On the first of the two occasions I met Thomas Kuhn, we immediately plunged into a ferocious but very friendly argument about incommensurability. He was for it, I was against. Believing in incommensurability was Kuhn’s worst mistake. If it is to be found anywhere in science, it would be in theoretical physics. But revolutions in theoretical physics have one striking feature in common: they all embody theoretical unification. Revolutions associated with Galileo, Newton, Faraday and Maxwell, Einstein, Bohr, Schrödinger, Dirac, (...) Tomonaga, Schwinger and Feynman, Weinberg and Salam, have all been unifying revolutions. 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. Once this is recognized, it becomes clear that we need a new 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 view makes explicit that we can improve assumptions and associated methods – aims and methods – as we proceed with physics, and knowledge improves. There is something like positive feedback between improving knowledge, and improving aims and methods – the nub of scientific rationality, and the methodological key to the great success of science. 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. I describe basic features of this hierarchical view, and give reasons why it should be accepted. (shrink)
If realism about possible worlds is to succeed in eliminating primitive modality, it must provide an 'analysis' of possible world: nonmodal criteria for demarcating one world from another. This David Lewis has done. Lewis holds, roughly, that worlds are maximal unified regions of logical space. So far, so good. But what Lewis means by 'unification' is too narrow, I think, in two different ways. First, for Lewis, all worlds are (almost) 'globally' unified: at any world, (almost) every part is (...) directly linked to (almost) every other part. I hold instead that some worlds are 'locally' unified: at some worlds, parts are directly linked only to "neighboring" parts. Second, for Lewis, each world is (analogically) 'spatio-temporally' unified; every world is 'spatio-temporally' isolated from every other. I hold instead: a world may be unified by nonspatio-temporal relations; every world is 'absolutely' isolated from every other. If I am right, Lewis's conception of logical space is impoverished: perfectly respectable worlds are missing. (shrink)
This paper represents a response to the criticisms made by Eric Barnes in “Explanatory Unification and the Problem of Asymmetry” and “Explanatory Unification and Scientific Understanding” against the thesis of Explanatory Unification. This paper responds to Barnes‟ two main criticisms, that of derivational skepticism and causal asymmetry, and successfully refutes his objections. This paper also defends the plausibility of the unificationist account of scientific explanation because of its ability to render coherent the notion of scientific understanding, focusing (...) in particular on the work by Michael Friedman and Philip Kitcher. (shrink)
Pluralism with respect to the structure of explanations of facts is not uncommon. Wesley Salmon, for instance, distinguished two types of explanation: causal explanations (which provide insight in the causes of the fact we want to explain) and unification explanations (which fit the explanandum into a unified world view). The pluralism which Salmon and others have defended is compatible with several positions about the exact relation between these two types of explanations. We distinguish four such positions, and argue in (...) favour of one of them. We also compare our results with the views of some authors who have recently written on this subject. (shrink)
In this paper I examine Don Ross’s application of unificationism as a methodological criterion of theory appraisal in economics and cognitive science. Against Ross’s critique that explanations of the preference reversal phenomenon by the ‘heuristics and biases’ programme is ad hoc or ‘Ptolemaic’, I argue that the compatibility hypothesis, one of the explanations offerd by this programme, is theoretically and empirically well-motivated. A careful examination of this hypothesis suggests several strengths of a procedural approach to modelling cognitive processes underlying individual (...) decision making, compared to a multiple-agent approach which Ross promotes. I argue that the debate between economists and psychologists are both theoretical and empirical, but cannot be resolved by appealing to the ideal of unification. (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.
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)
Astroparticle physics is a recent sub-discipline of physics that emerged from early cosmic ray studies, astrophysics, and particle physics. Its theoretical foundations range from quantum field theory to general relativity, but the underlying “standard models” of cosmology and particle physics are far from being unified. The paper explores the pragmatic strategies employed in astroparticle physics in order to unify a disunified research field, the concept of observation involved in these strategies, and their relations to scientific realism.
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)
The two major modern accounts of explanation are the causal and unification accounts. My aim in this paper is to provide a kind of unification of the causal and the unification accounts, by using the central technical apparatus of the unification account to solve a central problem faced by the causal account, namely, the problem of determining which parts of a causal network are explanatorily relevant to the occurrence of an explanandum. The end product of my (...) investigation is a causal account of explanation that has many of the advantages of the unification account. (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)
Physics seems to tell us that there are four fundamental force-fields in nature: the gravitational, the electromagnetic, the weak, and the strong (or interactions). But it also seems to tell us that gravity cannot possibly be a force-field, in the same sense as the other three are. And yet the search for a grand unification of all four force-fields is today one of the hottest pursuits. Is this the result of a simple confusion? This article aims at clarifying this (...) situation by (i) reviewing the gauge-field programme and its conception of unification of force-fields, (ii) examining the various attempts at a gauge theory of gravity, and (iii) articulating the nature of "gauging" and using it to explain the difference between gravity and the other force-fields. (shrink)
In the literature on scientific explanation, there is a classical distinction between explanations of facts and explanations of laws. This paper is about explanations of facts. Our aim is to analyse the role of unification in explanations of this kind. We discuss five positions with respect to this role, argue for two of them and refute the three others.
This paper addresses a central question of contemporary theoretical physics: Can a unified account be provided for the known forces of nature? The issue is brought into focus by considering the recently revived Kaluza-Klein approach to unification, a program entailing dimensional transformation through cosmogony. First it is demonstrated that, in a certain sense, revitalized Kaluza-Klein theory appears to undermine the intuitive foundations of mathematical physics, but that this implicit consequence has been repressed at a substantial cost. A fundamental reformulation (...) of the Kaluza-Klein strategy is then undertaken, one that casts it within a new intuitive context. This is followed by a provisional application of the suggested approach to the specific problem of cosmic evolution. The paper concludes by exploring the far-reaching epistemological implications of the "neo-intuitive" proposal set forth. (shrink)
For two decades, the integrated causal model of evolutionary psychology (EP) has constituted an interdisciplinary nucleus around which a single unified theoretical and empirical behavioral science has been crystallizing – while progressively resolving problems (such as defective logical and statistical reasoning) that bedevil Gintis's beliefs, preferences, and constraints (BPC) framework. Although both frameworks are similar, EP is empirically better supported, theoretically richer, and offers deeper unification. (Published Online April 27 2007).
Given that scientific realism is based on the assumption that there is a connection between a model's predictive success and its truth, and given the success of multiple incompatible models in scientific practice, the realist has a problem. When the different models can be shown to arise as different approximations to a unified theory, however, one might think the realist to be able to accommodate such cases. I discuss a special class of models (generated as non-uniform limits of a unified (...) theory) and argue that a realist interpretation has to understand these models of a system as ‘perspectival’, in close analogy to different spatial perspectives onto the same object. For this sort of case, I also respond to Morrison's recent claim that in the process of unifying models into an overarching theory, explanatory and descriptive power are lost, leaving the unified theory with less of a claim to a realist interpretation than the models themselves. Introduction Perspectival models from singular perturbation problems Unification of perspectives without losses of explanatory power Perspectives as different levels of a system Perspectival models, idealizations and pluralism. (shrink)
Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with epistemology. The complexity of the issue of course precludes addressing it tout court in one paper, and I’ll just be laying some early foundations here. To this end I’ll narrow the field in two ways. First, I’ll address a specific account of explanation and understanding that applies naturally to mathematical reasoning: the view proposed (...) by Philip Kitcher and Michael Friedman of explanation or understanding as involving the unification of theories that had antecedently appeared heterogeneous. For the second narrowing, I’ll take up one specific feature (among many) of theories and their basic concepts that is sometimes taken to make the theories and concepts preferred: in some fields, for some problems, what is counted as understanding a problem may involve finding a way to represent the problem so that it (or some aspect of it) can be visualized. The final section develops a case study which exemplifies the way that this consideration – the potential for visualizability – can rationally inform decisions as to what the proper framework and axioms should be. The discussion of unification (in sections 3 and 4) leads to a mathematical analogue of Goodman’s problem of identifying a principled basis for distinguishing grue and green. Just as there is a philosophical issue about how we arrive at the predicates we should use when making empirical predictions, so too there is an issue about what properties best support many kinds of mathematical reasoning that are especially valuable to us. The issue becomes pressing via an examination of some physical and mathematical cases that make it seem unlikely that treatments of unification can be as straightforward as the philosophical literature has hoped. Though unification accounts have a grain of truth (since a phenomenon (or cluster of phenomena) called “unification” is in fact important in many cases) we are far from an analysis of what “unification” is.. (shrink)
Myrvold (2003) has proposed an attractive Bayesian account of why theories that unify phenomena tend to derive greater epistemic support from those phenomena than do theories that fail to unify them. It is argued, however, that "unification" in Myrvold's sense is both too easy and too difficult for theories to achieve. Myrvold's account fails to capture what it is that makes unification sometimes count in a theory's favor.
I examine the relation between explanation and unification in both the original Kaluza–Klein theory, which originated in the works of Theodor Kaluza and Oskar Klein in the 1920s, and in the modern Kaluza–Klein theories which date back to the late 1970s and which are still considered by the majority of the physics community to be the best hope for a complete unified theory of all fundamental interactions. I use the conclusions of this case study to assess the merits of (...) Philip Kitcher's account of explanation as unification. I also draw lessons about physicists’ pursuit of the higher dimensional unification of the fundamental forces of nature. (shrink)
I argued that the frameworks and mechanisms that produce unification do not enable us to explain why the unified phenomena behave as they do. That is, we need to look beyond the unifying process for an explanation of these phenomena. Anya Plutynski ([2005]) has called into question my claim about the relationship between unification and explanation as well as my characterization of it in the context of the early synthesis of Mendelism with Darwinian natural selection. In this paper (...) I argue that her methodological criticisms rest on a misinterpretation of my views on explanation and defend my historical interpretation of the work of Fisher and Wright. A statement of the problem Methodological differences: how to characterize explanation Historical matters: disagreements about details Explanation revisited: the possible versus the ‘merely actual’. (shrink)
A Bayesian account of the virtue of unification is given. On this account, the ability of a theory to unify disparate phenomena consists in the ability of the theory to render such phenomena informationally relevant to each other. It is shown that such ability contributes to the evidential support of the theory, and hence that preference for theories that unify the phenomena need not, on a Bayesian account, be built into the prior probabilities of theories.
Philip Kitcher has proposed a theory of explanation based on the notion of unification. Despite the genuine interest and power of the theory, I argue here that the theory suffers from a fatal deficiency: It is intrinsically unable to account for the asymmetric structure of explanation, and thus ultimately falls prey to a problem similar to the one which beset Hempel's D-N model. I conclude that Kitcher is wrong to claim that one can settle the issue of an argument's (...) explanatory force merely on the basis of considerations about the unifying power of the argument pattern the argument instantiates. (shrink)
This article is a commentary on Machery (2009) Doing without Concepts. Concepts are mental symbols that have semantic structure and processing structure. This approach (1) allows for different disciplines to converge on a common subject matter; (2) it promotes theoretical unification; and (3) it accommodates the varied processes that preoccupy Machery. It also avoids problems that go with his eliminativism, including the explanation of how fundamentally different types of concepts can be co-referential.
Although Trautman (1966) appears to give a unified-field treatment of electrodynamics in Newtonian spacetime, there are difficulties in cogently interpreting it as such in relation to the facts of electromagnetic and magneto-electric induction. Presented here is a covariant, non-unified field treatment of the Maxwell-Lorentz theory with absolute space. This dispels a worry in Earman (1989) as to whether there are any historically realistic examples in which absolute space plays an indispenable role. It also shows how Trautman`s formulation can be rendered (...) coherent, albeit at the cost of de-unification, by reinterpreting the Maxwell tensor as a composite object involving, in part, elements from Newtonian spacetime. (shrink)
In three recent papers, Wayne Myrvold (1996, 2003) and Timothy McGrew (2003) have developed Bayesian accounts of the virtue of unification. In his account, McGrew demonstrates that, ceteris paribus, a hypothesis that unifies its evidence will have a higher posterior probability than a hypothesis that does not. Myrvold, on the other hand, offers a specific measure of unification that can be applied to individual hypotheses. He argues that one must account for this measure in order to calculate correctly (...) the degree of confirmation that a hypothesis receives from its evidence. Using the probability calculus, I prove that the two accounts of unification require the same underlying inequality; thus, McGrew and Myrvold have accounted for unification in fundamentally identical probabilistic terms. I then evaluate five putative counterexamples to this account and show that these examples, far from disqualifying it, serve to clarify our notion of unification by disentangling it from a host of other concepts. (shrink)
This article has three aims. The first is to give a partial explication of the concept of unification. My explication will be partial because I confine myself to unification of particular events, because I do not consider events of a quantitative nature, and discuss only deductive cases. The second aim is to analyze how unification can be reached. My third aim is to show that unification is an intellectual benefit. Instead of being an intellectual benefit (...) class='Hi'>unification could be an intellectual harm, i.e., a state of mind we should try to avoid by all means. By calling unification an intellectual benefit, we claim that this form of understanding has an intrinsic value for us. I argue that unification really has this alleged intrinsic value. (shrink)
According to Philip Kitcher, scientific unification is achieved via the derivation of numerous scientific statements from economies of argument schemata. I demonstrate that the unification of selection phenomena across domains in which it is claimed to occur--evolutionary biology, immunology and, speculatively, neurobiology--is unattainable on Kitcher's view. I then introduce an alternative method for rendering the desired unification based on the concept of a mechanism schema. I conclude that the gain in unification provided by the alternative account (...) suggests that Kitcher's view is defective. (shrink)
The theory of explanatory unification was first proposed by Friedman (1974) and developed by Kitcher (1981, 1989). The primary motivation for this theory, it seems to me, is the argument that this account of explanation is the only account that correctly describes the genesis of scientific understanding. Despite the apparent plausibility of Friedman's argument to this effect, however, I argue here that the unificationist thesis of understanding is false. The theory of explanatory unification as articulated by Friedman and (...) Kitcher thus emerges as fundamentally misconceived. (shrink)
P. Kitcher's unification theory of explanation appears to endorse a reductionistic view of scientific explanation that is inconsistant with scientific practice. In this paper, I argue that this appearance is illusory. The existence of multiply realizable generalizations enable the unification theory to also count many high-level accounts as explanatory.
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). Key Words: scientific explanation • explanatory unification • unity of economics • economic methodology. (shrink)
Do we need principles of the unification of our agency, our mode of acting? Immanuel Kant and Christine Korsgaard argue that the reflective structure of our mind forces us to have some conception of ourselves, others and the world—including our agency—and that it is through will and reason, and in particular principles of our agency, that we take upon ourselves to unify and test the way(s) in which we make our lives consistent. I argue that the principles suggested—the hypothetical (...) imperative and the categorical imperative—function to unify our understanding of ourselves and others as agents as efficacious and autonomous and that the extent to which those concerned render themselves efficacious and autonomous in cosmopolitan education or elsewhere is due to the extent to which they act in accordance with and are motivated by the suggested principles and in particular the categorical one. I first discuss how the principles function to unify our agency and how the categorical imperative functions as a test of maxims for our actions, how the will is the source of our morality, and how we are forced to have practical identities. I end with some remarks on what it means to acknowledge the mentioned principles in cosmopolitan education. (shrink)
Chomsky's current Biolinguistic (Minimalist) methodology is shown to comport with what might be called 'established' aspects of biological method, thereby raising, in the biolinguistic domain, issues concerning biological autonomy from the physical sciences. At least current irreducibility of biology, including biolinguistics, stems in at least some cases from the very nature of what I will claim is physiological, or inter-organ/inter-component, macro-levels of explanation which play a new and central explanatory role in Chomsky's inter-componential (interface-based) explanation of certain (anatomical) properties of (...) the syntactic component of Universal Grammar. Under this new mode of explanation, certain physiological functions of cognitive mental organs are hypothesized, in an attempt to explain aspects of their internal anatomy. Thus, the internal anatomy of the syntactic component exhibits features that enable it to effectively interface with (i.e. function in a coordinated fashion with) other 'adjacent' organs, such as the Conceptual-Intensional (C-I) ('meaning') system and the Sensory- Motor (SM) ('sound') system. These two interface systems take as their inputs the assembled outputs of the syntactic component and, as a result of the very syntactic structure imposed by the syntax (as opposed to countless imaginable alternatives) are then able to assign their (linearized) sound and (compositional) meaning interpretations. If this is an accurate characterization, Chomsky's long-standing postulation of mental organs, and I will argue, the advancement of new hypotheses concerning physiological inter-organ functions, has attained in current biolinguistic Minimalist method a significant unification with foundational aspects of physiological explanation in other areas of biology. (shrink)
I motivate the concept of styles of scientific investigation, and differentiate two styles, formal and compositional. Styles are ways of doing scientific research. Radically different styles exist. I explore the possibility of the unification of biology and social science, as well as the possibility of unifying the two styles I identify. Recent attempts at unifying biology and social science have been premised almost exclusively on the formal style. Through the use of a historical example of defenders of compositional biological (...) social science, the Ecology Group at the University of Chicago from, roughly, the 1930s to the 1950s, I attempt to show the coherence and possibility, if not utility, of employing the compositional style to effect the synthesis of biology and social science. I also relate the efforts of the Ecology Group to those of investigators in the Sociology Department of the University of Chicago. In my conclusion, I discuss the usefulness both of employing the category of styles of scientific investigation in historical and philosophical studies of science, as well as the concept of compositionality in scientific studies. I end the paper with some tentative suggestions regarding the importance of compositionality for an analysis of human society. (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.
A newly emerged field within economics, known as geographical economics claims to have provided a unified approach to the study of spatial agglomerations at different spatial scales by showing how these can be traced back to the same basic economic mechanisms. We analyze this contemporary episode of explanatory unification in relation to major philosophical accounts of unification. In particular, we examine the role of argument patterns in unifying derivations, the role of ontological convictions and mathematical structures in shaping (...)unification, the distinction between derivational and ontological unification, the issue of how explanation and unification relate and finally the idea that unification comes in degrees. (shrink)
We provide an algorithm for determining a categorial grammar from linguistic data that essentially uses unification of type-schemes assigned to atoms. The algorithm presented here extends an earlier one restricted to rigid categorial grammars, introduced in [4] and [5], by admitting non-rigid outputs. The key innovation is the notion of an optimal unifier, a natural generalization of that of a most general unifier.
Kitcher's unification theory of explanation seems to suggest that only the most reductive accounts can legitimately be termed explanatory. This is not what we find in actual scientific practice. In this paper, I attempt to reconcile these ideas. I claim that Kitcher's theory picks out ideal explanations, but that our term explanation is used to cover other accounts that have a certain relationship with the ideal accounts. At times, versions and portions of ideal explanations can also be considered explanatory.
Wayne Myrvold (2003) has captured an important feature of unified theories, and he has done so in Bayesian terms. What is not clear is whether the virtue of such unification is most clearly understood in terms of Bayesian confirmation. I argue that the virtue of such unification is better understood in terms of other truth-related virtues such as predictive accuracy.
In this paper the notion of unifier is extended to the infinite set case. The proof of existence of the most general unifier of any infinite, unifiable set of types (terms) is presented. Learning procedure, based on infinite set unification, is described.
In this paper I try to capture Newton's notion and practice of unification (I will mainly focus on the Principia). I will use contemporary theories on unification in philosophy of science as analytic tools (Kitcher, Schurz and Salmon). I will argue that Salmon's later work on the topic provides a good starting point to characterize Newton's notion and practice. However, in order to fully grasp Newton's idea and practice of unification, Salmon's model needs to be fleshed out (...) and extended. (shrink)
Green and Shapiro's critique of rational choice theory underestimates the value of unification and the necessity of universalism in science. The central place of intentionality in social life makes both unification and universalism feasible norms in social science. However, ?universalism? in social science may be partial, in that the independence hypothesis?that the causal mechanism governing action is context independent?may hold only locally in certain classes of choice domains.
Wayne Myrvold (2003) has captured an important feature of unified theories, and he has done so in Bayesian terms. What is not clear is whether the virtue of such unification is most clearly understood in terms of Bayesian confirmation. I argue that the virtue of such unification is better understood in terms of other truth-related virtues such as predictive accuracy.
The paper discusses examples of integrative metatheoretical and theoretical work undertaken in the spirit of unification. Unification is defined as a recursive process in which the outcome of any one integrative episode provides ideas that may enter into further such episodes. The conceptual materials entering into integration exist at different levels and in distinct contexts. At the metatheoretical level, the examples relate to a number of contexts and issues, including methodological individualism versus holism. At the theoretical level, two (...) examples of the idea of a unification episode are described. In each instance, the ideas entering into the integrative episode are drawn from distinct research programs. It is argued that the spirit of unification, as embodied in theoretical practice along the lines suggested by the examples, can create bridges between disparate theory enterprises so as to help break down particularistic barriers within sociological theory. (shrink)
Unification grammars are widely accepted as an expressive means for describing the structure of natural languages. In general, the recognition problem is undecidable for unification grammars. Even with restricted variants of the formalism, off-line parsable grammars, the problem is computationally hard. We present two natural constraints on unification grammars which limit their expressivity and allow for efficient processing. We first show that non-reentrant unification grammars generate exactly the class of context-free languages. We then relax the constraint (...) and show that one-reentrant unification grammars generate exactly the class of mildly context-sensitive languages. We thus relate the commonly used and linguistically motivated formalism of unification grammars to more restricted, computationally tractable classes of languages. (shrink)
We define an order independent version of default unification on typed feature structures. The operation is one where default information in a feature structure typed with a more specific type, will override default information in a feature structure typed with a more general type, where specificity is defined by the subtyping relation in the type hierarchy. The operation is also able to handle feature structures where reentrancies are default. We provide a formal semantics, prove order independence and demonstrate the (...) utility of this version of default unification in several linguistic applications. First, we show how it can be used to define multiple orthogonal default inheritance in the lexicon in a fully declarative fashion. Secondly, we show how default lexical specifications (introduced via default lexical inheritance) can be made to usefully persist beyond the lexicon and interact with syntagmatic rules. Finally, we outline how persistent default unification might underpin default feature propagation principles and a more restrictive and constraint-based approach to lexical rules. (shrink)
In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including -ω, ω/2, 1/ω, \sqrt{ω} and ω-π to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG (von Neumann—Bernays—Gödel set theory with global (...) choice), it may be said to contain “All Numbers Great and Small.” In this respect, No bears much the same relation to ordered fields that the system ℝ of real numbers bears to Archimedean ordered fields. In Part I of the present paper, we suggest that whereas ℝ should merely be regarded as constituting an arithmetic continuum (modulo the Archimedean axiom), No may be regarded as a sort of absolute arithmetic continuum (modulo NBG), and in Part II we draw attention to the unifying framework No provides not only for the reals and the ordinals but also for an array of non-Archimedean ordered number systems that have arisen in connection with the theories of non-Archimedean ordered algebraic and geometric systems, the theory of the rate of growth of real functions and nonstandard analysis. In addition to its inclusive structure as an ordered field, the system No of surreal numbers has a rich algebraico-tree-theoretic structure—a simplicity hierarchical structure—that emerges from the recursive clauses in terms of which it is defined. In the development of No outlined in the present paper, in which the surreals emerge vis-à-vis a generalization of the von Neumann ordinal construction, the simplicity hierarchical features of No are brought to the fore and play central roles in the aforementioned unification of systems of numbers great and small and in some of the more revealing characterizations of No as an absolute continuum. (shrink)
The apparent underdetermination of the formalism of quantum field theory (QFT) as between a particle and a field interpretation is studied in this paper through a detour over the problem of unifying QFT with general relativity. All we have at present is a partial or approximate unification, QFT in non-Minkowskian spaces. The nature of this hybrid and the problem of its internal consistency are discussed. One of its most striking implications is that particles do not have an observer-independent existence. (...) We trace the ways in which physicists reacted to this at first highly implausible ontological consequence. We conclude that quantum fields rather than particles are after all the basic entities in QFT. (shrink)
In this article the problem of unification of mathematical theories is discussed. We argue, that specific problems arise here, which are quite different than the problems in the case of empirical sciences. In particular, the notion of unification depends on the philosophical standpoint. We give an analysis of the notion of unification from the point of view of formalism, Gödel's platonism and Quine's realism. In particular we show, that the concept of “having the same object of study” (...) should be made precise in the case of mathematical theories. In the appendix we give a working proposal of a certain understanding of this notion. (shrink)
A method is described for inducing a type-logical grammar from a sample of bare sentence trees which are annotated by lambda terms, called term-labelled trees . Any type logic from a permitted class of multimodal logics may be specified for use with the procedure, which induces the lexicon of the grammar including the grammatical categories. A first stage of semantic bootstrapping is performed, which induces a general form lexicon from the sample of term-labelled trees using Fulop’s (J Log Lang Inf (...) 14(1):49–86, 2005) procedure. Next we present a two-stage procedure for performing distributional learning by unifying the lexical types that are initially discovered. The first structural unification algorithm in essence unifies the initial family of sets of types so that the resulting grammar will generate all term-labelled trees that follow the usage patterns evident from the learning sample. Further altering the lexical categories to generate a recursively extended language can be accomplished by a second unification. The combined unification algorithm is shown to yield a new type-logical lexicon that extends the learning sample to a possibly infinite (and possibly context-sensitive) language in a principled fashion. Finally, the complete learning strategy is analyzed from the perspective of algorithmic learning theory; the range of the procedure is shown to be a class of term-labelled tree languages which is finitely learnable from good examples (Lange et al in Algorithmic learning theory, Vol 872 of lecture notes in artificial intelligence, Springer, Berlin, pp 423–437), and so is identifiable in the limit as a corollary. (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).
The dynamical hypothesis is strong in that, for it to be true, every cognitive phenomenon must be best modeled by a dynamical system. Depending on how it is interpreted, however, the hypothesis may be seen as probably false or even unfalsifiable. Strengthening the hypothesis to require unification, or at least coherence, across models in different cognitive domains alleviates this problem.
Pluralism with respect to the structure of explanations of facts is not uncommon. Wesley Salmon, for instance, distinguished two types of explanation: causal explanations (which provide insight in the causes of the fact we want to explain) and unification explanations (which fit the explanandum into a unified world view). The pluralism which Salmon and others have defended is compatible with several positions about the exact relation between these two types of explanations. We distinguish four such positions, and argue in (...) favour of one of them. We also compare our results with the views of some authors who have recently written on this subject. (shrink)
This article originated in a “cultural futures” course I taught in Seoul in 2007.1 As part of their semester project, students interviewed friends and family to identify futures that were likely to precipitate profound cultural shifts in their lives. Not surprisingly, “Korean unification” was at the top of students’ lists. After all, then-president Roh Moo-hyun had in many ways continued the “Sunshine” policies of his predecessor, President Kim Dae-jung, culminating in a largely symbolic train journey from the South to (...) the North in May 2007 and, perhaps more meaningfully, a new wave of emotional “separated family reunions” (isan’gajok sangbong). But what cultural and societal shifts might unification bring? Here .. (shrink)
Cartesian closed categories (CCCs) have played and continue to play an important role in the study of the semantics of programming languages. An axiomatization of the isomorphisms which hold in all Cartesian closed categories discovered independently by Soloviev and Bruce, Di Cosmo and Longo leads to seven equalities. We show that the unification problem for this theory is undecidable, thus settling an open question. We also show that an important subcase, namely unification modulo the linear isomorphisms, is NP-complete. (...) Furthermore, the problem of matching in CCCs is NP-complete when the subject term is irreducible. CCC-matching and unification form the basis for an elegant and practical solution to the problem of retrieving functions from a library indexed by types investigated by Rittri. It also has potential applications to the problem of polymorphic type inference and polymorphic higher-order unification, which in turn is relevant to theorem proving and logic programming. (shrink)
We show that the D A -unification problem is undecidable. That is, given two binary function symbols $\bigoplus$ and $\bigotimes$ , variables and constants, it is undecidable if two terms built from these symbols can be unified provided the following D A -axioms hold: \begin{align*}(x \bigoplus y) \bigotimes z &= (x \bigotimes z) \bigoplus (y \bigotimes z),\\x \bigotimes (y \bigoplus z) &= (x \bigotimes y) \bigoplus (x \bigotimes z),\\x \bigoplus (y \bigoplus z) &= (x \bigoplus y) \bigoplus z.\end{align*} Two (...) terms are D A -unifiable (i.e. an equation is solvable in D A ) if there exist terms to be substituted for their variables such that the resulting terms are equal in the equational theory D A . This is the smallest currently known axiomatic subset of Hilbert's tenth problem for which an undecidability result has been obtained. (shrink)
We present a kind of logic named multideductive logic and outline an application of it in the problem of theoretic-formal unification of physical theories dealing with the Bohr atom theory. This is just a preliminary study that will be developed in future papers.
We propose related algorithms for unification and constraint simplification in }F’&, a refinement of the simply-typed A-calculus with subtypes and bounded intersection types. }F""’ is intended as the basis of a logical framework in order to achieve more succinct and declarative axiomatiza-.
The epistemological problems of unification of two distinct theories are discussed. An approach related to the work of Soviet authors (Stepin, Podgoretzky and Smorodinsky) is used and developed. The notion of ‘crossbred objects’—theoretical objects with contradictory properties which are part of the domain of application of two independent theories—is introduced which helps to describe the dynamics of revolutionary theory change. The occurrence of the cross-contradiction of two theories is reconstructed and the reductionistic and the synthetic means of its elimination (...) are proposed. The results of the methodological analysis are applied to the paradox of equivalence. (shrink)
Higher order unification is a way of combining information (or equivalently, solving equations) expressed as terms of a typed higher order logic. A suitably restricted form of the notion has been used as a simple and perspicuous basis for the resolution of the meaning of elliptical expressions and for the interpretation of some non-compositional types of comparative construction also involving ellipsis. This paper explores another area of application for this concept in the interpretation of sentences containing intonationally marked focus, (...) or various semantic constructs which are sensitive to focus.Similarities and differences between this approach, and theories using alternative semantics, structured meanings, or flexible categorial grammars, are described. The paper argues that the higher order unification approach offers descriptive advantages over these alternatives, as well as the practical advantage of being capable of fairly direct computational implementation. (shrink)
In this paper two different approaches to unification will be compared, Relational Blockworld (RBW) and Hiley’s implicate order. Both approaches are monistic in that they attempt to derive matter and spacetime geometry ‘at once’ in an interdependent and background independent fashion from something underneath both quantum theory and relativity. Hiley’s monism resides in the implicate order via Clifford algebras and is based on process as fundamental while RBW’s monism resides in spacetimematter via path integrals over graphs whereby space, time (...) and matter are co-constructed per a global constraint equation. RBW’s monism therefore resides in being (relational blockworld) while that of Hiley’s resides in becoming (elementary processes). Regarding the derivation of quantum theory and relativity, the promises and pitfalls of both approaches will be elaborated. Finally, special attention will be paid as to how Hiley’s process account might avoid the blockworld implications of relativity and the frozen time problem of canonical quantum gravity. (shrink)
Unification grammars are known to be Turing-equivalent; given a grammar G and a word w, it is undecidable whether w L(G). In order to ensure decidability, several constraints on grammars, commonly known as off-line parsability (OLP), were suggested, such that the recognition problem is decidable for grammars which satisfy OLP. An open question is whether it is decidable if a given grammar satisfies OLP. In this paper we investigate various definitions of OLP and discuss their interrelations, proving that some (...) of the OLP variants are indeed undecidable. We then present a novel, decidable OLP constraint which is more liberal than the existing decidable ones. (shrink)
Daniel Steel argues that a causal theory of explanation can account for Ferguson's anthropological theory of Yanomami warfare but that a unification theory of explanation cannot. I argue that a unification theory can explain such an account, in a manner similar to Hempel's view of explanation in history. I go on to argue that the unification theory allows for different explanations of specific and general social circumstances.
In this paper we integrate a sorted unification calculus into free variable tableau methods for logics with term declarations. The calculus we define is used to close a tableau at once, unifying a set of equations derived from pairs of potentially complementary literals occurring in its branches. Apart from making the deduction system sound and complete, the calculus is terminating and so, it can be used as a decision procedure. In this sense we have separated the complexity of sorts (...) from the undecidability of first order logic. (shrink)
According to the traditional requirement, formulated already by William Whewell in his account of the “consilience of inductions” in 1840, an explanatory scientific theory should be independently testable by new kinds of phenomena. A good theory should have unifying power in the sense that it explains and predicts several mutually independent phenomena. This paper studies the prospects of Bayesianism to motivate this kind of unification criterion for abductive confirmation.
We present a kind of logic named multideductive logic and outline an application of it in the problem of theoretic-formal unification of physical theories dealing with the Bohr atom theory. This is just a preliminary study that will be developed in future papers.
A scientific theory, in order to be accepted as a part of theoretical scientific knowledge, must satisfy both empirical and non-empirical requirements, the latter having to do with simplicity, unity, explanatory character, symmetry, beauty. No satisfactory, generally accepted account of such non-empirical requirements has so far been given. Here, a proposal is put forward which, it is claimed, makes a contribution towards solving the problem. This proposal concerns unity of physical theory. In order to satisfy the non-empirical requirement of unity, (...) a physical theory must be such that the same laws govern all possible phenomena to which the theory applies. Eight increasingly demanding versions of this requirement are distinguished. Some implications for other non-empirical requirements, and for our understanding of science are indicated. (shrink)
This article generalizes the explanationist account of inference to the best explanation (IBE). It draws a clear distinction between IBE and abduction and presents abduction as the first step of IBE. The second step amounts to the evaluation of explanatory power, which consist in the degree of explanatory virtues that a hypothesis exhibits. Moreover, even though coherence is the most often cited explanatory virtue, on pain of circularity, it should not be treated as one of the explanatory virtues. Rather, coherence (...) should be equated with explanatory power and considered to be derivable from the other explanatory virtues: unification, explanatory depth and simplicity. (shrink)
In this note, I clarify the point of my paper “The Nature of Semantics: On Jackendoff’s Arguments” (NS) in light of Ray Jackendoff’s comments in his “Linguistics in Cognitive Science: The State of the Art.” Along the way, I amplify my remarks on unification.
The various behavioral disciplines model human behavior in distinct and incompatible ways. Yet, recent theoretical and empirical developments have created the conditions for rendering coherent the areas of overlap of the various behavioral disciplines. The analytical tools deployed in this task incorporate core principles from several behavioral disciplines. The proposed framework recognizes evolutionary theory, covering both genetic and cultural evolution, as the integrating principle of behavioral science. Moreover, if decision theory and game theory are broadened to encompass other-regarding preferences, they (...) become capable of modeling all aspects of decision making, including those normally considered “psychological,” “sociological,” or “anthropological.” The mind as a decision-making organ then becomes the organizing principle of psychology. (Published Online April 27 2007) Key Words: behavioral game theory; behavioral science; evolutionary theory; experimental psychology; gene-culture coevolution; rational actor model; socialization. (shrink)
Explanations contribute to our understanding of the world byembedding phenomena into general nomic patterns that we recognize in the world. Manyof these patterns are, of course, causal ones, but the declaration as ``causal'' often fails to determinethe explanatory power of the pattern. More important is the systematization capacity and the empiricalcontent of the pattern or theory with respect to explanations. We can specify these parameters moreprecisely within the framework of the structuralist view of theories.
Why did Einstein tirelessly study unified field theory for more than 30 years? In this book, the author argues that Einstein believed he could find a unified theory of all of nature's forces by repeating the methods he used when he formulated general relativity. The book discusses Einstein's route to the general theory of relativity, focusing on the philosophical lessons that he learnt. It then addresses his quest for a unified theory for electromagnetism and gravity, discussing in detail his efforts (...) with Kaluza-Klein and, surprisingly, the theory of spinors. From these perspectives, Einstein's critical stance towards the quantum theory comes to stand in a new light. This book will be of interest to physicists, historians and philosophers of science. (shrink)
In the paper it is shown that every physically sound Birkhoff – von Neumann quantum logic, i.e., an orthomodular partially ordered set with an ordering set of probability measures can be treated as partial infinite-valued Łukasiewicz logic, which unifies two competing approaches: the many-valued, and the two-valued but non-distributive, which have co-existed in the quantum logic theory since its very beginning.
This chapter examines four solutions to the problem of many models, and finds some fault or limitation with all of them except the last. The first is the naïve empiricist view that best model is the one that best fits the data. The second is based on Popper’s falsificationism. The third approach is to compare models on the basis of some kind of trade off between fit and simplicity. The fourth is the most powerful: Cross validation testing.
Carl Hempel1 set the tone for subsequent philosophical work on scientific explanation by resolutely locating the problem he wanted to address outside of epistemology. “Hempel’s problem,” as I will call it, was not to say what counts as evidence that X is the explanation of Y. Rather, the question was what it means for X to explain Y. Hempel’s theory of explanation and its successors don’t tell you what to believe; instead, they tell you which of your beliefs (if any) (...) can be said to explain a given target proposition. (shrink)
Although Trautman (1966) appears to give a unified‐field treatment of electrodynamics in Newtonian spacetime, there are difficulties in cogently interpreting it as such in relation to the facts of electromagnetic and magneto‐electric induction. Presented here is a covariant, nonunified field treatment of the Maxwell‐Lorentz theory with absolute space. This dispels a worry in Earman (1989) as to whether there are any historically realistic examples in which absolute space plays an indispensable role. It also shows how Trautman's formulation can be rendered (...) coherent, albeit at the cost of deunification, by reinterpreting the Maxwell tensor as a composite object involving, in part, elements from Newtonian spacetime. (shrink)
John Polkinghorne claims there are no real distinctions between general providence, special providence and miracle. In this paper I determine whether this claim could be true given Polkinghorne’s wider account of these types of divine action. I conclude that this claim could be true, but only given a particular reading of Polkinghorne. I then defend this reading in light of two potential objections.
We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause source of the ellipsis, our analysis requires no such hidden ambiguity. Further, the analysis follows relatively directly from an abstract statement of the ellipsis interpretation problem. It predicts correctly a wide range of interactions between ellipsis and other semantic phenomena such as quantifier scope and bound anaphora. Finally, although the (...) analysis itself is stated nonprocedurally, it admits of a direct computational method for generating interpretations. (shrink)
A mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics is proposed. For this a Hilbert space H of functions of four variables x,t furnished with an additional indefinite inner product invariant under Poincare transformations is introduced. For a class of functions in H that are well localized in the time variable the usual formalism of non-relativistic quantum mechanics is derived. In particular, the interference in time for these functions is suppressed; a motion in H becomes (...) the usual Shrodinger evolution with t as a parameter. The relativistic invariance of the construction is proved. The usual theory of relativity on Minkowski space-time is shown to be ``isometrically and equivariantly embedded'' into H. That is, classical space-time is isometrically embedded into H, Poincare transformations have unique extensions to isomorphisms of H and the embedding commutes with Poincare transformations. (shrink)
I consider a way the concept of causation could be excised from chemical practice, suggested by Kitcher's view that causes are just a subset of unifying patterns which play a particular psychological role for us. Kitcherian chemistry is at first blush well equipped to handle explanatory tasks. However, it would force chemists to accept certain unifying patterns as explanatory, which they do not think are at all explanatory. This might head off some descriptive lines of enquiry and damage prospects for (...) the identification of potentially larger‐scale explanations. More important than this, to chemists, it could put them off from finding the explanatory patterns that are true—true because they get at the real structure of the chemical phenomena in the world. (shrink)
