From ancient times to the present, the discovery and presentation of new proofs of previously established theorems has been a salient feature of mathematical practice. Why? What purposes are served by such endeavors? And how do mathematicians judge whether two proofs of the same theorem are essentially different? Consideration of such questions illuminates the roles that proofs play in the validation and communication of mathematical knowledge and raises issues that have yet to be resolved by mathematical logicians. The Appendix, in (...) which several proofs of the Fundamental Theorem of Arithmetic are compared, provides a miniature case study. (shrink)

John Etchemendy has argued that it is but "a fortuitous accident" that Tarski's work on truth has any signifance at all for semantics. I argue, in response, that Etchemendy and others, such as Scott Soames and Hilary Putnam, have been misled by Tarski's emphasis on definitions of truth rather than theories of truth and that, once we appreciate how Tarski understood the relation between these, we can answer Etchemendy's implicit and explicit criticisms of neo-Davidsonian semantics.

Religious considerations in medical decision-making have enjoyed newfound attention in recent years, challenging the assumption that the domains of biological and spiritual flourishing can be cleanly separated in clinical practice. A surprising majority of patients desire their physicians to engage their religious and spiritual concerns, yet most never receive such attention, particularly in cases near the end of life where such attention seems most warranted.1–3 As physicians Aparna Sajja and Christina Puchalski recently wrote in the AMA Journal of Ethics theme (...) issue on ‘Religion and Spirituality in Healthcare Practice’, modern medical training is ‘falling short of preparing physicians to help patients with the metaphysical needs of their illness’.4 It would seem then that both patients and physicians might challenge the conclusions proffered by philosophers Jake Greenblum and Ryan Hubbard in ‘Responding to Religious Patients: Why Physicians Have No Business Doing Theology’, in which they claim that physicians ought not to engage religious reasoning for medical decisions. Their conclusion relies on two core arguments: a ‘public reason’ argument and a ‘fiduciary argument’, both of which contend that theology and religious considerations have no place in medical reasoning. We find that two central errors undergird these arguments. First is the fraught notion of an epistemically and ethically normative public reason, and second is a fundamental mischaracterisation of the fiduciary nature of the patient–physician relationship and the nature of medicine itself. In response, we argue that all physicians essentially ‘do theology’ and that, rather than divorcing theology from medical practice, clinicians should make it their business to do theology well. To support the exclusion of religious reasoning from medical decision-making, the authors open with a ‘public reason argument’, suggesting that physicians serve in roles closely resembling those of public officials. As such, the physician as public official ought to limit himself …. (shrink)

Some people have found my distinction between meaning and significance useful. In the following revision of that distinction, I hope to improve its accuracy and perhaps, therefore, its utility as well. My impulse for making the revision has been my realization, very gradually achieved, that meaning is not simply an affair of consciousness and unconsciousness. In 1967, in Validity in Interpretation, I roundly asserted that “there is no magic land of meanings outside human consciousness.” 1 That assertion would be true (...) if, godlike, we could oversee the whole of human consciousness, past, present, and future. But we language users, being limited creatures, intend our verbal meanings to go beyond what we can pay attention to at any moment. We intend our meanings to transcend our momentary limitations of attention and knowledge. Hence there is a land of meanings beyond past and present human consciousness—the land of the future. What I should have said originally is that there is no magic lance of meanings beyond the whole extent of human consciousness, past, present, and future. This correction of my original statements leads to a deepening of the concept of meaning.In 1960 I first proposed the analytical distinction between two aspects of textual interpretation. One of them, meaning, was fixed and immutable; the other, significance, was open to change.2 I acknowledged that significance, changeable or not, is the more valuable object of interpretation, because it typically embraces the present use of texts, and present use is present value. But I argued that, in academic criticism, the significance and use of a text ought to be rooted in its fixed meaning, since otherwise criticism would lack a stable object of inquiry and would merely float on tides of preference. The claim that one reader’s opinion is as valid as another’s would then be right, despite any indignant protest to the contrary. I did not wish to dissuade people from floating on the tides of preference if that was what they wished to do. I intended to provide a firm justification for those who wished to pursue historical scholarship. 3 I also assumed that even those who did not pursue historical scholarship might sometimes wish to exploit the possibility of historically fixed meaning. In my experience, even antiauthorial theorists sometimes with to regard their own texts as having a historically fixed meaning and will complain if someone misunderstands that meaning. 1. E. D. Hirsch, Jr., Validity in Interpretation, p. 4.2. See my “Objective Interpretation,” PMLA 75 : 463-79.3. See, for instance, W. K. Wimsatt, Jr., and Monroe C. Beardsley, “The Intentional Fallacy,” in Wimsatt, The Verbal Icon: Studies in the Meaning of Poetry, which ends:We submit that this is the true and objective way of criticism, as contrasted to what the very uncertainty of exegesis might tempt a second kind of critic to undertake: the way of biographical or genetic inquiry …. Our point is that such an answer to such an inquiry would have nothing to do with the poem “Prufrock”; it would not be a critical inquiry. Critical inquiries, unlike bets, are not settled in this way. Critical inquiries are not settled by consulting the oracle. [P. 18] E. D. Hirsch, Jr., professor of English at the University of Virginia, is the author of numerous works, including Validity in Interpretation and The Aims of Interpretation. His previous contributions to Critical Inquiry are “Against Interpretation?”, “The Politics of Theories of Interpretation, and “Stylistics and Synonymity”. (shrink)

This short essay was published by Shelterforce, the journal of affordable of housing and community development published by the National Housing Institute. It is largely taken from my law review article entitled "'We Shall Not Be Moved': Eminent Domain, Urban Redevelopment and the Socioeconomics of Just Compensation" published by St. John's Law Review. That article can be downloaded from SSRN at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=904224 This shorter piece focuses on the two proposals outlined in the second part of the law review article that (...) are designed to curb abuses of eminent domain in the urban redevelopment context without destroying its effectiveness as a tool for community revitalization and, even, community empowerment. Specifically, homeowners should not be subject to eminent domain pursuant to a redevelopment plan until the majority of them have approved the plan. To further solidify resident ownership of redevelopment, the right to continued residency in the community should be protected by amending relocation laws to guarantee an alienable entitlement to be offered replacement housing in the redeveloped district area. Together, these two legislative reforms express a more nuanced balance of property and liability rules that will facilitate a more productive interface between community residents and redevelopment officials. (shrink)

This paper presents a method for investigating counterfactual histories of science. A central notion to our theory of science are "advances" , which are units passed among scientists and which would be conserved in passing from one possible history to another. Advances are connected to each other by nets of causal influence, and we distinguish strong and weak influences. Around sixty types of advances are grouped into ten classes. As our case study, we examine the beginning of the Old Quantum (...) Theory, using a computer to store and process historical information. We describe four plausible possible histories, along with six other implausible ones. (shrink)

Skeptics try to persuade us of our ignorance with arguments like the following: 1. I don't know that I am not a handless brain-in-a-vat [BIV]. 2. If I don't know that I am not a handless BIV, then I don't know that I have hands. Therefore, 3. I don't know that I have hands. The BIV argument is valid, its premises are intuitively compelling, and yet, its conclusion strikes us as a absurd. Something has to go, but what? Contextualists contend (...) that an adequate solution to the skeptical problem must: (i) retain epistemic closure, (ii) explain the intuitive force of skeptical arguments by explaining why their premises initially seem so compelling, and (iii) account for the truth of our commonsense judgment that we do possess lots of ordinary knowledge. Contextualists maintain that the key to such a solution is recognizing that the semantic standards for 'knows' vary from context to context such that in skeptical contexts the skeptic's premises are true and so is her conclusion; but in ordinary contexts, her conclusion is false and so is her first premise. Despite its initial attractiveness, the contextualist solution comes at a significant cost, for contextualism has many counterintuitive results. After presenting the contextualist solution, I identify a number of these costs. I then offer a noncontextualist solution that meets the adequacy constraint identified above, while avoiding the costs associated with contextualism. Hence, one of the principal reasons offered for adopting a contextualist theory of knowledge -- its supposedly unique ability to adequately resolve the skeptical problem -- is undermined. (shrink)

On first blush the Jim Crow Era may seem an odd place to locate anything meaningful about democratic, equal citizenship and the promise of the fourteenth amendment. This article argues to the contrary. The period of Jim Crow, in its negation of democratic citizenship, in fact reveals import aspects about the nature of democratic citizenship. This occurred in two ways. First, whites who implemented white supremacy implicitly understood that freedom and citizenship manifest themselves in a multiplicity of spheres, which is (...) why white supremacists sought to subordinate blacks not just politically but across all social spheres. Second, the resistance to comprehensive subordination revealed the multiplicity of the spirit of freedom and equality in actions and arguments African Americans. African Americans created spaces of democratic citizenship within the dominant culture of subordination. This article suggests that, in studying both the implementation of white supremacy and the resistance to it, we can learn more about how equal and democratic citizenship can be affirmed and implemented rather than negated, and also about the role of law as a tool for both subordination and resistance. (shrink)

The dominant argument for the introduction of propensities or chances as an interpretation of probability depends on the difficulty of accounting for single case probabilities. We argue that in almost all cases, the "single case" application of probability can be accounted for otherwise. "Propensities" are needed only in theoretical contexts, and even there applications of probability need only depend on propensities indirectly.

Taxation and government policy related to it have only episodic appearance in classical Protestant ethical sources. Of the early sixteenth century reformers, Luther gave most attention to the subject, justifying taxation in general as necessary for the just service of government to the public good and calling the princes to spend tax monies for that good rather than their own luxury. Calvin made much the same claims but called more clearly for official church scrutiny of all government than did Luther. (...) Two centuries later John Wesley criticized English tax policy, appealing to standards of economic efficiency and compassion for the poor with little reference overtly to theology. The churches of colonial and post-revolutionary America developed no systematic, theologically rooted rationale for taxation ethics, either; but official Protestant denominational concern for such ethics has grown measurably in the most recent fifteen years. After a survey of these recent national church statements, and on the basis of them and the slender Protestant heritage on this issue, we end by posing four questions which we see as worthy of much serious thinking by contemporary American Protestant ethicists and church bodies. (shrink)

Among philosophers as well as linguists the battle is still joined between those who view the correlation between meaning and linguistic form as strictly determined by convention and those who argue for the essential indeterminacy of the relationship between meaning and form.1 Plato's Cratylus aside, the philosphical dialogue that forms the locus classicus of this debate is the following: "You're holding it upside down!" Alice interrupted. "To be sure I was!" Humpty Dumpty said gaily, as she turned it round for (...) him. "I thought it looked a little queer. As I was saying. that seems to be done right - though I haven't time to look it over thoroughly just now - and that shows that there are three hundred and sixty-four days when you might get un-birthday presents -" "Certainly," said Alice. "And only one for birthday presents, you know. There's glory for you!" "I don't know what you mean by 'glory,'" Alice said. Humpty Dumpty smiled contemptuously. "Of course you don't - till I tell you. I meant 'there's a nice knock-down argument for you!'" "But 'glory' doesn't mean 'a nice knock-down argument,'" Alice objected. "When I use a word," Humpty Dumpty said in rather a scornful tone, "it means just what I choose it to mean - neither more nor less."2 · 1. This should not be taken as an argument for the indeterminacy of linguistic meaning itself. Quite the contrary; it is because meaning can be stable and determinate despite variations in mental acts and linguistic forms that the relation between form and meaning must be indeterminate on the basis merely of rules and conventions.· 2. Lewis Carroll, Through the Looking Glass, chap. 6. E. D. Hirsch, Jr. is Kenan Professor of English at the University of Virginia. He is the author of Validity in Interpretation and Wordsworth and Schelling: A Typological Study of Romanticism. A second edition of his book on Blake, Innocence and Experience, will appear next year, as will a new book on critical theory. (shrink)

Open peer commentary on the target article “Arguments Opposing the Radicalism of Radical Constructivism” by Gernot Saalmann. Excerpt: Gernot Saalmann uses the term “radical” in the sense of something “extreme.” For example, in §1, he contrasts “radical” constructivists with “moderate” constructivists. This adjectival usage of the word “radical” as “extreme” is a slang usage from the American sub-culture called “Surfers” which originated in the late 1950s or early 1960s. “Radical,” in their slang means: “At or exceeding limits of control or (...) safety…” (Oxford English Dictionary OED 2007) . (shrink)