Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...) non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four (...) main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. (shrink)

The concept of truth and competing philosophical theories on what truth amounts to have an important place in contemporary philosophy. The aim of this chapter is to give a synopsis of different theories of truth and the particular philosophical issues related to the concept of truth. The literature on this topic is vast, and we must necessarily be rather selective and very brief about complex questions of interpretation of various philosophers. The focus of the chapter is mainly on selected systematic (...) issues and the most influential and well-established philosophical theories and key concepts. (shrink)

The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ other than what they are, (...) there’d be no apparent contradiction. But the meaning is what it is, and changing the meaning of our terms to avoid the apparent contradiction of Christ is an apparent flight from reality. What, in the end, is the explanation of the apparent contradiction of Christ? Theologians and philosophers have long advanced many consistency-seeking answers, all of which increase the metaphysical or semantical complexity of the otherwise strikingly simple but radical core of Christianity’s GodMan. In this paper, I put the simplest explanation on the theological table: namely, Christ appears to be contradictory because Christ is contradictory. This explanation may sound complicated to the many who are steeped in the mainstream account of logic according to which logic precludes the possibility of true contradictions. But the mainstream account of logic can and should be rejected. Ridding theology of the dogma of mainstream logic illuminates the simple though striking explanation of the apparent contradiction of Christ — namely, that Christ is a contradictory being. Just as the simplest explanation to the apparent roundness of the earth has earned due acceptance, so too should the simplest explanation of the apparent contradiction of Christ. (shrink)

Este texto tem como objetivo apresentar a principal motivação filosófica para se defender uma teoria causal da memória, que é explicar como pode um evento que se deu no passado estar relacionado a uma experiência mnêmica que se dá no presente. Para tanto, iniciaremos apresentando a noção de memória de maneira informal e geral, para depois apresentar elementos mais detalhados. Finalizamos apresentando uma teoria causal da memória que se beneficia da noção de veritação (truthmaking).

This paper presents four key results. Firstly, it distinguishes between _partial_ and _consistent_ assertion of a sentence, and introduces the concept of an _equivocal_ sentence, which is both partially asserted and partially denied. Secondly, it proposes a novel definition of truth, stating that _a true sentence is one that is consistently asserted_. This definition is immune from the Liar paradox, does not restrict classical logic, and can be applied to declarative sentences in the language used by any particular person. Thirdly, (...) the paper introduces an epistemic model of language, known as _assertional language_, which is used to formalize the definition of truth. Finally, it provides an argument for the falsity of so-called Liar sentences. The paper also discusses Tarski's solution to the Liar paradox and argues for the abandonment of the Tarski Scheme: _'p' is true if and only if p_, in the context of everyday language. The proposed definition of truth can be viewed as a formal account of the correspondence theory. The epistemic model is a powerful concept on its own that allows for combining different languages in a meaningful way. This model is uniquely capable of reflecting on epistemic inconsistencies, such as logical paradoxes, in a consistent manner. (shrink)

Davidson conjectured that suitably formulated Tarski-style theories of truth can “do duty” as theories of meaning for the spoken languages that humans naturally acquire. But this conjecture faces a pair of old objections that are, in my view, fatal when combined. Foster noted that given any theory of the sort Davidson envisioned, for a language L, there will be many equally true theories whose theorems pair endlessly many sentences of L with very different specifications of whether or not those sentences (...) are true. And if L includes words ‘true’, then for reasons stressed by Tarski, it’s hard to see how any truth theory for L could be correct. Moreover, each of these concerns amplifies the other. Appealing to possible worlds will not help with Foster’s Problem, for reasons that Chomsky discussed in the 1950s, and appealing to trivalent models of truth will not avoid concerns illustrated with Liar Sentences. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic can be obtained? We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-capture’ versions of standard theorems, given suitable restrictions and background assumptions; but the shift (...) to non-classical logic may recast the meanings of these apparently ‘absolute’ theorems. (shrink)

Dialetheists believe some sentences are both true and false. Objectors have argued that this makes it unclear how people can disagree with each other because, given the dialetheist’s commitments, if I make a claim and you tell me my claim is false, we might both be correct. Graham Priest (2006a) thinks that people disagree by rejecting or denying what is said rather than ascribing falsehood to it. We build on the work of Julien Murzi and Massimiliano Carrara (2015) and show (...) that Priest’s approach cannot succeed: given the same dialetheist’s commitments you may be correct to reject a claim that I correctly believe. We argue further that any attempt to solve the problem by identifying a new attitude of disagreement will also fail. The culprit, we claim, is the attempt to find a pair of attitudes that satisfy ‘exclusivity’—that is, attitudes such that both cannot be simultaneously correct. Instead of identifying disagreement by the kinds of attitudes involved, we propose dialetheists focus on the normative landscape and identify it in part by whether parties have reasons to change their attitudes. We offer our own normative theory of disagreement to help dialetheists with this challenge. (shrink)

Truth is a fundamental philosophical concept that, despite its common and everyday use, has resisted common-sense formulations. At this point, one may legitimately wonder if there even is a common-sense notion of truth or what it could look like. In response, I propose here a common-sense account of truth based on four “truisms” that set a baseline for how to go about building an account of truth. Drawing on both ordinary language philosophy and contemporary pragmatic approaches to truth, I defend (...) a pragmatic, common-sense theory of truth. The result is a theory that focuses the use and function of truth while also emphasizing its “subject-independence.”. (shrink)

This book is a running commentary of Tarski’s momentous monograph ‘The Concept of Truth in Formalized Languages’, published in Polish in 1933, with special focus on discrepancies...

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