This article compares the moral significance of two types of immigration, that which is based on the unification of citizens and non-citizens and that which is based on the skilled labor needs of the receiving society. I assess the interests of both citizens and non-citizens affected by each of these types of inflows and argue that unification admissions should be given priority over skilled workers but states retain a qualified moral permission to incentivize skilled worker migration.

Liberal societies typically prefer relatives and spouses of their members over other prospective immigrants seeking admission. Giving this preferential treatment to only certain categories of relationships requires justification. In this paper, I provide a defense of a category-based system for "unification admissions," non-members seeking admission for the purpose of living in the same society with members on a stable basis, that is compatible with liberalism and, in particular, does not violate the requirement of liberal neutrality. This defense does (...) not commit liberal theorists to the traditional state sovereignty view on immigration, according to which societies have wide latitude to exclude immigrants as they see fit, and shows that, contra Ferracioli, societies are not required to treat relatives, spouses, friends, and creative partners of their members on a par in matters of immigration policy. (shrink)

Liberal societies typically prefer relatives and spouses of their members over other prospective immigrants seeking admission. Giving this preferential treatment to only certain categories of relationships requires justification. In this paper, I provide a defense of a category-based system for “unification admissions,” non-members seeking admission for the purpose of living in the same society with members on a stable basis, that is compatible with liberalism and, in particular, does not violate the requirement of liberal neutrality. This defense does (...) not commit liberal theorists to the traditional state sovereignty view on immigration, according to which societies have wide latitude to exclude immigrants as they see fit, and shows that, contra Ferracioli, societies are not required to treat relatives, spouses, friends, and creative partners of their members on a par in matters of immigration policy. (shrink)

In this paper we study the admissible rules of intermediate logics. We establish some general results on extensions of models and sets of formulas. These general results are then employed to provide a basis for the admissible rules of the Gabbay–de Jongh logics and to show that these logics have finitary unification type.

We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking (...) just unifiability of formulas with coefficients also works via verification of admissibility. (shrink)

We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.

This paper contains a proof-theoretic account of unification in transitive reflexive modal logics, which means that the reasoning is syntactic and uses as little semantics as possible. New proofs of theorems on unification types are presented and these results are extended to negationless fragments. In particular, a syntactic proof of Ghilardi’s result that $\mathsf {S4}$ has finitary unification is provided. In this approach the relation between classical valuations, projective unifiers, and admissible rules is clarified.

This piece outlines an argument against recent changes in U.S. immigration policy that aim to give priority in admissions to skilled workers rather than family members seeking unification. I argue that democratic states have a moral obligation to admit individuals seeking unification with family members, rather than give priority to skilled workers.

We characterize all finitary consequence relations over S4.3, both syntactically, by exhibiting so-called passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic L extending S4 has projective unification if and only if L contains S4.3. In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the (...) known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relations over S4.3 is countable and distributive and it forms a Heyting algebra. (shrink)

This paper offers a brief analysis of the unification problem in modal transitive logics related to the logic S4 : S4 itself, K4, Grz and Gödel-Löb provability logic GL . As a result, new, but not the first, algorithms for the construction of ‘best’ unifiers in these logics are being proposed. The proposed algorithms are based on our earlier approach to solve in an algorithmic way the admissibility problem of inference rules for S4 and Grz . The first algorithms (...) for the construction of ‘best’ unifiers in the above mentioned logics have been given by S. Ghilardi in [ 16 ]. Both the algorithms in [ 16 ] and ours are not much computationally efficient. They have, however, an obvious significant theoretical value a portion of which seems to be the fact that they stem from two different methodological approaches. (shrink)

Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties (in logics) are exhibited. Consequently, RA and products of S5 as well as representable diagonal-free n-dimensional cylindric algebras, RDfn, are almost structurally complete but not structurally complete. In case of S5n a basis for admissible rules and the form of all passive rules are provided.

A term td is called a ternary deductive term for a variety of algebras V if the identity td≈r holds in V and ∈θ yields td≈td for any A∈V and any principal congruence θ on A. A connective f is called td-distributive if td)≈ f,…,td). If L is a propositional logic and V is a corresponding variety that has a TD term td, then any admissible in L rule, the premises of which contain only td-distributive operations, is derivable, and the (...) substitution r↦td is a projective L-unifier for any formula containing only td-distributive connectives. The above substitution is a generalization of the substitution introduced by T. Prucnal to prove structural completeness of the implication fragment of intuitionistic propositional logic. (shrink)

We show that some common varieties of modal K4-algebras have finitary unification type, thus providing effective best solutions for equations in free algebras. Applications to admissible inference rules are immediate.

The most majestic scientific achievement, of this century in mathematical beauty, axiomatic consistency, and experimental verifications has been special relativity with its unitary structure at the operator level, and canonical structure at the classical levels, which has turned out to be exactly valid for point particles moving in the homogenenous and isotropic vacuum (exterior dynamical problems). In recent decades a number of authors have studied nonunitary and noncanonical theories, here generally calleddeformations for the representation of broader conditions, such as extended (...) and deformable particles moving within inhomogeneous and anisotrophic physical media (interior dynamical problems). In this paper we show that nonunitary deformations, including, q-, k-, quatum-, Lie-isotopic, Lie-admissible, and other deformations, even thoughmathematically correct, have a number of problematic aspects ofphysical character when formulated on conventional spaces over conditional fields, such as lack of invariance of the basic space-time units, ambiguous applicability to measurements, loss of Hermiticity-observability in time, lack of invariant numerical predictions, loss of the axions of special relativity, and others. We then show that the classical noncanonical counterparts of the above nonunitary deformations are equally afflicted by corresponding problems of physical consistency. We also show that the contemporary formulation of gravity is afflicted by similar problematic aspects because Riemannian spaces are noncanonical deformations of Minkowskian spaces, thus having noninvariant space-time units. We then point out that new mathematical methods, calledisotopies, genotopies, hyperstructures and their isoduals, offer the possibilities of constructing a nonunitary theory, known asrelativistic hadronic mechanics which: (1) is as axiomatically consistent as relativistic quantum mechanics, (2) preserves the abstract axioms of special relativity, and (3) results in a completion of the conventional mechanics much along the celebrated Einstein-Podolski-Rosen argument. A number of novel applications are indicated, such as a geometric unification of the special and general relativity via the isominkowskian geometry in which the two relativities are differentiated via the invariant basic unit, while preserving conventional Riemannian metrics, Einstein's field equations, and related experimental verifications; a novel operator form of gravity verifying the axioms of relativistic quantum mechanics under the universal isopoincaré symmetry; a new structure model of hadrons with conventional massive particles as physical constituents which is compatile with composite quarks and with established unitary classifications; and other novels applications in nuclear physics, astrophysics, theoretical biology, and other fields. The paper ends with the proposal of a number of new experiments, some of which may imply new practical applications, such as conceivable new forms of recycling nuclear waste. The achievement of axiomatic consistency in the study of the above physical problems has been possible for the first time in this paper thanks to mathematical advances that recently appeared in a special issue of theRendiconti Circolo Matematico Palermo, and in other journals identified in the Acknowledgements. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Concepts, Judgments, and Unity in Kant's Metaphysical Deduction of the Relational Categories CHARLES NUSSBAUM 1. INTRODUCTION TO ANY ATTENTIVEREADERof the section of the Critique of Pure Reason' known as the "Metaphysical Deduction of the Categories" (A67/B92-A83/B to9), one paragraph in that section stands out particularly by virtue of its special importance for Kant's developing argument: The same function Which gives unity to the various representations in ajudgment also gives (...) unity to the mere synthesis of various representations in an intuition; and this unity, in its most general expression, we entitle the pure concept of the understanding. The same understanding, through the same operations by which in concepts, by means of analytical unity, it produced the logical form of a judgment, also introduces a transcendental content into its representations, by means of the synthetic unity of the manifold of intuition in general.... (CPR A79/B loS) The importance of this paragraph is, however, more than equaled by its difficulties, which center on the question of how the function which operates by means of analytical unity can be the same as one that operates by means of the synthetic unity of the manifold of intuition in general. Put shortly, the problem is this. If the functions are really the same, then how do we distinguish at all between analytic and synthetic operations? But if they are different, then how can these forms of judgment serve as a clue for the discovery of the categories? ' Immanuel Kant, Critiqueof Pure Reason, trans. Norman KempSmith (London: Macmillan and Co., Ltd., 1963).Hereafter CPR. [89] 9~ JOURNAL OF THE HISTORY OF PHILOSOPHY 28:1 JANUARY 1990 The results of this dilemma which can be observed in the literature are not surprising: commentators tend to grasp one horn or the other. They either emphasize the difference between analysis and synthesis, and reject or dilute the claims as to sameness of function; or they take seriously Kant's argument concerning sameness of functions, and try to minimize the difference between analysis and synthesis. The major twentieth-century representant of the former approach is Kemp Smith," and of the latter, Paton. 3 This latter approach has found a formidable contemporary champion in the person of Henry Allison. By Allison's own admission,4 however, his position on this controversial topic was suggested (in part) by arguments first put forward over fifty years ago by Klaus Reich in a most remarkable book entitled Die Volls~ndigkeit der Kantischen Urteilstafel, 5 a book, by the way, also greatly admired by Paton. 6 In the first section of this paper I will try to show that Reich's arguments are rather more subtle than Allison apparently takes them to be, and that Reich is one commentator who attempts to go between the horns of the dilemma described above, and who essays an interpretation of our crucial paragraph that unifies its seemingly divergent tendencies. In the second section of the paper I will introduce some interpretive elements of my own. 2. Let us begin by reacquainting ourselves with Kant's notion of analytical unity, one aspect of this debate which is not particularly controversial and is largely agreed upon by all parties. For Kant, analytical unity is the sort of unity achieved by all general concepts (conceptus communes) insofar as they abstract from all differences that subsist between the objects under them, or the lower concepts subordinated to them. 7 A general concept unifies these objects or concepts by means of a common mark or set of marks. Thus Kant's example at CPR A69/B94 of the unification of bodies under the concepts 'body' and 'divisible' is a perfectly representative instance of unification via analytical unity, as the function upon which such concepts "rest." Let us note that the " Norman KempSmith,A CommentarytoKant's "Cr/t~rueofPureReason"(NewYork:HumanitiesPress, 196~). 3 H.J. Paton, Kant's MetaphysicofExperience, 2 vols.(London:George Allenand Unwin,Ltd., 1936). 4 Henry Allison,Kant's TranscendentalIdealum (NewHaven:YaleUniversityPress, 1983), 144 n. 3o. Hereafter KTI. 5 KlausReich,Die Vollst~ndigkeitderKantischenUrteilstafel,3rd. ed. (Hamburg: Meiner, 1986). Hereafter VKU. 6 Paton, Kant's Metaphysic, 1:302. Kant, we should note, does not makethis important logicaldistinctionbetweensubordination... (shrink)

In this paper significant challenges are raised with respect to the view that explanation essentially involves unification. These objections are raised specifically with respect to the well-known versions of unificationism developed and defended by Michael Friedman and Philip Kitcher. The objections involve the explanatory regress argument and the concepts of reduction and scientific understanding. Essentially, the contention made here is that these versions of unificationism wrongly assume that reduction secures understanding.

Explanatory unification—the urge to “explain much by little”—serves as an ideal of theorizing not only in natural sciences but also in the social sciences, most notably in economics. The ideal is occasionally challenged by appealing to the complexity and diversity of social systems and processes in space and time. This article proposes to accommodate such doubts by making a distinction between two kinds of unification and suggesting that while such doubts may be justified in regard to mere derivational (...) unification (which serves as a formal constraint on theories), it is less justified in the case of ontological unification (which is a result of factual discovery of the actual degree of underlying unity in the world). (shrink)

We characterize (both from a syntactic and an algebraic point of view) the normal K4-logics for which unification is filtering. We also give a sufficient semantic criterion for existence of most general unifiers, covering natural extensions of K4.2⁺ (i.e., of the modal system obtained from K4 by adding to it, as a further axiom schemata, the modal translation of the weak excluded middle principle).

In this paper I challenge two widespread convictions about unification in physics: unification is an aim of physics and unification is driven by metaphysical or metatheoretical presuppositions. I call these external explanations of why there is unification in physics. Against this, I claim that unification is a by-product of physical research and unification is driven by basic methodological strategies of physics alone. I call this an internal explanation of why there is unification in (...) physics. To support my claims, I will investigate the actual practice undertaken in physics in paradigmatic examples of unification. (shrink)

The official model of explanation proposed by the logical empiricists, the covering law model, is subject to familiar objections. The goal of the present paper is to explore an unofficial view of explanation which logical empiricists have sometimes suggested, the view of explanation as unification. I try to show that this view can be developed so as to provide insight into major episodes in the history of science, and that it can overcome some of the most serious difficulties besetting (...) the covering law model. (shrink)

__In this paper I investigate unification as a virtue of explanation. I the first part of the paper I give a brief exposition of the unification account of Schurz and Lambert and Schurz. I illustrate the advantages of this account in comparison to the older unification accounts of Friedman and Kitcher. In the second part I discuss several comments and objections to the Schurz-Lambert account that were raised by Weber and van Dyck, Gijsberg and de Regt. In (...) the third and final part, I argue that explanation should be understood as a prototype concept which contains nomic expectability, causality and unification as prototypical virtues of explanations, although none of these virtues provides a sufficient and necessary "defining condition" of explanation. (shrink)

In this paper, I argue that unification is neither necessary nor sufficient for explanation. Focusing on the versions of the unificationist theory of explanation of Kitcher and of Schurz and Lambert, I establish three theses. First, Kitcher’s criterion of unification is vitiated by the fact that it entails that every proposition can be explained by itself, a flaw that it is unable to overcome. Second, because neither Kitcher’s theory nor that of Schurz and Lambert can solve the problems (...) of asymmetry and accidental generalizations, it follows that unification is not sufficient to ground explanation. Third, some good explanations are disunifying, which entails that unification is not necessary for explanation either. (shrink)

The?-admissibility is one of the most important problems in the realm of relevant logics. To prove the 7-admissibility, either the method of normal models or the method using metavaluations may be employed. The?-admissibility of a wide class of relevant modal logics has been discussed in Part I based on a former method, but the?-admissibility based on metavaluations has not hitherto been fully considered. Sahlqvist axioms are well known as a means of expressing generalized forms of formulas with modal operators. This (...) paper shows that? is admissible for relevant modal logics with restricted Sahlqvist axioms in terms of the method using metavaluations. (shrink)

We investigate finitarity of unification types in locally finite varieties of Heyting algebras, giving both positive and negative results. We make essential use of finite dualities within a conceptualization for E-unification theory 733–752) relying on the algebraic notion of a projective object.

In this paper, we defend a novel, multidimensional account of representational unification, which we distinguish from integration. The dimensions of unity are simplicity, generality and scope, non-monstrosity, and systematization. In our account, unification is a graded property. The account is used to investigate the issue of how research traditions contribute to representational unification, focusing on embodied cognition in cognitive science. Embodied cognition contributes to unification even if it fails to offer a grand unification of cognitive (...) science. The study of this failure shows that unification, contrary to what defenders of mechanistic explanation claim, is an important mechanistic virtue of research traditions. (shrink)

Which objects and properties are represented in perceptual experience, and how are we able to determine this? The papers in this collection address these questions together with other fundamental questions about the nature of perceptual content. The book draws together papers by leading international philosophers of mind, including Alex Byrne (MIT), Alva Noë (University of California, Berkeley), Tim Bayne (St Catherine’s College, Oxford), Michael Tye (University of Texas, Austin), Richard Price (All Souls College, Oxford) and Susanna Siegel (Harvard University) Essays (...) address the central questions surrounding the content of perceptual experience Investigates how are we able to determine the admissible contents of experience Published in association with the journal Philosophical Quarterly . (shrink)

Cognitive science is an interdisciplinary conglomerate of various research fields and disciplines, which increases the risk of fragmentation of cognitive theories. However, while most previous work has focused on theoretical integration, some kinds of integration may turn out to be monstrous, or result in superficially lumped and unrelated bodies of knowledge. In this paper, I distinguish theoretical integration from theoretical unification, and propose some analyses of theoretical unification dimensions. Moreover, two research strategies that are supposed to lead to (...) unification are analyzed in terms of the mechanistic account of explanation. Finally, I argue that theoretical unification is not an absolute requirement from the mechanistic perspective, and that strategies aiming at unification may be premature in fields where there are multiple conflicting explanatory models. (shrink)

In the current literature on scientific explanation unification became unfashionable in favour of causal approaches. We want to bring unification back into the picture. In this paper we demonstrate that resemblance questions do occur in scientific practice and that they cannot be properly answered without unification. Our examples show that resemblance questions about particular facts demand what we call causal network unification, while resemblance questions about regularities require what we call mechanism unification. We clarify how (...) these types of unification relate to Philip Kitcher’s account, but also to causal and mechanistic accounts of explanation. (shrink)

Predictive processing (PP) has been repeatedly presented as a unificatory account of perception, action, and cognition. In this paper, we argue that this is premature: As a unifying theory, PP fails to deliver general, simple, homogeneous, and systematic explanations. By examining its current trajectory of development, we conclude that PP remains only loosely connected both to its computational framework and to its hypothetical biological underpinnings, which makes its fundamentals unclear. Instead of offering explanations that refer to the same set of (...) principles, we observe systematic equivocations in PP‐based models, or outright contradictions with its avowed principles. To make matters worse, PP‐based models are seldom empirically validated, and they are frequently offered as mere just‐so stories. The large number of PP‐based models is thus not evidence of theoretical progress in unifying perception, action, and cognition. On the contrary, we maintain that the gap between theory and its biological and computational bases contributes to the arrested development of PP as a unificatory theory. Thus, we urge the defenders of PP to focus on its critical problems instead of offering mere re‐descriptions of known phenomena, and to validate their models against possible alternative explanations that stem from different theoretical assumptions. Otherwise, PP will ultimately fail as a unified theory of cognition. (shrink)

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.

It is proved that Ackermann’s rule δ is admissible in a wide spectrum of relevant logics satisfying certain syntactical properties.

This article examines our moral obligations to refugees and stateless people. I argue that in order to understand our moral obligations to stateless people, both de jure refugees and de facto stateless people, we ought to reconceptualize the harm of statelessness as entailing both a legal/political harm (the loss of citizenship) and an ontological harm, a deprivation of certain fundamental human qualities. To do this, I draw on the work of Hannah Arendt and show that the ontological deprivation has three (...) distinct though interconnected elements: a reduction to the merely human or bare life, a separation from the common realm of humanity and abandonment, and the diminishment of agency or ability to act in the Arendtian sense. If we pull apart the legal/political harm of statelessness from the ontological harm, we are better able to see that we can address some of the features of the ontological deprivation even though we may not be able to rectify the political harm. I conclude this article by discussing some suggestions that follow from a recognition of the reality and harm of the ontological deprivation. (shrink)

This is the second of the three volumes comprising, Scholastic Humanism and the Unification of Europe. Focussing on the period from c.1090-1212, the volume explores the lives, scholarly resources, and contributions of a wide sample of people who either took part in the creation of the scholastic system of thought or gave practical effect to it in public life. The second volume of a compelling, original work which will redefine our perceptions of medieval civilization, the renaissance and the evolution (...) of modern Europe. Written by a man who was widely regarded as the greatest medieval historian. (shrink)

The admissibility of Ackermann's rule? is one of the most important problems in relevant logic. While the?-admissibility of normal modal logics based on the relevant logic R has been previously discussed, the case for weaker relevant modal logics has not yet been considered. The method of normal models has often been used to prove the?-admissibility. This paper discusses which relevant modal logics admit? from the viewpoint of the method of normal models.

The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special (...) attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)

Bridging the gap between the world of science and the realm of the spiritual, B. Alan Wallace introduces a natural theory of human consciousness that has its roots in contemporary physics and Buddhism. Wallace's "special theory of ontological relativity" suggests that mental phenomena are _conditioned_ by the brain, but do not _emerge_ from it. Rather, the entire natural world of mind and matter, subjects and objects, arises from a unitary dimension of reality that is more fundamental than these dualities, as (...) proposed by Wolfgang Pauli and Carl Jung. To test his hypothesis, Wallace employs the Buddhist meditative practice of _samatha_, refining one's attention and metacognition, to create a kind of telescope to examine the space of the mind. Drawing on the work of the physicist John Wheeler, he then proposes a more general theory in which the participatory nature of reality is envisioned as a self-excited circuit. In comparing these ideas to the Buddhist theory known as the Middle Way philosophy, Wallace explores further aspects of his "general theory of ontological relativity," which can be investigated by means of _vipasyana_, or insight, meditation. Wallace then focuses on the theme of symmetry in reference to quantum cosmology and the "problem of frozen time," relating these issues to the theory and practices of the Great Perfection school of Tibetan Buddhism. He concludes with a discussion of the general theme of complementarity as it relates to science and religion. The theories of relativity and quantum mechanics were major achievements in the physical sciences, and the theory of evolution has had an equally deep impact on the life sciences. However, rigorous scientific methods do not yet exist to observe mental phenomena, and naturalism has its limits for shedding light on the workings of the mind. A pioneer of modern consciousness research, Wallace offers a practical and revolutionary method for exploring the mind that combines the keenest insights of contemporary physicists and philosophers with the time-honored meditative traditions of Buddhism. (shrink)

In this article I argue that there are two different types of understanding: the understanding we get from explanations, and the understanding we get from unification. This claim is defended by first showing that explanation and unification are not as closely related as has sometimes been thought. A critical appraisal of recent proposals for understanding without explanation leads us to discuss the example of a purely classificatory biology: it turns out that such a science can give us understanding (...) of the world through unification of the phenomena, even though it does not give us any explanations. The two types of understanding identified in this paper, while strictly separate, do have in common that both consist in seeing how the individual phenomena of the universe hang together. Explanations give us connections between the phenomena through the asymmetric, ‘vertical’ relation of determination; unifications give us connections through the symmetric, ‘horizontal’ relation of kinship. We then arrive at a general definition of understanding as knowledge of connections between the phenomena, and indicate that there might be more than two types of understanding. (shrink)

The object of this paper is to reply to Morrison's ([2000]) claim that while ‘structural unity’ was achieved at the level of the mathematical models of population genetics in the early synthesis, there was explanatory disunity. I argue to the contrary, that the early synthesis effected by the founders of theoretical population genetics was unifying and explanatory both. Defending this requires a reconsideration of Morrison's notion of explanation. In Morrison's view, all and only answers to ‘why’ questions which include the (...) ‘cause or mechanism’ for some phenomenon count as explanatory. In my view, mathematical demonstrations that answer ‘how possibly’ and ‘why necessarily’ questions may also count as explanatory. The authors of the synthesis explained how evolution was possible on a Mendelian system of inheritance, answered skepticism about the sufficiency of selection, and thus explained why and how a Darwinian research program was warranted. While today we take many of these claims as obvious, they required argument, and part of the explanatory work of the formal sciences is providing such arguments. Surely, Fisher and Wright had competing views as to the optimal means of generating adaptation. Nevertheless, they had common opponents and a common unifying and explanatory goal that their mathematical demonstrations served. Introduction: Morrison's challenge Fisher v. Wright revisited The early synthesis Conclusion: unification and explanation reconciled. (shrink)

Recent interest in the idea that there can be scientific understanding without explanation lends new relevance to Duhem's notion of natural classification. According to Duhem, a classification that is natural teaches us something about nature without being explanatory. However, Duhem's conception of naturalness leaves much to be desired. In this paper, I argue that we can measure the naturalness of classification by using an amended version of the notion of unification as defined by Schurz and Lambert. If this thesis (...) is correct, it both leads to a better conceptual understanding of scientific understanding, and also gives the nascent literature on this topic some much-needed precision. (shrink)

In this article we criticize two recent articles that examinethe relation between explanation and unification. Halonen and Hintikka (1999), on the one hand,claim that no unification is explanation. Schurz (1999), on the other hand, claims that all explanationis unification. We give counterexamples to both claims. We propose a pluralistic approach to the problem:explanation sometimes consists in unification, but in other cases different kinds of explanation(e.g., causal explanation) are required; and none of these kinds is more fundamental.

Summary: Throughout the history of science, indeed throughout the history of knowledge, unification has been touted as a central aim of intellectual inquiry. We’ve always wanted to discover not only numerous bare facts about the universe, but to show how such facts are linked and interrelated. Large amounts of time and effort have been spent trying to show diverse arrays of things can be seen as different manifestations of some common underlying entities or properties. Thales is said to have (...) originated philosophy and science with his declaration that everything was, at base, a form of water. Plato’s theory of the forms was thought to be a magnificent accomplishment because it gave a unified solution to the separate problems of the relation between knowledge and belief, the grounding of objective values, and how continuity is possible amid change. Pasteur made numerous medical advancements possible by demonstrating the interconnection between microorganisms and human disease symptoms. Many technological advances were aided by Maxwell’s showing that light is a kind of electromagnetic radiation. The attempt to unify the various known forces is often referred to as “The Holy Grail” of physics. Some philosophers have even suggested that providing explanations is itself just a sort of unifying of our knowledge. But while unification (like simplicity) has often been hailed as a tremendous virtue in science, the meaning of the term is not altogether clear. Scientists often don’t specify what, precisely, they mean by unification. And in cases where what they mean is clear, different thinkers plainly mean different things by the term. What are the various senses of unification, and why has unification been such an important aim in the history of inquiry? (shrink)

Unification was originally introduced in automated deduction and term rewriting, but has recently also found applications in other fields. In this article, we give a survey of the results on unification obtained in two closely related, yet different, application areas of unification: description logics and modal logics.

This paper examines the impact of education reforms on school admissions policies and practices. It discusses the changes that are needed to improve the current system, especially in areas where the market is highly developed. It is concluded that the new legislation to be enacted by the current Labour Government should be beneficial, but that more far-reaching changes are needed for the admissions process to be equitable, transparent and accountable.

Incommensurability was Kuhn’s worst mistake. If it is to be found anywhere in science, it would be in physics. But revolutions in theoretical physics all embody theoretical unification. Far from obliterating the idea that there is a persisting theoretical idea in physics, revolutions do just the opposite: they all actually exemplify the persisting idea of underlying unity. Furthermore, persistent acceptance of unifying theories in physics when empirically more successful disunified rivals can always be concocted means that physics makes a (...) persistent implicit assumption concerning unity. To put it in Kuhnian terms, underlying unity is a paradigm for paradigms. We need a conception of science which represents problematic assumptions concerning the physical comprehensibility and knowability of the universe in the form of a hierarchy, these assumptions becoming less and less substantial and more and more such that their truth is required for science, or the pursuit of knowledge, to be possible at all, as one goes up the hierarchy. This hierarchical conception of science has important Kuhnian features, but also differs dramatically from the view Kuhn expounds in his The Structure of Scientific Revolutions. In this paper, I compare and contrast these two views in a much more detailed way than has been done hitherto. I show how the hierarchical view can be construed to emerge from Kuhn’s view as it is modified to overcome objections. I argue that the hierarchical conception of science is to be preferred to Kuhn’s view. (shrink)