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Logics of Formal Inconsistency
 Handbook of Philosophical Logic
"... 1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory ..."
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1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory
Diamonds are a Philosopher's Best Friends. The Knowability Paradox and Modal Epistemic Relevance Logic (Extended Abstract)
 Journal of Philosophical Logic
, 2002
"... Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the ..."
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Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution o#ered is in the spirit of the constructivist attitude usually maintained by defenders of the antirealist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.
Clues to the paradoxes of knowability: reply to Dummett and Tennant. Analysis 62
 New Waves in Epistemology. Aldershot: Ashgate
"... truth as knowability. He ponders Fitch’s paradox of knowability, 1 which threatens any such conception. Dummett maintains that the antirealist’s error is to offer a blanket characterization of truth, expressed by the following knowability principle: any statement A is true if and only if it is poss ..."
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truth as knowability. He ponders Fitch’s paradox of knowability, 1 which threatens any such conception. Dummett maintains that the antirealist’s error is to offer a blanket characterization of truth, expressed by the following knowability principle: any statement A is true if and only if it is possible to know A. Formally, Tr(A) iff ‡K(A) To remedy the error, Dummett’s proposes the following inductive characterization of truth: (i) Tr(A) iff ‡K(A), if A is a basic statement; (ii) Tr(A and B) iff Tr(A) & Tr(B); (iii) Tr(A or B) iff Tr(A) v Tr(B); (iv) Tr(if A, then B) iff (Tr(A) Æ Tr(B)); (v) Tr(it is not the case that A) iff ¬Tr(A), where the logical constant on the righthand side of each biconditional clause is understood as subject to the laws of intuitionistic logic. 2 The only other principle in play in Dummett’s discussion is
doi:10.1111/j.17552567.2011.01119.x Everything is Knowable – How to Get to Know Whether a Proposition is Truetheo_1119 1..22
, 2012
"... Abstract: Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Mooresentences is that not all propositions are known af ..."
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Abstract: Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Mooresentences is that not all propositions are known after their announcement, i.e., not every proposition is successful. Fitch’s and Moore’s results are related, as they equally apply to standard notions of knowledge and belief (S 5 and KD45, respectively). If we interpret ‘successful ’ as ‘known after its announcement ’ and ‘knowable ’ as ‘known after some announcement’, successful implies knowable. Knowable does not imply successful: there is a proposition j that is not known after its announcement but there is another announcement after which j is known. We show that all propositions are knowable in the more general sense that for each proposition, it can become known or its negation can become known. We can get to know whether it is true: �(Kj ⁄ K¬j). This result comes at a price. We cannot get to know whether the proposition was true. This restricts the philosophical relevance of interpreting ‘knowable ’ as ‘known after an announcement’. Keywords: modal logic, knowability, Fitch’s paradox, dynamic epistemics, public announcements 1. Successful – the Historical Record
Ineffability and Nonsense
 in Proceedings of the Aristotelian Society Supp
, 2003
"... ABSTRACT There are criteria of ineffability whereby, even if the concept of ineffability can never serve to modify truth, it can sometimes (nontrivially) serve to modify other things, specifically understanding. This allows for a reappraisal of the dispute between those who adopt a traditional read ..."
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ABSTRACT There are criteria of ineffability whereby, even if the concept of ineffability can never serve to modify truth, it can sometimes (nontrivially) serve to modify other things, specifically understanding. This allows for a reappraisal of the dispute between those who adopt a traditional reading of Wittgenstein’s Tractatus and those who adopt the new reading recently championed by Diamond, Conant, and others. By maintaining that what the nonsense in the Tractatus is supposed to convey is ineffable understanding, rather than ineffable truth, we can do considerable justice to each of these readings. We can also do considerable justice to the Tractatus. I David Lewis holds that there are inexpressible truths. The following argument, which is a variant of an argument that he discusses, can be used to motivate this view. 1 Suppose that S is an item that can express a proposition, in the minimal sense that, for some proposition p and for some possible
BonJour, L. [1985], The Structure of Empirical Knowledge (Cambridge,
"... ing of justifi cation is, in my terms, that (1) the epistemologist has to choose between (a) mindinternalist foundationalism (e.g., evidentialism), (b) mindexternalist foundationalism (e.g., process reliabilism), and (c) mindinternalist coherentism (e.g., simple coherentism), and (2) objections s ..."
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ing of justifi cation is, in my terms, that (1) the epistemologist has to choose between (a) mindinternalist foundationalism (e.g., evidentialism), (b) mindexternalist foundationalism (e.g., process reliabilism), and (c) mindinternalist coherentism (e.g., simple coherentism), and (2) objections such as the AlternativeSystems Objection and the Isolation Objection dictate against choosing (c) and, therefore, in favor of choosing either (a) or (b). I have challenged this orthodox line on two fronts. I have argued, fi rst, that the epistemologist has a fourth option: (d) mindexternalist coherentism. I have argued, second, that mindexternalist coherentism is immune to both the AlternativeSystems Objection and the Isolation Objection—so that even if these objections are decisive against mindinternalist coherentism, it in no way follows that the epistemologist has to choose between mindinternalist foundationalism and
Antirealist Truth
"... Antirealists have hitherto offered at best sketches of a theory of truth. This paper presents an antirealist theory of truth in some formal detail. It is shown that the theory is able to deal satisfactorily with some problems that are standardly taken to beset antirealism. According to antirealists, ..."
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Antirealists have hitherto offered at best sketches of a theory of truth. This paper presents an antirealist theory of truth in some formal detail. It is shown that the theory is able to deal satisfactorily with some problems that are standardly taken to beset antirealism. According to antirealists, there is an intimate connection between truth and human cognitive capacities which holds of conceptual necessity. While antirealists differ about the exact nature of the connection, the point of conceptual necessity is undisputed; it distinguishes the antirealist conception of truth from a realist one accompanied by some methodological view to the effect that, by natural selection or just by good fortune perhaps, our epistemic powers happen to be so attuned to the world we inhabit that there exist no truths which are beyond our ken in principle. So far antirealists have proposed constraints to be met by antirealist theories of truth, and even a sporadic “informal elucidation ” of antirealist truth (Putnam [1981:56]), but an antirealist theory of truth, comparable, if only just remotely, in formal precision to Tarski’s [1956] theory
(to appear in J. Salerno, ed., New Essays on the Knowability Paradox, Oxford: Oxford University Press) Tennant’s Troubles
"... First, some reminiscences. In the years 197380, when I was an undergraduate and then graduate student at Oxford, Michael Dummett’s formidable and creative philosophical presence made his arguments impossible to ignore. In consequence, one pole of discussion was always a form of antirealism. It end ..."
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First, some reminiscences. In the years 197380, when I was an undergraduate and then graduate student at Oxford, Michael Dummett’s formidable and creative philosophical presence made his arguments impossible to ignore. In consequence, one pole of discussion was always a form of antirealism. It endorsed something like the replacement of truthconditional semantics by verificationconditional semantics and of classical logic by intuitionistic logic, and the principle that all truths are knowable. It did not endorse the principle that all truths are known. Nor did it mention the now celebrated argument, first published by Frederic Fitch (1963), that if all truths are knowable then all truths are known. Even in 1970s Oxford, intuitionistic antirealism was a strictly minority view, but many others regarded it as a live theoretical option in a way that now seems very distant. As the extreme verificationist commitments of the view have combined with accumulating decades of failure to reply convincingly to criticisms of the arguments in its favour or to carry out the programme of generalizing intuitionistic semantics for 1 mathematics to empirical discourse, even in toy examples, the impression has been
1 An Axiomatic Version of Fitch’s Paradox
"... Abstract. A variation of Fitch’s Paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundn ..."
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Abstract. A variation of Fitch’s Paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s Paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the paradox. 1.
Knowability from a Logical Point of View
, 2010
"... The wellknown ChurchFitch paradox shows that the verificationist knowability principle all truths are knowable, yields an unacceptable omniscience property. Our semantic analysis establishes that the knowability principle fails because it misses the stability assumption ‘the proposition in questio ..."
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The wellknown ChurchFitch paradox shows that the verificationist knowability principle all truths are knowable, yields an unacceptable omniscience property. Our semantic analysis establishes that the knowability principle fails because it misses the stability assumption ‘the proposition in question does not change from true to false in the process of discovery, ’ hidden in the verificationist approach. Once stability is made explicit, the resulting stable knowability principle accurately represents verificationist knowability, does not yield the omniscience property, and can be offered as a resolution of the knowability paradox. Two more principles are considered: total knowability stating that it is possible to know whether a proposition holds or not, and monotonic knowability stemming from the intrinsically intuitionistic reading of knowability. The study of these four principles yields a “knowability diamond ” describing their logical strength. These results are obtained within a logical framework which opens the door to the systematic study of knowability from a logical point of view. 1