Philosophers of information, according to Luciano Floridi (The philosophy of information. Oxford University Press, Oxford, 2010, p 32), study how information should be “adequately created, processed, managed, and used.” A small number of epistemologists have employed the concept of information as a cornerstone of their theoretical framework. How this concept can be used to make sense of seemingly intractable epistemological problems, however, has not been widely explored. This paper examines Fred Dretske’s information-based epistemology, in particular his response to radical epistemological (...) skepticism. We discuss the relationship between information, evidence and knowledge in relation to the problem of skepticism and the options available to an information-based epistemology for dealing with it. (shrink)

The Church-Turing Thesis (CTT) is often paraphrased as ``every computable function is computable by means of a Turing machine.'' The author has constructed a family of equational theories that are not Turing-decidable, that is, given one of the theories, no Turing machine can recognize whether an arbitrary equation is in the theory or not. But the theory is called pseudorecursive because it has the additional property that when attention is limited to equations with a bounded number of variables, one obtains, (...) for each number of variables, a fragment of the theory that is indeed Turing-decidable. In a 1982 conversation, Alfred Tarski announced that he believed the theory to be decidable, despite this contradicting CTT. The article gives the background for this proclamation, considers alternate interpretations, and sets the stage for further research. (shrink)

Although it is conceded that distinct knowledge domains do presentparticular problems of coming to know, in thispaper it is argued that it is possible to construct a domain independent modelof the processes of coming to know, one inwhich observers share understandings and do soin agreed ways. The model in question is partof the conversation theory of Gordon Pask. CT, as a theory of theory construction andcommunication, has particular relevance forfoundational issues in science and scienceeducation. CT explicitly propounds a ``radicalconstructivist'' epistemology. (...) A briefaccount is given of the main tenets of RC andCT's place in that tradition and the traditionsof cybernetics. The paper presents a briefnon-technical account of the main concepts ofCT including elaborations by Laurillard andHarri-Augstein and Thomas. As part of CT, Pask also elaborated a methodology – knowledgeand task analysis – for analysing the structureof different knowledge domains; thismethodology is sketched in outline. (shrink)

Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.

During the first half of the twentieth century, mainstream answers to the foundational crisis, mainly triggered by Russell and Gödel, remained largely perfectibilist in nature. Along with a general naturalist wave in the philosophy of science, during the second half of that century, this idealist picture was finally challenged and traded in for more realist ones. Next to the necessary preliminaries, the present paper proposes a structured view of various philosophical accounts of mathematics indebted to this general idea, laying the (...) ground for a desirable integration of their strenghts. (shrink)

A cornerstone of modern mathematical logic is the diagonal lemma of Gödel and Carnap. It is used in e.g. the classical proofs of the theorems of Gödel, Rosser and Tarski. From its first explication in 1934, just essentially one proof has appeared for the diagonal lemma in the literature; a proof that is so tricky and hard to relate that many authors have tried to avoid the lemma altogether. As a result, some so called diagonal-free proofs have been given for (...) the above mentioned fundamental theorems of logic. In this paper, we provide new proofs for the semantic formulation of the diagonal lemma, and for a weak version of the syntactic formulation of it. (shrink)

During the first half of the twentieth century, mainstream answers to the foundational crisis, mainly triggered by Russell and Gödel, remained largely perfectibilist in nature. Along with a general naturalist wave in the philosophy of science, during the second half of that century, this idealist picture was finally challenged and traded in for more realist ones. Next to the necessary preliminaries, the present paper proposes a structured view of various philosophical accounts of mathematics indebted to this general idea, laying the (...) ground for a desirable integration of their strenghts. (shrink)