation, in that it ascribes only structural properties to typical mathematical objects. However, I also argue that this success depends on the adoption of a strict typing system which (...) undermines the metaphysical seriousness of this structuralism. Homotopy type theory adds to CST a distinctive theory of identity between sets, which arguably allows its objects to be seen as ante rem structures. I examine the prospects for such a view, and address many other interpretive problems as they arise. (shrink)

Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form 'gamma entails phi'—to normative constraints on reasoning. This paper argues for two claims. First, for the time being at least, Harman’s (...) challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form 'gamma does not entail phi' to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic. (shrink)

ABSTRACT This paper is concerned with the ontological status of linguistic types. According to a widely held view, linguistic types are abstract objects that are instantiated or represented by tokens. The same types might be tokened by both speech, signing and text. This view has implications for how we consider what it is to know a language since knowledge of language is typically taken to be knowledge of linguistic types. We argue below that linguistic types are not abstract objects but (...) action-types and that these action-types are individuated by the capacities that they manifest. The picture that results from this view is that to know a language is to have the capacities required to perform these action-types. (shrink)

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)

In this article I explore some implications of the correspondence that went on between Ludwig Wittgenstein and the logician and mathematician Gottlob Frege. Part of this exchange was focused on the envisaged publication of Wittgenstein’s Tractatus Logico-Philosophicus, and on the philosophical or literary character of that work. The problem discussed concerned the question of whether the Tractatus should be seen not as a scientific but as an artistic achievement. My first goal is to present what, given Frege’s writings, his phrase (...) “an artistic rather than a scientific achievement” could be understood to mean in terms of the Tractatus itself. Secondly, I seek to determine the extent to which traces of Frege’s understanding of such terms as “mock thoughts,” “fiction,” “elucidation,” “paintings” and “colouring” are to be found in the language of the Tractatus. This should then make it possible to show how Wittgenstein’s work, viewed from a Fregean perspective, can be seen as furnishing a logic and semantics not only for the languages of logic and natural science, but also for something that is “an artistic rather than a scientific achievement”, while also indicating that the content of the Tractatus as a whole could not have been captured independently of the unified form Wittgenstein himself gave it. (shrink)

This paper aims to answer the question of whether or not Frege's solution limited to value-ranges and truth-values proposed to resolve the "problem of indeterminacy of reference" in section 10 of Grundgesetze is a violation of his principle of complete determination, which states that a predicate must be defined to apply for all objects in general. Closely related to this doubt is the common allegation that Frege was unable to solve a persistent version of the Caesar problem for value-ranges. It (...) is argued that, in Frege’s standards of reducing arithmetic to logic, his solution to the indeterminacy does not give rise to any sort of Caesar problem in the book. (shrink)

“Feminicity” is the term for a predicate register that enables feminist work be accounted for as relational “active-points” that collectively can be seen through what they have achieved. But going further, it marks where those active-points contribute to the dynamic field of feminist epistemologies and where change occurs. This article contributes to my larger project’s discussion of this concept. Broadly, feminicity argues that the active-points of feminist practices need to be understood within their situated fields as materialist informatics. In the (...) digital era, examples of the affects of digital feminicity are as identified in works such as those by Wajcman ; Haraway, Hayles, VNSMatrix, Adam, Plant. Collectively, such authors and artists opened a creative, and sometimes radical discourse of the digital field as multidirectional, multidimensional, multitemporal platform of “gender actions”. Taken as a predicated field sense of the term “predicate”), this work contributes to the feminist materialist reappraisal of feminist epistemology, and larger radical feminist deconstructive projects. Thus conceived, the genealogy of digital feminicity problematizes the monopolitical terms of feminism in its collation of actions, enabling a re-situation of feminist practices as positive material interventions and expressions of the ontological constitution of the political sphere. Feminicity does not propose a chronological account of the active-points, but processually and systemically addresses the terms of generational epistemological political change. This article describes the ways in which a materialist constructed register – “feminicity”– can be used to think about encounters between the domains of gender, politics and technology, as manifested by materialist informatics. For reasons of brevity, this article focuses on just two aspects of feminicity: the terms of predication of the female as gendered, and the issue of the image, as digital informatics, comprised of activitypoints of feminist practice. Consequently, these are measurable and offer practical resources for the general problem of gendering politics that operate in governance, resource distribution and a non-equal opportunity social/cultural power structure, under which minorities are disadvantaged. Feminist practice here refers to forms produced through feminist activities, ie, forms generated through relations with the matter of life through specific modalities of needs-based practices. (shrink)

This paper concerns the three great modal dichotomies: (i) the necessary/contingent dichotomy; (ii) the a priori/empirical dichotomy; and (iii) the analytic/synthetic dichotomy. These can be combined to produce a tri-dichotomy of eight modal categories. The question as to which of the eight categories house statements and which do not is a pivotal battleground in the history of analytic philosophy, with key protagonists including Descartes, Hume, Kant, Kripke, Putnam and Kaplan. All parties to the debate have accepted that some categories are (...) void. This paper defends the contrary view that all eight categories house statements—a position I dub ‘octopropositionalism’. Examples of statements belonging to all eight categories are given. (shrink)

I attempt to explain Frege's handling of the Julius Caesar issue in terms of his more general philosophical commitments. These only became fully explicit in his middle-period writings, but his earlier moves are best explained, I suggest, if we suppose them to be implicit in his earlier thinking. These commitments conditionally justify Frege in rejecting Hume's Principle as either a definition or axiom but in accepting Axiom V. However, the general epistemological picture they constitute has serious problems in accounting for (...) how knowledge is possible at all of such propositions as that Julius Caesar is not a number. (shrink)

In his late fragment, ‘Sources of Knowledge of Mathematics and Natural Sciences’ Frege laments the tendency to confuse functions with objects and says, ‘It is here that the tendency of language by its use of the definite article to stamp as an object what is a function and hence a non-object, proves itself to be the source of inaccurate and misleading expressions and also of errors of thought. Probably most of the impurities that contaminate the logical source of knowledge have (...) their origins in this.’ This paper applies Frege’s logical insights to a series of influential modal arguments for the existence of souls or minds, in order to demonstrate that they hinge on the error of treating functions as objects. Related arguments have also resulted in the claim that identity statements are necessary, and that apparent identities ‘really’ involve relations of constitution. Here it is argued that once we recognise that all these arguments involve the assimilation of objects and concepts (which Frege identifies with functions) they can be seen to be defective. (shrink)

The paper offers a new account of Spinoza's conception of “substance”, the fundamental building block of reality. It shows that it can be demonstrated apriori within Spinoza's metaphysical framework that (i) contrary to Idealist readings, for Spinoza there can be no substance that is not determined or modified by some other entity produced by substance; and that (ii) there can be no substance (and hence no being) that is not a thinking substance.

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

Two different conceptions of language dominate philosophical reflection on the nature of human language and of human linguistic powers. The first is the conception of language as a calculus of meaning, and of understanding as computational interpretation. This conception is rooted in the exigencies of function-theoretic logic. The notions pivotal to this conception are truth, truth-condition, sense and force, naming and describing (representation), and theory of meaning for natural languages. The alternative conception is an anthropological one, which conceives of language (...) above all as a form of human communicative behaviour, constituted by human practices and manifest in human action. The notions pivotal to this conception are practice, language-game, use and rule of use as given by explanations of meaning, understanding and criteria of understanding. The fundamental principles that inform each of these conceptions are explained. The radical flaws of calculus conceptions of language are laid bare. (shrink)

Conceptual primitivism is the view that truth is among our most basic and fundamental concepts. It cannot be defined, analyzed, or reduced into concepts that are more fundamental. Primitivism is opposed to both traditional attempts at defining truth (in terms of correspondence, coherence, or utility) and deflationary theories that argue that the notion of truth is exhausted by means of the truth schema. Though primitivism might be thought of as a view of last resort, I believe that the view is (...) independently attractive, and can be argued for directly. In this paper I offer what I take to be the strongest argument in favor of conceptual primitivism, which relies upon the Fregean doctrine of the omnipresence of truth. (shrink)

This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...) independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance. (shrink)

This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.

Wittgenstein responds in his Notes on Logic to a discussion of Russell's Principles of Mathematics concerning assertion. Russell writes: "It is plain that, if I may be allowed to use the word assertion in a non-psychological sense, the proposition "p implies q" asserts an implication, though it does not assert p or q. The p and the q which enter into this proposition are not strictly the same as the p or the q which are separate propositions." (PoM p35) Wittgenstein (...) replies: "Assertion is merely psychological. In not-p, p is exactly the same as if it stands alone; this point is absolutely fundamental." (NB p95) Wittgenstein's response is intriguing, not least because of the centrality to his Tractatus of the idea that a proposition says something. This paper will examine that idea, distinguishing it from 'merely psychological' assertion, and explore in this context how we should understand the occurrence of a Tractarian proposition within another. (shrink)

I have three main objectives in this essay. First, in chapter 2, I shall put forward and justify what I call worldlessness, by which I mean the following: All truths (as well as falsehoods) are wholly independent of any circumstances, not only time and place but also possible worlds. It follows from this view that whatever is actually true must be taken as true with respect to every possible world, which means that all truths are (in a sense) necessary. However, (...) the account I shall propound is different from what is known in the trade as necessitarianism, i.e. the view that there is only one possible world, viz. the actual one, for the doctrine of the worldlessness of truth values, despite its commitment to the necessity of truths and falsehoods, is quite compatible with the idea of there being other possible worlds. Another important issue in chapter 2, explored in particular in section 2.12, is the claim that there is no real change in the world. Secondly, in chapter 3 I consider the eminent traditional argument for determinism, deriving from Aristotle, namely, logical determinism, i.e. determinism justified by an appeal to the logical principle of bivalence (that all proper statements, including those concerning the future, are either true or false). In this connection I try to show that, (i), the formulation of the conclusion of this argument as "Whatever will happen will happen of necessity" is implausible, at least from the modern point of view, (ii), the formulation as "Whatever will happen will happen inevitably" is more to the point, and (iii), on the basis of the worldless and timeless aspect advocated in chapter 2, this latter formulation is quite harmless, essentially amounting to the trivial statement, "Whatever will happen will happen". Thirdly, in chapter 4 I study theological determinism, or determinism that arises from God's supposed providential control over everything that happens. In this connection, I shall survey some historical accounts of the relation between human free will and determinism (not only theological but also causal determinism); the philosophers the views of whom I shall attend to include Chrysippus, St. Augustine, Boethius and Aquinas. I shall in particular consider G.W. Leibniz' theodicean aspirations, viz. his solution to the problem of evil and, especially, his compatibilist attempts to reconcile human free will with the strictly deterministic flow of actual events. I think it is important to try to explicate Leibniz' ingenious account of these matters, since it seems that it has not been fully appreciated in the literature, not even by contemporary Leibniz scholars (such as B. Mates, R.C. Sleigh, C. Wilson, R.M. Adams and D. Rutherford). In providing the Leibnizian compatibilist solution of the problem of determinism and freedom in chapter 4, I shall utilize the approach of chapter 2. (shrink)

This paper explores the relationship between Hume's Prinicple and Basic Law V, investigating the question whether we really do need to suppose that, already in Die Grundlagen, Frege intended that HP should be justified by its derivation from Law V.

The paper argues, as against Thau and Caplan, that the traditional interpretation that Frege abandoned his earlier views about identity and identity--statements is correct.

It is argued that the finitist interpretation of wittgenstein fails to take seriously his claim that philosophy is a descriptive activity. Wittgenstein's concentration on relatively simple mathematical examples is not to be explained in terms of finitism, But rather in terms of the fact that with them the central philosophical task of a clear 'ubersicht' of its subject matter is more tractable than with more complex mathematics. Other aspects of wittgenstein's philosophy of mathematics are touched on: his view that mathematical (...) propositions are 'grammatical propositions' (and so, Strictly speaking, Not genuine propositions at all) and his view that in mathematics 'everything is algorithm, Nothing meaning'. His views on consistency and his anti-Foundationalism are linked with this central thesis. (shrink)

Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different (...) formalizations of arithmetic. In Peano's formalization the domain is a restricted class of individuals, while the universe of discourse is the unrestricted class of all individuals. In Gödel's formalization the domain is a restricted class of individuals as in Peano's formalization, but the universe of discourse coincides with the domain. In Whitehead-Russell's formalization the domain is a class of logical notions in Tarski's sense, that are necessarily not individuals, whereas the universe of discourse is the unrestricted class of individuals as in Peano's formalization. The present approach emphasizes the viewpoint that the universe of discourse of a given discourse is important in determining which propositions are expressed by which sentences. (shrink)

This paper examines some of the most important metaphors and analogies that epistemologists have used to discuss the structure and validity of knowledge. After reviewing foundational, coherentist, and other metaphors for knowledge, we discuss the metaphilosophical significance of the prevalence of such metaphors. We argue that they support a view of philosophy as akin to science rather than poetry or rhetoric. Keywords: epistemology, metaphor, analogy, metaphilosophy, foundations, coherence.

Are Fregean thoughts compositionally complex and composed of senses? We argue that, in Begriffsschrift, Frege took 'conceptual contents' to be unstructured, but that he quickly moved away from this position, holding just two years later that conceptual contents divide of themselves into 'function' and 'argument'. This second position is shown to be unstable, however, by Frege's famous substitution puzzle. For Frege, the crucial question the puzzle raises is why "The Morning Star is a planet" and "The Evening Star is a (...) planet" have different contents, but his second position predicts that they should have the same content. Frege's response to this antinomy is of course to distinguish sense from reference, but what has not previously been noticed is that this response also requires thoughts to be compositionally complex, composed of senses. That, however, raises the question just how thoughts are composed from senses. We reconstruct a Fregean answer, one that turns on an insistence that this question must be understood as semantic rather than metaphysical. It is not a question about the intrinsic nature of residents of the third realm but a question about how thoughts are expressed by sentences. (shrink)

I shall compare two views of legal concepts: as nodes in inferential nets and as categories in an ontology (a conceptual architecture). Firstly, I shall introduce the inferential approach, consider its implications, and distinguish the mere possession of an inferentially defined concept from the belief in the concept’s applicability, which also involves the acceptance of the concept’s constitutive inferences. For making this distinction, the inferential and eliminative analysis of legal concepts proposed by Alf Ross will be connected to the views (...) on theoretical concepts in science advanced by Frank Ramsey and Rudolf Carnap. Consequently, the mere comprehension of a legal concept will be distinguished from the application of the concept to a particular legal system, since application presupposes a doctrinal commitment, namely, the belief that the inferences constituting the concept hold in that system. Then, I shall consider how concepts can be characterised by defining the corresponding terms and placing them within an ontology. Finally, I shall argue that there is a tension between the inferential and the ontological approach, but that both need to be taken into account, to capture the meaning and the cognitive function of legal concepts. (shrink)

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...) from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas. (shrink)

Is there only one logic? Or are there several equally adequate logics? What does it mean, after all, that different logics can be equally adequate? And they would be adequate with respect to what?This article intends to analyze the different answers to these questions, that is, we will evaluate the central arguments of the debate between pluralism, relativism and logical monism. We will explain,on the one hand, the main assumptions of this discussion and, on the other hand, its philosophical ramifications. (...) We will end by indica-ting the development of a possible logical pluralism using the notion of paraconsistentization of logics, which will be explained afterward.We do not intend to refute, once and for all, logical monism. We will show that the main arguments put forward by a monist against logical pluralism are unsound and therefore the existence of some form of logical pluralism remains possible. (shrink)

One of the most striking differences between Frege's Begriffsschrift (logical system) and standard contemporary systems of logic is the inclusion in the former of the judgement stroke: a symbol which marks those propositions which are being asserted , that is, which are being used to express judgements . There has been considerable controversy regarding both the exact purpose of the judgement stroke, and whether a system of logic should include such a symbol. This paper explains the intended role of the (...) judgement stroke in a way that renders it readily comprehensible why Frege insisted that this symbol was an essential part of his logical system. The key point here is that Frege viewed logic as the study of inference relations amongst acts of judgement , rather than – as in the typical contemporary view – of consequence relations amongst certain objects (propositions or well-formed formulae). The paper also explains why Frege's use of the judgement stroke is not in conflict with his avowed anti-psychologism, and why Wittgenstein's criticism of the judgement stroke as 'logically quite meaningless' is unfounded. The key point here is that while the judgement stroke has no content , its use in logic and mathematics is subject to a very stringent norm of assertion. (shrink)

This article treats three aspects of Frege's discussions of definitions. First, I survey Frege's main criticisms of definitions in mathematics. Second, I consider Frege's apparent change of mind on the legitimacy of contextual definitions and its significance for recent neo-Fregean logicism. In the remainder of the article I discuss a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend: do the logical structures of the definientia reflect the understanding of arithmetical terms prevailing prior to (...) Frege's analyses? Unless they do, it is unclear how Frege's proofs demonstrate the analyticity of the arithmetic in use before logicism. Yet, especially in late writings, Frege characterizes definitions as arbitrary stipulations of the senses or references of expressions unrelated to pre-definitional understanding. I conclude by examining some options for conceiving of the status of Frege's logicism in light of this apparent tension, and outline a suggestion for a philosophically fruitful way of resolving this tension. (shrink)

Barnes, A. and P. Thagard Empathy and analogy. Dialogue: Canadian Philosophical Review, 36: 705-720. HTML Croft, D., & Thagard, P.. Dynamic imagery: A computational model of motion and visual analogy. In L. Magnani and N. Nersessian, Model-based reasoning: Science, technology, values. New York: Kluwer/Plenum, 259-274. PDF only. HTML description of program and code for DIVA.

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

Poincaré was a persistent critic of logicism. Unlike most critics of logicism, however, he did not focus his attention on the basic laws of the logicists or the question of their genuinely logical status. Instead, he directed his remarks against the place accorded to logical inference in the logicist's conception of mathematical proof. Following Leibniz, traditional logicist dogma (and this is explicit in Frege) has held that reasoning or inference is everywhere the same — that there are no principles of (...) inference specific to a given local topic. Poincaré, a Kantian, disagreed with this. Indeed, he believed that the use of non-logical reasoning was essential to genuinely mathematical reasoning (proof). In this essay, I try to isolate and clarify this idea and to describe the mathematical epistemology which underlies it. Central to this epistemology (which is basically Kantian in orientation, and closely similar to that advocated by Brouwer) is a principle of epistemic conservation which says that knowledge of a given type cannot be extended by means of an inference unless that inference itself constitutes knowledge belonging to the given type. (shrink)

Thorough a detailed analysis of version III of Gödel's Is mathematics syntax of language?, we propose a new interpretation of Gödel's criticism against the conventionalist point of view in mathematics. When one reads carefully Gödel's text, it brings out that, contrary to the opinion of some commentators, Gödel did not overlook the novelty of Carnap's solution, and did not criticise him from an old-fashioned conception of science. The general aim of our analysis is to restate the Carnap/Gödel debate in the (...) Fregean heritage. We stress the way both of them try to answer, from different Fregean perspectives, to the question of the nature of logic and mathematics in knowledge. (shrink)

L'A. étudie la théorie classique du jugement telle qu'elle apparait dans «La logique» de A. Arnauld et P. Nicole et oppose la sémantique des termes généraux de Port-Royal à celles de Kant et Frege.

George Boolos has argued that the iterative conception of set justifies most, but not all, the ZFC axioms, and that a second conception of set, the Frege-von Neumann conception (FN), justifies the remaining axioms. This article challenges Boolos's claim that FN does better than the iterative conception at justifying the axioms in question.

If I lose my key in Canada, for instance, and I search for it in the United Kingdom, how long will I take to find it? This paper argues that problems in education are caused by non-professional teachers who are employed when trained teachers move in search of promotion friendly activities or financially rewarding duties. This shift of focus means that policy makers in education act without adequate professional guidance. The problems in education, therefore, result from demands made on mainstream (...) education based on misconceptions about what education can offer. It is argued that the implementation of e-learning in education faces the risk of developing on the basis of unproven theories. This scenario increasingly sees the replacement of formal education activities in institutions of learning with non-formal and informal education practices. Given that the contents and influences of non-formal and informal education are not under the control of the teacher, the experiences that learners bring to education settings are increasingly difficult to manage. The paper proposes that by integrating e-learning in teacher education and rewarding 'good teaching', there is a potential for a successful e-learning revolution in education. (shrink)

Simon Blackburn has shown that there is an analogy between the problem of moral motivation in ethics (how can moral reasons move us?) and the problem of what we might call the power of logical reasons (how can logical reasons move us, what is the force of the 'logical must?'). In this paper, I explore further the parallel between the internalism problem in ethics and the problem of the power of logical reasons, and defend a version of psychologism about reasons, (...) although not one of the Humean form. I discuss two forms of cognitivism: (i) a pure cognitivism and 'hard' realism modelled after Dancy's parallel conception in ethics: when we grasp logical reasons we grasp facts, which are directly known to us; (ii) a Kantian form of cognitivism, based on the idea that compulsion by reason goes with the capacity of reflection. I argue that (i) is implausible, and that (ii) fails to meet the internalist requirement. One would then seem to be left with what Dancy calls, about practical reasoning, psychologism about reasons. I sketch what might be such a psychologism. But it fails to account for the objectivity of logical reasons. I argue that the relevant state here is a form of dispositional knowledge of logical reasons. (shrink)