John Calvin holds that the fall radically changed humanity’s moral and epistemic capacities. Reco... more John Calvin holds that the fall radically changed humanity’s moral and epistemic capacities. Recognizing that should lead Christian philosophers to see that philosophical questions require at least two sets of answers: one reflecting our nature and capacities before the fall, and the other reflecting our nature and capacities after the fall. Our prelapsarian knowledge of God, the right, and the good is direct and noninferential; our postlapsarian knowledge of them is mostly indirect, inferential, and filled with moral and epistemic risk. Only revelation can move us beyond fragmentary and indeterminate moral and theological knowledge.
I extend theories of nonmonotonic reasoning to account for reasons allowing free choice. My appro... more I extend theories of nonmonotonic reasoning to account for reasons allowing free choice. My approach works with a wide variety of approaches to nonmonotonic reasoning and explains the connection between reasons for kinds of action and reasons for actions or subkinds falling under them. I use an Anderson–Kanger reduction of reason statements, identifying key principles in the logic of reasons.
Aristotle (384-322 BC), the founder of the discipline of logic, also founded the study of quantif... more Aristotle (384-322 BC), the founder of the discipline of logic, also founded the study of quantification. Normally, Aristotle begins a topic by reviewing the common opinions, including the opinions of his chief predecessors. In logic, however, he could not adopt the same strategy; before him, he reports, "there was nothing at all" (Sophistical Refutations 183b34-36). Aristotle's theory dominated logical approaches to quantification until the nineteenth century. That is not to say that others did not make important contributions. Medieval logicians elaborated Aristotle's theory, structuring it in the form familiar to us today. They also contemplated a series of problems the theory generated, devising increasingly complex theories of semantic relations to account for them. Textbook treatments of quantification in the seventeenth and nineteenth centuries made important contributions while also advancing some peculiar theories based on medieval contributions. Modern quantification theory emerged from mathematical insights in the middle and late nineteenth century, displacing Aristotelian logic as the dominant theory of quantifiers for roughly a century. It has become common to see the history of logic as little more than a prelude to what we now call classical first-order logic, the logic of Frege, Peirce, and their successors. Aristotle's theory of quantification is nevertheless in some respects more powerful than its modern replacement. Aristotle's theory combines a relational conception of quantifiers with a monadic conception of terms. The modern theory combines a monadic conception of quantifiers with a relational theory of terms. Only recently have logicians combined relational conceptions of quantifiers and terms to devise a theory of generalized quantifiers capable of combining the strengths of the Aristotelian and modern approaches. There is no theory-neutral way of defining quantification, or even of delineating the class of quantifiers. Some logicians treat determiners such as 'all,' ''every,' 'most,' 'no,' 'some,' and the like as quantifiers; others think of them as denoting quantifiers. Still others think of quantifiers as noun phrases containing such determiners ('all men,' 'every book,' etc.). Some include other noun phrases ('Aristotle,' 'Peter, Paul, and John,' etc.). Some define quantifiers as variable-binding expressions; others lack the concept of a variable. My sketch of the history of our understanding of quantification thus traces the development of understandings of what is to be explained as much as how it is to be explained.
This paper develops a metaphysically flexible theory of quantification broad enough to incorporat... more This paper develops a metaphysically flexible theory of quantification broad enough to incorporate many distinct theories of objects. Quite different, mutually incompatible conceptions of the nature of objects and of reference find representation within it. Some conceptions yield classical first-order logic; some yield weaker logics. Yet others yield notions of validity that are proper extensions of classical logic. Keywords Quantification • Semantics • Metaphysics • Objects • Ontology Since Quine declared that 'to be is to be a value of a variable' [9], philosophers and logicians have recognized an intimate connection between quantification and ontology. Most directly, they have seen the quantificational structure of a theory as revealing its ontological commitments. This presupposes an objectual interpretation of the quantifiers, according to which ∀xA is true iff every object in the domain satisfies A. But many philosophers have also seen the logic of quantification as cloaking a theory of objects. Intuitionists, for example, have felt compelled to rewrite the semantics of quantification (and other logical operators) to accord with their nonclassical
A~ air Macintyre entitled a recent book on ethics and political theory, ose Justice? Which Ration... more A~ air Macintyre entitled a recent book on ethics and political theory, ose Justice? Which Rationality? Those questions ought to be asked of teaching in contemporary philosophy courses. Courses on ethics and contemporary moral problems are popular throughout the country, focusing on, among other things, justice. Logic courses, if not quite so popular, are also perennially full of students. Whose conception of justice and which conception of rationality do these courses teach? We have undertaken a study of recent textbooks on contemporary moral problems and on logic. We have found that, overwhelmingly, these books adopt a liberal to left-wing political stance. The ethics books imply that liberals or leftists have the stronger arguments on topics ranging from abortion to capital punishment to affirmative action. The logic books suggest that conservative reasoning is routinely fallacious. These findings are disturbing because while, for most students, one or another of these courses is their first exposure to philosophy, for many, it is their last. At stake, therefore, is no less than how most students of this generation will understand not only justice and rationality, but philosophy itself. Will students think of philosophy as a open search for truth, wherever it lies, or as a process of partisan debunking whose goal is to ratify contemporary ideological preferences? The Case of Logic Textbooks Logic seems like a paradigm of an objective, apolitical discipline. Despite recent trends in other areas, there is no such thing as specifically "feminist" or "deconstructionist" logic. There are no left-right disputes concerning logical theory. Nevertheless, many logic textbooks reveal a bias against specific thinkers and positions, mostly conservative ones. We first began to suspect that the teaching of logic was not immune from politics when a referee criticized a manuscript by one of us for a logic textbook, not only for including too few quotations from non-Western thinkers, but also for presenting as an example of fallacious reasoning the following quotation from M. Y. Latsis, chief of Lenin's secret police, the Cheka:
Justice is a concept by far more subtle and indefinite than is yielded by mere obedience to a rul... more Justice is a concept by far more subtle and indefinite than is yielded by mere obedience to a rule.-Benjamin N. Cardozo wO wne ofJohn Rawls's most abiding contributions to moral and political philosophy is his idea of reflective equilibrium. Even many who dissent from Rawls's principles of justice or contractarian framework find reflective equilibrium an apt characterization of philosophical method. Rawls provides a compelling if somewhat vague account of ethical reflection as going "back and forth" between consideredjudgments and principles, adjusting each in light of the other. Why, however, should we expect the process of reflection Rawls outlines to lead to equilibrium? Surprisingly, Rawls offers little argument. In defining that state, he makes it clear that equilibrium is simply an assumption. "By going back and forth," Rawls writes, "...I assume that eventually we shall find a description of the initial situation that both expresses reasonable conditions and yields principles which match our considered judgments duly pruned and adjusted."' Most other writers have been no less sanguine. Michael Sandel, for example, discussing the process of mutual adjustment, simply remarks, "a final product emerges."2 * I delivered a version of this paper at a symposium in memory of John Rawls at the University of Texas at Austin in March 2003. I am grateful to my fellow participants and audience members-especially James Fishkin, David Braybrooke, T. K. Seung, Jay Budziszewski, Benjamin Gregg, Paul Lyon, and Michael O'Connor-for their helpful comments and advice, and to an anonymous referee, Bryan Register, John Messerly, and especially Anthony Gillies for their comments on later drafts. 'A Theory ofJustice (Cambridge: Harvard, 1971), p. 20, my emphasis; hereafter TJ. 2 Liberalism and the Limits of Justice (New York: Cambridge, 1982), p. 48. The exception that proves the rule: Geoffrey Sayre-McCord recognizes that "actually achieving a comprehensive reflective equilibrium will almost surely remain always at most an ideal"-"Coherentist Epistemology and Moral Theory," in Walter Sinnott-Armstrong and Mark Timmons, eds., Moral Knowledge? (New York: Oxford, 1996), pp. 137-89, on p. 142. His concerns are primarily practical rather than theoretical. We do however share a crucial premise: that reflection does not merely cull initially given intuitive judgments and principles but also generates them. As he puts it, "new commitments will come on board thanks sometimes just to expanding experience, and other times to seeing what is implicit in, or required by, what else one believes" (p. 141). This is an important distinction. Judgments at equilibrium are not immune to all revision; they remain stable unless "expanding experience" alters them. So, new commitments arising from expanding experience do not challenge the possibility of reflective equilibrium. Those arising from responses to currently held judgments and principles, however, do.
Contemporary students of logic tend to think of the logic of the connectives as the most basic ar... more Contemporary students of logic tend to think of the logic of the connectives as the most basic area of the subject, which can then be extended with a logic of quantifiers. Historically, however, the logic of the quantifiers, in the form of the Aristotelian theory of the syllogism, came first. Truth conditions for negation, conjunction, and disjunction were well understood in ancient times, though not until Leibniz did anyone appreciate the algebraic features of these connectives. Approaches to the conditional, meanwhile, depended on drawing an analogy between conditionals and universal affirmative propositions. That remained true throughout the ancient, medieval, and early modern periods, and extended well into the nineteenth century, when Boole constructed an algebraic theory designed to handle sentential and quantificational phenomena in one go. The strength of the analogy, moreover, undercuts a common and otherwise appealing picture of the history of logic, according to which sentential and quantificational threads developed largely independently and, sometimes, in opposition to each other, until Frege wove them together in what we now consider classical logic. Frege did contribute greatly to our understanding of the connectives as well as the quantifiers. But his contribution consists in something other than unifying them into a single theory. 1 Aristotelian Foundations Aristotle (384-322 BC), the founder of logic, develops a logic of terms rather than a logic of propositions. He nevertheless argues for and against certain broad metaprinciples with direct relevance to propositional logic. In Metaphysics Γ 4, for example, he famously argues in favor of the principle of noncontradiction in the form "it is impossible for anything at the same time to be and not to be," maintaining that anyone who opposes it is "no better than a vegetable." In De Interpretatione 9 he argues against the principle of bivalence, contending that, if every proposition is either true or false, everything must be taken to happen by necessity and not by chance. He correspondingly denies that 'There will be a sea battle tomorrow' is either true or false. These are important discussions, raising central logical and philosophical issues. But they fall far short of a logic of propositional connectives. That has not stopped scholars from finding the core of such a logic in Aristotle.
Advances in genomic science create both opportunities and challenges for future generations. Both... more Advances in genomic science create both opportunities and challenges for future generations. Both adolescents and adults may benefit or be harmed by decisions they make in response to this new science. Using a qualitative descriptive design, the authors interviewed 22 adolescents (11 who were aged 14-17 years and 11 who were 18-21 years) and 11 parents to determine levels of knowledge and approaches to decision making. It was found that younger adolescents and their parents have very limited knowledge about genetics and genetic testing. Older adolescents have more complete information and consider a broader range of points in making decisions about hypothetical situations involving genetic testing. Adolescents and parents need much more information to enhance their ability to make decisions about using genetic services. These findings have implications for developing interventions and public health policy highlighted by the need for improved education about the benefits and harms of...
Lennart Aqvist (1984) explains why most contemporary deontic logics use a primitive binary condit... more Lennart Aqvist (1984) explains why most contemporary deontic logics use a primitive binary conditional obligation operator. He then points to an account of prima facie obligation as the primary outstanding problem facing these logics. Solving that problem, I hope to show, also solves the puzzles that motivated such theories in the first place. The crucial feature of obligation sentences to which the puzzles point is that such sentences, and evaluative sentences more generally, are defeasible. They may be warranted, given some information, only to be defeated by further information. A theory that recognizes this no longer needs to see conditional obligation as anything more than a simple combination of unary obligation and the conditional. My title may thus be overly provocative. I do not mean to deny that some obligations hold only if some condition is fulfilled. Nor do I mean to deny that sentences Kant would have called hypothetical imperatives, such as If you like Mexican food, you should try Jorge's, express such obligations. Finally, I do not mean to deny that there is anything wrong with the common strategy of using a primitive conditional obligation operator such as O(q0p) in a logical or philosophical theory of deontic concepts. It usefully avoids commitments about the relative roles of obligation and the conditional. What I do want to attack is the idea that a theory with a primitive conditional obligation operator-a binary theory, as I shall call it-can be a final logical or philosophical theory about deontic concepts. At the very least, a theorist using a conditional obligation operator owes us an explanation of how the semantics of the operator depends on the semantics for obligation and the conditional simpliciter. Sentences expressing conditional obligations are intelligible to anyone understanding should (or ought to) and if. The combination of these words is no idiom. The meanings of such sentences, therefore, should be explicable in terms
John Calvin holds that the fall radically changed humanity’s moral and epistemic capacities. Reco... more John Calvin holds that the fall radically changed humanity’s moral and epistemic capacities. Recognizing that should lead Christian philosophers to see that philosophical questions require at least two sets of answers: one reflecting our nature and capacities before the fall, and the other reflecting our nature and capacities after the fall. Our prelapsarian knowledge of God, the right, and the good is direct and noninferential; our postlapsarian knowledge of them is mostly indirect, inferential, and filled with moral and epistemic risk. Only revelation can move us beyond fragmentary and indeterminate moral and theological knowledge.
I extend theories of nonmonotonic reasoning to account for reasons allowing free choice. My appro... more I extend theories of nonmonotonic reasoning to account for reasons allowing free choice. My approach works with a wide variety of approaches to nonmonotonic reasoning and explains the connection between reasons for kinds of action and reasons for actions or subkinds falling under them. I use an Anderson–Kanger reduction of reason statements, identifying key principles in the logic of reasons.
Aristotle (384-322 BC), the founder of the discipline of logic, also founded the study of quantif... more Aristotle (384-322 BC), the founder of the discipline of logic, also founded the study of quantification. Normally, Aristotle begins a topic by reviewing the common opinions, including the opinions of his chief predecessors. In logic, however, he could not adopt the same strategy; before him, he reports, "there was nothing at all" (Sophistical Refutations 183b34-36). Aristotle's theory dominated logical approaches to quantification until the nineteenth century. That is not to say that others did not make important contributions. Medieval logicians elaborated Aristotle's theory, structuring it in the form familiar to us today. They also contemplated a series of problems the theory generated, devising increasingly complex theories of semantic relations to account for them. Textbook treatments of quantification in the seventeenth and nineteenth centuries made important contributions while also advancing some peculiar theories based on medieval contributions. Modern quantification theory emerged from mathematical insights in the middle and late nineteenth century, displacing Aristotelian logic as the dominant theory of quantifiers for roughly a century. It has become common to see the history of logic as little more than a prelude to what we now call classical first-order logic, the logic of Frege, Peirce, and their successors. Aristotle's theory of quantification is nevertheless in some respects more powerful than its modern replacement. Aristotle's theory combines a relational conception of quantifiers with a monadic conception of terms. The modern theory combines a monadic conception of quantifiers with a relational theory of terms. Only recently have logicians combined relational conceptions of quantifiers and terms to devise a theory of generalized quantifiers capable of combining the strengths of the Aristotelian and modern approaches. There is no theory-neutral way of defining quantification, or even of delineating the class of quantifiers. Some logicians treat determiners such as 'all,' ''every,' 'most,' 'no,' 'some,' and the like as quantifiers; others think of them as denoting quantifiers. Still others think of quantifiers as noun phrases containing such determiners ('all men,' 'every book,' etc.). Some include other noun phrases ('Aristotle,' 'Peter, Paul, and John,' etc.). Some define quantifiers as variable-binding expressions; others lack the concept of a variable. My sketch of the history of our understanding of quantification thus traces the development of understandings of what is to be explained as much as how it is to be explained.
This paper develops a metaphysically flexible theory of quantification broad enough to incorporat... more This paper develops a metaphysically flexible theory of quantification broad enough to incorporate many distinct theories of objects. Quite different, mutually incompatible conceptions of the nature of objects and of reference find representation within it. Some conceptions yield classical first-order logic; some yield weaker logics. Yet others yield notions of validity that are proper extensions of classical logic. Keywords Quantification • Semantics • Metaphysics • Objects • Ontology Since Quine declared that 'to be is to be a value of a variable' [9], philosophers and logicians have recognized an intimate connection between quantification and ontology. Most directly, they have seen the quantificational structure of a theory as revealing its ontological commitments. This presupposes an objectual interpretation of the quantifiers, according to which ∀xA is true iff every object in the domain satisfies A. But many philosophers have also seen the logic of quantification as cloaking a theory of objects. Intuitionists, for example, have felt compelled to rewrite the semantics of quantification (and other logical operators) to accord with their nonclassical
A~ air Macintyre entitled a recent book on ethics and political theory, ose Justice? Which Ration... more A~ air Macintyre entitled a recent book on ethics and political theory, ose Justice? Which Rationality? Those questions ought to be asked of teaching in contemporary philosophy courses. Courses on ethics and contemporary moral problems are popular throughout the country, focusing on, among other things, justice. Logic courses, if not quite so popular, are also perennially full of students. Whose conception of justice and which conception of rationality do these courses teach? We have undertaken a study of recent textbooks on contemporary moral problems and on logic. We have found that, overwhelmingly, these books adopt a liberal to left-wing political stance. The ethics books imply that liberals or leftists have the stronger arguments on topics ranging from abortion to capital punishment to affirmative action. The logic books suggest that conservative reasoning is routinely fallacious. These findings are disturbing because while, for most students, one or another of these courses is their first exposure to philosophy, for many, it is their last. At stake, therefore, is no less than how most students of this generation will understand not only justice and rationality, but philosophy itself. Will students think of philosophy as a open search for truth, wherever it lies, or as a process of partisan debunking whose goal is to ratify contemporary ideological preferences? The Case of Logic Textbooks Logic seems like a paradigm of an objective, apolitical discipline. Despite recent trends in other areas, there is no such thing as specifically "feminist" or "deconstructionist" logic. There are no left-right disputes concerning logical theory. Nevertheless, many logic textbooks reveal a bias against specific thinkers and positions, mostly conservative ones. We first began to suspect that the teaching of logic was not immune from politics when a referee criticized a manuscript by one of us for a logic textbook, not only for including too few quotations from non-Western thinkers, but also for presenting as an example of fallacious reasoning the following quotation from M. Y. Latsis, chief of Lenin's secret police, the Cheka:
Justice is a concept by far more subtle and indefinite than is yielded by mere obedience to a rul... more Justice is a concept by far more subtle and indefinite than is yielded by mere obedience to a rule.-Benjamin N. Cardozo wO wne ofJohn Rawls's most abiding contributions to moral and political philosophy is his idea of reflective equilibrium. Even many who dissent from Rawls's principles of justice or contractarian framework find reflective equilibrium an apt characterization of philosophical method. Rawls provides a compelling if somewhat vague account of ethical reflection as going "back and forth" between consideredjudgments and principles, adjusting each in light of the other. Why, however, should we expect the process of reflection Rawls outlines to lead to equilibrium? Surprisingly, Rawls offers little argument. In defining that state, he makes it clear that equilibrium is simply an assumption. "By going back and forth," Rawls writes, "...I assume that eventually we shall find a description of the initial situation that both expresses reasonable conditions and yields principles which match our considered judgments duly pruned and adjusted."' Most other writers have been no less sanguine. Michael Sandel, for example, discussing the process of mutual adjustment, simply remarks, "a final product emerges."2 * I delivered a version of this paper at a symposium in memory of John Rawls at the University of Texas at Austin in March 2003. I am grateful to my fellow participants and audience members-especially James Fishkin, David Braybrooke, T. K. Seung, Jay Budziszewski, Benjamin Gregg, Paul Lyon, and Michael O'Connor-for their helpful comments and advice, and to an anonymous referee, Bryan Register, John Messerly, and especially Anthony Gillies for their comments on later drafts. 'A Theory ofJustice (Cambridge: Harvard, 1971), p. 20, my emphasis; hereafter TJ. 2 Liberalism and the Limits of Justice (New York: Cambridge, 1982), p. 48. The exception that proves the rule: Geoffrey Sayre-McCord recognizes that "actually achieving a comprehensive reflective equilibrium will almost surely remain always at most an ideal"-"Coherentist Epistemology and Moral Theory," in Walter Sinnott-Armstrong and Mark Timmons, eds., Moral Knowledge? (New York: Oxford, 1996), pp. 137-89, on p. 142. His concerns are primarily practical rather than theoretical. We do however share a crucial premise: that reflection does not merely cull initially given intuitive judgments and principles but also generates them. As he puts it, "new commitments will come on board thanks sometimes just to expanding experience, and other times to seeing what is implicit in, or required by, what else one believes" (p. 141). This is an important distinction. Judgments at equilibrium are not immune to all revision; they remain stable unless "expanding experience" alters them. So, new commitments arising from expanding experience do not challenge the possibility of reflective equilibrium. Those arising from responses to currently held judgments and principles, however, do.
Contemporary students of logic tend to think of the logic of the connectives as the most basic ar... more Contemporary students of logic tend to think of the logic of the connectives as the most basic area of the subject, which can then be extended with a logic of quantifiers. Historically, however, the logic of the quantifiers, in the form of the Aristotelian theory of the syllogism, came first. Truth conditions for negation, conjunction, and disjunction were well understood in ancient times, though not until Leibniz did anyone appreciate the algebraic features of these connectives. Approaches to the conditional, meanwhile, depended on drawing an analogy between conditionals and universal affirmative propositions. That remained true throughout the ancient, medieval, and early modern periods, and extended well into the nineteenth century, when Boole constructed an algebraic theory designed to handle sentential and quantificational phenomena in one go. The strength of the analogy, moreover, undercuts a common and otherwise appealing picture of the history of logic, according to which sentential and quantificational threads developed largely independently and, sometimes, in opposition to each other, until Frege wove them together in what we now consider classical logic. Frege did contribute greatly to our understanding of the connectives as well as the quantifiers. But his contribution consists in something other than unifying them into a single theory. 1 Aristotelian Foundations Aristotle (384-322 BC), the founder of logic, develops a logic of terms rather than a logic of propositions. He nevertheless argues for and against certain broad metaprinciples with direct relevance to propositional logic. In Metaphysics Γ 4, for example, he famously argues in favor of the principle of noncontradiction in the form "it is impossible for anything at the same time to be and not to be," maintaining that anyone who opposes it is "no better than a vegetable." In De Interpretatione 9 he argues against the principle of bivalence, contending that, if every proposition is either true or false, everything must be taken to happen by necessity and not by chance. He correspondingly denies that 'There will be a sea battle tomorrow' is either true or false. These are important discussions, raising central logical and philosophical issues. But they fall far short of a logic of propositional connectives. That has not stopped scholars from finding the core of such a logic in Aristotle.
Advances in genomic science create both opportunities and challenges for future generations. Both... more Advances in genomic science create both opportunities and challenges for future generations. Both adolescents and adults may benefit or be harmed by decisions they make in response to this new science. Using a qualitative descriptive design, the authors interviewed 22 adolescents (11 who were aged 14-17 years and 11 who were 18-21 years) and 11 parents to determine levels of knowledge and approaches to decision making. It was found that younger adolescents and their parents have very limited knowledge about genetics and genetic testing. Older adolescents have more complete information and consider a broader range of points in making decisions about hypothetical situations involving genetic testing. Adolescents and parents need much more information to enhance their ability to make decisions about using genetic services. These findings have implications for developing interventions and public health policy highlighted by the need for improved education about the benefits and harms of...
Lennart Aqvist (1984) explains why most contemporary deontic logics use a primitive binary condit... more Lennart Aqvist (1984) explains why most contemporary deontic logics use a primitive binary conditional obligation operator. He then points to an account of prima facie obligation as the primary outstanding problem facing these logics. Solving that problem, I hope to show, also solves the puzzles that motivated such theories in the first place. The crucial feature of obligation sentences to which the puzzles point is that such sentences, and evaluative sentences more generally, are defeasible. They may be warranted, given some information, only to be defeated by further information. A theory that recognizes this no longer needs to see conditional obligation as anything more than a simple combination of unary obligation and the conditional. My title may thus be overly provocative. I do not mean to deny that some obligations hold only if some condition is fulfilled. Nor do I mean to deny that sentences Kant would have called hypothetical imperatives, such as If you like Mexican food, you should try Jorge's, express such obligations. Finally, I do not mean to deny that there is anything wrong with the common strategy of using a primitive conditional obligation operator such as O(q0p) in a logical or philosophical theory of deontic concepts. It usefully avoids commitments about the relative roles of obligation and the conditional. What I do want to attack is the idea that a theory with a primitive conditional obligation operator-a binary theory, as I shall call it-can be a final logical or philosophical theory about deontic concepts. At the very least, a theorist using a conditional obligation operator owes us an explanation of how the semantics of the operator depends on the semantics for obligation and the conditional simpliciter. Sentences expressing conditional obligations are intelligible to anyone understanding should (or ought to) and if. The combination of these words is no idiom. The meanings of such sentences, therefore, should be explicable in terms
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