In the year of our Lord 1862, Polish painter Jan Matejko finished his first famous work, Stańczyk, fully translated into English as “Stańczyk during a ball at the court of Queen Bona in the face of the loss of Smolensk.”1 The piece was painted in oils and depicts a famous political figure of Renaissance Poland, Stańczyk the court jester. Stańczyk, an influential figure of Polish history who was as much a political philosopher as a funny man, is depicted in this (...) scene sitting alone and apoplectic as a royal party rages on just outside his door. As the illustration implies, he and the partygoers have just received some correspondence that declares the Polish territory of Smolensk has been besieged, and, appallingly.. (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)

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)

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)

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).

The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical (...) philosophy, and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant. (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.

The teaching of ethics in science within the disciplines provides an avenue to deepen students’ scientific understanding and to develop their critical thinking skills. This study showcases a module which connects ethics to science within a large introductory geoscience course. The module components, a tutorial plus homework assignment and an exam question, require students to decide on ethical issues using a 5-step approach that mirrors the scientific decision-making process. The assignment is graded using a developed rubric. An analysis of exam (...) question responses reveals that students correctly identify stakeholders and mention contributions by geoscientists, but have difficulties recognizing their own assumptions. Furthermore, many acknowledge the complexity of the ethical issue at hand. The module provides an example of how disciplinary instructors can include ethics in their teaching and assess students’ ethical decision-making process. (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.

Zhuangzi and Henry David Thoreau share a critical interest in the relations between wandering, nature, and experience. Their attitudes toward nature provide a basis for their views of human well-being, which in turn inform their attitudes toward language, society, and politics. Both celebrate nature as a source of constant novelty, change, and nourishing life. These values clash against social conformity and political homogeneity. For both Zhuangzi and Thoreau, how we experience life is already constitutive of human well-being. Wandering thus provides (...) a unique vision of freedom, one that binds experience, nature, and social-political criticism. (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)