Unknowable Truths Research Articles

Knowability paradox, decidability solution?

AbstractFitch'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.

I Am Not All the Way Here

I Am Not All the Way Here

Making sense of (in)determinate truth: the semantics of free variables

It is argued that truth value of a sentence containing free variables in a context of use (or the truth value of the proposition it expresses in a context of use), just as the reference of the free variables concerned, depends on the assumptions and posits given by the context. However, context may under-determine the reference of a free variable and the truth value of sentences in which it occurs. It is argued that in such cases a free variable has indeterminate reference and a sentence in which it occurs may have indeterminate truth value. On letting, say, x be such that x^2=4, the sentence ‘Either x=2 or x=-2’ is true but the sentence ‘x=2’ has an indeterminate truth value: it is determinate that the variable x refers to either 2 or -2, but it is indeterminate which of the two it refers to, as a result ‘x=2’ has a truth value but its truth value is indeterminate. The semantic indeterminacy is analysed in a ‘radically’ supervaluational (or plurivaluational) semantic framework closely analogous to the treatment of vagueness in McGee and McLaughlin (South J Philos 33:203–251, 1994, Linguist Philos 27:123–136, 2004) and Smith (Vagueness and degrees of truth, Oxford University Press, Oxford, 2008), which saves bivalence, the T-schema and the truth-functional analysis of the boolean connectives. It is shown that on such an analysis the modality ‘determinately’ is quite clearly not an epistemic modality, avoiding a potential objection raised by Williamson (Vagueness, Routledge, London, 1994) against such ‘radically’ supervaluational treatments of vagueness, and that determinate truth (rather than truth simpliciter) is the semantic value preserved in classically valid arguments. The analysis is contrasted with the epistemicist proposal of Breckenridge and Magidor (Philos Stud 158:377–400, 2012) which implies that (in the given context) ‘x=2’ has a determinate but unknowable truth value.

Why Knowledge Should Not Be Typed: An Argument against the Type Solution to the Knowability Paradox

The Knowability Paradox is a logical argument to the effect that, if there are truths not actually known, then there are unknowable truths. Recently, Alexander Paseau and Bernard Linsky have independently suggested a possible way to counter this argument by typing knowledge. In this article, we argue against their proposal that if one abstracts from other possible independent considerations supporting reasons for typing knowledge and considers the motivation for a type- theoretic approach with respect to the Knowability Paradox alone, there is no substantive philo- sophical motivation to type knowledge, except that of solving the paradox. Every attempt to independently justify the typing of knowledge is doomed to failure.

Necessary limits to knowledge: unknowable truths

The paper seeks a perfectly general argument regarding the non-contingent limits to any (human or non-human) knowledge. After expressing disappointment with the history of philosophy on this score, an argument is grounded in Fitch’s proof, which demonstrates the unknowability of some truths. The necessity of this unknowability is then defended by arguing for the necessity of Fitch’s premise—viz., there this is in fact some ignorance.

Possible knowledge of unknown truth

Fitch’s argument purports to show that for any unknown truth, p, there is an unknowable truth, namely, that p is true and unknown; for a contradiction follows from the assumption that it is possible to know that p is true and unknown. In earlier work I argued that there is a sense in which it is possible to know that p is true and unknown, from a counterfactual perspective; that is, there can be possible, non-actual knowledge, of the actual situation, that in that situation, p is true and unknown. Here I further elaborate that claim and respond to objections by Williamson, who argued that there cannot be non-trivial knowledge of this kind. I give conditions which suffice for such non-trivial counterfactual knowledge.

Fitch’s Paradox and Probabilistic Antirealism

Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.

Unknowable truths: a reply to Cook

In ‘Knights, knaves and unknowable truths’, Roy T. Cook (2006) argues that even if it is impossible for it to be known of any particular sentence that it is both true and unknowable, we may still know that there are unknowable truths. That is, even if the Constructive Unknowable Propositions Principle: C: (∃P)K(P& ¬ K(P)) is inconsistent, the weaker Non-constructive Unknowable Propositions Principle: N: K(∃P)(P& ¬ K(P)) may yet be true. Cook offers an argument in favour of this latter principle. I will suggest that Cook’s argument for this conclusion does not succeed, since his argument depends on paradoxical reasoning. Cook frames his argument in the context of Smullyan’s (1978) island of knights and knaves. Every inhabitant of this island is either a knight or a knave, where a knight tells only truths and a knave, only falsehoods....

Unknowable truths: a reply to Cook

Arrow, K. J. 1965. Aspects of the Theory of Risk Bearing. Helsinki: Yrjo Jahnssonin Saatio. Brennan, G. and A. Hamlin. 2004. Analytic conservatism. British Journal of Political Science 34: 675-91. Broome, J. 1991. Weighing Goods. Oxford: Basil Blackwell. Chang, R. 1998. Incommensurability, Incompatibility and Practical Reason. Cam bridge Mass.: Harvard University Press. Lerner, A. 1944/1976. The Economics of Control. Clifton, NJ: Augustus M. Kelley.

Knights, knaves and unknowable truths

Knights, knaves and unknowable truths Get access Roy T. Cook Roy T. Cook Arché: The AHRC Centre for the Philosophy of Logic, Language, Mathematics, and Mind University of St AndrewsSt Andrews Fife KY16 9AL, Scotland, UK and Villanova University VillanovaPA 19085, USARoy.cook@villanova.edu Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 66, Issue 1, January 2006, Pages 10–16, https://doi.org/10.1093/analys/66.1.10 Published: 01 January 2006

Knights, knaves and unknowable truths

1 Sometimes knowability, unlike actual knowledge, is not factive. For example, it is plausible that 'I am now thinking this very sentence' is knowable at any time by any sufficiently rational agent, even though it is not necessarily true at those times. Here I ignore such phenomena, however, since these sorts of epistemic puzzles, although interesting and important in their own right, seem orthogonal to the issue at hand.

Knowability and Epistemic Truth

The so-called knowability paradox results from Fitch's argument that if there are any unknown truths, then there are unknowable truths. This threatens recent versions of semantical antirealism, the central thesis of which is that truth is epistemic. When this is taken to mean that all truths are knowable, antirealism is thus committed to the conclusion that no truths are unknown. The correct antirealistic response to the paradox should be to deny that the fundamental thesis of the epistemic nature of truth entails the knowability of all truths. Correctly understood, the antirealistic conditions on a proposition's truth do not require that the proposition possess a verification-procedure which, when executed under the given conditions, issues in an agent's recognition of truth, but merely that there be a verification-procedure which, under these conditions, takes the value true. The knowability paradox and the related idealism problem (that antirealism seems, but is not, committed to the necessary existence of an epistemic agent) draw attention to the fact that certain propositions, those that are about verification-procedures themselves, may under certain conditions take the value true despite their unperformability under these circumstances. Thus these propositions' procedures can only be performed when the propositions are false, and they gain the appearance of antirealistic impossibility (e.g., that there is an unknown truth). This differs from the unperformability that antirealists object to, pertaining merely to matters of execution rather than to the logical structure of the procedures themselves. The force of antirealism's notion of epistemic truth is piecemeal, rather than consisting in a blanket characterization of truth as knowable.

Shattered Pasts, Fractured Selves: Trauma and Memory in Desirada

Maryse Conde's published in 1997, chronicles the lives of three generations of women, Nina, Reynalda and Marie-Noelle Titane. The story begins shortly before 1928 with the birth of Nina in la Desirade, Guadeloupe, and ends in 1990s Boston with the story of Marie-Noelle. The lives of all three women are marked by separation from home, rape and sexual abuse. In this essay I shall attempt to analyze the intergenerational impact of these traumatic events on the lives of the characters. Such analysis implies a theoretical exploration of the nature of trauma and of the structure and functioning of memory. In this, I am inspired by the works of Cathy Caruth and Dori Laub, M.D., whose work in the field of trauma theory has contributed to the re-examining of these questions that originate in psychoanalysis within the framework of literature. Nina, Reynalda and Marie-Noelle share certain events in their lives that have made indelible mark on their being. These events are characterized by their profoundly traumatic nature. All three women are torn from the place of their birth, where, despite the harsh conditions, they feel rooted in a sense of well-being and belonging. Nina is raped and Reynalda is either molested or raped, or indeed both. Marie-Noelle escapes the violence of tape, but becomes a witness to a form of insidious sexual violence in her role as watchdog for her friend's wretched sexual activity, which is a heart-breaking attempt at procuring the necessities of everyday life. Furthermore, all three women grow up in the shadow of the missing father and, perhaps more significantly, in the shadow of the missing mother. For in the case of Reynalda and Marie-Noelle, the mothers are emotionally absent from their lives, while in the case of Nina, the mother has died. The looming presence of Il Lago di Como signals and conceals unknowable truth about the history of the three women. It is the most significant site for the transmission of memory, as their individual encounters with it mark each woman deeply. The pathology of these three women is first and foremost characterized by a rupture in the continuity of their history, a fissure in their being, a wound on their psyche, a trauma. The American Psychiatric Association defines trauma as an event outside the range of human experience. And indeed, all three women experience such event, not just once, but repeatedly. All three are traumatized by having been wrested away from their homes, from the land of their birth, a place to which all show a great attachment despite the harshness of their life there. Let us look at three passages uttered by Nina, Reynalda and Marie-Noelle, respectively: Nina indulges in the following reflection, Quand je reflechis, je m'apercois que ces annees-la n'ont pas ete les plus dures de ma vie malgre le travail et la faim. J'avais ma Bonne-Maman [ ... ] Ma Bonne-Maman qui ne parlait pas beaucoup, mais qui avait toujours une douceur pour moi, cachee dans son corsage, des topinambours, un sucre a coco tete-rose, un nougat pistache. These memories are echo of similar thoughts revealed by Reynalda, C'est a la Desirade que je suis nee. Les gens de la Guadeloupe ont une mauvaise idee de la Desirade a cause des sacripants et des lepreux qu'on y envoyait dans le temps et aussi, parce que rien n'y pousse. [ ... ] Mais pour moi, petite fille, c'etait vraiment Desirada, ile desiree surgie sur la mer devant les yeux des marins de Christophe Colombe apres des jours et des jours. Je possedais tous ses recoins. Je respirais son odeur quand le soleil qui l'a chauffee toute la journee repose enfin sa tete au fond de l'eau. Je pouvais soulever une roche et nommer avec certitude le nom de l'insecte cache en dessous. Je connaissais ses razye. [ ... ] Elle (Nina) a donne un tour de cle a la porte et nous voila parties. Moi, j'etais a l'agonie. …

Epistemicist Models: Comments on Gómez‐Torrente and Graff

Every philosopher should wish for commentators as thoughtful and rigorous as Mario G6mez-Torrente and Delia Graff. Their papers contribute significantly to our understanding of the fine structure of vagueness, but not by undermining its epistemicist interpretation. According to epistemicism, there is an unknowable truth of the matter in borderline cases. Either is bald or he is not, but we cannot know which. Why not? Suppose that in fact is bald; the argument is similar if he is not. Then we speak truly if we say Harry is But since the case is borderline, we might easily have uttered the same words even if our overall pattern of use had been slightly different so as slightly to shift the boundary of 'bald' in that context, making 'Harry is bald' express a different and false proposition. Thus even if we actually make the true judgement that is bald in this case, we do so on an insufficiently reliable basis to count as knowing that is bald. This is a conceptual analogue of more familiar kinds of ignorance, in which limits on our powers of perceptual discrimination prevent us from knowing the exact values of physical quantities by ordinary perception. Such limits on our knowledge can be expressed as margin for error principles (Williamson 1992, 1994: pp. 216-47). Gomez-Torrente points out that in perceptual cases we can discover the values of the quantities exactly (or at least far less inexactly) by scientific measurement; the unknowability is relative to limited cognitive means. He suggests that the epistemicist explanation establishes at most a similarly limited ignorance in borderline cases, thereby missing the depth of the phenomenon to be explained. The epistemicist explanation is as general as its underlying assumptions. In this context the relevant ones are: (a) the boundary of a vague term is unstable with respect to small changes in use because there is no natural line for it to follow; (b) because our use of such a term is not perfectly co-ordinated internally, a small change in one aspect of use (enough to shift the boundary a little) can easily be combined with preservation of another aspect

Unknowable Truths and the Doctrine of Omniscience

Unknowable Truths and the Doctrine of Omniscience

On knowledge of the unknowable

If it is an unknown truth that p, it is an unknowable truth that it is an unknown truth that p (cf F. B. Fitch, 'A logical analysis of some value concepts', The Journal of Symbolic Logic 28, 1963, pp. 135-42, at p. 138). It follows, by classical logic, that if all truths are knowable then all truths are known. This hardish fact makes life difficult for the verificationist who wishes to assert that all truths are knowable, but to deny that all truths are known. He might try rejecting classical logic (cf. my 'Intuitionism disproved?', ANALYSIS 42.4, October, 1982, pp. 203-7). Dorothy Edgington has recently suggested a different way out (cf. 'The paradox of knowability', Mind 94, 1985, pp. 557-68). She admits that there are unknowable truths in the sense of Fitch's argument, but interestingly revises the verificationist principle, to give it this form: if, in a situation s, it is a truth that p, then there is a possible situation s' in which it is known that, in s, p. Although the truth (for some values of '/?') that, in s, it is an unknown truth that p cannot be known in s, it might be known in some possible situation other than s. I have argued elsewhere that this account faces difficulties of principle in explaining how the knower in s' can pick out the situations in thought with adequate specificity (cf. 'On the paradox of knowability', Mind forthcoming). I waive those objections here, to examine Edgington's application of her principle to a particular case of knowledge in one situation that something is an unknown truth in another. I shall argue that her account does not generalize to the full range of cases which it needs to cover.

Voice and Eye in Faulkner's Fiction by Hugh M. Ruppersburg (review)

240Reviews Starting from those recognitions, Wolford builds to show that Crane's fiction included, among the enormous repudiations that H.G. Wells noted, an understanding of and reaction against the epic tradition. Inevitably Wolford goes too far, his focus on one aspect of Crane's work obscuring the rest that is there. He also commits some minor blunders along the way, such as taking Crane's schoolmate Harvey Wickham seriously and thinking Crane's "An Experiment in Misery" and "An Experiment in Luxury" experimental fiction. Wolford's accomplishment, however, makes his lapses pale into relative insignificance. In this book he traces an important aspect of Crane's Realistic vision—the ire he felt at the way tradition of any kind interferes with people who either must confront life as it is or perish. What Wolford does is important, and he does it well. University of South CarolinaJoseph Katz Ruppersburg, Hugh M. Voice and Eye in Faulkner's Fiction. Athens: Univ. of Georgia Press, 1983. 189 pp. Cloth: $16.00. "Out of the metaphor of individual perception blossom his innovations in point of view, one of the most important and distinctive elements in his writing" (p. 8); "Narrative structure reflects meaning. It also becomes meaning" (p. 28). These sentences identify the focus and the thesis of this study of William Faulkner's narrative structure. In his first chapter, Hugh M. Ruppersburg labels and defines a series of terms that provide a vocabulary for discussing Faulkner's techniques and narrative structure. Though the Faulkner scholar will encounter no new insights, the chapter is a useful and informative description of various types of narrators that appear in the fiction. These include characters who serve as narrators, focal characters through whose consciousness the narrative is developed, and a number of other narrator variations that make point of view in Faulkner's fiction integral to its meaning. In individual essays the narrative techniques of Light in August, Pylon, Absalom, Absalom', and Requiem for a Nun are described effectively and in great detail. The choice of Pylon and Requiem for a Nun and the absence of essays on The Sound and the Fury and As I Lay Dying, the more obvious choices in a study of narrative structure, raise the question of Professor Ruppersburg's rationale. Anticipating such a question, he states in his introduction that the choice of these particular novels is "arbitrary, reflecting my own personal interests." His disclaimer that consideration of more than these "four novels would quickly lead to redundancy" does not erase the impression that the dictates of a thesis had little to do with determining the structure of this book. The author aptly identifies his study as primarily descriptive, and, when he is describing , he provides a valuable discussion of Faulkner's narrative techniques and structure. When he digresses into interpretation, he tends to intrude upon the narrative process. He stresses, for example, that Faulkner's use of unreliable narrating characters in such novels as Light in August "leave all 'facts' in doubt" (p. 28). Nevertheless, he accepts as fact that Joe Christmas is black. With that creative leap into unknowable truth, he can conclude that this novel illustrates Faulkner's belief that the "individual derives his identity from his participation in society, even if that society is hostile to him. Joe Christmas's quest for identity proves self-destructive because he seeks to live outside his community" (p. 152). I suppose that means that if Joe had just admitted that he was black and accepted the status that his society accorded blacks, he would not have been a misanthrope "who tries both to ignore and to flagrantly violate community values" (p. 152). Studies in American Fiction241 In the essay on Pylon, Ruppersburg is so eager to support the idea that Laverne is a sacrificial heroine that he undercuts much of his presentation about the role of narrators and the absence of an authoritative authorial voice. "External narrative," he states, "free of biased character perspectives, portrays Laverne objectively." The "'real' Laverne" is presented to us in chapter one as a traditional woman with "numerous 'feminine' traits: modesty, neatness, cleanliness, for example." Because she has a "conventional desire for hearth and...

Wealden petrology : The Top Ashdown Pebble Bed and the Top Ashdown Sandstone

Wealden petrology : The Top Ashdown Pebble Bed and the Top Ashdown Sandstone