Incompatible Propositions Research Articles

Entitlement, generosity, relativism, and structure‐internal goods

AbstractCrispin Wright is widely known for having introduced epistemic entitlement, a species of non‐evidential warrant, as a response to certain skeptical challenges. This paper investigates a fundamental issue concerning entitlement: it appears to be quite generous, as it appears to apply indiscriminately to anti‐skepticial hypotheses as well as a range of radically different—indeed, even incompatible—propositions. It argues that the generosity of entitlement is reflective of an underlying commitment to a form of epistemic relativism. In addition, the paper presents an axiology that helps entitlement theorists to address the pressing issue of how, given the absence of evidence, there can be anything epistemically good about acceptance of anti‐skeptical hypotheses and other cornerstones for inquiry. Lastly, the paper argues that the issues of generosity and epistemic relativism are rather deeply rooted: they surface at the level of value. It explains why.

Rational Degree of Belief Ceases to Be Additive When the Dutch Book Argument Is Transported to a New Environment

The strength of a person’s beliefs can be measured by the buying and selling prices they offer on contingent promissory notes. Consider a promissory note contingent on a proposition; it pays off one unit of money if the proposition is true and nothing otherwise. The more strongly a person believes the proposition, the higher the minimum price would be at which they would sell it. The same would apply to the maximum purchase price. The well-known Dutch Book Argument claims that, if the person’s beliefs are rational, their buying/selling prices should combine additively, meaning that the price of a promissory note contingent on the disjunction of two incompatible propositions should be the sum of the prices of the promissory notes contingent on the individual incompatible propositions. This paper shows that the essence of the Dutch Book Argument is that rational belief is additive because money is additive. It is proved that, if the structure of the Dutch Book Argument is kept, but a nonadditive resource is substituted for money, then rational belief will follow a nonadditive combining rule. It is also shown how rational buying/selling prices behave when the pay-off amount of a contingent note changes.

Probability, Approximate Truth, and Truthlikeness: More Ways out of the Preface Paradox

ABSTRACTThe so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including a recent one advanced by Hannes Leitgeb (Analysis 74.1).

A problem of scope for the free energy principle as a theory of cognition

Those who endorse the free energy principle as a theory of cognition (as well as a theory of biological homeostasis) are committed to three propositions that are jointly incompatible but which will cohere if one of them is denied. The first of these is that the free energy principle gives us a self-sufficient explanation of what all cognitive systems consist in: a specific computational architecture. The second is that all adaptive behavior is driven by the free energy principle and the process of model-based inference it entails. The third is that cognition is not ubiquitous. These three incompatible propositions together comprise a problem of scope for the free energy principle as a theory of cognition. The prospects for rejecting each of these propositions are considered. To drop either the first or the second would limit the explanatory success of the principle. However, there are plausible ways to bite the bullet on denial of the third proposition. In particular, I argue that it is possible for the free energy theorist to admit that cognition is ubiquitous in biological systems while reserving conceptual space exclusively for human cognitive capacities.

Fallibilism, Verisimilitude, and the Preface Paradox

The Preface Paradox apparently shows that it is sometimes rational to believe logically incompatible propositions. In this paper, I propose a way out of the paradox based on the ideas of fallibilism and verisimilitude (or truthlikeness). More precisely, I defend the view that a rational inquirer can fallibly believe or accept a proposition which is false, or likely false, but verisimilar; and I argue that this view makes the Preface Paradox disappear. Some possible objections to my proposal, and an alternative view of fallible belief, are briefly discussed in the final part of the paper.

Is Hume's Account of the Soul Contradictory?

Is Hume's Account of the Soul Contradictory? Alan Schwerin Abstract In his Treatise of Human Nature Hume argues for a provocative account of the soul; the soul - or self, as he prefers to call it - is nothing but a bundle of perceptions. But this bold thesis, concedes Hume, gives rise to a predicament concerning two incompatible propositions, or principles as he calls them: one on the nature of perceptions, the other on the capabilities of the mind: "In short, there are two principles, which I cannot render consistent; nor is it in my power to renounce either of them, viz. that all our distinct perceptions are distinct existences, and that the mind never perceives any real connexion among distinct existences". But the situation is not hopeless, thinks Hume. Someone might be able to show that these principles are actually consistent: "Others, perhaps, or myself, upon more mature reflection, may discover some hypothesis, that will reconcile those contradictions". (Treatise 636, my emphasis) My paper is an attempt to throw light on this important component in Hume’s analysis of his account of the self. In the course of our investigation of Hume's suggestion that an hypothesis can resolve his contradiction we will learn more about his conception of a contradiction - ultimately enriching our understanding of his account of the soul. Full Text: PDF DOI: 10.15640/ijpt.v2n4a4

The place of parties in contemporary democracies

. Edited by RICHARDGUNTHER, JOSE RAMON MONTERO and JUAN J. LINZ. Oxford:Oxford University Press, 2002. pp.380, £16.99, ISBN 0199246742.The body of scholarly literature on political parties in modern democraciesis essentially built around two seemingly incompatible propositions. Thefirst one is that, as Schattschneider famously asserted more than half acentury ago, ‘modern democracy is unthinkable save in terms of politicalparties’.

Blasphemy and Heresy: The Modernist Challenge.A Review Article

The word blasphemy, once considered a relic of the benighted middle ages, is enjoying something of a popular revival especially in the west. This is not because it has its own particular currency as an ongoing practice but because it has usefulness in providing an index to the uneven development of world societies, as well as establishing the status of their laws in guaranteeing fundamental liberties of speech and the degree of tolerance that their civil societies are inclined to show. It is no accident that two recent, identically titled books on blasphemy, albeit written from quite different perspectives, culminate in the Rushdie as an exemplary case study to explicate the cultural meanings of blasphemy. Thefatwa against Rushdie is the ostensible starting point for a retrospective view of the stages through which European history has passed, as well as the end point for the dangers posed to western society by religious fundamentalism, particularly militant Islamic fundamentalism.' David Lawton specifically states at the outset that his interest in blasphemy [was] re-awakened by the Rushdie affair and proclaims that he does not address this book to anyone who supports killing writers, as if all those who took offense with Rushdie's novel also endorsed his death penalty. Lawton's is a voice that speaks for an enlightened multiculturalism against the perverted and already transcultured monoculturalism of militant Muslims like Yusuf Islam and Doctor Siddiqi.2 The terms of the debate are clear and unambiguous, firmly establishing that blasphemy prosecution and a tolerant society are incompatible propositions. If blasphemy as a concept denotes the past of the European world, it is also put to use to mark the present of the non-European world. The narrative organization of both works views blasphemy as helping to demarcate the west from the Islamic world far more usefully than any other signifier-cultural, geographical, or political. Leonard Levy's Blasphemy: Verbal Offense against

Ignorance versus False Belief: A Developmental Lag in Attribution of Epistemic States

HOGREFE, G.-JUERGEN; WIMMER, HEINZ; and PERNER, JOSEF. Ignorance versus False Belief: A Developmental Lag in Attribution of Epistemic States. CHILD DEVELOPMENT, 1986, 57, 567-582. 3-6-year-old children were either put into real-life situations or were read stories in which another person or story character was excluded from certain information. Their competence in attributing absence of knowledge (ignorance) was compared to their competence in attributing a false belief to the other. A marked difference between attributions was found. In a transitional stage at 3-4 years children were able to attribute ignorance but failed to attribute the resulting false belief. The same developmental gap for children about 2 years older was found between the attribution of secondorder ignorance and second-order false belief. Results are interpreted to show that children at a transitional stage find it difficult to represent the incompatible propositions describing the true state of affairs and the state of affairs falsely believed to be true by the other. Such a complexity is not involved in the understanding of ignorance where it has just to be represented that the other does not share the representation of the true state of affairs.

Cultural relativism and comparative criminology

The recent spate of comparative studies of crime is long overdue as a potential palliative to the traditional ethnocentrism of American criminology. But their comparative method is uncritically taken from two incompatible propositions derived from Durkheimian empiricism. As such, the generalizations about criminal behavior that these studies advance should be treated more with caution than optimism. This essay discusses the alleged advances over Durkheimian empiricism made by two distinct forms of cultural relativism. If what every man believes as a result of perception is indeed to be true for him; if, just as no one is to be a better judge of what another experiences, so no one is better entitled to consider what another thinks is true or false... then, my friend, where is the wisdom of Protagoras, to justify his setting up to teach others and to be handsomely paid for it? Socrates, in Plato'sTheaetetus

A Problem about Identity

1. The problem: Here are three plausible but incompatible propositions:(1) The answer to Locke's question (23):Could we suppose two distinct incommunicable consciousnesses acting the same body, the one constantly by day, the other by night … I ask … whether the day and the night man would not be two as distinct persons as Socrates and Plato ?is yes.(2) I am a human being. More generally, human persons are human beings.(3) Identity is not relative.

The Discourse on Inequality and The Social Contract

My Purpose is twofold: first, to interpret Rousseau's The Social Contract in terms of a serious interpretation of the Discourse on the Origin and Foundations of Inequality and second, to use as the principal interpretative concept for both, the concept of independence. One gets the impression in reading commentators that the Discourse on Inequality is not taken seriously in its own right but rather is treated as what it is, an essay which was suitable for submission as a prize essay, with the required clever rhetorical style, flashes of paradox and yet withal solemnly addressing itself to a virtually impossible question. However, if it is taken, in part, as Rousseau's social and psychological analysis of modern society, as an account of “men as they are” (The Social Contract, ed. Cranston, p.49), then it is not only worthy of serious study in itself, it also helps one to see that still puzzling book, The Social Contract, from a new perspective. Moreover, Rousseau's concept of independence is both interesting and helpful. What Rousseau means by “independence” may diner from what he means by “freedom”, but for most of this essay I shall draw from the latter a working definition of the former and thus shall mean by independence: (1) not being subject to or under the control of another person or persons, and (2) not being subject to or under the control of one's passions. The advantage of attending to the concept of independence is that it enables one to recognize that Rousseau is asserting three seemingly incompatible propositions: first, man is independent, second, no man is independent and in the given circumstances can be and, third, man must become dependent in order to become independent.

Algebra of Observation

Birkof£-von Neumann's contention') that observational propositions in Quantum Mechanics do not obey the Boolean logic, but the modular logic was suggested by the structure of the Hilbert space, and only indirectly related to the nature of observation in physics. Husimi2 ) was the first to undertake the task of establishing directly experiment:J.l foundation of quantum logic. The present paper has the same aim as Husimi's early paper,') but adopts a different approach. A feature of the present paper is its methodology of extracting an algebraic structure from a pro­ babilistic structure. A concrete observational interpretation is given for the first time to the conjunction of two incompatible propositions. A side benefit of this work is clarification of the origin of the Booleanity of the ordinary logic, which has to be sought outside the implicational lattice.