Soames (Philos Top 15:44–87, 1987 , J Philos Logic 37:267–276, 2008 ) has argued that propositions cannot be sets of truth-supporting circumstances. This argument is criticized for assuming that various singular terms are directly referential when in fact there are good grounds to doubt this.

Contrary to a claim made by Kaplan (Mind 114:933–1003, 2005) and Neale (Mind 114:809–871, 2005), the readings available to sentences containing definite descriptions embedded under propositional attitude verbs and conditionals do pose a significant problem for the Russellian theory of definite descriptions. The Fregean theory of descriptions, on the other hand, deals easily with the relevant data.

In the last two decades, there has been increasing interest in a re-evaluation of Frege’s stance towards consistency- and independence proofs. Papers by several authors deal with Frege’s views on these topics. In this note, I want to discuss one particular problem, which seems to be a main reason for Frege’s reluctant attitude towards his own proposed method of proving the independence of axioms, namely his view that thoughts, that is, intensional entities are the objects of metatheoretical investigations. This stands (...) in contrast to more straightforward interpretations, which claim that Frege’s hesitancy is mainly due to worries concerning the logical constants or what counts as a logical inference. (shrink)

There are many kinds of negation and denial. Perhaps the most common is the Boolean negation not that applies to propositions-in-extension, i.e. truth-values. The others are, inter alia, the property of propositions of not being true which applies to propositions; the complement function which applies to sets; privation which applies to properties; negation as failure applied in logic programming; negation as argumentation ad absurdum, and many others. The goal of this paper is neither to provide a complete list, nor to (...) analyse all of them. Rather, I am going to deal with negation of propositions that come attached with a presupposition that is entailed by the positive as well as negated form of a given proposition. However, there are two kinds of negation, namely internal and external negation. I am going to prove that while the former is presupposition-preserving, the latter is presupposition-denying. This issue has much in common with the difference between topic and focus articulation within a sentence. Whereas articulating the topic of a sentence activates a presupposition, articulating the focus frequently yields merely an entailment. The main contribution of this paper is the proof that the two kinds of negation are not equivalent. While the Russellian wide-scope (external) negation gets the truthconditions of a sentence right for a subject occurring as a focus, Strawsonian narrow-scope (internal) negation is validly applicable for a subject occurring as the topic. I also deal with other kinds of presupposition triggers, in particular factive attitudes and prerequisites of a given property. My background theory is Transparent Intensional Logic (TIL). TIL is an expressive logic apt for the analysis of sentences with presuppositions, because in TIL we work with partial functions, in particular with propositions with truth-value gaps. Moreover, the procedural semantics of TIL make it possible to uncover the hidden semantic features of sentences, make them explicit and logically tractable. (shrink)

Descriptions have been the object of attention of many philosophers. The goal of this article is to inquire into the meaning of those descriptions which, due to the peculiar character of the objects of description, have been interpreted in different ways, and to investigate in which sense one is able to speak of the existence (or non-existence) of an object of description. The various sorts of descriptions are inquired; the question which entities exist and which do not is dealt with, (...) and, in relation to this, how ‘meaning’ is to be understood. (shrink)

ABSTRACT This paper reveals David Hilbert’s position in the philosophy of mathematics, circa 1900, to be a form of non-eliminative structuralism, predating his formalism. I argue that Hilbert withstands the pressing objections put to him by Frege in the course of the Frege-Hilbert controversy in virtue of this early structuralist approach. To demonstrate that this historical position deserves contemporary attention I show that Hilbertian structuralism avoids a recent wave of objections against non-eliminative structuralists to the effect that they cannot distinguish (...) between structurally identical but importantly distinct mathematical objects, such as the complex roots of $-1$. (shrink)

Este artigo procura mostrar que,apesar de emergir de uma visão tradicional emetafísica da linguagem, a teoria husserliana dosignificado enquanto espécie ideal nas mvestigaçõesLógicas não é redutível a urna expressãolingüística de uma adequação essencialista erepresentacional, mas antes enfatiza o papel daintencionalidade, a idealidade da linguagem e ocaráter constitutivo da consciência no preenchimentoda "significação".

In the last decade the enterprise of formal semantics has been under attack from several philosophical and linguistic perspectives, and it has certainly suffered from its own scattered state, which hosts quite a variety of paradigms which may seem to be incompatible. It will not do to try and answer the arguments of the critics, because the arguments are often well-taken. The negative conclusions, however, I believe are not. The only adequate reply seems to be a constructive one, which puts (...) several pieces of formal semantics, in particular dynamic semantics, together again.In this paper I will try and sketch an overview of tasks, techniques, and results, which serves to at least suggest that it is possible to develop a coherent overall picture of undeniably important and structural phenomena in the interpretation of natural language. The idea is that the concept of meanings as truth conditions after all provides an excellent start for an integrated study of the meaning and use of natural language, and that an extended notion of goal directed pragmatics naturally complements this picture. None of the results reported here are really new, but we think it is important to re-collect them. (shrink)

It is widely assumed that the identity relation is, among other things, transitive. Some have proposed that the identity relation might hold between objects contingently or occasionally. If, on those proposals, identity is shown to not be transitive, then there is reason to reject such proposals. One such argument attempts to show that the identity relation on such proposals violates transitivity in cases of ‘simultaneous’ fissions and fusion. I argue that, even in those cases, contingent identity and occasional identity are (...) transitive. (shrink)

I review and reconsider some of the themes of ‘Two notions of necessity’ (Davies and Humberstone, 1980) and attempt to reach a deeper understanding and appreciation of Gareth Evans’s reflections (in ‘Reference and contingency’, 1979) on both modality and reference. My aim is to plot the relationships between the notions of necessity that Humberstone and I characterised in terms of operators in two-dimensional modal logic, the notions of superficial and deep necessity that Evans himself described, and the epistemic notion of (...) a priority. (shrink)

Las interpretaciones tradicionales de Frege tienden a explicar su antipsicologismo como indicando que ninguna consideración subjetivista debe interferir en la elaboración de un lenguaje lógico; dichas interpretaciones, sin embargo, tienen problemas para explicar el énfasis dado por el mismo Frege a conceptos como el de fuerza asertiva. Este artículo pretende solucionar esta extrañeza investigando, a partir de su concepto de ciencia, algunas de las ideas epistemológicas de Frege. Esto nos llevará a concluir que una concepción de la verdad como fenómeno (...) esencialmente público puede resolver este y otros problemas interpretativos. (shrink)

Near the beginning of De Gen. et Cor. II.1, Aristotle claims that the generation and corruption of all naturally constituted substances are “not without the perceptible bodies”. It is not clear what he intends by this. In this paper I offer a new interpretation of this assertion. I argue that the assumption behind the usual reading, namely, that these “perceptible bodies” ought to be distinguished from the naturally constituted substances, is flawed, and that the assertion is best understood as a (...) claim that Aristotle has established in the second half of the first book of the De Gen. et Cor. (shrink)

In this paper I will analyze some philosophically relevant aspects involved in the dissolution of Benacerraf’s problem of fixing the identity of natural numbers by Shapiro’s structuralism. My fundamental aim is to present three criticisms to Shapiro’s position –to his conception of language, to his characterization of structures as ante rem, and to his dramatic conception of ontology. Some of these criticisms will also be directed to Benacerraf’s identification problem.

In this paper I argue for the idea that, throughout the history of science, there are some cases of theory change that would show how science develops with no referential continuity. For this purpose, I analyze Psillos’ proposal of a theory of reference used to account for referential continuity in conceptual transitions. This kind of continuity is requested by Psillos —as by other philosophers— in his defense of scientific realism. By means of a historical case, the theory of germplasm of (...) August Weismann, I intend to demonstrate that Psillos’ demand for reference continuity can be found to be inadequate. DOI:10.5007/1808-1711.2010v14n3p335. (shrink)

Esse artigo contém uma leitura da semântica fregeana na qual sentidos são parafraseados como regras cognitivas e a existência e a verdade em termos da aplicabilidade dessas regras. Nesse contexto ideias objetáveis da semântica fregeana são substituídas por outras mais intuitivas e plausíveis, sendo as consequências disso especulativamente consideradas.

O principal objetivo desse artigo é interpretativo. Trata-se de historiar as tradicionais teorias descritivistas dos nomes próprios sugeridas por Frege, Russell, Wittgenstein e Searle, demonstrando que, diversamente do que é suposto, elas não constituem teorias diversas a competir entre si, mas apresentações algo diversas de um mesmo modo de ver.

The paper discusses the emergence of Frege's puzzle and the introduction of the celebrated distinction between sense and reference in the context of Frege's logicist project. The main aim of the paper is to show that not logicism per se is mainly responsible for this introduction, but Frege's constant struggle against formalism. Thus, the paper enlarges the historical context, and provides a reconstruction of Frege's philosophical development from this broader perspective.

The Distributional Compositional Categorical model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated methods that (...) could build vectors for a full sentence. This success can be attributed to a conceptually motivated mathematical underpinning, something which the other methods lack, by integrating qualitative compositional type-logic and quantitative modelling of meaning within a category-theoretic mathematical framework. The type-logic used in the DisCoCat model is Lambekʼs pregroup grammar. Pregroup types form a posetal compact closed category, which can be passed, in a functorial manner, on to the compact closed structure of vector spaces, linear maps and tensor product. The diagrammatic versions of the equational reasoning in compact closed categories can be interpreted as the flow of word meanings within sentences. Pregroups simplify Lambekʼs previous type-logic, the Lambek calculus. The latter and its extensions have been extensively used to formalise and reason about various linguistic phenomena. Hence, the apparent reliance of the DisCoCat on pregroups has been seen as a shortcoming. This paper addresses this concern, by pointing out that one may as well realise a functorial passage from the original type-logic of Lambek, a monoidal bi-closed category, to vector spaces, or to any other model of meaning organised within a monoidal bi-closed category. The corresponding string diagram calculus, due to Baez and Stay, now depicts the flow of word meanings, and also reflects the structure of the parse trees of the Lambek calculus. (shrink)

Two-dimensional approaches to semantics, broadly understood, recognize two "dimensions" of the meaning or content of linguistic items. On these approaches, expressions and their utterances are associated with two different sorts of semantic values, which play different explanatory roles. Typically, one semantic value is associated with reference and ordinary truth-conditions, while the other is associated with the way that reference and truth-conditions depend on the external world. The second sort of semantic value is often held to play a distinctive role in (...) analyzing matters of cognitive significance and/or context-dependence. (shrink)

Like other sciences, biosemiotics also has its time-honoured archive, consisting, among other things, of writings by those who have been invented and revered as ancestors of the discipline. One such example is Jakob von Uexküll who has been hailed as a precursor of semiotics, developing his theory of “sign” and “meaning” independently of Saussure and Peirce. The juxtaposition of “sign” and “meaning” is revelatory because one can equally legitimately claim Uexküll as a hermeneutician in the same way as others having (...) claimed him as a semiotician. Such a novel temptation can be justified by Uexküll’s prolonged obsession with Sinn and Bedeutung since his first book in 1909. This paper attempts to reconstruct the immediate intellectual horizon of Uexküll’s historicity, a discursive space traversed by his contemporaries Frege and Husserl, in order to see how Uexküll’s discussions of Zeichen and Gegenstand, Sinn and Bedeutung, were informedby other philosophers of language, and to establish Uexküll as a phenomenological hermeneutician in the tradition of Husserl, Heidegger and Gadamer. To forestall and counter possible criticism that hermeneutics is primarily concerned with textual interpretation, while Uexküll is at most an interpreter of animal life, the paper will discuss his unfinished parody of the Platonic dialogue Meno, which is entitled Die ewige Frage: Biologische Variationen über einen platonischen Dialog (1943). It is through such textual practice that one witnesses the emergence of an Uexküll who embodies at once the addressee exercising his understanding of ancient texts as well as the second addresser recoding his explanation to another group of targeted addressees. This textual practice already goes beyond the confines of biology and in fact involves the linguistic pragmatics of rhetoric and speech act. (shrink)

When I say ‘Hesperus is Phosphorus’, I seem to express a proposition. And when I say ‘Joan believes that Hesperus is Phosphorus’, I seem to ascribe to Joan an attitude to the same proposition. But what are propositions? And what is involved in ascribing propositional attitudes?

What is involved in the meaning of our expressions? Frege suggested that there is an aspect of an expression.

This article is about the conception of truth and signification in Augustine's early philosophical writings. In the first, semantic-linguistic part, the gradual shift of Augustine's position towards the Academics is treated closely. It reveals that Augustine develops a notion of sign which, by integrating elements of Stoic epistemology, is suited to function as a transmitter of true knowledge through linguistic expressions. In the second part, both the ontological structure of signified (sensible) things and Augustine's solution to the apparent tautologies of (...) mathematical truths are examined. Again his notion of sign turns out to be the keystone; this time, however, the natural in contrast to the conventional sign of linguistic expressions. In their complementarity, both parts show how Augustine intensely struggles with and (partially) overcomes the skepticism of the sensible world through his conception of sign and signification. (shrink)

Thanks to David Kaplan (1989a, 1989b), we all know how to handle indexicals like ‘I’. ‘I’ doesn’t refer to an object simpliciter; rather, it refers to an object only relative to a context. In particular, relative to a context C, ‘I’ refers to the agent of C. Since different contexts can have different agents, ‘I’ can refer to different objects relative to different contexts. For example, relative to a context cwhose agent is Gottlob Frege, ‘I’ refers to Frege; relative to (...) a context 0* whose agent is Alexius.. (shrink)

Thanks to David Kaplan, we all know how to handle indexicals like ‘I’. ‘I’ doesn’t refer to an object simpliciter; rather, it refers to an object only relative to a context. In particular, relative to a context C, ‘I’ refers to the agent of C. Since different contexts can have different agents, ‘I’ can refer to different objects relative to different contexts. For example, relative to a context c whose agent is Gottlob Frege, ‘I’ refers to Frege; relative to a (...) context c* whose agent is Alexius Meinong, ‘I’ refers to Meinong. (shrink)

E. E. Constance Jones was one of the first women to study philosophy at the University of Cambridge. This paper focuses on her claim from her first major work, Elements of Logic as a Science of Propositions, that each thing has a unique existence. Jones’s claim follows from claims about tropes and haecceities; but, I suggest, it’s not claims about tropes and haecceities that lead her to accept it. Rather, I suggest, it’s claims about what she calls the denomination of (...) names and the quantitiveness of things that lead her to accept it. Her claim that each thing has a unique existence thus fits within her more general views in Elements of Logic. (shrink)

Here, I offer a rapid overview of the theory of metaphor, in order to situate the contributions to this volume in relation to one another and within the field more generally.

The causal theory of reference (CTR) provides a well-articulated and widely-accepted account of the reference relation. On CTR the reference of a term is fixed by whatever property causally regulates the competent use of that term. CTR poses a metaethical challenge to realists by demanding an account of the properties that regulate the competent use of normative predicates. CTR might pose a challenge to ethical theorists as well. Long argues that CTR entails the falsity of any normative ethical theory. First-order (...) theory attempts to specify what purely descriptive property is a fundamental right-making property (FRM). Long contends that the notion that the FRM causally regulates competent use of the predicate ‘right’ leads to a reductio. The failure of this argument is nevertheless instructive concerning a point at which ethics and metaethics overlap. (shrink)

In “Real Patterns” Daniel Dennett developed an argument about the reality of beliefs on the basis of an analogy with patterns and noise. Here I develop Dennett’s analogy into an argument for descriptivism, the view that belief reports do no specify belief contents but merely describe what someone believes, and show that this view is also supported by empirical evidence. No description can do justice to the richness and specificity or “noisiness” of what someone believes, and the same belief can (...) be described by different sentences or propositions (which is illustrated by Dennett’s analogy, some Gettier cases, and Frege’s puzzle), but in some contexts some of these competing descriptions are misleading or even false. Faithful (or truthful) description must be guided by a principle (or principles) related to the principle of charity: belief descriptions should not attribute irrationality to the believer or have other kinds of “deviant” implications. (shrink)

This paper identifies a tension in Frege’s philosophy and offers a diagnosis of its origins. Frege’s Context Principle can be used to dissolve the problem of propositional unity. However, Frege’s official response to the problem does not invoke the Context Principle, but the distinction between ‘saturated’ and ‘unsaturated’ propositional constituents. I argue that such a response involves assumptions that clash with the Context Principle. I suggest, however, that this tension is not generated by deep-seated philosophical commitments, but by Frege’s occasional (...) attempt to take a dubious shortcut in the justification of his conception of propositional structure. (shrink)

Scott Soames has recently argued that traditional accounts of propositions as n-tuples or sets of objects and properties or functions from worlds to extensions cannot adequately explain how these abstract entities come to represent the world. Soames’ new cognitive theory solves this problem by taking propositions to be derived from agents representing the world to be a certain way. Agents represent the world to be a certain way, for example, when they engage in the cognitive act of predicating, or cognizing, (...) an act that takes place during cognitive events, such as perceiving, believing, judging and asserting. On the cognitive theory, propositions just are act types involving the act of predicating and certain other mental operations. This theory, Soames argues, solves not only the problem of how propositions come to represent but also a number of other difficulties for traditional theories, including the problem of de se propositions and the problems of accounting for how agents are capable of grasping propositions and how they come to stand in the relation of expression to sentences. I argue here that Soames’ particular version of the cognitive theory makes two problematic assumptions about cognitive operations and the contents of proper names. I then briefly examine what can count as evidence for the nature of the constituents of the cognitive operation types that produce propositions and argue that the common nature of cognitive operations and what they operate on ought to be determined empirically in cross-disciplinary work. I conclude by offering a semantics for cognitive act types that accommodates one type of empirical evidence. (shrink)

Abstract:According to his own account, Russell was “led to” the Theory of Descriptions by “the desire to avoid Meinong’s unduly populous realm of being”. This “official view” has been subjected to severe criticism. However stimulating this criticism may be, it is too extreme and therefore not critical enough. It fails to fully acknowledge both the way it is itself opposed to Russell and the way Russell and Meinong were opposed to their opponents. In order to avoid these failures, a more (...) “dialectical” kind of analysis will be applied. It leads to unravelling two confusions shared by the official and the unofficial views: the confusion between conception and adoption of the theory of descriptions and the confusion between three varieties of Meinongianism. By means of these distinctions both a significant kernel of truth contained in Russell’s account and the underlying motive for his distortion of the historical facts can be laid bare. (shrink)

This paper will critically examine two solutions to Frege’s puzzle: the Millian-Russellian solution proposed by Salmon and Braun, which invokes non-semantic modes of presentation (guises, ways of believing or the like); and Fine’s relationalist solution, which appeals to semantic coordination. Special attention will be devoted to discussing the conception of modes of presentation as mental files and to elucidating the nature of coordination. A third solution to Frege’s puzzle will be explored which, like Salmon’s and Braun’s, adopts the Millian-Russellian semantics (...) but, like Fine’s, involves coordination instead of modes of presentation; however, coordination will not be conceived as a semantic relation but as a cognitive and subjective relation, which provides no contribution to semantic content. This novel Millian-Russellian account involving cognitive coordination will be labelled cognitive relationism. (shrink)

ABSTRACT In this paper, I argue that a number of influential Millian responses to Frege’s puzzle, which consist in denying that Frege’s data apply to natural languages, are not viable if logic is to play its role in legitimizing the logical appraisal of rational subjects. A notion of validity which does justice to the normativity of logic must make room for a distinction between valid inferences and enthymemes. I discuss the prospects of formal, relevant and manifest validity as candidates for (...) a notion which complies with this desideratum. Their success, or failure is argued to hang on the viability of a semantical account of de jure co-reference, which is in tension with standard Millian tenets. I conclude that these Millian theories face the following dilemma: either accept that there is no notion of logical validity which makes logic normative for reasoning, thus jeopardizing our well entrenched practices of rational appraisal; or accept that de jure co-reference is a real semantical relation. (shrink)

Rooth & Partee (1982) and Rooth (1985) have shown that the English-specific rule-by-rule system of PTQ can be factored out into function application plus two transformations for resolving type mismatch (type lifting and variable binding). Building on these insights, this article proposes a universal system for type-driven translation, by adding two more innovations: local type determination for gaps (generalizing Montague 1973) and a set of semantic filters (extending Cooper 1983). This system, dubbed Cross-Linguistic Semantics (XLS), is shown to account for (...) various phenomena — including scope relations in English and Greenlandic Eskimo, internally headed relative clauses in Lakhota, serial verbs in Yoruba and VP ellipsis in English. (shrink)

In the earliest phase of his logical investigations, Peirce adopts Mill's doctrine of real Kinds as discussed in the System of Logic and adapts it to the logical conceptions he was then developing. In Peirce's definition of natural class, a crucial role is played by the notion of information: a natural class is a class of which some non-analytical proposition is true. In Peirce's hands, Mill's distinction between connotative and non-connotative terms becomes a distinction between symbolic and informative and pseudo-symbolic (...) and non-informative forms of representation. A symbol is for Peirce a representation which has information. Just as for Mill all names of Kind connote their being such, so for Peirce all symbols profess to correspond to a natural class. (shrink)

In this paper it is shown how a partial semantics for presuppositions can be given which is empirically more satisfactory than its predecessors, and how this semantics can be integrated with a technically sound, compositional grammar in the Montagovian fashion. Additionally, it is argued that the classical objection to partial accounts of presupposition projection, namely that they lack “flexibility,” is based on a misconception. Partial logics can give rise to flexible predictions without postulating any ad hoc ambiguities. Finally, it is (...) shown how the partial foundation can be combined with a dynamic system of common-ground maintenance to account for accommodation. (shrink)

In this paper I develop a theory of contrastive why questions that establishes under what conditions it is sensible to ask "why p rather than q?". p and q must be outcomes of a single type of causal process.

Biosemiotics is the synthesis of biology and semiotics, and its main purpose is to show that semiosis is a fundamental component of life, i.e., that signs and meaning exist in all living systems. This idea started circulating in the 1960s and was proposed independently from enquires taking place at both ends of the Scala Naturae. At the molecular end it was expressed by Howard Pattee’s analysis of the genetic code, whereas at the human end it took the form of Thomas (...) Sebeok’s investigation into the biological roots of culture. Other proposals appeared in the years that followed and gave origin to different theoretical frameworks, or different schools, of biosemiotics. They are: (1) the physical biosemiotics of Howard Pattee and its extension in Darwinian biosemiotics by Howard Pattee and by Terrence Deacon, (2) the zoosemiotics proposed by Thomas Sebeok and its extension in sign biosemiotics developed by Thomas Sebeok and by Jesper Hoffmeyer, (3) the code biosemiotics of Marcello Barbieri and (4) the hermeneutic biosemiotics of Anton Markoš. The differences that exist between the schools are a consequence of their different models of semiosis, but that is only the tip of the iceberg. In reality they go much deeper and concern the very nature of the new discipline. Is biosemiotics only a new way of looking at the known facts of biology or does it predict new facts? Does biosemiotics consist of testable hypotheses? Does it add anything to the history of life and to our understanding of evolution? These are the major issues of the young discipline, and the purpose of the present paper is to illustrate them by describing the origin and the historical development of its main schools. (shrink)

The topic of this article is the ontology of practical reasons. We draw a critical comparison between two views. According to the first, practical reasons are states of affairs; according to the second, they are propositions. We first isolate and spell out in detail certain objections to the second view that can be found only in embryonic form in the literature – in particular, in the work of Jonathan Dancy. Next, we sketch possible ways in which one might respond to (...) each one of these objections. A careful evaluation of these complaints and responses, we argue, shows that the first view is not as obviously compelling as it is thought by Dancy. Indeed, it turns out that the view that practical reasons are propositions is by no means unworkable and in fact, at least under certain assumptions, explicit considerations can be made in favour of a propositional construal of reasons. (shrink)

The article deals with the interpretation of propositional attitudes in the framework of modal predicate logic. The first part discusses the classical puzzles arising from the interplay between propositional attitudes, quantifiers and the notion of identity. After comparing different reactions to these puzzles it argues in favor of an analysis in which evaluations of de re attitudes may vary relative to the ways of identifying objects used in the context of use. The second part of the article gives this analysis (...) a precise formalization from a model-and proof-theoretic perspective. (shrink)

Mitä oleva on? Omaisuus ja elämä pureutuu tähän filosofian peruskysymykseen seuraten kahta länsimaisen filosofian jättiläistä, Aristotelestä ja Heideggeria. Siinä missä Aristoteles kysyy olevaa substantiivina ja tilana, etsii Heidegger olemisen mieltä verbinä ja tapahtumana. Nämä kaksi merkitystä löytyvät myös suomen olla-verbistä: "omistaa jotakin" ja "olla olemassa, elossa". Omaisuus ja elämä antavat peruslähtökohdat olevan tulkitsemiselle. Kirja vie lukijansa filosofian kreikkalaisille juurille ja sen uusimpiin, Heideggerin avaamiin mahdollisuuksiin.

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. (...) Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method. (shrink)

From the Editor’s Introduction: "The Internal Limitations of Human Understanding." We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. -/- The limitations (...) in view here are not due to the mere finitude of our understanding of ourselves and of the world in which we live. They are limitations that come automatically and necessarily with any form of understanding. They are, as we shall see, part and parcel of any organization or ordering of data that we call information. -/- The consequences of these limitations are varied: As a result of them, hermeneutics cannot help but be hermetic; scientific theories of necessity are circumscribed by the boundaries of the ideas that define them; formal systems must choose between consistency and comprehensiveness; philosophical study, because it includes itself within its own proper subject matter, is forced to be reflexive in its self-enclosure. The fundamental dynamic shared by all forms of understanding testifies to an internal limitative keystone. (shrink)