Professor MerrieBergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The (...) major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems. (shrink)
This outstanding book is a leading text for symbolic or formal logic courses. All techniques and concepts are presented with clear, comprehensive explanations and numerous, carefully constructed examples. Its flexible organization (all chapters are complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose.
Taking into account pragmatic considerations and recent linguistic and psychological studies, the author forges a new understanding of the relation between metaphoric and literal meaning. The argument is illustrated with analysis of metaphors from literature, philosophy, science, and everyday language.
A three-valued propositional logic is presented, within which the three values are read as ?true?, ?false? and ?nonsense?. A three-valued extended functional calculus, unrestricted by the theory of types, is then developed. Within the latter system, Bochvar analyzes the Russell paradox and the Grelling-Weyl paradox, formally demonstrating the meaninglessness of both.
In this paper I am concerned with two questions: What is sexist humor? and what is wrong with it? To answer the first question, I briefly develop a theory of humor and then characterize sexist humor as humor in which sexist beliefs (attitudes/norms) are presupposed and are necessary to the fun. Concerning the second question, I criticize a common sort of argument that is supposed to explain why sexist humor is offensive: although the argument explains why sexist humor feels offensive, (...) it does not place responsibility for the offense in the humorist or audience that enjoys sexist humor. I develop an alternate account of the offense in sexist humor that places responsibility for offense in precisely those quarters. (shrink)
The typical rules for truth-trees for first-order logic without functions can fail to generate finite branches for formulas that have finite models–the rule set fails to have the finite tree property. In 1984 Boolos showed that a new rule set proposed by Burgess does have this property. In this paper we address a similar problem with the typical rule set for first-order logic with identity and functions, proposing a new rule set that does have the finite tree property.
In 1987, Crispin Wright argued that degree-theoretic (fuzzy) solutions to the Sorites paradox fail because the solutions do not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic solutions also work when the paradox is stated with a conjunctive major premise.
Virtually all philosophers agree that for a belief to be epistemically justified, it must satisfy certain conditions. Perhaps it must be supported by evidence. Or perhaps it must be reliably formed. Or perhaps there are some other "good-making" features it must have. But does a belief's justification also require some sort of awareness of its good-making features? The answer to this question has been hotly contested in contemporary epistemology, creating a deep divide among its practitioners. Internalists, who tend to focus (...) on scientific or theoretical beliefs as the ideal, insist that such awareness is required for justification. Externalists, who think children's ordinary beliefs in obvious facts are paradigm cases of justified belief, say it isn't required. Michael Bergmann's book offers a decisive refutation of internalism and a sustained defense of externalism. (shrink)
Some evidential arguments from evil rely on an inference of the following sort: 'If, after thinking hard, we can't think of any God-justifying reason for permitting some horrific evil then it is likely that there is no such reason'. Sceptical theists, us included, say that this inference is not a good one and that evidential arguments from evil that depend on it are, as a result, unsound. Michael Almeida and Graham Oppy have argued (in a previous issue of this journal) (...) that Michael Bergmann's way of developing the sceptical theist response to such arguments fails because it commits those who endorse it to a sort of scepticism that undermines ordinary moral practice. In this paper, we defend Bergmann's sceptical theist response against this charge. (shrink)
Challenges to Moral and Religious Belief contains fourteen original essays by philosophers, theologians, and social scientists on challenges to moral and religious belief from disagreement and evolution. Three main questions are addressed: Can one reasonably maintain one's moral and religious beliefs in the face of interpersonal disagreement with intellectual peers? Does disagreement about morality between a religious belief source, such as a sacred text, and a non-religious belief source, such as a society's moral intuitions, make it irrational to continue trusting (...) one or both of those belief sources? Should evolutionary accounts of the origins of our moral beliefs and our religious beliefs undermine our confidence in their veracity? This volume places challenges to moral belief side-by-side with challenges to religious belief, sets evolution-based challenges alongside disagreement-based challenges, and includes philosophical perspectives together with theological and social science perspectives, with the aim of cultivating insights and lines of inquiry that are easily missed within a single discipline or when these topics are treated in isolation. The result is a collection of essays--representing both skeptical and non-skeptical positions about morality and religion--that move these discussions forward in new and illuminating directions. -/- Contributors: Robert Audi, University of Notre Dame; Michael Bergmann, Purdue University; Sarah Brosnan, Georgia State University; William FitzPatrick, University of Rochester; John Hare, Yale University; Timothy P. Jackson, Emory University; Patrick Kain, Purdue University; Jordan Kiper, University of Connecticut; Dustin Locke, Claremont McKenna College; Charles Mathewes, University of Virginia; Mark C. Murphy, Georgetown University; John Pittard, Yale Divinity School; Walter Sinnott-Armstrong, Duke University; Richard Sosis, University of Connecticut; Sharon Street, New York University; Joshua Thurow, University of Texas at San Antonio; Ralph Wedgwood, University of Southern California. (shrink)
Stephen Law has recently argued (Think 9), using a dialogue set on the fictional planet Eth, that traditional belief in God is . Bergmann and Brower argue that theists on Earth should not be convinced.
Some evidential arguments from evil rely on an inference of the following sort: ‘If, after thinking hard, we can't think of any God-justifying reason for permitting some horrific evil then it is likely that there is no such reason’. Sceptical theists, us included, say that this inference is not a good one and that evidential arguments from evil that depend on it are, as a result, unsound. Michael Almeida and Graham Oppy have argued that Michael Bergmann's way of developing (...) the sceptical theist response to such arguments fails because it commits those who endorse it to a sort of scepticism that undermines ordinary moral practice. In this paper, we defend Bergmann's sceptical theist response against this charge. (shrink)
On March 12, 1938 the German army crossed the border into Austria. By the following September Gustav Bergmann had managed to send his first wife, Anna, and his daughter, Hanna, to safety in England. In October he managed to leave Austria himself. He first went to the Hague in the Netherlands to see Otto Neurath, who gave him enough money to assist his passage to New York. Bergmann’s prospects were quite uncertain at that time and it was not (...) clear that he would ever be able to repay Neurath. Neurath told Bergmann not to worry about repayment; he merely requested that Bergmann writes something about his recollections of the Vienna Circle. Bergmann wrote the following letter on the S. S. Staatendam while enroute to New York City to begin his new life. (shrink)
Internalists tend to impose on justification higher-level requirements, according to which a belief is justified only if the subject has a higher-level belief (i.e., a belief about the epistemic credentials of a belief). I offer an error theory that explains the appeal of this requirement: analytically, a belief is not justified if we have a defeater for it, but contingently, it is often the case that to avoid having defeaters, our beliefs must satisfy a higher-level requirement. I respond to the (...) objection that externalists who endorse this error theory will be forced to accept a radical form of scepticism. (shrink)
Skeptical theists endorse the skeptical thesis (which is consistent with the rejection of theism) that we have no good reason for thinking the possible goods we know of are representative of the possible goods there are. In his newest formulation of the evidential arguments from evil, William Rowe tries to avoid assuming the falsity of this skeptical thesis, presumably because it seems so plausible. I argue that his new argument fails to avoid doing this. Then I defend that skeptical thesis (...) against objections, thereby supporting my contention that relying on its falsity is a weakness in an argument. (shrink)
The question I consider is this: -/- The Question: Can two people–who are, and realize they are, intellectually virtuous to about the same degree–both be rational in continuing knowingly to disagree after full disclosure (by each to the other of all the relevant evidence they can think of) while at the same time thinking that the other may well be rational too? -/- I distinguish two kinds of rationality–internal and external–and argue in section 1 that, whichever kind we have in (...) mind, the answer to The Question is ‘yes’ (though that positive answer is less wholehearted in the case of external rationality). Then, in section 2, I briefly make some more general remarks about when discovering a disagreement provides a defeater and when it doesn't. In the final section, I consider an important objection to the answer given in section 1 to The Question. (shrink)
It’s not implausible to think that whenever I have a justified noninferential belief that p, it is caused by a seeming that p. It’s also tempting to think that something contributes to the justification of my belief only if I hold my belief because of that thing. Thus, given that many of our noninferential beliefs are justified and that we hold them because of seemings, one might be inclined to hold a view like Phenomenal Conservatism, according to which seemings play (...) a crucial role—perhaps the only crucial role—in the justification of our noninferential beliefs. But Phenomenal Conservatism seems to conflict, in a number of ways, with externalist accounts of justification. As a result, the attractiveness of the intuitions appealed to in support of views like Phenomenal Conservatism present something of a challenge to externalism. The purpose of this paper is to deal with that challenge by developing and defending an externalist-friendly account of the role of seemings in the formation and justification of our noninferential beliefs—an account that incorporates what is attractive in views like Phenomenal Conservatism. Because this externalist-friendly account is compatible with both externalist accounts of justification and the plausible elements of views like Phenomenal Conservatism, the challenge to externalism inspired by such views is thereby undermined. (shrink)
Despite various attempts to rectify matters, the internalism-externalism (I-E) debate in epistemology remains mired in serious confusion. I present a new account of this debate, one which fits well with entrenched views on the I-E distinction and illuminates the fundamental disagreements at the heart of the debate. Roughly speaking, the I-E debate is over whether or not certain of the necessary conditions of positive epistemic status are internal. But what is the sense of internal here? And of which conditions of (...) which positive epistemic status are we speaking? I argue that an adequate answer to these questions requires reference to what I call the no-defeater condition which is satisfied by a subjects belief B just in case she does not believe that B is defeated. I close by stating succinctly the main positions taken in the I-E debate, identifying the basic points of disagreement and suggesting fruitful courses for future discussion. (shrink)
This paper is a response to Peter Klein's "Human Knowledge and the Infinite Progress of Reasoning". After briefly discussing what Klein says about the requirement, for doxastic justification, that a belief be formed in the right way, I'll make the following three points: Klein's solution to the regress problem isn't an infinitist solution, Klein's position on doxastic justification faces a troubling dilemma, and Klein's objection to foundationalism fails.
Predication is an indisputable part of our linguistic behavior. By contrast, the metaphysics of predication has been a matter of dispute ever since antiquity. According to Plato—or at least Platonism, the view that goes by Plato’s name in contemporary philosophy—the truths expressed by predications such as “Socrates is wise” are true because there is a subject of predication (e.g., Socrates), there is an abstract property or universal (e.g., wisdom), and the subject exemplifies the property.1 This view is supposed to be (...) general, applying to all predications, whether the subject of predication is a person, a planet, or a property.2 Despite the controversy surrounding the metaphysics of predication, many theistic philosophers—including the majority of contemporary analytic theists—regard Platonism as extremely attractive. At the same time, however, such philosophers are also commonly attracted to a form of traditional theism that has at its core the thesis that God is an absolutely independent.. (shrink)
One thing all forms of foundationalism have in common is that they hold that a belief can be justified noninferentially--i.e., that its justification need not depend on its being inferred from some other justified (or unjustified) belief. In some recent publications, Peter Klein argues that in virtue of having this feature, all forms of foundationalism are infected with an unacceptable arbitrariness that makes it irrational to be a practicing foundationalist. In this paper, I will explain why his objections to foundationalism (...) fail. (shrink)
Adherents of traditional western Theism have espoused CONJUNCTION: God is essentially perfectly good and God is thankworthy for the good acts he performs . But suppose that (i) God’s essential perfect goodness prevents his good acts from being free, and that (ii) God is not thankworthy for an act that wasn’t freely performed.