This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and significance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the nonalgebraizable fragments of relevance logic are considered.

This paper develops an order-theoretic generalization of Blok and Pigozziʼs notion of an algebraizable logic. Unavoidably, the ordered model class of a logic, when it exists, is not unique. For uniqueness, the definition must be relativized, either syntactically or semantically. In sentential systems, for instance, the order algebraization process may be required to respect a given but arbitrary polarity on the signature. With every deductive filter of an algebra of the pertinent type, the polarity associates a reflexive and transitive relation (...) called a Leibniz order, analogous to the Leibniz congruence of abstract algebraic logic . Some core results of AAL are extended here to sentential systems with a polarity. In particular, such a system is order algebraizable if the Leibniz order operator has the following four independent properties: it is injective, it is isotonic, it commutes with the inverse image operator of any algebraic homomorphism, and it produces anti-symmetric orders when applied to filters that define reduced matrix models. Conversely, if a sentential system is order algebraizable in some way, then the order algebraization process naturally induces a polarity for which the Leibniz order operator has properties –. (shrink)

A quasivariety of algebras has the joint embedding property (JEP) if and only if it is generated by a single algebra A. It is structurally complete if and only if the free ℵ0‐generated algebra in can serve as A. A consequence of this demand, called ‘passive structural completeness’ (PSC), is that the nontrivial members of all satisfy the same existential positive sentences. We prove that if is PSC then it still has the JEP, and if it has the JEP and (...) its nontrivial members lack trivial subalgebras, then its relatively simple members all belong to the universal class generated by one of them. Under these conditions, if is relatively semisimple then it is generated by one ‐simple algebra. We also prove that a quasivariety of finite type, with a finite nontrivial member, is PSC if and only if its nontrivial members have a common retract. The theory is then applied to the variety of De Morgan monoids, where we isolate the sub(quasi)varieties that are PSC and those that have the JEP, while throwing fresh light on those that are structurally complete. The results illuminate the extension lattices of intuitionistic and relevance logics. (shrink)

Two constructions for adding an involution operator to residuated ordered monoids are investigated. One preserves integrality and the mingle axiom x 2x but fails to preserve the contraction property xx 2. The other has the opposite preservation properties. Both constructions preserve commutativity as well as existent nonempty meets and joins and self-dual order properties. Used in conjunction with either construction, a result of R.T. Brady can be seen to show that the equational theory of commutative distributive residuated lattices (without involution) (...) is decidable, settling a question implicitly posed by P. Jipsen and C. Tsinakis. The corresponding logical result is the (theorem-) decidability of the negation-free axioms and rules of the logic RW, formulated with fusion and the Ackermann constant t. This completes a result of S. Giambrone whose proof relied on the absence of t. (shrink)

This paper establishes several algebraic embedding theorems, each of which asserts that a certain kind of residuated structure can be embedded into a richer one. In almost all cases, the original structure has a compatible involution, which must be preserved by the embedding. The results, in conjunction with previous findings, yield separative axiomatizations of the deducibility relations of various substructural formal systems having double negation and contraposition axioms. The separation theorems go somewhat further than earlier ones in the literature, which (...) either treated fewer subsignatures or focussed on the conservation of theorems only. (shrink)

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMImin has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMImin is decidable.

For (finitary) deductive systems, we formulate a signature‐independent abstraction of the weak excluded middle law (WEML), which strengthens the existing general notion of an inconsistency lemma (IL). Of special interest is the case where a quasivariety algebraizes a deductive system ⊢. We prove that, in this case, if ⊢ has a WEML (in the general sense) then every relatively subdirectly irreducible member of has a greatest proper ‐congruence; the converse holds if ⊢ has an inconsistency lemma. The result extends, in (...) a suitable form, to all protoalgebraic logics. A super‐intuitionistic logic possesses a WEML iff it extends. We characterize the IL and the WEML for normal modal logics and for relevance logics. A normal extension of has a global consequence relation with a WEML iff it extends, while every axiomatic extension of with an IL has a WEML. (shrink)

A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR+ and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices.

Relatively congruence regular quasivarieties and quasivarieties of logic have noticeable similarities. The paper provides a unifying framework for them which extends the Blok-Pigozzi theory of elementarily algebraizable (and protoalgebraic) deductive systems. In this extension there are two parameters: a set of terms and a variable. When the former is empty or consists of theorems, the Blok-Pigozzi theory is recovered, and the variable is redundant. On the other hand, a class of ‘membership logics’ is obtained when the variable is the only (...) element of the set of terms. For these systems the appropriate variant of equivalent algebraic semantics encompasses the relatively congruence regular quasivarieties. (shrink)

Before military action, and even before mobilization, the decision on whether to go to war is debated by politicians, pundits, and the public. As they address the right or wrong of such action, it is also a time when, in the language of the just war tradition, the wise would deeply investigate their true claim to jus ad bellum (“the right of war”). Wars have negative consequences, not the least impinging on human life, and offer infrequent and uncertain benefits, yet (...) war is part of the human condition. James G. Murphy’s insightful analysis of the jus ad bellum criteria—competent authority, just cause, right intention, probability of success, last resort, and proportionality—is grounded in a variety of contemporary examples from World War I through Vietnam, the "soccer war" between Honduras and El Salvador, Afghanistan, and the Middle East conflict. Murphy argues persuasively that understanding jus ad bellum requires a primary focus on the international common good and the good of peace. Only secondarily should the argument about going to war hinge on the right of self-defense; in fact, pursuing the common good requires political action, given that peace is not simply the absence of violence. He moves on to demonstrate the interconnectedness of the jus ad bellum criteria, contending that some criteria depend logically on others—and that competent authority, not just cause, is ultimately the most significant criterion in an analysis of going to war. This timely study will be of special interest to scholars and students in ethics, war and peace, and international affairs. (shrink)

This book offers a thought-provoking examination of the state of contemporary anthropology, identifying key issues that have confronted the discipline in recent years and linking them to neoliberalism. The volume explores the effect of the economic crisis on funding and support for higher education, and addresses the sense that anthropology has 'lost its way', with uncertainty over the purpose and future of the discipline. Carrier considers how anthropology has come to resemble key elements of neoliberalism and neoclassical economics in rejecting (...) the idea of system in favour of individuals. He also suggests how the discipline can overcome its difficulties and place itself on a firmer foundation. (shrink)

This chapter contains section titled: Introduction Darwin's Life Darwin's Darwinism Philosophical Problems with Darwin's Darwinism The Core Problems and Darwinism Conclusion References Further Reading.

It was Ayn Rand's conviction that philosophy is a life and death matter, both for individuals and cultures. She was not a historian of philosophy, but a philosopher deeply interested in its history. This chapter discusses the approach Rand took in her exploration of the history of philosophy, and later in writing about that history. This provides us with the needed framework for looking at a number of distinctive conclusions she derives from her study of the history of philosophy, which (...) lead her to reject some of the standard ways of unifying and distinguishing “schools” of philosophy and locating figures within these schools. Finally, with that background as context, the chapter deals with her provocative claims about the place of Aristotle and Immanuel Kant in the history of philosophy and culture generally. (shrink)

In addition to being one of the world's most influential philosophers, Aristotle can also be credited with the creation of both the science of biology and the philosophy of biology. He was the first thinker to treat the investigations of the living world as a distinct inquiry with its own special concepts and principles. This book focuses on a seminal event in the history of biology - Aristotle's delineation of a special branch of theoretical knowledge devoted to the systematic investigation (...) of animals. Aristotle approached the creation of zoology with the tools of subtle and systematic philosophies of nature and of science that were then carefully tailored to the investigation of animals. The papers collected in this volume, written by a pre-eminent figure in the field of Aristotle's philosophy and biology, examine Aristotle's approach to biological inquiry and explanation, his concepts of matter, form and kind, and his teleology. (shrink)

It is often claimed that one of Darwin''s chief accomplishments was to provide biology with a non-teleological explanation of adaptation. A number of Darwin''s closest associates, however, and Darwin himself, did not see it that way. In order to assess whether Darwin''s version of evolutionary theory does or does not employ teleological explanation, two of his botanical studies are examined. The result of this examination is that Darwin sees selection explanations of adaptations as teleological explanations. The confusion in the nineteenth (...) century about Darwin''s attitude to teleology is argued to be a result of Darwin''s teleological explanations not conforming to either of the dominant philosophical justifications of teleology at that time. Darwin''s explanatory practices conform well, however, to recent defenses of the teleological character of selection explanations. (shrink)

Stuart Glennan, and the team of Peter Machamer, Lindley Darden, and Carl Craver have recently provided two accounts of the concept of a mechanism. The main difference between these two versions rests on how the behavior of the parts of the mechanism is conceptualized. Glennan considers mechanisms to be an interaction of parts, where the interaction between parts can be characterized by direct, invariant, change-relating generalizations. Machamer, Darden, and Craver criticize traditional conceptualizations of mechanisms which are based solely on parts (...) interacting and introduce a new conceptactivity. This essay is an attempt at carving out a relationship between these two philosophical interpretations of a mechanism. I will claim that, rather than being in conflict, Glennan's concept of interaction and Machamer, Darden, and Craver's notion of activity actually complement one another, each emphasizing a missing element of the other. (shrink)

Aristotle is a rarity in the history of philosophy and science - he is a towering figure in the history of both disciplines. Moreover, he devoted a great deal of philosophical attention to the nature of scientific knowledge. How then do his philosophical reflections on scientific knowledge impact his actual scientific inquiries? In this book James Lennox sets out to answer this question. He argues that Aristotle has a richly normative view of scientific inquiry, and that those norms are (...) of two kinds: a general, question-guided framework applicable to all scientific inquiries, and domain-specific norms reflecting differences in the target of inquiry and in the means of observation available to researchers. To see these norms of inquiry in action, the second half of this book examines Aristotle's investigations of animals, the soul, material compounds, the motions of heavenly bodies, and respiration. (shrink)

Variants on two approaches to the concept of health have dominated the philosophy of medicine, here referred to as ‘reductionist’ and ‘relativis’. These two approaches share the basic assumption that the concept of health cannot be both based on an empirical biological foundation and be evaluative, and thus adopt either the view that it is ‘objective’ or evaluative. It is here argued that there are a subset of value concepts that are formed in recognition of certain fundamental facts about living (...) organisms, among which is the concept of health. These are not yet moral concepts, but they are ‘normative’ or ‘evaluative’. The view is defended that health, so understood, is a fundamental concept in the process of medical diagnosis and treatment. Keywords: health, value, objectivity, function CiteULike Connotea Del.icio.us What's this? (shrink)

In this article I defend an account of Meteorology IV as providing a material-level causal account of the emergence of uniform materials with a wide range of dispositional properties not found at the level of the four elements—the emergence of material complexity. I then demonstrate that this causal account is used in the Generation of Animals and Parts of Animals as part of the explanation of the generation of the uniform parts (tissues) and of their role in providing nonuniform parts (...) (organs) with the dispositional properties needed to fulfill their functions. (shrink)

Kuhn closed the Introduction to The Structure of Scientific Revolutions with what was clearly intended as a rhetorical question: How could history of science fail to be a source of phenomena to which theories about knowledge may legitimately be asked to apply? (Kuhn 1970, 9) This paper argues that there is a more fruitful way of conceiving the relationship between a historical and philosophical study of science, which is dubbed the 'phylogenetic' approach. I sketch an example of this approach, and (...) take a first pass at an abstract characterization of the method. (shrink)

Perhaps the greatest determinant of individual and societal welfare is who raises children and with what degree of discretion. Philosophers have endeavored in myriad ways to provide normative justification for ascribing a right to be a legal parent and to possess particular legal powers as a parent. This Article shows why they fail and offers an alternative theoretical framework for delimiting parental rights. The prevailing tendency in philosophical writing on the topic is to begin with observations and intuitions specific to (...) parent-child relationships. Against that tendency, this Article demonstrates the need to begin with principles at a high level of generality, covering a broad range of human relationships. This yields a much more limited moral right in connection with parenthood than do accounts that fail to generalize. (shrink)

This essay outlines one aspect of a larger collaboration with John Beatty and Alan Love.2 The project’s focus is philosophical, but for reasons that will become clear momentarily, the method of approach is historical. All three of us share the conviction that philosophical issues concerning the foundations of the sciences are often illuminated by investigating their history. It is my hope that this paper both provides support for that thesis, and illustrates it. The focal philosophical issue can be stated in (...) the form of a puzzle about contemporary discussions of the conceptual foundations of evolutionary theory. The role of the concepts of “chance” and “randomness” in that theory is a significant part of .. (shrink)

Where does Aristotle stand in the debate between rationalism and empiricism? The locus classicus on this question, Posterior Analytics II. 19, seems clearly empiricist. Yet many commentators have resisted this conclusion. Here, I review their arguments and conclude that they rest in part on expectations for this text that go unfulfilled. I argue that this is because his views about norms of empirical inquiry are in the rich methodological passages in his scientific treatises. In support of this claim, I explore (...) such passages in On Parts of Animals and De anima. I argue that they reach distinct, though complementary, conclusions about the norms governing zoological and psychological inquiries. (shrink)

The Renaissance was a period of great intellectual change and innovation as philosophers rediscovered the philosophy of classical antiquity and passed it on to the modern age. Renaissance philosophy is distinct both from the medieval scholasticism, based on revelation and authority, and from philosophers of the seventeenth and eighteenth centuries who transformed it into new philosophical systems. Despite the importance of the Renaissance to the development of philosophy over time, it has remained largely understudied by historians of philosophy and professional (...) philosophers. This anthology aims to correct this by providing scholars and students of philosophy with representative translations of the most important philosophers of the Renaissance. Its purpose is to help readers appreciate philosophy in the Renaissance and its importance in the history of philosophy. The anthology includes translations from philosophers from the thirteenth to the seventeenth centuries, and it ranges from works on moral and political philosophy, to metaphysics, epistemology, and natural philosophy, thereby providing historians and students of philosophy with a sense for the nature, breadth, and complexity of philosophy in the Renaissance. Each translation is accompanied by an introduction by a historian of Renaissance philosophy, as well as select secondary sources, in order to encourage further study. (shrink)

T. H. Huxley (1825-1895) was not only an active protagonist in the religious and scientific upheaval that followed the publication of Darwin's theory of evolution but also a harbinger of the sociobiological debates about the implications of evolution that are now going on. His seminal lecture Evolution and Ethics, reprinted here with its introductory Prolegomena, argues that the human psyche is at war with itself, that humans are alienated in a cosmos that has no special reference to their needs, and (...) that moral societies are of necessity in conflict with the natural conditions of their existence. Seen in the light of current understanding of the mechanisms of evolution, these claims remain as controversial today as they were when Huxley proposed them. In this volume George Williams, one of the best-known evolutionary biologists of our time, asserts that recent biological ideas and data justify a more extreme condemnation of the "cosmic process" than Huxley advocated and more extreme denial that the forces that got us here are capable of maintaining a viable world. James Paradis, an expert in Victorian studies, has written an introduction that sets the celebrated lecture in the context of cultural history, revealing it to be an impressive synthesis of Victorian thinking, as well as a challenge to eighteenth-century assumptions about the harmony of of nature. With Huxley's lecture as a focal point, the three parts of this book unite philosophy and science in a shared quest that recalls their common origins as systems of knowledge. Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

A necessary condition for having a revolution named after you is that you are an innovator in your field. I argue that if Charles Darwin meets this condition, it is as a philosopher and methodologist. In 1991, I made the case for Darwin's innovative use of "thought experiment" in the "Origin." Here I place this innovative practice in the context of Darwin's methodological commitments, trace its origins back into Darwin's notebooks, and pursue Darwin's suggestion that it owes its inspiration to (...) Charles Lyell. (shrink)

Aristotle is without question the founder of the science of biology. In his treatise On the Parts of Animals, he develops his systematic principles for biological investigation, and explanation, and applies those principles to explain why the different animal kinds have the different parts that they do. It is one of the greatest achievements in the history of science. This new translation from the Greek aims to reflect the subtlety and detail of Aristotle's reasoning. The commentary provides help in understanding (...) each argument as well as an integrated account of the goals and methods of the work taken as a whole. (shrink)

In metaphysics and philosophy of science, a significant movement is making inroads, under the banner of ‘neo-Aristotelianism’. This movement has so far been focused primarily on the physical sciences; but given that Aristotle the natural scientist was above all a biologist, it is worth asking what a neo-Aristotelian philosophy of biology would look like? In this paper, I begin a discussion on precisely that question. One interesting result is that the fact that biology is now permeated by evolutionary ways of (...) thinking is all but irrelevant to answering that question. Far more important is how central are concepts of organic form, function and development to biology. Given recent developments, there are reasons to think at least some areas of the biological sciences would welcome a neo-Aristotelian philosophy of biology - i.e. a critical exploration of these concepts from an Aristotelian perspective. (shrink)

The main argument of this paper is that an evaluation of the overall explanatory power of a theory is less problematic and more relevant as an assessment of the state of knowledge than evaluation of statistical explanations of single occurrences in terms of likelihoods that are assigned to explananda.

Aristotle is without question the founder of the science of biology. In his treatise On the Parts of Animals, he develops his systematic principles for biological investigation, and explanation, and applies those principles to explain why the different animal kinds have the different parts that they do. It is one of the greatest achievements in the history of science. This new translation from the Greek aims to reflect the subtlety and detail of Aristotle's reasoning. The commentary provides help in understanding (...) each argument as well as an integrated account of the goals and methods of the work taken as a whole. (shrink)