[Michael Friedman] This paper considers the extent to which Kant's vision of a distinctively 'transcendental' task for philosophy is essentially tied to his views on the foundations of the mathematical and physical sciences. Contemporary philosophers with broadly Kantian sympathies have attempted to reinterpret his project so as to isolate a more general philosophical core not so closely tied to the details of now outmoded mathematical-physical theories (Euclidean geometry and Newtonian physics). I consider two such attempts, those of Strawson and (...) McDowell, and argue that they fundamentally distort the original Kantian impulse. I then consider Buchdahl's attempt to preserve the link between Kantian philosophy and the sciences while simultaneously generalizing Kant's doctrines in light of later scientific developments. I argue that Buchdahl's view, while not adequate as in interpretation of Kant in his own eighteenth century context, is nonetheless suggestive of an historicized and relativized revision of Kantianism that can do justice to both Kant's original philosophical impulse and the radical changes in the sciences that have occurred since Kant's day. /// [Graham Bird] Michael Friedman criticises some recent accounts of Kant which 'detach' his transcendental principles from the sciences, and do so in order to evade naturalism. I argue that Friedman's rejection of that 'detachment' is ambiguous. In its strong form, which I claim Kant rejects, the principles of Euclidean geometry and Newtonian physics are represented as transcendental principles. In its weak form, which I believe Kant accepts, it treats those latter principles as higher order conditions of the possibility of both science and ordinary experience. I argue also that the appeal to naturalism is unhelpful because that doctrine is seriously unclear, and because the accounts Friedman criticises are open to objections independent of any appeal to naturalism. (shrink)
Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.
Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.
It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never a real problem.
Abstract In this paper I undertake an in-depth examination of an oft mentioned but rarely expounded upon state: suspended judgment. While traditional epistemology is sometimes characterized as presenting a “yes or no” picture of its central attitudes, in fact many of these epistemologists want to say that there is a third option: subjects can also suspend judgment. Discussions of suspension are mostly brief and have been less than clear on a number of issues, in particular whether this third option should (...) be thought of as an attitude or not. In this paper I argue that suspended judgment is (or at least involves) a genuine attitude. Content Type Journal Article Pages 1-17 DOI 10.1007/s11098-011-9753-y Authors Jane Friedman, St Catherine’s College, University of Oxford, Oxford, OX1 3UJ UK Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (shrink)
In this collection of essays one of the preeminent philosophers of science writing today offers a reinterpretation of the enduring significance of logical positivism, the revolutionary philosophical movement centered around the Vienna Circle in the 1920s and '30s. Michael Friedman argues that the logical positivists were radicals not by presenting a new version of empiricism (as is often thought to be the case) but rather by offering a new conception of a priori knowledge and its role in empirical knowledge. (...) This collection will be mandatory reading for any philosopher or historian of science interested in the history of logical positivism in particular or the evolution of modern philosophy in general. (shrink)
In this new book, Michael Friedman argues that Kant's continuing efforts to find a metaphysics that could provide a foundation for the sciences is of the utmost ...
Women have historically been prevented from living autonomously by systematic injustice, subordination, and oppression. The lingering effects of these practices have prompted many feminists to view autonomy with suspicion. Here, Marilyn Friedman defends the ideal of feminist autonomy. In her eyes, behavior is autonomous if it accords with the wants, cares, values, or commitments that the actor has reaffirmed and is able to sustain in the face of opposition. By her account, autonomy is socially grounded yet also individualizing and (...) sometimes socially disruptive, qualities that can be ultimately advantageous for women. Friedman applies the concept of autonomy to domains of special interest to women. She defends the importance of autonomy in romantic love, considers how social institutions should respond to women who choose to remain in abusive relationships, and argues that liberal societies should tolerate minority cultural practices that violate women's rights so long as the women in question have chosen autonomously to live according to those practices. (shrink)
This paper raises some minor questions about Lisa Tessman’s book, Burdened Virtues. Friedman’s questions pertain, among other things, to the adequacy of a virtue ethical focus on character, the apparent implication of virtue ethics that oppressors suffer damaged characters and are not any better off than the oppressed, the importance of whether privileged persons may have earned their privileges, and the oppositional anger that movement feminists sometimes direct against each other.
: Nancy J. Hirschmann presents a feminist, social constructionist account of women's freedom. Friedman's discussion of Hirschmann's account deals with (1) some conceptual problems facing a thoroughgoing social constructionism; (2) three ways to modify social constructionism to avoid those problems; and (3) an assessment of Hirschmann's version of social constructionism in light of the previous discussion.
Michael Friedman's book develops a new and complete reading of this work and reconstructs Kant's main argument clearly and in great detail, explaining its relationship to both Newton's Principia and eighteenth-century scientific thinkers ...
Economist and evolutionary game theorist Daniel Friedman demonstrates that our moral codes and our market systems-while often in conflict-are really devices evolved to achieve similar ends, and that society functions best when morals and markets are in balance with each other.
Both realists and instrumentalists have found it difficult to understand (much less accept) Carnap’s developed view on theoretical terms, which attempts to stake out a neutral position between realism and instrumentalism. I argue that Carnap’s mature conception of a scientific theory as the conjunction of its Ramsey sentence and Carnap sentence can indeed achieve this neutral position. To see this, however, we need to see why the Newman problem raised in the context of recent work on structural realism is no (...) problem for Carnap’s conception; and we also need to locate Carnap’s work on theoretical terms within his wider program of Wissenschaftslogik or the logic of science. (shrink)
This paper considers the evolution of the problem of scientific rationality from Kant through Carnap to Kuhn. I argue for a relativized and historicized version of the original Kantian conception of scientific a priori principles and examine the way in which these principles change and develop across revolutionary paradigm shifts. The distinctively philosophical enterprise of reflecting upon and contextualizing such principles is then seen to play a key role in making possible rational intersubjective communication between otherwise incommensurable paradigms.
There has been much discussion about whether traditional epistemology's doxastic attitudes are reducible to degrees of belief. In this paper I argue that what I call the Straightforward Reduction - the reduction of all three of believing p, disbelieving p, and suspending judgment about p, ~p to precise degrees of belief for p, ~p that ought to obey the standard axioms of the probability calculus - cannot succeed. By focusing on suspension of judgment (agnosticism) rather than belief, we can see (...) why the Straightforward Reduction is bound to fail. I argue that, in general, suspending about p is not just a matter of having some specified standard credence for p, and in the end I suggest some ways to extend the arguments that will put pressure on other credence-theoretic accounts of belief and suspension of judgment as well. (shrink)
The logical positivists adopted Poincare's doctrine of the conventionality of geometry and made it a key part of their philosophical interpretation of relativity theory. I argue, however, that the positivists deeply misunderstood Poincare's doctrine. For Poincare's own conception was based on the group-theoretical picture of geometry expressed in the Helmholtz-Lie solution of the space problem, and also on a hierarchical picture of the sciences according to which geometry must be presupposed be any properly physical theory. But both of this pictures (...) are entirely incompatible with the radically new conception of space and geometry articulated in the general theory of relativity. The logical positivists's attempt to combine Poincare's conventionalism with Einstein's new theory was therefore, in the end, simply incoherent. Underlying this problem, moreover, was a fundamental philosophical difference between Poincare's and the positivists concerning the status of synthetic a priori truths. (shrink)
Skeptical problems arising for Kant's version of transcendental idealism have been raised from Kant's own time to the present day. By focussing on how such problems originally arose in the wake of Kant's work, and on the first formulations of absolute idealism by Schelling, I argue that the skeptical problems in question ultimately depend on fundamental features of Kant's philosophy of natural science. As a result, Naturphilosophie and the organic conception of nature cannot easily be separated from the deep and (...) insightful response to these problems offered by absolute idealism. (shrink)
I use recent work on Kant and diagrammatic reasoning to develop a reconsideration of central aspects of Kant’s philosophy of geometry and its relation to spatial intuition. In particular, I reconsider in this light the relations between geometrical concepts and their schemata, and the relationship between pure and empirical intuition. I argue that diagrammatic interpretations of Kant’s theory of geometrical intuition can, at best, capture only part of what Kant’s conception involves and that, for example, they cannot explain why Kant (...) takes geometrical constructions in the style of Euclid to provide us with an a priori framework for physical space. I attempt, along the way, to shed new light on the relationship between Kant’s theory of space and the debate between Newton and Leibniz to which he was reacting, and also on the role of geometry and spatial intuition in the transcendental deduction of the categories. (shrink)
Carl Hempel introduced what he called "Craig's theorem" into the philosophy of science in a famous discussion of the "problem of theoretical terms." Beginning with Hempel's use of 'Craig's theorem," I shall bring out some of the key differences between Hempel's treatment of the "problem of theoretical terms" and Carnap's in order to illuminate the peculiar function of Wissenschaftslogik in Carnap's mature philosophy. Carnap's treatment, in particular, is fundamentally antimetaphysical—he aims to use the tools of mathematical logic to dissolve rather (...) solve traditional philosophical problems—and it is precisely this point that is missed by his logically-minded contemporaries such as Hempel and Quine. (shrink)
Modal Platonism utilizes “weak” logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them.
What I call the dynamics of reason is a post-Kuhnian approach to the history and philosophy of science articulating a relativized and historicized version of the Kantian conception of the rationality and objectivity of the modern physical sciences. I here discuss two extensions of this approach. I argue that, although the relativized standards of rationality in question change over time, the particular way in which they do this still preserves the trans-historical rationality of the entire process. I also make a (...) beginning in extending my historical narrative from purely intellectual history (both philosophical and scientific) to the wider cultural context. (shrink)
Because it consists of an entire family of specific theories derived from the same first principles, rational choice offers one approach to generate explanations that provide for micro-macro links, and to attack a wide variety of empirical problems in macrosociology. The aims of this paper are (1) to provide a bare skeleton of all rational choice arguments; (2) to demonstrate their applicability to a range of macrosociological concerns by reviewing a sample of both new and classic works; and (3) to (...) discuss the weaknesses of current rational choice theory and the possibilities for its future development. (shrink)
Informal statements of Gödel's Second Incompleteness Theorem, referred to here as Informal Second Incompleteness, are simple and dramatic. However, current versions of Formal Second Incompleteness are complicated and awkward. We present new versions of Formal Second Incompleteness that are simple, and informally imply Informal Second Incompleteness. These results rest on the isolation of simple formal properties shared by consistency statements. Here we do not address any issues concerning proofs of Second Incompleteness.
We introduce insertion domains that support the placement of new, higher, vertices into finite trees. We prove that every nonincreasing insertion domain has an element with simple structural properties in the style of classical Ramsey theory. This result is proved using standard large cardinal axioms that go well beyond the usual axioms for mathematics. We also establish that this result cannot be proved without these large cardinal axioms. We also introduce insertion rules that specify the placement of new, higher, vertices (...) into finite trees. We prove that every insertion rule greedily generates a tree with these same structural properties; and every decreasing insertion rule generates (or admits) a tree with these same structural properties. It is also necessary and sufficient to use the same large cardinals (in the precise sense of Corollary D.25). The results suggest new areas of research in discrete mathematics called "Ramsey tree theory" and "greedy Ramsey theory" which demonstrably require more than the usual axioms for mathematics. (shrink)
The notion of interpretation is absolutely fundamental to mathematical logic and the foundations of mathematics. It is also crucial for the foundations and philosophy of science - although here some crucial conditions generally need to be imposed; e.g., “the interpretation leaves the mathematical concepts unchanged”.
A four dimensional approach to Newtonian physics is used to distinguish between a number of different structures for Newtonian space-time and a number of different formulations of Newtonian gravitational theory. This in turn makes possible an in-depth study of the meaning and status of Newton's Law of Inertia and a detailed comparison of the Newtonian and Einsteinian versions of the Law of Inertia and the Newtonian and Einsteinian treatments of gravitational forces. Various claims about the status of Newton's Law of (...) Inertia are critically examined including these: the Law of Inertia is not an empirical law but a definition; it is not a law simpliciter but a family of schemata; it is a convention and gravitational forces exist only by convention; it is (or is not) redundant; the concepts it embodies can be dispensed with in favor of operationally defined entities; it is unique for a given theory. More generally, the paper demonstrates the importance of space-time structure for the philosophy of space and time and provides support for a realist interpretation of space-time theories. (shrink)
Immanuel Kant's Metaphysical Foundations of Natural Science (1786) provides metaphysical foundations for the application of mathematics to empirically given nature. The application that Kant primarily has in mind is that achieved in Isaac Newton's Principia (1687). Thus, Kant's first chapter, the Phoronomy, concerns the mathematization of speed or velocity, and his fourth chapter, the Phenomenology, concerns the empirical application of the Newtonian notions of true or absolute space, time, and motion. This paper concentrates on Kant's second and third chapters—the Dynamics (...) and the Mechanics, respectively—and argues that they are best read as providing a transcendental explanation of the conditions for the possibility of applying the (mathematical) concept of quantity of matter to experience. Kant again has in mind the empirical measures of this quantity that Newton fashions in the Principia, and he aims to make clear, in particular, how Newton achieves a universal measure for all bodies whatsoever by projecting the static quantity of terrestrial weight into the heavens by means of the theory of universal gravitation. Kant is not attempting to prove a priori what Newton has established empirically but, rather, to clarify the character of Newton's mathematization by building Newton's empirical measures into the very concept of matter that is articulated in the Metaphysical Foundations. (shrink)
This book is the first in-depth study of the concepts of agency and structure in the context of international relations and politics. It is an important contribution, examing the ways in which explanations of social phenomenon integrate and account for the interrelationship between agency and structure.
The sensible response to conflicts of interest is impaired by misconceptions and sloppy usage of terminology. Apparent and potential are widely misused modifiers for conflicts. Excessive legislative focus on financial interests limits understanding of the scope and significance of researchers' conflicts of interest. There is no moral or ethical failing in having a conflict of interest; the problem occurs when conflicts are not disclosed appropriately and when conflicts are allowed to bias research, teaching, or practice. Avoidance and prevention should be (...) applied to bias, not conflicts. (shrink)
In the Foundational Life, philosophy is commonly used as a method for choosing and analyzing fundamental concepts, and mathematics is commonly used for rigorous development. The mathematics informs the philosophy and the philosophy informs the mathematics.
Part of the ambiguity lies in the various points of view from which this question might be considered. The crudest di erence lies between the point of view of the working mathematician and that of the logician concerned with the foundations of mathematics. Now some of my fellow mathematical logicians might protest this distinction, since they consider themselves to be just more of those \working mathematicians". Certainly, modern logic has established itself as a very respectable branch of mathematics, and there (...) are quite a few highly technical journals in logic, such as The Journal of Sym-. (shrink)
Feminist ethics supports the contemporary educational trend toward increased multiculturalism and a diminished emphasis on the Western canon. First, I outline a feminist ethical justification for this development. Second, I argue that Western canon studies should not be altogether abandoned in a multicultural curriculum. Third, I suggest that multicultural education should help combat oppression in addition to simply promoting awareness of diversity. Fourth, I caution against an arrogant moralism in the teaching of multiculturalism.
How do people decide which claims should be considered mere beliefs and which count as knowledge? Although little is known about how people attribute knowledge to others, philosophical debate about the nature of knowledge may provide a starting point. Traditionally, a belief that is both true and justified was thought to constitute knowledge. However, philosophers now agree that this account is inadequate, due largely to a class of counterexamples (termed ‘‘Gettier cases’’) in which a person’s justified belief is true, but (...) only due to luck. We report four experiments examining the effect of truth, justification, and ‘‘Gettiering’’ on people’s knowledge attributions. These experiments show that: (1) people attribute knowledge to others only when their beliefs are both true and justified; (2) in contrast to contemporary philosophers, people also attribute knowledge to others in Gettier situations; and (3) knowledge is not attributed in one class of Gettier cases, but only because the agent’s belief is based on ‘‘apparent’’ evidence. These findings suggest that the lay concept of knowledge is roughly consistent with the traditional account of knowledge as justified true belief, and also point to a major difference between the epistemic intuitions of laypeople and those of philosophers. (shrink)
In 1995 we gave a new simple principle of combinatorial set theory and showed that it implies the existence of a nontrivial elementary embedding from a rank into itself, and follows from the existence of a nontrivial elementary embedding from V into M, where M contains the rank at the first fixed point above the critical point. We then gave a “diamondization” of this principle, and proved its relative consistency by means of a standard forcing argument.
Introduction STEN EBBESEN In the second half of the 20th century scholarly research uncovered a wealth of interesting medieval discussions about issues ...
Mathematical Logic had a glorious period in the 1930s, which was briefly rekindled in the 1960s. Any Shock Value, such as it is, has surrounded unprovability from ZFC.
An extreme kind of logic skeptic claims that "the present formal systems used for the foundations of mathematics are artificially strong, thereby causing unnecessary headaches such as the Gödel incompleteness phenomena". The skeptic continues by claiming that "logician's systems always contain overly general assertions, and/or assertions about overly general notions, that are not used in any significant way in normal mathematics. For example, induction for all statements, or even all statements of certain restricted forms, is far too general - mathematicians (...) only use induction for natural statements that actually arise. If logicians would tailor their formal systems to conform to the naturalness of normal mathematics, then various logical difficulties would disappear, and the story of the foundations of mathematics would look radically different than it does today. In particular, it should be possible to give a convincing model of actual mathematical practice that can be proved to be free of contradiction using methods that lie within what Hilbert had in mind in connection with his program”. Here we present some specific results in the direction of refuting this point of view, and introduce the Strict Reverse Mathematics (SRM) program. (shrink)
In Aristotle's biological works, there is an apparent conflict between passages which seem to insist that only hypothetical necessity (anagk ex hypotheses) operates in the sublunary world, and passages in which some biological phenomena are explained as simply (hapls) necessary. Parallel to this textual problem lies the claim that explanations in terms of simple necessity render teleological explanations (in some of which Aristotle puts hypothetical necessity to use) superfluous. I argue that the textual conflict is only apparent, and that Aristotle's (...) notion of coincidental sameness allows him to avoid the superfluity problem. (shrink)
Whether refusal is an act of civil disobedience meant to challenge the state politically as a form of protest, or an action which reflects a deep moral objection to the policies of the state, selective conscientious objection presents the state and its citizens with a number of difficult legal and moral challenges. Appeals to authority outside of the state, whether religious or secular, influence both citizenship and the behavior of the government itself. As Israel raises funds to defend IDF officers (...) from charges of human rights violations in the United Kingdom, it may find itself in need of a better defense against those citizens hesitant to be placed in harm's way, militarily and legally. At some point in the future it may find itself unable to field soldiers for whom service in the Occupied Territories is prohibited by inviolable secular or religious law. And for those who will continue to argue that they cannot abide service in an army of occupation, an expression sounded in 1968 by Yeshayahu Leibowitz, the moral crisis of an individual conscience rent between obligations to the state and obligations to self, will linger along with the pain of a conscience nurtured and then rejected by this democratic society. (shrink)
Normal mathematical culture is overwhelmingly concerned with finite structures, finitely generated structures, discrete structures (countably infinite), continuous and piecewise continuous functions between complete separable metric spaces, with lesser consideration of pointwise limits of sequences of such functions, and Borel measurable functions between complete separable metric spaces.
: Beginning with Emerson's turn from his pulpit, many argue that American philosophy has rigorously held forth against supernaturalism and metaphysics. While most read self-reliance as a call for individualism, I argue that self-reliance is the application of the moral sentiment to the source of existence Emerson calls the Over-soul. Figures like George Kateb, Stanley Cavell, and Jeffrey Stout have presented a very different picture of American pragmatism. Stout, in particular, is responsible for building up what I call "the myth (...) of the Emersonian democrat." We find that a few philosophical positions generally constitute this myth. The Emersonian democrat is secular, sceptical, relativist, anti-realist, and anti-metaphysical. In fact, on my reading of the strand of pragmatism running from Emerson through James to Dewey, the pluralism of the Emersonian democrat depends on certain metaphysical commitments. The traditional reading of Emerson as anti-religion, and by extension, anti-religious, impedes a better understanding of self-reliance and obfuscates some of the Emersonian inheritances in James and Dewey. (shrink)
This paper explores the relationship between Kant's views on the metaphysical foundations of Newtonian mathematical physics and his more general transcendental philosophy articulated in the Critique of pure reason. I argue that the relationship between the two positions is very close indeed and, in particular, that taking this relationship seriously can shed new light on the structure of the transcendental deduction of the categories as expounded in the second edition of the Critique.
The space CS(R) has a unique “Borel structure” in the following sense. Note that there is a natural mapping from R¥ onto CS(R}; namely, taking ranges. We can combine this with any Borel bijection from R onto R¥ in order to get a “preferred” surjection F:R ® CS(R).
