The topics discussed in this volume include: transcending anti-foundationalism and two concurrent trends of "anthropological" and "practical" understanding of the foundations of mathematics, new approaches to mathematical realism, the “roots” of logic in a genetic perspective, the primacy of truth or satisfaction, and the “effectiveness” of mathematics in terms of categorical semantics.
The topics discussed in this volume include: transcending anti-foundationalism and two concurrent trends of "anthropological" and "practical" understanding of the foundations of mathematics, new approaches to mathematical realism, the “roots” of logic in a genetic perspective, the primacy of truth or satisfaction, and the “effectiveness” of mathematics in terms of categorical semantics.
Argumentation analysis and formal approaches to reasoning often focus the logical validity of arguments on inferences made in discourse from a god’s-eye perspective. In contrast, Breitholtz’s account emphasises the individual perspectives of interlocutors and the function and acceptability of their reasoning in context. This provides an analysis of interactions where interlocutors have access to different topoi and therefore make different inferences.
Argumentation analysis and formal approaches to reasoning often focus the logical validity of arguments on inferences made in discourse from a god’s-eye perspective. In contrast, Breitholtz’s account emphasises the individual perspectives of interlocutors and the function and acceptability of their reasoning in context. This provides an analysis of interactions where interlocutors have access to different topoi and therefore make different inferences.
The access to Brentano's philosophy is enhanced by this volume not only with regard to his logic as a theory of deductive inference, but also to his descriptive psychology, metaphysics, and philosophy of language.
The access to Brentano's philosophy is enhanced by this volume not only with regard to his logic as a theory of deductive inference, but also to his descriptive psychology, metaphysics, and philosophy of language.
The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of sand, or neither one is. The third claim is rendered plausible by an initial conviction that vague predicates like ‘heap’ tolerate small changes. However, the repeated application of a tolerance principle to the second claim yields the further proposition that one grain of sand does make a heap – which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates.
Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case.
The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of sand, or neither one is. The third claim is rendered plausible by an initial conviction that vague predicates like ‘heap’ tolerate small changes. However, the repeated application of a tolerance principle to the second claim yields the further proposition that one grain of sand does make a heap – which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates.
Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case.