Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie (...) the result is in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig. (shrink)

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. (shrink)

According to the “paradox of knowability”, the moderate thesis that all truths are knowable – ... – implies the seemingly preposterous claim that all truths are actually known – ... –, i.e. that we are omniscient. If Fitch’s argument were successful, it would amount to a knockdown rebuttal of anti-realism by reductio. In the paper I defend the nowadays rather neglected strategy of intuitionistic revisionism. Employing only intuitionistically acceptable rules of inference, the conclusion of the argument is, firstly, (...) not ..., but .... Secondly, even if there were an intuitionistically acceptable proof of ..., i.e. an argument based on a different set of premises, the conclusion would have to be interpreted in accordance with Heyting semantics, and read in this way, the apparently preposterous conclusion would be true on conceptual grounds and acceptable even from a realist point of view. Fitch’s argument, understood as an immanent critique of verificationism, fails because in a debate dealing with the justification of deduction there can be no interpreted formal language on which realists and anti-realists could agree. Thus, the underlying problem is that a satisfactory solution to the “problem of shared content” is not available. I conclude with some remarks on the proposals by J. Salerno and N. Tennant to reconstruct certain arguments in the debate on anti-realism by establishing aporias. (shrink)

Jago uses a Fitch-style argument in an attempt to demonstrate that every truth has a truthmaker. But Trueman shows that there is a parallel argument, this time to the conclusion that no truth has a truthmaker. Since we cannot accept both, we must ditch at least one Fitch. But which? Keywords: Truth, truthmaking, truthmaker maximalism, Fitch paradox, Robert Trueman.

If we want to say that all truths are knowable Fitch’s Paradox leads us to conclude that all truths are known. Is it a real philosophical problem or a mere modeling problem? Is it possible to express the idea of knowability using modal logic? The Knowability Principle is expressed by the formula: if Phi is true then it is possible to know that Phi. But what is the meaning of possibility in this context? Using standard modal operators under (...) what condition can we express the idea of knowability? We will in particular examine the subjacent relations of the modal operators in a Kripke Model. We will define the possibility as the possibility of learning opposed to an unclear possibility. Then we will show that Fitch’s Paradox becomes clearer and we will examine how the Knowability Principle could be expressed in such frame. (shrink)

1) We will begin by offering a short introduction to Epistemic Logic and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will proceed to presenting three Epistemic Temporal logical frameworks creat‑ ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL (Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal Public Announcement Logic with Labeled Past Operators). We will show how Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze his argument on (...) why this version of it is immune from paradox. (3) Edgington (1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s paradox and we will propose a way to formulate it in a TAPAL‑based lan‑ guage. The language we will use is a combination of TAPAL and TPAL+P ! with an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑ ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑ tive semantics for this language. We will investigate whether the tentative re‑ formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from paradox and adequate to Edgington’s ideas on how „all truths are knowable“ should be interpreted. (shrink)

In a recent paper, Alexander argues that relaxing the requirement that sound knowers know their own soundness might provide a solution to Fitch’s paradox and introduces a suitable axiomatic system where the paradox is avoided. In this paper an analysis of this solution is proposed according to which the effective move for solving the paradox depends on the axiomatic treatment of the ontic modality rather than the limitations imposed on the epistemic one. It is then shown (...) that, once the ontic modality is standardly introduced, the paradox still follows and, in addition, some puzzling consequences arise. (shrink)

Enligt ett realistiskt synsätt kan ett påstående vara sant trots att det inte ens i princip är möjligt att veta att det är sant. En sanningsteoretisk antirealist kan inte godta denna möjlighet utan accepterar en eller annan version av Dummetts vetbarhetsprincip: (K) Om ett påstående är sant, så måste det i princip vara möjligt att veta att det är sant. Det kan dock förefalla rimligt, även för en antirealist, att gå̊ med på̊ att det kan finnas sanningar som ingen faktiskt (...) vet (har vetat, eller kommer att veta) är sanna. Man kan därför tänka sig att en antirealist skulle acceptera principen (K) utan att därför gå med på den till synes starkare principen: (SK) Om ett påstående är sant, så måste det faktiskt finnas någon som vet att det är sant. Ett mycket omdiskuterat argument – som ytterst går tillbaka till Alonzo Church, men som först publicerades i en uppsats av Frederic Fitch i Journal of Symbolic Logic 1963 – tycks emellertid visa att principen (K) implicerar principen (SK). Anta nämligen att (K) är sann, medan (SK) inte är det. Men om (SK) är falsk, så finns det ett påstående som är sant men som ingen faktiskt vet är sant. Anta nu att p är ett sådant påstående. Låt Kp betyda att någon vet att p är sant. Det galler alltså̊ att p är sant samtidigt som Kp inte är det. Betrakta nu påståendet (p ∧ −Kp). Enligt antagandet är detta påstående sant. Enligt (K) måste det då vara möjligt att någon vet att (p ∧ −Kp). D.v.s., det måste vara möjligt att påståendet K(p ∧ −Kp) är sant. Men i så fall är det också̊ möjligt att påståendet Kp ∧ K−Kp är sant, vilket i sin tur implicerar att det är möjligt att Kp ∧ −Kp är sant, vilket ju är absurt. Således kan inte (K) vara sann samtidigt som (SK) är falsk. Vi tycks således kunna sluta oss till att (K) implicerar (SK). I uppsatsen diskuterar jag några olika sätt att undgå̊ Church-Fitch paradoxala slutsats. Ett tillvägagångssätt är att ersätta kunskapsoperatorn med en hierarki av kunskapspredikat. Ett annat är baserat på distinktionen mellan faktisk och potentiell kunskap och ett förkastande av den vanliga modallogiska formaliseringen av principen (K). Den senare typen av lösning betraktas både från ett realistiskt och ett icke-realistiskt perspektiv. Utifrån denna analys kommer jag fram till slutsatsen att vi, vare sig vi är realister eller antirealister rörande sanning, kan sluta oroa oss för vetbarhetsparadoxen och ändå uppskatta Church-Fitchs argument. (shrink)

Augment the propositional language with two modal operators: □ and ■. Define ⧫ to be the dual of ■, i.e. ⧫=¬■¬. Whenever (X) is of the form φ → ψ, let (X⧫) be φ→⧫ψ . (X⧫) can be thought of as the modally qualified counterpart of (X)—for instance, under the metaphysical interpretation of ⧫, where (X) says φ implies ψ, (X⧫) says φ implies possibly ψ. This paper shows that for various interesting instances of (X), fairly weak assumptions suffice for (...) (X⧫) to imply (X)—so, the modally qualified principle is as strong as its unqualified counterpart. These results have surprising and interesting implications for issues spanning many areas of philosophy. (shrink)

Fitch's knowability paradox shows that for each unknown truth there is also an unknowable truth, a result which has been thought both odd in itself and at odds with views which impose epistemic constraints on truth and/or meaningfulness. Here a solution is considered which has received little attention in the debate but which carries prima facie plausibility. The decidability solution is to accept that Fitch sentences are unknowably true but deny the significance of this on the grounds (...) that Fitch sentences are nevertheless decidable. The decidability solution is particularly attractive for those whose primary concern is an epistemic constraint on meaningfulness (‘verificationists’). For those whose main concern is truth (‘anti-realists’), the situation is more complex: Melia takes the solution to exonerate anti-realism completely; Williamson sees it as completely irrelevant. The truth lies between these two extremes: there is one broad anti-realist commitment to which the solution does not apply, but there is also one, the “fundamental tenet” of anti-realism according to Dummett, to which it does. (shrink)

Famously, the Church–Fitch paradox of knowability is a deductive argument from the thesis that all truths are knowable to the conclusion that all truths are known. In this argument, knowability is analyzed in terms of having the possibility to know. Several philosophers have objected to this analysis, because it turns knowability into a nonfactive notion. In addition, they claim that, if the knowability thesis is reformulated with the help of factive concepts of knowability, then omniscience can be avoided. (...) In this article we will look closer at two proposals along these lines :557–568, 1985; Fuhrmann in Synthese 191:1627–1648, 2014a), because there are formal models available for each. It will be argued that, even though the problem of omniscience can be averted, the problem of possible or potential omniscience cannot: there is an accessible state at which all truths are known. Furthermore, it will be argued that possible or potential omniscience is a price that is too high to pay. Others who have proposed to solve the paradox with the help of a factive concept of knowability should take note :53–73, 2010; Spencer in Mind 126:466–497, 2017). (shrink)

Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal (...) characterisations of the surprise notion, crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes. (shrink)

Antirealists who hold the knowability thesis, namely that all truths are knowable, have been put on the defensive by the Church-Fitch paradox of knowability. Rejecting the non-factivity of the concept of knowability used in that paradox, Edgington has adopted a factive notion of knowability, according to which only actual truths are knowable. She has used this new notion to reformulate the knowability thesis. The result has been argued to be immune against the Church-Fitch paradox, but (...) it has encountered several other triviality objections. Schlöder in a forthcoming paper defends the general approach taken by Edgington, but amends it to save it in turn from the triviality objections. In this paper I will argue, first, that Schlöder's justification for the factivity of his version of the concept of knowability is vulnerable to criticism, but I will also offer an improved justification that is in the same spirit as his. To the extent that some philosophers are right about our intuitive concept of knowability being a factive one, it is important to explore factive concepts of knowability that are made formally precise. I will subsequently argue that Schlöder's version of the knowability thesis overgenerates knowledge or, in other words, it leads to attributions of knowledge where there is ignorance. This fits a general pattern for the research programme initiated by Edgington. This paper also contains preliminary investigations into the internal and logical structure of lines of inquiries, which raise interesting research questions. (shrink)

It is often claimed that anti-realism is a form of transcendental idealism or that Kant is an anti-realist. It is also often claimed that anti-realists are committed to some form of knowability principle and that such principles have problematic consequences. It is therefore natural to ask whether Kant is so committed, and if he is, whether this leads him into difficulties. I argue that a standard reading of Kant does indeed have him committed to the claim that all empirical truths (...) are knowable and that this claim entails that there is no empirical truth that is never known. I extend the result to a priori truths and draw some general philosophical lessons from this extension. However, I then propose a re-examination of Kant’s notion of experience according to which he carefully eschews any commitment to empirical knowability. Finally I respond to a remaining problem that stems from a weaker, justified believability principle. (shrink)

Epistemic theories of truth, such as those presumed to be typical for anti-realism, can be characterised as saying that what is true can be known in principle: p → ◊Kp. However, with statements of the form “p & ¬Kp”, a contradiction arises if they are both true and known. Analysis of the nature of the paradox shows that such statements refute epistemic theories of truth only if the the anti-realist motivation for epistemic theories of truth is not taken into (...) account. The motivation in a link of understandability ans meaningful- ness suggests to change the above principle and to restrict the theory to logically simple sentences, in which case the paradox does not arise. This suggestion also allows to see the deep philosophical problems for anti-realism those counterexamples are pointing at. (shrink)

Marton ( 2019 ) argues that that it follows from the standard antirealist theory of truth, which states that truth and possible knowledge are equivalent, that knowing possibilities is equivalent to the possibility of knowing, whereas these notions should be distinct. Moreover, he argues that the usual strategies of dealing with the Church–Fitch paradox of knowability are either not able to deal with his modal-epistemic collapse result or they only do so at a high price. Against this, I (...) argue that Marton’s paper does not present any seriously novel challenge to anti-realism not already found in the Church–Fitch result. Furthermore, Edgington ( 1985 ) reformulated antirealist theory of truth can deal with his modal-epistemic collapse argument at no cost. (shrink)

This paper addresses a solution due to Michael Fara to the Church/Fitch paradox of knowability. Fara’s solution has significant interest but the paradox can beresurrected within his approach by considering a slightly more complex sentence. The issue of what counts as an epistemological capability for enhanced agents is then discussed with some emphasis on the developmental heritage of agents and their ability to transcend conceptual frameworks.

In an anonymous referee report written in 1945, Church suggested a sweeping argument against verificiationism, the thesis that every truth is knowable. The argument, which was published with due acknowledgement by Fitch almost two decades later, has generated significant attention as well as some interesting successor arguments. In this paper, we present the most important episodes in this intellectual history using the logic that Church himself favoured, and we give reasons for thinking that the arguments are less than decisive. (...) However, we present some new arguments against verificationism that we believe to be dialectically effective. (shrink)

A dynamic epistemic logic is presented in which the single agent can reason about his knowledge stages before and after announcements. The logic is generated by reinterpreting multi agent private announcements in a single agent environment. It is shown that a knowability principle is valid for such logic: any initially true ϕ can be known after a certain number of announcements.

Assuming that a paralogism is an unintentionally invalid reasoning, we give an exampli.

Anti-realism is plagued by Fitch’s paradox: the remarkable result that if one accepts that all truths are knowable, minimal assumptions about the nature of knowledge entail that every truth is known. Dorothy Edgington suggests to address this problem by understanding p is knowable to be a counterfactual claim, but her proposal must contend with a forceful objection by Timothy Williamson. I revisit Edgington’s basic idea and find that Williamson’s objection is obviated by a refined understanding of counterfactual knowability (...) that is grounded in possible courses of inquiry. I arrive at a precise definition of knowability that is not just a technical avoidance of paradox, but is metaphysically sound and does justice to the anti-realist idea. (shrink)

kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K⁠, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weakK¬K⁠, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weakK¬K are much stronger than (...) they initially appear. Jointly, they entail kk and K¬K⁠. And they are susceptible to variants of the standard arguments against kk and K¬K⁠. This has interesting implications for the debate on positive introspection and for deeper issues concerning the structure and limits of knowability. (shrink)

Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

We examine two competing solutions to Benardete paradoxes: causal finitism, according to which nothing can have infinitely many causes, and the unsatisfiable pair diagnosis (UPD), according to which such paradoxes are logically impossible and no metaphysical thesis need be adopted to avoid them. We argue that the UPD enjoys notable theoretical advantages over causal finitism. Causal finitists, however, have levelled two main objections to the UPD. First, they urge that the UPD requires positing a ‘mysterious force’ that prevents paradoxes from (...) arising. Since such a force is implausible, the UPD is in trouble. Second, they employ recombination or patchwork principles to argue that paradoxical situations would be possible if causal finitism were false. Since such situations are not possible, causal finitism is true, and so a substantive metaphysical thesis is needed to avoid the paradoxes. We argue that the UPD proponent can successfully respond to these objections. (shrink)

The paradox of pain refers to the idea that the folk concept of pain is paradoxical, treating pains as simultaneously mental states and bodily states. By taking a close look at our pain terms, this paper argues that there is no paradox of pain. The air of paradox dissolves once we recognize that pain terms are polysemous and that there are two separate but related concepts of pain rather than one.

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling (...) epistemic problem. Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

There is a very plausible principle linking abilities and possibilities: If S is able to Φ, then it is metaphysically possible that S Φ’s. Jack Spencer recently proposed a class of counterexamples to this principle involving the ability to know certain propositions. I renew an argument against these counterexamples based on the unknowability of Fitch propositions. In doing so, I provide a new argument for the unknowability of Fitch propositions and show that Spencer’s counterexamples are in tension with (...) a principle weaker than the one linking abilities and possibilities. (shrink)

In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. (...) I then show how this leads to the Infinity from Nothing paradox, in which we have the spontaneous eruption of infinite mass and energy out of nothing. I conclude by showing how our supertask models at least something of an old conundrum, the question of what happens when the immovable object meets the irresistible force. (shrink)

Neil Tennant was the first to propose a proof-theoretic criterion for paradoxicality, a framework in which a paradox, formalized through natural deduction, is derived from an unacceptable conclusion that employs a certain form of id est inferences and generates an infinite reduction sequence. Tennant hypothesized that any derivation in natural deduction that formalizes a genuine paradox would meet this criterion, and he argued that while the liar paradox is genuine, Russell's paradox is not. -/- The present (...) paper delves into Tennant's conjecture for genuine paradoxes and suggests that to validate the conjecture, one of two issues must be addressed. The first issue is the need for a philosophical consensus on the identification of a genuine paradox in an informal sense. The second issue is the requirement for a uniform approach to formalize paradoxes in natural deduction. If either of these issues is addressed, the conjecture could be validated, or at the very least, it could hold philosophical importance in delineating the proof-theoretic features of paradoxicality. (shrink)

Attention has turned from Hobbes the systematic thinker to his inconsistencies, as the essays in the Hobbes symposium published in the recent volume of Political Theory suggest. Deborah Baumgold, in “The Difficulties of Hobbes Interpretation,” shifted the focus to “the history of the book,” and Hobbes’s method of serial composition and peripatetic insertion, as a major source of his inconsistency. Accepting Baumgold’s method, the author argues that the manner of composition does not necessarily determine content and that fundamental paradoxes in (...) Hobbes’s work have a different provenance, for which there are also contextual answers. Hobbes was a courtier’s client, but one committed early to a materialist ontology and epistemology, and these commitments shackled him in treating the immediate political questions with which he was required to deal, leading to systemic paradoxes in his treatment of natural law, liberty, authorization, and consent. (shrink)

Solutions to ninety paradoxes, some old, some new.

Supererogatory acts—good deeds “beyond the call of duty”—are a part of moral common sense, but conceptually puzzling. I propose a unified solution to three of the most infamous puzzles: the classic Paradox of Supererogation (if it’s so good, why isn’t it just obligatory?), Horton’s All or Nothing Problem, and Kamm’s Intransitivity Paradox. I conclude that supererogation makes sense if, and only if, the grounds of rightness are multi-dimensional and comparative.

I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are impossible according (...) to Laissez Faire theories, while it seems hypodoxes are possible. (shrink)

Tullmann et Buckwalter (2014) ont récemment soutenu que le paradoxe de la fiction tenait plus de l’illusion que de la réalité. D’après eux, les théories contemporaines des émotions ne fourniraient aucune raison d’adopter une interprétation du terme « existence » qui rende les prémisses du paradoxe incompatibles entre elles. Notre discussion a pour but de contester cette manière de dissoudre le paradoxe de la fiction en montrant qu’il ne prend pas sa source dans les théories contemporaines des émotions. Bien plutôt, (...) son origine se situe dans ce que Radford (1975) décrit comme une incohérence dans nos réactions émotionnelles aux évènements fictionnels et non fictionnels. Malgré ce désaccord, nous concédons à Tullmann et Buckwalter qu’une solution satisfaisante au paradoxe de la fiction doit s’appuyer sur les théories des émotions. Ainsi, en guise de conclusion, nous expliquons comment il convient de comprendre l’incohérence en question et comment les théories des émotions pourraient contribuer à la résolution du paradoxe de la fiction. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

The present work outlines a logical and philosophical conception of propositions in relation to a group of puzzles that arise by quantifying over them: the Russell-Myhill paradox, the Prior-Kaplan paradox, and Prior's Theorem. I begin by motivating an interpretation of Russell-Myhill as depending on aboutness, which constrains the notion of propositional identity. I discuss two formalizations of of the paradox, showing that it does not depend on the syntax of propositional variables. I then extend to propositions a (...) modal predicative response to the paradoxes articulated by an abstraction principle for propositions. On this conception, propositions are “shadows” of the sentences that express them. Modal operators are used to uncover the implicit relation of dependence that characterizes propositions that are about propositions. The benefits of this approach are shown by application to other intensional puzzles. The resulting view is an alternative to the plenitudinous metaphysics of impredicative comprehension principles. (shrink)

Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists.” To this end they (...) recommend a radical solution to both paradoxes, involving a substructural logic, in particular, one without structural contraction. In this paper I argue that substructuralism is unnecessary. Diagnosing the “v-Curry” is complicated because of a multiplicity of readings of the principles it relies on. But these principles are not analogous to the principles of naive truth, and taken together, there is no reading of them that should have much appeal to anyone who has absorbed the morals of both the ordinary Curry paradox and the second incompleteness theorem. (shrink)

Counterfactuals are somewhat tolerant. Had Socrates been at least six feet tall, he need not have been exactly six feet tall. He might have been a little taller—he might have been six one or six two. But while he might have been a little taller, there are limits to how tall he would have been. Had he been at least six feet tall, he would not have been more than a hundred feet tall, for example. Counterfactuals are not just tolerant, (...) then, but bounded. This paper presents a surprising paradox: If counterfactuals are tolerant and bounded, then we can prove a flat contradiction using natural rules of inference. Something has to go then. But what? (shrink)

I present a paradoxical combination of desires. I show why it's paradoxical, and consider ways of responding. The paradox saddles us with an unappealing trilemma: either we reject the possibility of the case by placing surprising restrictions on what we can desire, or we deny plausibly constitutive principles linking desires to the conditions under which they are satisfied, or we revise some bit of classical logic. I argue that denying the possibility of the case is unmotivated on any reasonable (...) way of thinking about mental content, and rejecting those desire-satisfaction principles leads to revenge paradoxes. So the best response is a non-classical one, according to which certain desires are neither determinately satisfied nor determinately not satisfied. Thus, theorizing about paradoxical propositional attitudes helps constrain the space of possibilities for adequate solutions to semantic paradoxes more generally. (shrink)

Silence is a multifaceted concept which is not merely as an absence of sound but a presence with significant ontological, existential, and phenomenological implications. Through a thematic analysis, this paper deconstructs silence into various dimensions—its ontology, linguistic universality, and its function as cessation of speech, a form of listening, an act of kenosis, a form of ascesis, and a way of life. The study employs philosophical discourse and mathematical notation to delve into these aspects, demonstrating that while each perspective sheds (...) light on certain facets of silence, none can comprehensively encapsulate its essence. The research underscores the paradoxical nature of silence. It is both a universal phenomenon recognised across cultures and an intimate, personal experience that resists definitive categorisation. The paper concludes that the true nature of silence, particularly when considering the state of "being silent," remains indefinable and elusive, inviting deeper contemplation on its role in human experience. (shrink)

This paper explores the relationships between some the problems of the Fermi Paradox (FP), with its variety of possible answers; and the Problem of Induction, and thus the possibility of a Theory of Everything. We seek to improve the hierarchy of plausibility within answers to FP, given by what we call “preference criteria”, among which we particularly highlight culture-independence. We argue that, if the question of whether a Theory of Everything is possible is answered negatively, then FP becomes much (...) more serious than otherwise, and this makes many of FP’s solutions less preferable. This constitutes a further preference criterion. Armed with this tool, we try to outline a network of relative truths between FP and the Problem of Induction, in the form of a cross-answer table. Only two or three combinations of answers survive as preferable: 1) degenerate, pure solipsistic metaphysics; 2) accept Induction and the Anthropic Principle at the same time, thus saying that the human condition is a very rare one in the universe; or 3) that the Theory of Everything exists and its discovery is the Great Filter. This latter possibility is discussed with its implications for the current scientific and economic progress of our civilization. (shrink)

Essential for the concept of the law of nature is not only spatio-temporal universality, but also functionality in the sense of the dependency on physical conditions of natural entities. In the following it is explained in detail that just the neglect of this functional property is to be understood as the real reason for the occurrence of the Goodman paradox. As a consequence, the behavior of things seems to be completely at the mercy of the temporal change of unique (...) absolute temporal points. It is exactly this (mis-)understanding that also generated the induction problem. From the intrinsic connection between universality and functionality, however, - that is my claim - the ontological consequence of a nature results, for which the potentiality of lawfulness is coupled to essentially functionally defined time sequences. (shrink)

In the emerging literature on judgment aggregation over logically connected proposi- tions, expert rights or liberal rights have not been investigated yet. A group making collective judgments may assign individual members or subgroups with expert know- ledge on, or particularly affected by, certain propositions the right to determine the collective judgment on those propositions. We identify a problem that generalizes Sen's 'liberal paradox'. Under plausible conditions, the assignment of rights to two or more individuals or subgroups is inconsistent with (...) the unanimity principle, whereby unanimously accepted propositions are collectively accepted. The inconsistency can be avoided if individual judgments or rights satisfy special conditions. (shrink)

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for (...) a wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt. (shrink)

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends (...) classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)

Zeno’s paradoxes of motion, allegedly denying motion, have been conceived to reinforce the Parmenidean vision of an immutable world. The aim of this article is to demonstrate that these famous logical paradoxes should be seen instead as paradoxes of immobility. From this new point of view, motion is therefore no longer logically problematic, while immobility is. This is convenient since it is easy to conceive that immobility can actually conceal motion, and thus the proposition “immobility is mere illusion of the (...) senses” is much more credible than the reverse thesis supported by Parmenides. Moreover, this proposition is also supported by modern depiction of material bodies: the existence of a ceaseless random motion of atoms—the ‘thermal agitation’—in the scope of contemporary atomic theory, can offer a rational explanation of this ‘illusion of immobility’. Our new approach to Zeno’s paradoxes therefore leads to presenting the novel concept of ‘impermobility’, which we think is a more adequate description of physical reality. (shrink)