Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a (...) description of Mars. But whereas Mars is a physical object, the number 3 is (according to platonism) an abstract object. And abstract objects, platonists tell us, are wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal. Thus, on this view, the number 3 exists independently of us and our thinking, but it does not exist in space or time, it is not a physical or mental object, and it does not enter into causal relations with other objects. This view has been endorsed by Plato, Frege (1884, 1893-1903, 1919), Gödel (1964), and in some of their writings, Russell (1912) and Quine (1948, 1951), not to mention numerous more recent philosophers of mathematics, e.g., Putnam (1971), Parsons (1971), Steiner (1975), Resnik (1997), Shapiro (1997), Hale (1987), Wright (1983), Katz (1998), Zalta (1988), and Colyvan (2001). (shrink)

If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is (...) also the case with respect to the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way, namely, by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics. (shrink)

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed.

Contemporary philosophy’s three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion’s share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed more briefly (...) in section 6. (shrink)

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California (...) in 1988. Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought. (shrink)

Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects.

The incredible achievements of modern scientific theories lead most of us to embrace scientific realism: the view that our best theories offer us at least roughly accurate descriptions of otherwise inaccessible parts of the world like genes, atoms, and the big bang. In Exceeding Our Grasp, Stanford argues that careful attention to the history of scientific investigation invites a challenge to this view that is not well represented in contemporary debates about the nature of the scientific enterprise. The historical (...) record of scientific inquiry, Stanford suggests, is characterized by what he calls the problem of unconceived alternatives. Past scientists have routinely failed even to conceive of alternatives to their own theories and lines of theoretical investigation, alternatives that were both well-confirmed by the evidence available at the time and sufficiently serious as to be ultimately accepted by later scientific communities. Stanford supports this claim with a detailed investigation of the mid-to-late 19th century theories of inheritance and generation proposed in turn by Charles Darwin, Francis Galton, and August Weismann. He goes on to argue that this historical pattern strongly suggests that there are equally well-confirmed and scientifically serious alternatives to our own best theories that remain currently unconceived. Moreover, this challenge is more serious than those rooted in either the so-called pessimistic induction or the underdetermination of theories by evidence, in part because existing realist responses to these latter challenges offer no relief from the problem of unconceived alternatives itself. Stanford concludes by investigating what positive account of the spectacularly successful edifice of modern theoretical science remains open to us if we accept that our best scientific theories are powerful conceptual tools for accomplishing our practical goals, but abandon the view that the descriptions of the world around us that they offer are therefore even probably or approximately true. (shrink)

One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It's not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these (...) theories is also varied. Not only does mathematics help with empirical predictions, it allows elegant and economical statement of many theories. Indeed, so important is the language of mathematics to science, that it is hard to imagine how theories such as quantum mechanics and general relativity could even be stated without employing a substantial amount of mathematics. (shrink)

1. Preliminary Reconnaissance: Realism, Instrumentalism, and Interpretation On the one hand, I think it is fair to say that philosophers recognize a special problem or question about how we are to “interpret” scientific theories only in light of their concerns about whether we are really entitled to believe what those theories say when they are interpreted in what we see as the most natural or straightforward or intuitive way. On the other hand, this fundamental worry reaches all the way back (...) to the inception of scientific inquiry itself, no matter how liberally we conceive of that enterprise. Before the relatively recent professionalization of academic fields, such concerns were well-represented among the figures who served simultaneously as both the leading practitioners and the leading philosophers of science. This is nicely illustrated by the strident debates throughout this community in the 18th and 19th centuries concerning whether only pure inductive methods were legitimate for scientific inquiry and/or whether the competing “method of hypothesis” could produce any genuine knowledge of nature (see Laudan 1981 Ch. 8). (shrink)

UMI Number: 3319553 This study is a historical ethnography of religious diversity in post-revolutionary Nicaragua from the vantage point of Catholics who live in the city of Masaya located on the Pacific side of Nicaragua at the end of the twentieth century. My overarching research question is: How may ethnographically observed patterns in Catholic religious practices in contemporary Nicaragua be understood in historical context? Utilizing anthropological theory and method grounded in Weberian historical theory, I explore Catholic ritual as contested politico-religious (...) cultural terrain. The patron saint celebration of Masaya becomes a contested symbol in 1999 as those who carry Saint Jerome in street procession refuse to honor a sitting president, challenging his right to rule. The deep Marian devotion of the Nicaraguan people is reflected in the household and neighborhood celebrations of the Immaculate Conception of the Virgin Mary, while nation-building elites have a long history of claiming the Virgin as patron saint of the nation. While these traditional Catholic saint celebrations figure in imagining a nation, three "new" Catholic movements also compete for attention, while the polity is increasingly exposed to Protestant and Pentecostal groups. When Anastasio Somoza Debayle was overthrown in 1979, ending the 40-year family dictatorship, the Sandinista National Liberation Front (FSLN) ruled for a decade with the attention of the world placed on its religion of revolution, the Christian base community and liberation theology. At the same time, however, two other movements began growing quietly. They, like liberation theology, draw their justification from the second Vatican Council. In Masaya, Catholic Charismatic Renewal and the Neocatechumenal Way are "exemplary" prophetic movements gaining ground within the Catholic Church in competition with the "ethical" prophets of the Christian base community. Selectively adopting "protestant-like" forms of worship through these modern movements, the Nicaraguan Roman Catholic Church reacts to the challenge to its cultural hegemony coming from evangelical competitors. New history is continuously being made as people in this part of Nicaragua struggle over the direction of their country within a complex terrain of religious competition. (shrink)

The historical record of scientific inquiry, Stanford suggests, is characterized by what he calls the problem of unconceived alternatives. Past scientists have routinely failed even to conceive of alternatives to their own theories and lines of theoretical investigation, alternatives that were both well-confirmed by the evidence available at the time and sufficiently serious as to be ultimately accepted by later scientific communities. Stanford supports this claim with a detailed investigation of the mid-to-late 19th century theories of inheritance and (...) generation proposed in turn by Charles Darwin, Francis Galton, and August Weismann. He goes on to argue that this historical pattern strongly suggests that there are equally well-confirmed and scientifically serious alternatives to our own best theories that remain currently unconceived. Moreover, this challenge is more serious than those rooted in either the so-called pessimistic induction or the underdetermination of theories by evidence, in part because existing realist responses to these latter challenges offer no relief from the problem of unconceived alternatives itself.Stanford concludes by investigating what positive account of the spectacularly successful edifice of modern theoretical science remains open to us if we accept that our best scientific theories are powerful conceptual tools for accomplishing our practical goals, but abandon the view that the descriptions of the world around us that they offer are therefore even probably or approximately true."Stanford has genuinely advanced the philosophical discussion about scientific realism with his careful articulation of the problem of unconceived alternatives."-- The Review of Metaphysics "Stanford's book deserves to be widely read. Its central argument is clearly stated, its conclusion is radical, it engages in a productive fashion with detailed case studies, and it lays down several substantial challenges to scientific realism. Lastly, it is consistently thought-provoking."-Science. (shrink)

In this paper, I will discuss the need for a theory of essences within Object-Oriented Ontology (OOO) and then formulate one. I will do so by drawing on Graham Harman’s work on OOO and Martin Heidegger’s thought on the essence of being, presented in his Introduction to Metaphysics. Harman touches on essences, describing them as the tension between a withdrawn object and its withdrawn qualities, but fails to distinguish between essential and inessential qualities within this framework. To fill in the (...) gaps, I will turn to Heidegger’s explication of phusis in order to show that an essential aspect of being is how one enters into causal relations and continually reveals oneself to other beings. In bringing OOO and Heidegger together, I will find that each object has a unique way of exerting itself in the world and that the domestic relations that make up this unique profile are essential to it, while other domestic relations, those that do not influence its particular way of exerting itself, are inessential. Thus, the essence will be found to be the set of domestic relations that make up the determinate form, or unique causal profile, of the object. (shrink)

Scientific realists have suggested that changes in our scientific communities over the course of their history have rendered those communities progressively less vulnerable to the problem of unconcieved alternatives over time. I argue in response not only that the most fundamental historical transformations of the scientific enterprise have generated steadily mounting obstacles to revolutionary, transformative, or unorthodox scientific theorizing, but also that we have substantial independent evidence that the institutional apparatus of contemporary scientific inquiry fosters an exceedingly and increasingly theoretically (...) conservative form of that inquiry. I conclude that contemporary scientific communities are actually more vulnerable to the problem of unconceived alternatives than their historical predecessors, and I briefly suggest how we might seek to pursue scientific inquiry in a less theoretically conservative way. (shrink)

Scientific realists have suggested that changes in our scientific communities over the course of their history have rendered those communities progressively less vulnerable to the problem of unconcieved alternatives over time. I argue in response not only that the most fundamental historical transformations of the scientific enterprise have generated steadily mounting obstacles to revolutionary, transformative, or unorthodox scientific theorizing, but also that we have substantial independent evidence that the institutional apparatus of contemporary scientific inquiry fosters an exceedingly and increasingly theoretically (...) conservative form of that inquiry. I conclude that contemporary scientific communities are actually more vulnerable to the problem of unconceived alternatives than their historical predecessors, and I briefly suggest how we might seek to pursue scientific inquiry in a less theoretically conservative way. (shrink)

Advocates have sought to prove that underdetermination obtains because all theories have empirical equivalents. But algorithms for generating empirical equivalents simply exchange underdetermination for familiar philosophical chestnuts, while the few convincing examples of empirical equivalents will not support the desired sweeping conclusions. Nonetheless, underdetermination does not depend on empirical equivalents: our warrant for current theories is equally undermined by presently unconceived alternatives as well-confirmed merely by the existing evidence, so long as this transient predicament recurs for each theory and body (...) of evidence we consider. The historical record supports the claim that this recurrent, transient underdetermination predicament is our own. (shrink)

Advocates have sought to prove that underdetermination obtains because all theories have empirical equivalents. But algorithms for generating empirical equivalents simply exchange underdetermination for familiar philosophical chestnuts, while the few convincing examples of empirical equivalents will not support the desired sweeping conclusions. Nonetheless, underdetermination does not depend on empirical equivalents: our warrant for current theories is equally undermined by presently unconceived alternatives as well-confirmed merely by the existing evidence, so long as this transient predicament recurs for each theory and body (...) of evidence we consider. The historical record supports the claim that this recurrent, transient underdetermination predicament is our own. (shrink)

A range of empirical findings is first used to more precisely characterize our distinctive tendency to objectify or externalize moral demands and obligations, and it is then argued that this salient feature of our moral cognition represents a profound puzzle for evolutionary approaches to human moral psychology that existing proposals do not help resolve. It is then proposed that such externalization facilitated a broader shift to a vastly more cooperative form of social life by establishing and maintaining a connection between (...) the extent to which an agent is herself motivated by a given moral norm and the extent to which she uses conformity to that same norm as a criterion in evaluating candidate partners in social interaction generally. This connection ensures the correlated interaction necessary to protect those prepared to adopt increasingly cooperative, altruistic, and other prosocial norms of interaction from exploitation, especially as such norms were applied in novel ways and/or to novel circumstances and as the rapid establishment of new norms allowed us to reap still greater rewards from hypercooperation. A wide range of empirical findings is then used to support this hypothesis, showing why the status we ascribe to moral demands and considerations exhibits the otherwise puzzling combination of objective and subjective elements that it does, as well as showing how the need to effectively advertise our externalization of particular moral commitments generates features of our social interaction so familiar that they rarely strike us as standing in need of any explanation in the first place. (shrink)

I develop an account of predictive similarity that allows even Antirealists who accept a correspondence conception of truth to answer the Realist demand (recently given sophisticated reformulations by Musgrave and Leplin) to explain the success of particular scientific theories by appeal to some intrinsic feature of those theories (notwithstanding the failure of past efforts by van Fraassen, Fine, and Laudan). I conclude by arguing that we have no reason to find truth a better (i.e., more plausible) explanation of a theory's (...) success than predictive similarity, even of its success in making novel predictions. (shrink)

In the concluding chapter of Exceeding our Grasp Kyle Stanford outlines a positive response to the central issue raised brilliantly by his book, the problem of unconceived alternatives. This response, called "epistemic instrumentalism", relies on a distinction between instrumental and literal belief. We examine this distinction and with it the viability of Stanford's instrumentalism, which may well be another case of exceeding our grasp.

Deductivism says that a mathematical sentence s should be understood as expressing the claim that s deductively follows from appropriate axioms. For instance, deductivists might construe “2+2=4” as “the sentence ‘2+2=4’ deductively follows from the axioms of arithmetic”. Deductivism promises a number of benefits. It captures the fairly common idea that mathematics is about “what can be deduced from the axioms”; it avoids an ontology of abstract mathematical objects; and it maintains that our access to mathematical truths requires nothing (...) beyond our ability to make logical deductions. Sections 1 and 2 define and motivate deductivism in more detail. Section 3 covers four authors (Russell, Hilbert, Pasch, Curry) who have endorsed deductivism at some point. Section 4 aims to clarify what semantic claim deductivists make. Sections 5–9 review objections to deductivism and possible replies. (shrink)

Realists have responded to challenges from the historical record of successful but ultimately rejected theories with what I call the selective confirmation strategy: arguing that only idle parts of past theories have been rejected, while truly success‐generating features have been confirmed by further inquiry. I argue first, that this strategy is unconvincing without some prospectively applicable criterion of idleness for theoretical posits, and second, that existing efforts to provide one either convict all theoretical posits of idleness (Kitcher) or stand refuted (...) by detailed consideration of the very examples (optical/electromagnetic ether, caloric fluid) to which they appeal (Psillos). I also argue that available avenues for improving on these proposals are unpromising. (shrink)

Some scientific realists suggest that scientific communities have improved in their ability to discover alternative theoretical possibilities and that the problem of unconceived alternatives therefore poses a less significant threat to contemporary scientific communities than it did to their historical predecessors. I first argue that the most profound and fundamental historical transformations of the scientific enterprise have actually increased rather than decreased our vulnerability to the problem. I then argue that whether we are troubled by even the prospect of increasing (...) theoretical conservatism in science should depend on the position we occupy in the ongoing debate concerning scientific realism itself. (shrink)

I argue for accepting a pluralist approach to species, while rejecting the realism about species espoused by P. Kitcher and a number of other philosophers of biology. I develop an alternative view of species concepts as divisions of organisms into groups for study which are relative to the systematic explanatory interests of biologists at a particular time. I also show how this conception resolves a number of difficult puzzles which plague the application of particular species concepts.

Fish, S. Georgics of the mind: Bacon's philosophy and the experience of his Essays.--Brett, R. L. Thomas Hobbes.--Watt, I. Realism and the novel.--Tuveson, E. Locke and Sterne.--Kampf, L. Gibbon and Hume.--Frye, N. Blake's case against Locke.--Abrams, M. H. Mechanical and organic psychologies of literary invention.--Ryle, G. Jane Austen and the moralists.--Schneewind, J. B. Moral problems and moral philosophy in the Victorian period.--Donagan, A. Victorian philosophical prose: J. S. Mill and F. H. Bradley.--Pitcher, G. Wittgenstein, nonsense, and Lewis Carroll.--Bolgan, A. C. (...) The philosophy of F. H. Bradley and the mind and art of T. S. Eliot: an introduction.--Davie, D. Yeats, Berkeley, and Romanticism.--Ross, M. L. The mythology of friendship: D. H. Lawrence, Bertrand Russell, and "The Blind man".--Rosenbaum, S. P. The philosophical realism of Virginia Woolf.--Bibliography (p. 357-360). (shrink)

Recent years have seen the growing promise of cultural evolutionary theory as a new approach to bringing human behaviour fully within the broader evolutionary synthesis. This review of two recent seminal works on this topic argues that cultural evolution now holds the potential to bring together fields as disparate as neuroscience and social anthropology within a unified explanatory and ontological framework.

Sherri Roush ([2005]) and I ([2001], [2006]) have each argued independently that the most significant challenge to scientific realism arises from our inability to consider the full range of serious alternatives to a given hypothesis we seek to test, but we diverge significantly concerning the range of cases in which this problem becomes acute. Here I argue against Roush's further suggestion that the atomic hypothesis represents a case in which scientific ingenuity has enabled us to overcome the problem, showing how (...) her general strategy is undermined by evidence I have already offered in support of what I have called the 'problem of unconceived alternatives'. I then go on to show why her strategy will not generally (if ever) allow us to formulate and test exhaustive spaces of hypotheses in cases of fundamental scientific theorizing. (shrink)

While Maurice Merleau-Ponty thought that the natural sciences could offer partial explanations of the world, he maintained that they were incomplete and further understanding required an existential analysis or a study of the pre-theoretical and pre-reflective structures that are the conditions of the possibility of experience. He offered a series of arguments against both the possibility of the sciences explaining the world in general and their ability to explain the phenomenon of perception in particular.In his paper, "Merleau-Ponty's Phenomenological Critique of (...) Natural Science," Thomas Baldwin pushes back on both of these positions, arguing that Merleau-Ponty offered insufficient proof of his... (shrink)

The cell theory of Schleiden and Schwann is generalized to the effect that throughout the natural world, in physics, biology, and sociopsychology, there is a widespread phenomenon of the existence of organized cells, whose organization is usually protected by barriers. These barriers exist not only in space, but in time and even in other domains. These barriers typically not only protect the organization within the cell from external disturbance, but they actively participate in reducing the internal disorganization. It appears that (...) the quantum phase cell or its equivalent, the discrete quantum state, may be a physical analog of the organized biological cell. The sampling and ambiguity theorems of communication theory throw new light on phase cells. The quantum phase cell has both configuration and momentum elements, which are analogous respectively to the somatic elements in the cytoplasm of a cell and the genetic elements in the DNA. A biological cell or organism, a physical quantum state, and a human being as a sociopsychological entity each has a natural individuality. A natural individuality is a somewhat mysterious thing, since in addition to specificity, it also involves stochasticity and complementarity. There are some striking and unexplained spin-analog characteristics in biology which have a relation to boson- and fermion-analog characteristics in biology that corresponds with the known relation in physics. The hypothesis suggested in our earlier paper, that quantum mechanical entropy is diminished in interaction, is clarified and sharpened in this paper. (shrink)

We present a theoretical and an empirical challenge to Cushman's claim that rationalization is adaptive because it allows humans to extract more accurate beliefs from our non-rational motivations for behavior. Rationalization sometimes generates more adaptive decisions by making our beliefs about the world less accurate. We suggest that the most important adaptive advantage of rationalization is instead that it increases our predictability as potential partners in cooperative social interactions.

Evidence is presented to support the hypothesis that there is a set of basically similar phenomena or characteristics of physics, biology, and sociology. Six of these are identified. Five of them are usually associated with quantum mechanics. They are the existence of eigenstates, transform domains, bosons and fermions, particles and antiparticles, and complementarity. The sixth, namely alternation of generation, is usually associated with biology. The hypothesis leads to some new points of view and interpretations in biology, sociology, and physics.