Citations of:
Conceptions of truth in intuitionism
History and Philosophy of Logic 25 (2):13145 (2004)
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In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically (...) 

Here, I offer a rapid overview of the theory of metaphor, in order to situate the contributions to this volume in relation to one another and within the field more generally. 

Three influential forms of realism are distinguished and interrelated: realism about the external world, construed as a metaphysical doctrine; scientific realism about nonobservable entities postulated in science; and semantic realism as defined by Dummett. Metaphysical realism about everyday physical objects is contrasted with idealism and phenomenalism, and several potent arguments against these latter views are reviewed. / Three forms of scientific realism are then distinguished: (i) scientific theories and their existence postulates should be taken literally; (ii) the existence of unobservable (...) 

A survey of more philosophical applications of Gödel's incompleteness results. 

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of noncontradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify (...) 



From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle, this duality can be interpreted either ontologically or epistemically. An ontological interpretation of intuitionistic logic is Brouwer’s idealism; of paraconsistency is dialetheism. The epistemic interpretation of intuitionistic logic is (...) 

We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency. 

This paper considers logics which are formally dual to intuitionistic logic in order to investigate a coconstructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widelyheld assumptions, to a justification of bivalence. For example, we do not want to (...) 

In this paper it is argued that the understanding of Brouwer as replacing truth conditions with assertability or proof conditions, in particular as codified in the socalled BrouwerHeytingKolmogorov Interpretation, is misleading and conflates a weak and a strong notion of truth that have to be kept apart to understand Brouwer properly: truthasanticipation and truth incontent. These notions are explained, exegetical documentation provided, and semiformal recursive definitions are given. 

Michael Dummett's argument for intuitionism can be criticized for the implicit reliance on the existence of what might be called absolutely undecidable statements. Neil Tennant attacks epistemic optimism, the view that there are no such statements. I expose what seem serious flaws in his attack, and I suggest a way of defending the use of classical logic in arithmetic that circumvents the issue of optimism. I would like to thank an anonymous referee for helpful comments. CiteULike Connotea Del.icio.us What's this? 

I highlight the importance of the notion of falsity for a semantical consideration of intuitionistic logic. One can find two principal (and nonequivalent) versions of such a notion in the literature, namely, falsity as nontruth and falsity as truth of a negative proposition. I argue in favor of the first version as the genuine intuitionistic notion of falsity. 

Here the relationship between understanding and knowledge of meaning is discussed from two different perspectives: that of Dummettian semantic antirealism and that of the semantic externalism of Putnam and others. The question addressed is whether or not the truth of semantic externalism would undermine a central premise in one of Dummetts key arguments for antirealism, insofar as Dummetts premise involves an assumption about the transparency of meaning and semantic externalism is often taken to undermine such transparency. Several notions of transparency (...) 

Two kinds of justification logics are studied. Then, this article shows how the notion of quasitruth can be defined in these systems. 

Truth’s universal knowability entails its discovery. This threatens antirealism, which is thought to require it. Fortunately, antirealism is not committed to it. Avoiding it requires adoption (and extension) of Dag Prawitz’s position in his longterm disagreement with Michael Dummett on the notion of provability involved in intuitionism’s identification of it with truth. Antirealism (intuitionism generalized) must accommodate a notion of lostopportunity truth (a kind of recognitiontranscendent truth), and even truth consisting in the presence of unperformable verifications. Dummett’s position cannot abide (...) 

What is the appropriate notion of truth for sentences whose meanings are understood in epistemic terms such as proof or ground for an assertion? It seems that the truth of such sentences has to be identified with the existence of proofs or grounds, and the main issue is whether this existence is to be understood in a temporal sense as meaning that we have actually found a proof or a ground, or if it could be taken in an abstract, tenseless (...) 

The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verificationtranscendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or MartinLöf using the sort of propositional modal operators which are employed (...) 



This paper considers a topostheoretic structure for the interpretation of coconstructive logic for proofs and refutations following Trafford :22–40, 2015). It is notoriously tricky to define a prooftheoretic semantics for logics that adequately represent constructivity over proofs and refutations. By developing abstractions of elementary topoi, we consider an elementary topos as structure for proofs, and complement topos as structure for refutation. In doing so, it is possible to consider a dialogue structure between these topoi, and also control their relation such (...) 