This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis . But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)

Quine's well-known ‘Two Dogmas of Empiricism’ (1951) plays a key role in the debate about the analytic-synthetic distinction. Taking to task the ideas of Carnap in particular, Quine shows that logical positivism works with a concept of scientific rationality that is based dogmatically on, among other things, the opposition analytic-synthetic.

Contents: Acknowledgements. Conventions. Preface. Biographical sketch. 1 Introduction. 2 The Contributions. 3 Early work in analysis. 4 The Theory of Science . 5. Later mathematical studies. A On Kantian Intuitions. B The Bolzano-Cauchy Theorem.

D’après Bolzano, une proposition est logiquement analytique si et seulement si elle est soit logiquement valide, soit logiquement non valide. Bolzano dit aussi parfois qu’une proposition est logiquement valide si et seulement si elle est et reste vraie sous toute variation simultanée et uniforme de ses parties non logiques. C’est essentiellement la même définition que donne Quine dans son article « Carnap and Logical Truth » où il attribue à ce dernier l’idée qu’un énoncé logiquement vrai est un énoncé au (...) sein duquel seuls les termes logiques sont essentiels. Mais qu’en est-il des propositions et des énoncés vrais qui sont composés exclusivement de parties logiques ? Selon la définition précédente, elles s’avèreraient toutes logiquement valides ou logiquement vraies. Une proposition telle que « Il y a quelque chose » n’est toutefois manifestement pas logiquement valide selon Bolzano. La définition courante de la validité logique doit être modifiée de manière à répondre aux intuitions bolzaniennes. Dans cet article, je propose une telle modification.A proposition is logically analytic according to Bolzano if and only if it is either logically valid or logically non-valid. And a proposition is sometimes said to be logically valid according to Bolzano if and only if it is true and remains true under all simultaneous and uniform variations of all of its non-logical parts. Basically the same definition is provided by Quine in his paper “Carnap and Logical Truth” where he attributes to Carnap the view that a logically true sentence is a true sentence which involves only logical words essentially. But, what about true propositions and sentences which are composed exclusively of logical parts ? Due to the definition mentioned above, all of them will trivially turn out as logically valid or logically true. A proposition like “There is something”, however, is clearly not logically valid according to Bolzano. The common definition of logical validity must be modified in order to match Bolzano’s intuitions. In this paper, such a modification is presented. (shrink)

Jusqu'à maintenant, il semble qu'on n'ait pas établi de lien entre le rejet par Bolzano de la notation quantificationnelle des propositions universelles de la logique traditionnelle et l'articulation inédite de sa notion de validité universelle. C'est ce que je veux faire ici. En particulier, dans la mesure où l'analyticité est un cas spécial de la validité universelle, j'ai l'intention de défendre l'idée qui veut que la notion bolzanienne d'analyticité cherche à résoudre des problèmes qui sont intrinsèquement liés à la théorie (...) traditionnelle de la quantification universelle tels qu'ils surviennent, notamment avec le traitement kantien de l'analyticité. It seems that the connection between Bolzano's rejection of the traditional quantificational notation for universal propositions and the articulation of his notion of universal validity has remained, until today, perfectly unnoticed. In this paper, I will show that there is such a connection. Particularly, since analyticity is a special case of universal validity, my intention is to show that the problems to which Bolzano's perfectly original account of analyticity seeks to find an answer are intrinsically related to the traditional conception of universal quantification as it arises in the context of Kant's treatment of analyticity. (shrink)

Bolzano was the first to establish an explicit distinction between the deductive methods that allow us to recognise the certainty of a given truth and those that provide its objective ground. His conception of the relation between what we, in this paper, call "subjective consequence", i.e., the relation from epistemic reason to consequence and "objective consequence", i.e., grounding however allows for an interpretation according to which Bolzano advocates an "explicativist" conception of proof: proofs par excellence are those that reflect the (...) objective order of grounding. In this paper, we expose the problems involved by such a conception and argue in favour of a more rigorous demarcation between the ontological and the epistemological concern in the elaboration of a theory of demonstration. (shrink)

What I propose is to reconsider the interpretation of Bolzano’s concept of analytic propositions which was offered thirty years ago by Bar-Hillel. The claim of Bar-Hillel was that, in a late addition to his book, The Theory of Science, Bolzano actually had been radically improving his concept of analyticity, thus creating some inconsistencies with the previous, uncorrected version. This allows us to equate the new Bolzanian definition of analytic with what was to be defined, a century later, as logical truth (...) by W. V. Quine. Bar-Hillel’s interpretation has been uncritically accepted by commentators, although the historical issue has been rightly challenged by J. Berg. What I want to show is that, in spite of a surface analogy between Bolzano’s phrasing of the definition of ‘logical analytic’ and Quine’s definition, certain considerations should lead us to call that parallel into question. Attractive as it may be for a Quinian, such a view of Bolzano’s analytic can be shown as incompatible with the leading ideas of his philosophy of logic. Furthermore, there is enough evidence in other sections of the Theory of Science to show that Bolzano’s criterion of analyticity is grounded on purely semantical properties and is part of a general account of logical properties in terms of the mapping of propositions to corresponding models. (shrink)

The aim of the paper is to present and evaluate Bolzano's theory of grounding, that is, his theory of the concept expressed and the relation brought into play by 'because'. In the first part of the paper (Sections 1-4) the concept of grounding is distinguished from and related to three other concepts: the concept of an epistemic reason}, the concept of causality, and the concept of deducibility (i.e., logical consequence). In its second part (Sections 5-7) Bolzano's positive account of grounding (...) is reconstructed in axiomatic form and critically discussed. (shrink)

Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we will (...) propose a general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth. (shrink)

This paper concentrates on some aspects of the history of the analyticsynthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio exprincipiis. But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)

L'auteur expose la tentative faite par Bolzano de définir le concept de proposition en soi analytique à l'aide du concept de variation de représentation. Puis, il discute les difficultés qui résultent de ce modèle quant à la définition bolzanienne du concept étroit de vérité logiquement analytique ou de vérité logique. En conclusion, il compare la définition bolzanienne du concept de proposition en soi analytique et la définition husserlienne: celle-ci se découvre être une application de l'idée fondamentale de Bolzano — employer (...) la variation de représentation pour définir les concepts logiques fondamentaux. The author tries to outline Bolzano's proposal to define the concept of an analytic proposition by using the concept of idea variation. He discusses the problems that arise for Bolzano's attempt to define the concept of a logical truth on the same lines. He ends by comparing Bolzano's and Husserl's definition of the concept of an analytical proposition: Husserl's definition can be seen as an original application of Bolzano's basic idea to define basic logical notions with recourse to the concept of idea variation. (shrink)

Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora. These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science. In this paper we will do two things. First of all, we will propose a (...) general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth. (shrink)

Jacques Laz. exigences de rigueur, inconnues de la philosophie pratiquée dans des pays où elle voulut se penser dans la lignée de Kant. Depuis Brentano, Meinong et Ehrenfels, jusqu'aux membres du Cercle de Vienne et des penseurs  ...

In the second volume of his Wissenschaftslehre from 1837, the Bohemian philosopher, theologian, and mathematician Bernard Bolzano introduced his concept of consequence, named derivability, together with a variety of theorems and further considerations. Derivability is an implication relation between sentences in themselves, which are not meant to be linguistic symbols but the contents of declarative sentences as well as of certain mental episodes. When Schmidt utters the sentence ‘Schnee ist weiß’, and Jones judges that snow is white, the sentence in (...) itself expressed by Schmidt is the same as the one to which Jones agrees in thought. This sentence in itself is an abstract entity: in some sense, it exists; but it is unreal insofar as it lacks a position in space and time, does not stand in causal relationships, and is independent of the existence of thinking beings and languages. (shrink)

What I propose is to reconsider the interpretation of Bolzano’s concept of analytic propositions which was offered thirty years ago by Bar-Hillel. The claim of Bar-Hillel was that, in a late addition to his book, The Theory of Science, Bolzano actually had been radically improving his concept of analyticity, thus creating some inconsistencies with the previous, uncorrected version. This allows us to equate the new Bolzanian definition of analytic with what was to be defined, a century later, as logical truth (...) by W. V. Quine. Bar-Hillel’s interpretation has been uncritically accepted by commentators, although the historical issue has been rightly challenged by J. Berg. What I want to show is that, in spite of a surface analogy between Bolzano’s phrasing of the definition of ‘logical analytic’ and Quine’s definition, certain considerations should lead us to call that parallel into question. Attractive as it may be for a Quinian, such a view of Bolzano’s analytic can be shown as incompatible with the leading ideas of his philosophy of logic. Furthermore, there is enough evidence in other sections of the Theory of Science to show that Bolzano’s criterion of analyticity is grounded on purely semantical properties and is part of a general account of logical properties in terms of the mapping of propositions to corresponding models. (shrink)

Bernard Bolzano's most fruitful invention was his method of variation. He used it in defining such fundamental logical concepts as logical consequence, analyticity and probability. The following three puzzles concerning this method of variation seem particularly worth considering, (i) How can we define the range of variation of an idea or the categorial conformity of two ideas without already using the concept of variation? This question was raised by Mark Siebel in his M. A. thesis, (ii) Why must we define (...) analyticity by means of (simultaneous or successive) variation of several ideas rather than by means of replacing a single idea? This problem is suggested by an example due to W.V.O. Quine, John R. Myhill and Benson Mates, (iii) Must every 'there is...' sentence be synthetic for Bolzano, as his pupil Franz Příhonský claims in his booklet Neuer Anti-Kant, or can a 'there is...' sentence be logically analytic? (shrink)

Bernard Bolzano's most fruitful invention was his method of variation. He used it in defining such fundamental logical concepts as logical consequence, analyticity and probability. The following three puzzles concerning this method of variation seem particularly worth considering, (i) How can we define the range of variation of an idea or the categorial conformity of two ideas without already using the concept of variation? This question was raised by Mark Siebel in his M. A. thesis, (ii) Why must we define (...) analyticity by means of (simultaneous or successive) variation of several ideas rather than by means of replacing a single idea? This problem is suggested by an example due to W.V.O. Quine, John R. Myhill and Benson Mates, (iii) Must every 'there is...' sentence be synthetic for Bolzano, as his pupil Franz Příhonský claims in his booklet Neuer Anti-Kant, or can a 'there is...' sentence be logically analytic? (shrink)

By way of these investigations, we hope to understand better the rationale behind Kant's theory of intuition, as well as to grasp many facets of the relations ...

S. Lapointe s'interroge sur l'analyse logique, sur les différents procédés d'analyse qui en découlent et sur l'importance que l'on doit y accorder en philosophie. Avec des textes de B. Bolzano et E. Kant.

Die "Paradoxien des Unendlichen" sind ein Klassiker der Philosophie der Mathematik und zugleich eine gute Einführung in das Denken des "Urgroßvaters" der analytischen Philosophie. Das Unendliche - seit jeher ein Faszinosum für die philosophische Reflexion - wurde in der Zeit nach der Grundlegung der Analysis durch Leibniz und Newton in der Mathematik zunächst als Problem betrachtet, das sich nicht vollkommen widerspruchsfrei behandeln lässt. Bernard Bolzano, der heute als "Urgroßvater der analytischen Philosophie" (Michael Dummett) gilt, zeigt in diesem klassisch gewordenen Text (...) jedoch, dass es beim Nachdenken über das Unendliche, sofern man begrifflich differenziert argumentiert und klare Definitionen zugrunde legt, keine echten Widersprüche gibt und sich die "Paradoxien des Unendlichen" auflösen lassen. Bolzano setzt sich zunächst mit den Unendlichkeitsbegriffen der Mathematik und der (idealistisch geprägten) Philosophie seiner Zeit auseinander, bevor er sich Schritt für Schritt die analytischen Grundlagen einer konsistenten Theorie des Unendlichen erarbeitet. Bereits einige Jahrzehnte vor Georg Cantors bis heute maßgeblicher mathematischer Unendlichkeitsdefinition gelingt Bolzano mit diesem Werk, dessen logische Klarheit und dessen Grad an philosophischer Durchdachtheit bis heute Beispielcharakter haben, die Rehabilitation des Unendlichen für die Philosophie der Mathematik. Die "Paradoxien des Unendlichen" wurden zuerst 1851 aus dem Nachlass herausgegeben. Diese Neuausgabe beruht auf dem der Erstausgabe zugrundeliegenden Manuskript. (shrink)