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Mathematics. A Science of Patterns?
  • G. Oliveri
  • Philosophy, Computer Science
  • Synthese
  • 1 September 1997
It is shown that it is possible to construct a realist philosophy of mathematics which commits one neither to dream the dreams of Platonism nor to reduce the word 'realism' to mere noise. Expand
Reply to Prawitz
I am extremely happy that Professor Dag Prawitz took part in this conference. I owe a great deal to his pioneering researches into natural deduction and into the relation between theories of meaningExpand
Reply to Wright
Crispin Wright’s discussion of my paper on Godel’s incompleteness theorem has the great merit of linking the principal topic of that with the more celebrated thesis of Lucas, recently endorsed byExpand
Truth in Mathematics
1. Truth and the foundations of mathematics. An introduction 2. Truth and obvjectivity from a verificationist point of view 3. Constructive truth in practice 4. On founding the theory of algorithmsExpand
The Philosophy of Michael Dummett
Preface. Abbreviations. Part 1: Philosophy of Language. The Social Aspect of Language D. Davidson. Singular Terms B. Hale. Philosophical Theorizing and Particularism: Michael Dummett onExpand
An algebra for the manipulation of conceptual spaces in cognitive agents
This paper introduces an algebra for the manipulation of different conceptual spaces in order to formalise the process whereby an artificial agent rearranges its internal conceptual representations as a consequence of its perceptions, which are here rendered in terms of measurement processes. Expand
Acting on Conceptual Spaces in Cognitive Agents
In this work, a cognitive agent must also be able to ‘produce a new space’ by means of ‘global’ operations which, acting on a conceptual space taken as a whole, generate other conceptual spaces. Expand
Object, structure, and form
The main task of this paper is to develop the non-Platonist view of mathematics as a science of structures I have called, borrowing the label from Putnam, ‘realism with the human face’. According toExpand
Mathematics as a Quasi-Empirical Science
The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows byExpand
Pattern-Recognition: a Foundational Approach
This paper aims at giving a contribution to the ongoing attempt to turn the theory of pattern-recognition into a rigorous science. In this article we address two problems which lie at the foundationsExpand