This paper analyzes and evaluates Bolzano's remarks on the apagogic method of proof with reference to his juvenile booklet ‘Contributions to a better founded presentation of mathematics’ of 1810 and to his ‘Theory of science’ (1837). I shall try to defend the following contentions: (1) Bolzanos’ vain attempt to transform all indirect proofs into direct proofs becomes comprehensible as soon as one recognizes the following facts: (1.1) his attitude towards indirect proofs with an affirmative conclusion differs from his stance to (...) indirect proofs with a negative conclusion; (1.2) by Bolzano's lights arguments via consequentia mirabilis only seem to be indirect. (2) Bolzano does not deny that indirect proofs can be perfect certifications (Gewissmachungen) of their conclusion; what he denies is rather that they can provide grounds for their conclusions. (2.1) They cannot do the latter, since they start from false premises and (2.2) since they make an unnecessary detour. Equation(3) The far-reaching agreement between his early and late assessment of apagogical proofs (in the Beyträge of 1810 and the Wissenschaftslehre of 1837) is partly due to the fact that he develops his own position always against the background of Wolff's and Lambert's views. (shrink)

Much as we would like to conceive empirical thought as rationally grounded in experience, pitfalls await anyone who tries to articulate this position, and ...

The present article purports to answer the old question of whether the concept (and the method) of Hegelian dialectic can be clarified. Three arguments are advanced in defence of the claim that Hegel's conception is not in fact intelligible. The first argument shows that dialectical negation leads to an infinite regress. The second argument analyses Hegel's claim that the dialectical method yields a positive result and demonstrates that this claim remains completely unsubstantiated and unsubstantiable. The third argument comes to the (...) conclusion that Hegelian dialectic cannot pretend to be an acceptable explication of the “intuitive” understanding of negation. An APPENDIX examines critically a new attempt by D. Wandschneider of reconstructing the first steps of Hegelian dialectical logic by displaying “antinomic structures” and by employing (at least to a limited extent) the techniques of formal logic. (shrink)

How do rational minds make contact with the world? The empiricist tradition sees a gap between mind and world, and takes sensory experience, fallible as it is, to provide our only bridge across that gap. In its crudest form, for example, the traditional idea is that our minds consult an inner realm of sensory experience, which provides us with evidence about the nature of external reality. Notoriously, however, it turns out to be far from clear that there is any viable (...) conception of experience which allows it to do the job. The original problem is to show that thought is rationally constrained by external reality. If sensory experience is to provide the solution--in particular, if it is to provide the answer to sceptical challenges--it must therefore meet two criteria. First, it must itself be `receptive'--i.e., appropriately constrained by external reality. Second, it must be the kind of thing that can enter into a logical or rational relationship with belief--it must already be `conceptual,' in other words. In arguing against the idea that anything could serve both roles, Wilfred Sellars termed this conception of experience "the Myth of the Given.". (shrink)

Some authors have claimed that Hegel's ‘determinate negation’ should be distinguished from ‘logical’ or ‘formal’ negation, that is, from a view of negation as a contradictory forming operator. In contrast, I argue that dialectical determinate negation involves a view of negation as a contradictory forming operator, and can therefore count as formal negation in every respect. However, as it is clear in contemporary glutty semantics of negation, one may distinguish between different accounts of the relationship between negation, contradiction and content. (...) I suggest that, differently from classical negation, and as glutty negation, dialectical negation has partial content. (shrink)

In this article, I consider the possibility of interpreting Hegel’s dialectic as dialetheism. After a first basic recapitulation about the meaning of the words ‘dialetheism’ and ‘dialectic’ and a consideration of Priest’s own account of the relation between dialectical and dialetheic logic in 1989, I discuss some controversial issues, not directly considered by Priest. As a matter of fact, the reflection on paraconsistent logics and dialetheism has enormously grown in recent years. In addition, the reception of Hegel’s logic and metaphysics (...) has also impressively improved. So I suggest that the discussion about the binomial dialectic/dialetheism should be reopened, on these new bases. (shrink)

This dictionary introduces undergraduate and post-graduate students in philosophy, mathematics, and computer science to the main problems and positions in philosophical logic. Coverage includes not only key figures, positions, terminology, and debates within philosophical logic itself, but issues in related, overlapping disciplines such as set theory and the philosophy of mathematics as well. Entries are extensively cross-referenced, so that each entry can be easily located within the context of wider debates, thereby providing a valuable reference both for tracking the connections (...) between concepts within logic and for examining the manner in which these concepts are applied in other philosophical disciplines. Roy T. Cook is Assistant Professor in the Department of Philosophy at the University of Minnesota and an Associate Fellow at Arché, the Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology at the University of St Andrews. He works primarily in the philosophy of logic, language, and mathematics, and has also published papers on seventeenth century philosophy. (shrink)

This paper analyzes and evaluates Bolzano's remarks on the apagogic method of proof with reference to his juvenile booklet "Contributions to a better founded presentation of mathematics" of 1810 and to his ?Theory of science? (1837). I shall try to defend the following contentions: (1) Bolzanos vain attempt to transform all indirect proofs into direct proofs becomes comprehensible as soon as one recognizes the following facts: (1.1) his attitude towards indirect proofs with an affirmative conclusion differs from his stance to (...) indirect proofs with a negative conclusion; (1.2) by Bolzano's lights arguments via consequentia mirabilis only seem to be indirect. (2) Bolzano does not deny that indirect proofs can be perfect certifications (Gewissmachungen) of their conclusion; what he denies is rather that they can provide grounds for their conclusions. (2.1) They cannot do the latter, since they start from false premises and (2.2) since they make an unnecessary detour. (3) The far-reaching agreement between his early and late assessment of apagogical proofs (in the Beyträge of 1810 and the Wissenschaftslehre of 1837) is partly due to the fact that he develops his own position always against the background of Wolff's and Lambert's views. (shrink)

Günthers Untersuchungen zu Hegels Kritik der »formalen« Logik und ihrer metaphysischen Voraussetzungen demonstrieren die Begrenzung der klassischen, zweiwertigen Logik auf das Thema »Objektivität« (»Sein des Seienden«). Zum Verständnis des zweiten logischen Fundamentalthemas »Subjektivität und Reflexion« in der Philosophie des Deutschen Idealismus ist eine grundsätzliche Erweiterung der Konzeption der Logik unumgänglich. In ausführlicher systematischer Analyse der Reflexionstheorie Hegels arbeiten die »Grundzüge einer neuen Theorie des Denkens« den für den Aufbau einer transklassischen Logik grundlegenden Begriff der »logischen Thematik« heraus. Und damit ist (...) dieses Buch als Hegel-Interpretation zu verstehen und zugleich der Einstieg in die Günthersche Theorie exakter operativer Dialektik. (shrink)

Contrariamente a quanto si dice, non esistono oggi “molte filosofie”, ma un unico benché multiforme orientamento scettico, che definisce - con gradi di maggiore o minore radicalità - la “razionalità minimale” all'opera in qualsiasi discorso filosofico. Al centro (o al cuore) di questa grande koiné scettica agisce profondamente, ma con effetti avvertibili, l'idea che sia difficile o impossibile afferrare, o riconoscere, o definire la verità. Ma è davvero così? In quale senso può essere vero che la verità non esiste, o (...) è indefinibile, ineffabile, inafferrabile? Il libro ricostruisce la storia di un solo enunciato, “la verità non esiste”, e delle sue traduzioni e parafrasi: dai sofisti e dagli antichi scettici fino a Nietzsche e alle teorie contemporanee sulla scomparsa della verità. È una storia controversa, fin da principio segnata dalla consapevolezza che a normali condizioni logiche non si può negare la verità: perché se è vero che la verità non esiste, allora almeno una verità esiste. La ricostruzione storica aiuta a capire che la verità è “innegabile” come altri concetti fondamentali della tradizione filosofica: come l'essere, il pensiero, il linguaggio. Cosí come non può essere vero che la verità non esiste, non si può pensare l'assenza di pensiero, e dire l'assenza di linguaggio. Ma esistono, essere, pensiero, verità, linguaggio? La tesi del libro è che non ci si può disfare della verità (esattamente come non ci si può disfare di altri concetti-fondamenti) se e in quanto si intende rimanere all'interno della filosofia, ossia di un discorso preliminare e generale (e in una certa misura libero e neutrale) su teorie, visioni della realtà, modi di dare conto della realtà. (shrink)

This 2007 book examines the possibilities for the rehabilitation of Hegelian thought within analytic philosophy. From its inception, the analytic tradition has in general accepted Bertrand Russell's hostile dismissal of the idealists, based on the claim that their metaphysical views were irretrievably corrupted by the faulty logic that informed them. These assumptions are challenged by the work of such analytic philosophers as John McDowell and Robert Brandom, who, while contributing to core areas of the analytic movement, nevertheless have found in (...) Hegel sophisticated ideas that are able to address problems which still haunt the analytic tradition after a hundred years. Paul Redding traces the consequences of the displacement of the logic presupposed by Kant and Hegel by modern post-Fregean logic, and examines the developments within twentieth-century analytic philosophy which have made possible an analytic re-engagement with a previously dismissed philosophical tradition. (shrink)

An important collection of essays that rectifies a long-standing misconception in the history of the relation between Hegel and analytic philosophy.>.

Den Ausgangspunkt des Aufsatzes bildet Dieter Henrichs These, daß die Negation in Hegels Wissenschaft der Logik selbstreferentiell und autonomisiert vorkommt. Sie wird als exegetische These an dem daseinslogischen Sachverhalt des Anderen seiner selbst sowie am Übergang von der Seins- zur Wesenslogik bewährt und wie folgt differenziert: In der Seinslogik erscheint die Selbstbeziehung der Negation als mit Unmittelbarem kontaminiert, erst in der Wesenslogik trifft sie autonomisiert hervor. Mittel der Differenzierung ist der mengentheoretische Begriff der Unfundiertheit, der es ferner erlaubt, die These (...) von der Selbstbeziehung der Negation auch der Sache nach zu verteidigen und sie für eine Nichtstandarddiagnose der Lügnerantinomie fruchtbar zu machen. (shrink)