Events by Frode A . Bjørdal
This was the 4th world congress organized about the square of opposition after very succesful pre... more This was the 4th world congress organized about the square of opposition after very succesful previous editions in Montreux, Switzerland 2007, Corté, Corsica 2010, Beirut, Lebanon, 2012. An interdisciplinary event gathering logicians, philosophers, mathematicians, semioticians, theologians, cognitivists, artists and computer scientists.
http://www.square-of-opposition.org/square2014.html
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Papers by Frode A . Bjørdal
Logic and Logical Philosophy, Jun 13, 2013
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Mathematical Reviews, 2019
This paper analyzes the use of diagrams in mathematical reasoning and puts forward examples where... more This paper analyzes the use of diagrams in mathematical reasoning and puts forward examples where diagrams are useful. It is not suggested that diagrammatic reasoning is sometimes necessary to justify mathematical results, but rather that such reasoning in some cases may be useful in discovering new theorems or in their communication. The topic could to a large extent have been treated by psychological research, it seems. Some typos interfere with the presentation. In the references, the title of the article and the page numbers of the article by Barwise and Etchemendy have been replaced by the information for the article by De Cruz
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arXiv (Cornell University), Dec 22, 2022
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Springer eBooks, 2015
The main purpose of this article is to discuss and clarify philosophical issues in connection wit... more The main purpose of this article is to discuss and clarify philosophical issues in connection with the librationst set theory £. We take technical results in and upon £ for granted though make references to them as that is useful. We defend the view that £ is neither an inconsistent nor a contradictory system and point out that it is neither paraconsistent nor dialetheist; in contrast we consider £ a bialethic and paracoherent theory.
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We present a strategy to avoid versions of Humean and counterfactual skepticism based upon a deon... more We present a strategy to avoid versions of Humean and counterfactual skepticism based upon a deontologist theory of justification, a partial guideline for how to side step Gettier problems for certain statements and the assumption that certain statements are compelling. As an upshot the threats of Humean skeptical arguments disappear for some subjects and classes of statements
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arXiv (Cornell University), Jul 15, 2014
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The Review of Symbolic Logic, 2010
We show that a paraconsistent set theory proposed in Weber (2010) is strong enough to provide a q... more We show that a paraconsistent set theory proposed in Weber (2010) is strong enough to provide a quite classical nonprimitive notion of identity, so that the relation is an equivalence relation and also obeys full substitutivity: a = b → (F(a) → F(b)). With this as background it is shown that the proposed theory also proves ∀x(x ≠ x). While not by itself showing that the proposed system is trivial in the sense of proving all statements, it is argued that this outcome makes the system inadequate.
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With the avoidance of Russell’s paradox and its cognates as one paramount motivation, and the avo... more With the avoidance of Russell’s paradox and its cognates as one paramount motivation, and the avoidance of ungrounded mathematical objects as another, the twentieth century from early on saw the initiation of various foundational theories which altogether avoided an invocation of infinite power sets. This is famously the case in the predicativist tradition going back to Herman Weyl’s Das Kontinuum, and further investigated later principally by Solomon Feferman, but also by others. This was clearly also an important motivational aspect of the perhaps less rigorously formulated original intent of Luitzen Brouwer’s intuitionist program, and it is presently manifest much more precisely within parts of the intuitionist tradition in that Per Martin Lof’s constructive Type Theory lacks an analogue of the infinitary power-set operation, as does Peter Aczel’s constructive set theory CZF. The reverse mathematics program initiated by Harvey Friedman seemed to have established that only a very ...
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Events by Frode A . Bjørdal
http://www.square-of-opposition.org/square2014.html
Papers by Frode A . Bjørdal
http://www.square-of-opposition.org/square2014.html