In diesem Aufsatz wird ein neues Paradoxon vorgestellt, der Super-Lügner. Er ist stärker als alle bekannten Lügner-Sätze, nicht mehr eindeutig selbstreferentiell und läßt sich darüber hinaus in eindeutig in die Tarski-Hierarchie einordnen. Eine unendlich große Familie von Super-Lügnern auf Metaebenen ist konstruierbar. Schließlich widersetzt sich der Super-Lügner der Auflösung durch die neue vielversprechende Reflexionslogik LR von U. Blau.

In diesem Aufsatz wird ein neues Paradoxon vorgestellt, der Super-Lügner. Er ist stärker als alle bekannten Lügner-Sätze, nicht mehr eindeutig selbstreferentiell und läßt sich darüber hinaus in eindeutig in die Tarski-Hierarchie einordnen. Eine unendlich große Familie von Super-Lügnern auf Metaebenen ist konstruierbar. Schließlich widersetzt sich der Super-Lügner der Auflösung durch die neue vielversprechende Reflexionslogik LR von U. Blau.

I propose an account of the metaphysics of the expressions of a mathematical language which brings together the structuralist construal of a mathematical object as a place in a structure, the semantic notion of indexicality and Kit Fine's ontological theory of qua objects. By contrasting this indexical qua objects account with several other accounts of the metaphysics of mathematical expressions, I show that it does justice both to the abstractness that mathematical expressions have because they are mathematical objects and to (...) the element of concreteness that they have because they are also used as signs. In a concluding section, I comment on the pragmatic element that has entered ontology by way of the notion of indexicality and use it to give an answer to a question Stewart Shapiro has recently posed about the status of meta-mathematics in the structuralist philosophy of mathematics. (shrink)

The article addresses two closely related questions: What are the criteria of adequacy of logical formalization of natural language arguments, and what gives logic the authority to decide which arguments are good and which are bad? Our point of departure is the criticism of the conception of logical formalization put forth, in a recent paper, by M. Baumgartner and T. Lampert. We argue that their account of formalization as a kind of semantic analysis brings about more problems than it solves. (...) We also argue that the criteria of adequate formalization need not be based on truth conditions associated with logical formulas; in our view, they are better based on structural (inferential) grounds. We then put forward our own version of the criteria. The upshot of the discussion that follows is that the quest for an adequate formalization in a suitable logical language is best conceived of as the search for a Goodmanian reflective equilibrium. (shrink)

A direct path that has been missed for 100 years leads from the oldest paradoxes straight to mysticism, via (the concept of) logical and mathematical truth, since the purely formal truth is an absolutely univocal, absolutely timeless and absolutely unbounded reference. I present three theses in passing: (1) logicians fail to fully appreciate the basic mathematical idea of truth and consequently push the semantic paradoxes aside. Otherwise they would have come to adopt the reflexive logic LR* right after Cantor (more (...) on this briefly in Sect. 4. For a more precise elaboration see my Logik der Unbestimmtheiten und Paradoxien (Blau 2008)). (2) Mathematicians fail to fully appreciate the basic mathematical concept of number and push Zeno’s paradoxes aside. Otherwise they would have come to adopt linear arithmetic ${\mathbb{L}^{*}}$ right after Cantor (more on this briefly in Sects. 1 and 5, for further elaboration see my planned Grundparadoxien und grenzenlose Arithmetik. The technical parts are complete, yet philosophically it is as incomplete as Sect. 6). (3) Philosophers fail to fully appreciate the paradox of subject and object and push the Darwinian argument for Cartesian (mind–body)-interaction aside, otherwise they would have been en route towards mysticism since Darwin’s times (more on this in Sect. 6, for a little more precise elaboration see Blau in Die Logik der Unbestimmtheiten und Paradoxien. Synchron Publishers, Heidelberg, 2008, Ch. 1.5). (shrink)

Hegel's Science of Logic makes the just not low claim to be an absolute, ultimate-grounded knowledge. This project, which could not be more ambitious, has no good press in our post-metaphysical age. However: That absolute knowledge absolutely cannot exist, cannot be claimed without self-contradiction. On the other hand, there can be no doubt about the fundamental finiteness of knowledge. But can absolute knowledge be finite knowledge? This leads to the problem of a self-explication of logic (in the sense of Hegel) (...) and further, as will be shown, to a new definition of the dialectical procedure. The stringency of which results from the fact that always exactly that implicit content is explicated that was generated by the preceding explication step itself and is thus concretely comprehensible. At the same time, a new implicit content is generated by this act of explication, which requires a new explication step, and so forth. In the dialectical procedure reinterpreted in this way, dialectical arguments are not beheld, guessed at or even surreptitiously obtained, but are methodically accountable. Thereby dialectics is understood as a self-explication of logic by logical means and thus as a proof of the possibility of ultimate-grounding in the form of absolute and nevertheless finite – and thus also fallible – knowledge. (shrink)

This book contains a representationalist theory of self-consciousness and of the phenomenal first-person perspective. It draws on empirical data from the cognitive and neurosciences.

Quine's metalogical 'quasiquotation' is formally added to classical first-Order logic; the resulting system lq is stronger and more natural than all former systems of quotational logic. Lq contains object-Variables ranging over the universe u and expression-Variables ranging over the set e of all expressions of lq; e is a subset of u. Object-Quantifiers are referential, Expression-Quantifiers are substitutional; only the latter ones bind into quasiquotations. Lq contains its own syntactic metatheory and arithmetics. Natural proofs of godel's and tarski's theorems are (...) given for lq. (shrink)