It is well-known that feature structures can be fruitfully viewed as forming a Scott domain. Once a linguistically motivated notion of set value in feature structures is countenanced, however, this is no longer possible inasmuch as unification of set values in general fails to yield a unique result. In Pollard and Moshier 1990 it was shown that, while falling short of forming a Scott domain, the set of feature structures possibly containing set values satisfies the weaker condition of forming (...) a 2/3 SFP domain when equipped with an appropriate notion of subsumption: that is, for any finite setS of feature structures, there is a finite setM of minimal upper bounds ofS such that any upper bound ofS is approximated by a member ofM. Unfortunately, the 2/3 SFP domains are not as pleasant to work with as Scott domains since they are not closed under all the familiar domain constructions; and the question has remained open whether the feature structure domain satisfies the added condition of profiniteness. In this paper we resolve this question in the affirmative. (shrink)

Though my title speaks of Kant’s mathematical realism, I want in this essay to explore Kant’s relation to a famous mathematical anti-realist. Specifically, I want to discuss Kant’s influence on L. E. J. Brouwer, the 20th-century Dutch mathematician who built a contemporary philosophy of mathematics on constructivist themes which were quite explicitly Kantian. Brouwer’s theory is perhaps most notable for its belief that constructivism requires us to abandon the traditional logic of mathematical reasoning in favor of different canon of reasoning, (...) called intuitionistic logic. Brouwer thought that classical logic is intrinsically bound up with a nonconstructive view of mathematics. This means that, according to Brouwer, when we do mathematics we must give up bivalence, we must no longer use such familiar logical laws as excluded middle, and we must sometimes forebear from the classic method of reductio ad absurdum. All of these are intuitionistically invalid classical principles. (shrink)

Environmental governance has emerged as a recent perspective to explain the link between corporate governance mechanisms and environmental performance such as pollution reduction. We extend current models by incorporating the crucial role of the underlying institutional logics in terms of an a priori focus on either shareholder rights or stakeholder inclusion, which, in turn, can be traced back to the legal origin of a specific country. Using data on a sample of common and civil law countries, we find support for (...) our predictions that a shareholder-focused common law legal origin is associated with significantly higher emissions of CO2, and also that international environmental agreements like the Kyoto protocol seem to have a more pronounced effect in shareholder-centric economies than thus far assumed. (shrink)

Behavioral biologists have long sought to link behavioral units (e.g., aggression, depression, sociopathy) with biological units (e.g., genes, neurotransmitters, hormones, neuroanatomical loci). These units, originally contrived for descriptive purposes, often lead to misunderstandings when they are reified for purposes of causal analysis. This genetic and biochemical explanation for sociopathy reflects such problems.

volume 1. The critical philosophy and its roots.

“It has been our fate as a nation not to have ideologies,” Richard Hofstadter famously wrote, “but to be one.” Defining that “American ideology” or “American creed” obsessed scholars of the consensus era, who celebrated Americans’ allegiance to a limited liberal vocabulary of rights, freedoms, and markets. The cultural transformations begun in the 1960s seemed to question the very idea of a unitary culture or creed, but some historians responded by exploring alternative ideological founding myths to the liberal consensus. Over (...) the ensuing decades scholars mounted formidable efforts to support republicanism or millennial Christianity as challengers, but liberalism proved a resilient foe. And it seemed to have contemporary history on its side: during the Reagan revolution of the century's final decades the classic liberal combination of scaled-down government and free markets carried the day as Americans’ ideal if not their reality. The Lockean liberal tradition that Louis Hartz described a half-century earlier still appeared the only game in town, although scholars continued to argue over its terms, history, and boundaries. (shrink)

Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. (...) It also includes the most important recent work on Kant's philosophy of mathematics. The essays bring to bear a wealth of detailed Kantian scholarship, together with powerful new interpretative tools drawn from modern mathematics, logic and philosophy. The cumulative effect of this collection upon the reader will be a deeper understanding of the centrality of mathematics in all aspects of Kant's thought and a renewed respect for the power of Kant's thinking about mathematics. The essays contained in this volume will set the agenda for further work on Kant's philosophy of mathematics for some time to come. (shrink)

Benacerraf’s Problem about mathematical truth displays a tension, indeed a seemingly unbridgeable gap, between Platonist foundations for mathematics on the one hand and Hilbert’s ‘finitary standpoint’ on the other. While that standpoint evinces an admirable philosophical unity, it is ultimately an effete rival to Platonism: It leaves mathematical practice untouched, even the highly non-constructive axiom of choice. Brouwer’s intuitionism is a more potent finitist rival, for it engenders significant deviation from standard (classical) mathematics. The essay illustrates three sorts of intuitionistic (...) deviations (weakening, refinement and outright contradiction), and goes on to sketch the technical tools and arguments that engender those clashes with classical mathematics and the philosophical principles underlying those arguments. Those philosophical principles coalesce into a “standpoint” no less unified and no less finitary that Hilbert’s. This intuitionistic standpoint is sufficiently detailed that it itself provides a benchmark for comparing all the rival positions; and it is sufficiently robust that it dissolves the Benacerrafian dichotomy. However, the intuitionistic refutation of the axiom of choice reveals two distinct sub-streams within that intuitionistic standpoint. Distinguishing these streams suggests perhaps that in spite of that robustness, intuitionism has an internal dichotomy parallel to the Benacerrafian split. The Benacerrafian split is a crack in the foundations of mathematics. But I shall argue that this internal intuitionistic dichotomy is not at all a foundational gap; it is rather a special insight about the nature of mathematical thought. (shrink)

It is argued that the tensed theory of the creative subject provides a natural formulation of the logic underlying Brouwer's notion of unextendable order and explains the link between that notion and virtual order. The tensed theory of the creative subject is also shown to be a useful tool for interpreting recent evidence about the stages of Brouwer's thinking concerning these two notions of order.

L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation (...) for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth. (shrink)

An examination and evaluation of Hegel's most important works including The Philosophy of History, The Philosophy of Right and Law, and The Science of Logic.

The ArgumentL. E. J. Brouwer and David Hubert, two titans of twentieth-century mathematics, clashed dramatically in the 1920s. Though they were both Kantian constructivists, their notoriousGrundlagenstreitcentered on sharp differences about the foundations of mathematics: Brouwer was prepared to revise the content and methods of mathematics (his “Intuitionism” did just that radically), while Hilbert's Program was designed to preserve and constructively secure all of classical mathematics.Hilbert's interests and polemics at the time led to at least three misconstruals of intuitionism, misconstruals which (...) last to our own time: Current literature often portrays popular views of intuitionism as the product of Brouwer's idiosyncratic subjectivism; modern logicians view intuitionism as simply applying a non-standard formal logic to mathematics; and contemporary philosophers see that logic as based upon a pure assertabilist theory of meaning. These pictures stem from the way Hilbert structured the controversy.Even though Brouwer's own work and behavior occasionally reinforce these pictures, they are nevertheless inaccurate accounts of his approach to mathematics. However, the framework provided by the Brouwer-Hilbert debate itself does not supply an adequate correction of these inaccuracies. For, even if we eliminate these mistakes within that framework, Brouwer's position would still appear fragmented and internally inconsistent. I propose a Kantian framework — not from Kant's philosophy of mathematics but from his general metaphysics — which does show the coherence and consistency of Brouwer's views. I also suggest that expanding the context of the controversy in this way will illuminate Hilbert's views as well and will even shed light upon Kant's philosophy. (shrink)

The Battle for the American Mind brings together religion, politics, economics, science, and literature to present a compelling history of the American people. In this brief and entertaining book, noted historian Carl J. Richard argues that there have been three worldviews that have dominated American thought—theism, humanism, and skepticism. By clearly explaining what Americans believed, exploring why they did so, and showing how that impacted the nation's development, Richard presents a unique portrait of the United States—past and present.

Languishing in exile after Louis Napoleon's coup d'état of December 1851 shut down socialist agitation, the followers of the utopian theorist Charles Fourier turned their attention to the New World as an "asylum" where Fourierism's communal ideals might be realized. In so doing they joined a long line of utopian dreamers who saw the young United States as a promised land of free expression and social experimentation. The head of the French Fourierists, Victor Considerant, made contacts with the remnant of (...) the American Fourierist movement, toured the United States in 1853, and was thrilled by the vast open spaces of Texas. Considerant discounted the fate of another French socialist group, the disciples... (shrink)

IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).

MICHAEL DUMMETT, Elements of intuitionism. With the assistance of Robert Minio. Oxford: Oxford University Press, 1977. xii + 466 pp. No price stated.