Much of cognitive neuroscience as well as traditional cognitive science is engaged in a quest for mechanisms through a project of decomposition and localization of cognitive functions. Some advocates of the emerging dynamical systems approach to cognition construe it as in opposition to the attempt to decompose and localize functions. I argue that this case is not established and rather explore how dynamical systems tools can be used to analyze and model cognitive functions without abandoning the use of (...) class='Hi'>decomposition and localization to understand mechanisms of cognition. (shrink)
Michael Dummett has long argued that Frege is committed to recognizing a distinction between two sorts of analysis of propositional contents: 'analysis', which reveals the entities that one must grasp in order to apprehend a given propositional content; and 'decomposition', which is used in recognizing the validity of certain inferences. Whereas any propositional content admits of a unique ultimate 'analysis' into simple constituents, it also admits of distinct 'decompositions', no one of which is ultimately privileged over the others. I (...) argue that although Russell accepts this distinction between analysis and decomposition, Frege does not. In particular, I consider claims which Dummett makes regarding how 'analysis' and 'decomposition' are related to two different models Frege at least suggests in discussing the composition of thoughts, the part/whole model and the function/argument model; and I argue that in each case, while Russell accepts views which Dummett attributes to Frege, Frege does not. (shrink)
The idea that quotidian, middle-level concepts typically have internal structure -- definitional, statistical, or whatever -- plays a central role in practically every current approach to cognition. Correspondingly, the idea that words that express quotidian, middle-level concepts have complex representations "at the semantic level" is recurrent in linguistics; it's the defining thesis of what is often called "lexical semantics," and it unites the generative and interpretive traditions of grammatical analysis. Recently, Hale and Keyser (1993) have provided a budget of sophisticated (...) and persuasive arguments for the claim that `denominal' verbs are typically derived from phrases containing the corresponding nouns: `singvtr' is supposed to come from something like DO A SONG; `saddlevtr' is supposed to come from something like PUT A SADDLE ON; `shelvevtr' is supposed to come from something like PUT ON A SHELF, and so forth.1 We think these are among the most persuasive arguments for lexical decomposition in the linguistics literature. Still, this paper is going to claim that they are finally unconvincing. In Part 1, we will show that there are quite serious arguments of a familiar kind against the decompositional analyses that Hale and Keyser (henceforth, HK) propose; in Part 2 we'll show that the arguments that HK offer in favor of their analyses are flawed. (shrink)
In this paper we argue that an operational organism concept can help to overcome the structural deficiency of mathematical models in biology. In our opinion, the structural deficiency of mathematical models lies mainly in our inability to identify functionally relevant biological characters in biological systems, and not so much in a lack of adequate mathematical representations of biological processes. We argue that the problem of character identification in biological systems is linked to the question of a properly formulated organism concept. (...) Lastly, we demonstrate how a decomposition of an organism into independent characters in the context of a specific biological process--such as adaptation by means of natural selection--depends on the dynamical properties and invariance conditions of the equations that describe this process. (shrink)
De Finetti's representation theorem is a special case of the ergodic decomposition of stationary probability measures. The problems of the interpretation of probabilities centred around de Finetti's theorem are extended to this more general situation. The ergodic decomposition theorem has a physical background in the ergodic theory of dynamical systems. Thereby the interpretations of probabilities in the cases of de Finetti's theorem and its generalization and in ergodic theory are systematically connected to each other.
Frege seems to hold two incompatible theses:(i) that sentences differing in structure can yet express the same sense; and (ii) that the senses of the meaningful parts of a complex term are determinate parts of the sense of the term. Dummett offered a solution, distinguishing analysis from decomposition. The present paper offers an embellishment of Dummett?s distinction by providing a way of depicting the internal structures of complex senses?determinate structures that yield distinct decompositions. Decomposition is then shown to (...) be adequate as a foundation for the informativity and analyticity of logic. (shrink)
De Finetti's representation theorem is a special case of the ergodic decomposition of stationary probability measures. The problems of the interpretation of probabilities centred around de Finetti's theorem are extended to this more general situation. The ergodic decomposition theorem has a physical background in the ergodic theory of dynamical systems. Thereby the interpretations of probabilities in the cases of de Finetti's theorem and its generalization and in ergodic theory are systematically connected to each other.
We obtain a p-adic semilinear cell decomposition theorem using methods developed by Denef in [Journal fur die Reine und Angewandte Mathematik, vol. 369 (1986), pp. 154-166]. We also prove that any set definable with quantifiers in (0, 1, +, =, λq, Pn){n∈N,q∈Qp} may be defined without quantifiers, where λq is scalar multiplication by q and Pn is a unary predicate which denotes the nonzero nth powers in the p-adic field Qp. Such a set is called a p-adic semilinear set (...) in this paper. Some further considerations are discussed in the last section. (shrink)
We introduce here and investigate the notion of an alternative tree of decomposition. We show (Theorem 5) a general method of finding out all non-alternative trees of the alternative tree determined by a diagram of decomposition.
This paper defends cognitive neuroscience’s project of developing mechanistic explan- ations of cognitive processes through decomposition and localization against objections raised by William Uttal in The New Phrenology. The key issue between Uttal and researchers pursuing cognitive neuroscience is that Uttal bets against the possibility of decomposing mental operations into component elementary operations which are localized in distinct brain regions. The paper argues that it is through advancing and revising what are likely to be overly simplistic and incorrect decompositions (...) that the goals of cognitive neuroscience are likely to be achieved. (shrink)
I discuss two subjects in Samir Okasha’s excellent book, Evolution and the Levels of Selection. In consonance with Okasha’s critique of the conventionalist view of the units of selection problem, I argue that conventionalists have not attended to what realists mean by group, individual, and genic selection. In connection with Okasha’s discussion of the Price equation and contextual analysis, I discuss whether the existence of these two quantitative frameworks is a challenge to realism.
To have an ontology is to interpret a world. In this paper we argue that the brain, viewed as a representational system aimed at interpreting our world, possesses an ontology too. It creates primitives and makes existence assumptions. It decomposes target space in a way that exhibits a certain invariance, which in turn is functionally significant. We will investigate which are the functional regularities guiding this decomposition process, by answering to the following questions: What are the explicit and implicit (...) assumptions about the structure of reality, which at the same time shape the causal profile of the brain's motor output and its representational deep structure, in particular of the conscious mind arising from it (its ''phenomenal output'')? How do they constrain high-level phenomena like conscious experience, the emergence of a first-person perspective, or social cognition? By reviewing a series of neuroscientific results and integrating them with a wider philosophical perspective, we will emphasize the contribution the motor system makes to this process. As it will be shown, the motor system constructs goals, actions, and intending selves as basic constituents of the world it interprets. It does so by assigning a single, unified causal role to them. Empirical evidence demonstrates that the brain models movements and action goals in terms of multimodal representations of organism-object-relations. Under a representationalist analysis, this process can be conceived of as an internal, dynamic representation of the intentionality-relation itself. We will show how such a complex form of representational content, once it is in place, can later function as a functional building block for social cognition and for a more complex, consciously experienced representation of the first-person perspective as well. (shrink)
In this paper, I suggest that the notion of module explicitly defined by Peter Carruthers in The Architecture of The Mind (Carruthers 2006) is not really In use in the book. Instead, a more robust notion seems to be actually in play. The more robust notion, albeit implicitly assumed, seems to be far more useful for making claims about the modularity of mind. Otherwise, the claims would become trivial. This robust notion will be reconstructed and improved upon by putting it (...) into a more general framework of mental architecture. I defend the view that modules are the outcome of structural rather than functional decomposition and that they should be conceived as near decomposable systems. (shrink)
Kant is gaining popularity in business ethics because the categorical imperative rules out actions such as deceptive advertising and exploitative working conditions, both of which treat people merely as means to an end. However, those who apply Kant in this way often hold businesses themselves morally accountable, and this conception of collective responsibility contradicts the kind of moral agency that underlies Kant's ethics. A business has neither inclinations nor the capacity to reason, so it lacks the conditions necessary for constraint (...) by the moral law. Instead, corporate policies ought to be understood as analogous to legal constraints. They may encourage or discourage certain actions, but they cannot determine a person's maxim - which for Kant is the focus of moral judgment. Because there is no collective intention apart from any intentions of the individual agents who act as members of the corporation, an organization itself has no moral obligations. This poses a dilemma: either apply the categorical imperative to the actions of particular businesspeople and surrender the notion of collective responsibility, or apply a different moral theory to the actions of businesses themselves. Given the diffusion of responsibility in a bureaucracy, the explanatory usefulness of collective responsibility may force business ethicists to abandon Kant's moral philosophy. (shrink)
This study is in two parts. In the first part, various important principles of classical extensional mereology are derived on the basis of a nice axiomatization involving ‘part of’ and fusion. All results are proved here with full Fregean (and Gentzenian) rigor. They are chosen because they are needed for the second part. In the second part, this natural-deduction framework is used in order to regiment David Lewis’s justification of his Division Thesis, which features prominently in his combination of mereology (...) with class theory. The Division Thesis plays a crucial role in Lewis’s informal argument for his Second Thesis in his book Parts of Classes. In order to present Lewis’s argument in rigorous detail, an elegant new principle is offered for the theory that combines class theory and mereology. The new principle is called the Canonical Decomposition Thesis. It secures Lewis’s Division Thesis on the strong construal required in order for his argument to go through. The exercise illustrates how careful one has to be when setting up the details of an adequate foundational theory of parts and classes. The main aim behind this investigation is to determine whether an anti-realist, inferentialist theorist of meaning has the resources to exhibit Lewis’s argument for his Second Thesis—which is central to his marriage of class theory with mereology—as a purely conceptual one. The formal analysis shows that Lewis’s argument, despite its striking appearance to the contrary, can be given in the constructive, relevant logic IR. This is the logic that the author has argued, elsewhere, to be the correct logic from an anti-realist point of view. The anti-realist is therefore in a position to regard Lewis’s argument as purely conceptual. (shrink)
I attempt to complement my earlier critiques of human sociobiology, by offering an account of how evolutionary ideas might legitimately be employed in the study of human social behavior. The main emphasis of the paper is the need to integrate studies of proximate mechanisms and their ontogenesis with functional/evolutionary research. Human psychological complexity makes it impossible to focus simply on specific types of human behavior and ask for their functional significance. For any of the kinds of behavior patterns that have (...) occupied human sociobiologists, the underlying proximate mechanisms are very likely to be linked to a broad spectrum of types of behavior, and we cannot expect that natural selection will have acted directly on any individual element from this spectrum. I illustrate this general point with a specific example, considering the traditional sociobiological account of human incest-avoidance and outlining an alternative approach to the phenomena. The example is intended to show the possibility of a more rigorous and sophisticated successor to human sociobiology, which I call "human behavioral ecology". (shrink)
My main reaction to MCGivern’s paper was one of dialectical puzzlement. Block argues that, Macro Non-Reduction: [all] macro properties are irreducible to the micro properties on which they supervene..
Book review of Bechtel and Richardson, Discovering Complexity (1993). Review suggests that one theme of the book -- that scientific reason is "constituted" in part by a cognitive strategy of finding complexity -- is not fully supported.
The main goal of the paper is to suggest some analytic proof systems for LC and its finite-valued counterparts which are suitable for proof-search. This goal is achieved through following the general Rasiowa-Sikorski methodology for constructing analytic proof systems for semantically-defined logics. All the systems presented here are terminating, contraction-free, and based on invertible rules, which have a local character and at most two premises.
Given two incomparable c.e. Turing degrees a and b, we show that there exists a c.e. degree c such that c = (a ⋃ c) ⋂ (b ⋃ c), a ⋃ c | b ⋃ c, and c < a ⋃ b.
Functions of type n are characteristic functions on n-ary relations. In Beyond the Frege Boundary [6], Keenan established their importance for natural language semantics, by showing that natural language has many examples of irreducible type n functions, where he called a function of type n reducible if it can be represented as a composition of functions of type 1 . We will give a normal form theorem for functions of type n , and use this to show that natural language (...) has many examples of irreducible type n functions in a much stronger sense, where we take a function to be reducible if it can be represented as a composition of functions of lower types. (shrink)
Ernie Lepore and Jerry Fodor have published a series of original and controversial essays on issues relating to compositionality in language and mind; they have...
Frege’s writings contain arguments for the thesis (i) that a thought expressed by a sentence S is a structured object whose composition pictures the composition of S, and for the thesis (ii) that a thought is an unstructured object. I will argue that Frege’s reasons for both (i) and (ii) are strong. Frege’s explanation of the difference in sense between logically equivalent sentences rests on assumption (i), while Frege’s claim that the same thought can be decomposed differently makes (ii) plausible. (...) Thoughts are supposed to do work that requires that they be structured and work that requires that they be unstructured. But this cannot be! While the standard response to this problem is to reject either (i) or (ii), I propose a charitable repair in the spirit of Frege’s theory that accepts both. The key idea can be found in Frege’s Basic Laws of Arithmetic(BL, GGA). Frege argues that the thought expressed by a sentence is determined by the truth-conditions that can be derived from the semantic axioms for the sentence constituents. The fact that the same axiomatic truth-condition can be derived in different ways from different semantic axioms suggests a Fregean solution of the dilemma: A thought is a type that is instantiated by all sequences of senses (decomposed thoughts) that have the same axiomatic truth-conditions. This allows for multiple decomposability of the same thought (for different decomposed thoughts can have the same axiomatic truth-conditions) and for a notion of containment (the decomposed thought contains those senses whose semantic axioms are needed in the derivation of the truth-conditions). My proposal combines the virtues of (i) and (ii) without inheriting their vices. (shrink)
Might the world be structured, as Leibniz thought, so that every part of matter is divided ad infinitum? The Physicist David Bohm accepted infinitely decomposable matter, and even Steven Weinberg, a staunch supporter of the idea that science is converging on a final theory, admits the possibility of an endless chain of ever more fundamental theories. However, if there is no fundamental level, physicalism, thought of as the view that everything is determined by fundamental phenomena and that all fundamental phenomena (...) are physical, turns out false, for in such a world, there are no fundamental phenomena, and so fundamental phenomena determine nothing. While some take physicalism necessarily to posit a fundamental level, here I present a thesis of physicalism that allows for its truth even in an infinitely decomposable world. (shrink)
In this paper, we describe the conceptual elusiveness of the notion of function as used in engineering practice. We argue that it should be accepted as an ambiguous notion, and then review philosophical argumentations in which engineering functions occur in order to identify the consequences of this ambiguity. Function is a key notion in engineering, yet is used by engineers systematically in a variety of meanings. First, we demonstrate that this ambiguous use is rational for engineers by considering the role (...) of functions in design methods and by analysing the ambiguity in terms of Kuhn’s notion of methodological incommensurability. Second, we discuss ontological and mereological analyses of engineering functions and describe a proof that subfunctions cannot formally be taken as parts of the functions they decompose. Engineering functions figure sometimes in philosophical work and are then typically taken as having an unambiguous, well-defined meaning. Finally, we therefore revisit work in philosophy of technology on the dual nature of technical artefacts, in philosophy of science on functional and mechanistic explanations, and in philosophy of biology on biological functions, and explore the consequences of the fact that engineering function is an ambiguous notion. It is argued that one of these consequences may be that also the notion of biological function has an ambiguous meaning. (shrink)
Artificial intelligence research has foundered on the issue of representation. When intelligence is approached in an incremental manner, with strict reliance on interfacing to the real world through perception and action, reliance on representation disappears. In this paper we outline our approach to incrementally building complete intelligent Creatures. The fundamental decomposition of the intelligent system is not into independent information processing units which must interface with each other via representations. Instead, the intelligent system is decomposed into independent and parallel (...) activity producers which all interface directly to the world through perception and action, rather than interface to each other particularly much. The notions of central and peripheral systems evaporateeverything is both central and peripheral. Based on these principles we have built a very successful series of mobile robots which operate without supervision as Creatures in standard office environments. (shrink)
Among the most pervasive and fundamental assumptions in cognitive science is that the human mind (or mind-brain) is a mechanism of some sort: a physical device com- posed of functionally specifiable subsystems. On this view, functional decomposition – the analysis of the overall system into functionally specifiable parts – becomes a central project for a science of the mind, and the resulting theories of cognitive archi- tecture essential to our understanding of human psychology.
It is commonplace in cognitive science that concepts are individuated in terms of the roles they play in the cognitive lives of thinkers, a view that Jerry Fodor has recently been dubbed ‘Concept Pragmatism’. Quinean critics of Pragmatism have long argued that it founders on its commitment to the analytic/synthetic distinction, since without such a distinction there is plausibly no way to distinguish constitutive from non-constitutive roles in cognition. This paper considers Fodor’s empirical arguments against analyticity, and in particular his (...) arguments against lexical decomposition and definitions, and argues that Concept Pragmatists have two viable options with respect to them. First, Concept Pragmatists can confront them head-on, and argue that they do not show that lexical items are semantically primitive or that lexical concepts are internally unstructured. Second, Pragmatists may accept that these arguments show that lexical concepts are atomic, but insist that this need not entail that Pragmatism is false. For there is a viable version of Concept Pragmatism that does not take lexical items to be semantically structured or lexical concepts to be internally structured. Adopting a version of Pragmatism that takes meaning relations to be specified by inference rules, or meaning postulates, allows one to accept the empirical arguments in favor of Concept Atomism, while at the same time deny that such arguments show that there are no analyticities. The paper concludes by responding to Fodor’s recent objection that such a version of Concept Pragmatism has unhappy consequences concerning the relation between concept constitution and concept possession. (shrink)
Chomsky’s conception of semantics must contend with both philosophical skepticism and contrary traditions in linguistics. In “Two Dogmas” Quine argued that “...it is non-sense, and the root of much non-sense, to speak of a linguistic component and a factual component in the truth of any individual statement.” If so, it follows that language as the object of semantic investigation cannot be separated from collateral information. F. R. Palmer pursues a similar contention in his recent survey of issues in semantic theory: (...) “...it is impossible even in theory to draw a clear line between the meaning of a word or sentence and all possible relevant information about it.” In spite of such skepticism, and through a variety of theories, devotion to lexical decomposition and truth dependent on language has not abated. The purpose of this paper is to focus related criticism and briefly put forward an alternative conception of empirical semantics. (shrink)
In Logical Properties, Colin McGinn offers a new theory of truth, which he describes as “thick disquotationalism.” In keeping with wider theme of the book, truth emerges as conceptually primitive. Echoing Moore, it is simple and unanalyzable. Though truth cannot be analyzed, in the sense of giving a conceptual decomposition, McGinn argues that truth can be defined. A non-circular statement of its application conditions can be given. This makes truth a singularly remarkable property. Indeed, by McGinn’s lights, it is (...) the only property which enjoys being both unanalyzable and definable. (shrink)
Contemporary arguments for forms of psycho-physical dualism standardly depart from phenomenal aspects of consciousness ('what it is like' to have some particular conscious experience). Conceptual aspects of conscious experience, as opposed to phenomenal or visual/perceptual ones, are often taken to be within the scope of functionalist, reductionist, or physicalist theories. I argue that the particular conceptual structure of human consciousness makes this asymmetry unmotivated. The argument for a form of dualism defended here proceeds from the empirical premise that (...) conceptual structure in a linguistic creature like us is a combinatorial and compositional system that implicates a distinction between simple and complex, or 'atomic' and 'molecular' concepts. The argument is that conceptual atoms, qua atoms, are irreducible to anything else. If so, and if the atoms are essentially semantic, a form of dualism follows: though positively inviting naturalistic inquiry into the semantic and mental aspects of nature, it requires that we look at the mental as a primitive domain of nature. Schematically, then, the argument is as follows: (1) Human consciousness/thought is conceptually structured. (2) The human conceptual system is a 'particulate' system at a syntactic and semantic level of representation (the notion of a 'particulate' system is developed in Section 2). (3) This implies the existence of conceptual 'particles', concepts that have no further semantic decomposition ('atoms'). (4) A conceptual atom cannot be explained in terms of anything that does not involve its own intrinsic properties (Section 3). (5) Physicalism as normally conceived is inconsistent with (3) and (4) (Section 4). (shrink)
Although there has been much recent discussion on mechanisms in philosophy of science and social theory, no shared understanding of the crucial concept itself has emerged. In this paper, a distinction between two core concepts of mechanism is made on the basis that the concepts correspond to two different research strategies: the concept of mechanism as a componential causal system is associated with the heuristic of functional decomposition and spatial localization and the concept of mechanism as an abstract form (...) of interaction is associated with the strategy of abstraction and simple models. The causal facts assumed and the theoretical consequences entailed by an explanation with a given mechanism differ according to which concept of mechanism is in use. Research strategies associated with mechanism concepts also involve characteristic biases that should be taken into account when using them, especially in new areas of application. (shrink)
Richard Levins’ distinction between aggregate, composed and evolved systems acquires new significance as we recognize the importance of mechanistic explanation. Criteria for aggregativity provide limiting cases for absence of organization, so through their failure, can provide rich detectors for organizational properties. I explore the use of failures of aggregativity for the analysis of mechanistic systems in diverse contexts. Aggregativity appears theoretically desireable, but we are easily fooled. It may be exaggerated through approximation, conditions of derivation, and extrapolating from some conditions (...) of decomposition illegtimately to others. Evolved systems particularly may require analyses under alternative complementary decompositions. Exploring these conditions helps us to better understand the strengths and limits of reductionistic methods. (shrink)
I resolve an argument over “flat” versus “dimensioned” theories of realization. The theories concern, in part, whether realized and realizing properties are instantiated by the same individual (the flat theory) or different individuals in a part-whole relationship (the dimensioned theory). Carl Gillett has argued that the two views conflict, and that flat theories should be rejected on grounds that they fail to capture scientific cases involving a dimensioned relation between individuals and their constituent parts. I argue on the contrary that (...) the two types of theory complement one another, even on the same range of scientific cases. I illustrate the point with two popular functionalist versions of flat and dimensioned positions – causal-role functionalism and a functional analysis by decomposition – that combine into a larger picture I call “comprehensive functional realization.” I also respond to some possible objections to this synthesis of functionalist views. (shrink)
In the context of mechanistic explanation, reductionistic research pursues a decomposition of complex systems into their component parts and operations. Using research on circadian rhythms and memory consolidation as exemplars, we consider the gains to be made by finding genes and proteins that figure in mechanisms underlying behavioral phenomena. However, we also show that such research is insufficient to explain the initial phenomenon. Accordingly, researchers have increasingly recognized the need to consider higher-level organization and integration with other systems. This (...) illustrates a common need to complement reductionistic inquiry with investigations at higher levels and identifies a trajectory whereby cognitive science can embrace molecular neuroscience without surrendering its own contributions. (shrink)
Explaining the complex dynamics exhibited in many biological mechanisms requires extending the recent philosophical treatment of mechanisms that emphasizes sequences of operations. To understand how nonsequentially organized mechanisms will behave, scientists often advance what we call dynamic mechanistic explanations. These begin with a decomposition of the mechanism into component parts and operations, using a variety of laboratory-based strategies. Crucially, the mechanism is then recomposed by means of computational models in which variables or terms in differential equations correspond to properties (...) of its parts and operations. We provide two illustrations drawn from research on circadian rhythms. Once biologists identified some of the components of the molecular mechanism thought to be responsible for circadian rhythms, computational models were used to determine whether the proposed mechanisms could generate sustained oscillations. Modeling has become even more important as researchers have recognized that the oscillations generated in individual neurons are synchronized within networks; we describe models being employed to assess how different possible network architectures could produce the observed synchronized activity. (shrink)
There has been much interest in the possibility of connectionist models whose representations can be endowed with compositional structure, and a variety of such models have been proposed. These models typically use distributed representations that arise from the functional composition of constituent parts. Functional composition and decomposition alone, however, yield only an implementation of classical symbolic theories. This paper explores the possibility of moving beyond implementation by exploiting holistic structure-sensitive operations on distributed representations. An experiment is performed using Pollack’s (...) Recursive Auto-Associative Memory. RAAM is used to construct distributed representations of syntactically structured sentences. A feed-forward network is then trained to operate directly on these representations, modeling syn- tactic transformations of the represented sentences. Successful training and generalization is obtained, demonstrating that the implicit structure present in these representations can be used for a kind of structure-sensitive processing unique to the connectionist domain. (shrink)
Some theorists who emphasize the complexity of biological and cognitive systems and who advocate the employment of the tools of dynamical systems theory in explaining them construe complexity and reduction as exclusive alternatives. This paper argues that reduction, an approach to explanation that decomposes complex activities and localizes the components within the complex system, is not only compatible with an emphasis on complexity, but provides the foundation for dynamical analysis. Explanation via decomposition and localization is nonetheless extremely challenging, and (...) an analysis of recent cognitive neuroscience research on memory is used to illustrate what is involved. Memory researchers split between advocating memory systems and advocating memory processes, and I argue that it is the latter approach that provides the critical sort of decomposition and localization for explaining memory. The challenges of linking distinguishable functions with brain processes is illustrated by two examples: competing hypotheses about the contribution of the hippocampus and competing attempts to link areas in frontal cortex with memory processing. (shrink)
This paper is about the semantic analysis of referentially opaque verbs like seek and owe that give rise to nonspecific readings. It is argued that Montague's categorization (based on earlier work by Quine) of opaque verbs as properties of quantifiers runs into two serious difficulties: the first problem is that it does not work with opaque verbs like resemble that resist any lexical decomposition of the seek ap try to find kind; the second one is that it wrongly predicts (...) de dicto (i.e. narrow scope) readings due to quantified noun phrases in the object positions of such verbs. It is shown that both difficulties can be overcome by an analysis of opaque verbs as operating on properties. This is a strongly modified version of a paper entitled lsquoDo We Bear Attitudes towards Quantifiers?rsquo that I have presented at conferences in Gosen (Gesellschaft für Sprachwissenschaft), Ithaca (SALT I), and Konstanz (Lexikon). I owe a special debt to Hans Kamp and Arnim von Stechow for shaping my views on the subject of this paper during the past ten years or so. Comments from and discussions with the following friends and colleagues have also led to considerable improvements: Heinrich Beck, Steve Berman, David Dowty, Veerle van Geenhoven, Fritz Hamm, Irene Heim, Wolfgang Klein, Angelika Kratzer, Michael Morreau, Barbara Partee, Mats Rooth, Roger Schwarzschild, Wolfgang Sternefeld, Emil Weydert, Henk Zeevat, and three referees. (shrink)
The idea that quotidian, middle-level concepts typically have internal structure-definitional, statistical, or whatever—plays a central role in practically every current approach to cognition. Correspondingly, the idea that words that express quotidian, middle-level concepts have complex representations "at the semantic level" is recurrent in linguistics; it is the defining thesis of what is often called "lexical semantics," and it unites the generative and interpretive traditions of grammatical analysis. Hale and Keyser (HK) (1993) have endorsed a version of lexical decomposition according (...) to which "denominal" verbs are typically derived from phrases containing the corresponding nouns: ‘singvtr’ is supposed to come from something like DO A SONG; ‘saddlevtr’ is supposed to come from something like PUT A SADDLE ON; ‘shelvevtr’ is supposed to come from something like PUT ON A SHELF; and so forth.1 Their case for these claims revives a form of argument, the "impossible-word" argument, which has for some time been in eclipse. In this article we will claim that, whatever the right account of lexical decomposition eventually turns out to be, impossible-word arguments are infirm and should be discounted. We will use HK's paper as a text for this critique. (shrink)
Social Judgement Theory (SJT) evolved from Egon Brunswik's Probabilistic Functionalist psychology coupled with multiple correlation and regression-based statistical analysis. Through its representational device, the Lens Model, SJT has become a widely used, systems-oriented perspective for analysing human judgement in specific ecological circumstances. Judgements are assumed to result from the integration of different cues or sources of perceptual information from the environment. Special advantages accrue to the SJT approach when criterion values (or correct values) for judgement are also available, as this (...) permits the comparison of judgement processes to environmental processes and leads naturally to the generation of cognitive feedback as an aid to facilitate learning. In contrast to more prescriptive approaches to decision analysis, the SJT approach analyses judgements by decomposing the judgement process after judgements have been rendered. This a posteriori decomposition is accomplished by first using multiple regression analysis to recover prediction equations for both the judgement and ecological systems and then using the Lens Model Equation to compare those systems. SJT methods maintain close contact with ecological circumstances by employing the principle of representative design (which focuses on how the researcher obtains the stimuli for judgement) and avoiding unwarranted over-generalisations from nomothetic aggregation (e.g. averaging across judges) through the use of idiographic statistical analysis. SJT methods have proven valuable in the analysis of individual judgements as well as groupbased judgements where conflict becomes likely. (shrink)
I propose to sketch my views on several aspects of the philosophy of mathematics that I take to be especially relevant to philosophy as a whole. The relevance of my discussion would, I think, become more evident, if the reader keeps in mind the function of (the philosophy of) mathematics in philosophy in providing us with more transparent aspects of general issues. I shall consider: (1) three familiar examples; (2) logic and our conceptual frame; (3) communal agreement and objective certainty; (...) (4) the transcommunal universality of mathematics; (5) the big jump to the potential infinite; (6) the reconciliation of local creation with the hypothesis of discovery; (7) Platonism as realism plus conceptualism; (8) foundational studies and mathematical practice; and (9) the decomposition of philosophical disagreements. The views of Gödel and Wittgenstein are emphasized in order to add specificity to the discussions. (shrink)
The representational dynamics of the brain is a subsymbolic process, and it has to be conceived as an "agent-free" type of dynamical self-organization. However, in generating a coherent internal world-model, the brain decomposes target space in a certain way. In doing so, it defines an "ontology": to have an ontology is to interpret a world. In this paper we argue that the brain, viewed as a representational system aimed at interpreting the world, possesses an ontology too. It decomposes target space (...) in a way that exhibits certain invariances, which in turn are functionally significant. A challenge for empirical research is to determine which are the functional regularities guiding this decomposition process. What are the explicit and implicit assumptions about the structure of reality, which at the same time shape the causal profile of the brain's motor output and the representational deep structure of the conscious mind arising from it (its "phenomenal output")? How do they constrain high-level phenomena like conscious experience, the emergence of a first-person perspective, or social cognition? By reviewing a series of neuroscientific results, we focus on the contribution the motor system makes to this process. As it turns out, the motor system constructs goals, actions, and intending selves as basic constituents of the world it interprets. It does so by assigning a single, unified causal role to them. Empirical evidence now clearly shows how the brain actually codes movements and action goals in terms of multimodal representations of organism-object relations. Under a representationalist analysis, this process can be interpreted as an internal representation of the intentionality relation itself. We try to show how such a more complex form of representational content, once it is in place, can later function as the building block for social cognition and a for more complex, consciously experienced representation of the first-person perspective as well. The motor system may therefore play a decisive role in understanding how the functional ontology of the human brain could be gradually extended into the subjective and social domains. (shrink)
Transcranial magnetic stimulation (TMS) is a method capable of transiently modulating neural excitability. Depending on the stimulation parameters information processing in the brain can be either enhanced or disrupted. This way the contribution of different brain areas involved in mental processes can be studied, allowing a functional decomposition of cognitive behavior both in the temporal and spatial domain, hence providing a functional resolution of brain/mind processes. The aim of the present paper is to argue that TMS with its ability (...) to draw causal inferences on function and its neural representations is a valuable neurophysiological tool for investigating the causal basis of neuronal functions and can provide substantive insight into the modern interdisciplinary and (anti)reductionist neurophilosophical debates concerning the relationships between brain functions and mental abilities. Thus, TMS can serve as a heuristic method for resolving causal issues in an arena where only correlative tools have traditionally been available. (shrink)
In this paper, we compare the mechanisms of protein synthesis and natural selection. We identify three core elements of mechanistic explanation: functional individuation, hierarchical nestedness or decomposition, and organization. These are now well understood elements of mechanistic explanation in fields such as protein synthesis, and widely accepted in the mechanisms literature. But Skipper and Millstein have argued (2005) that natural selection is neither decomposable nor organized. This would mean that much of the current mechanisms literature does not apply to (...) the mechanism of natural selection. (shrink)
According to one of Leibniz's theories of contingency a proposition is contingent if and only if it cannot be proved in a finite number of steps. It has been argued that this faces the Problem of Lucky Proof , namely that we could begin by analysing the concept ‘Peter’ by saying that ‘Peter is a denier of Christ and …’, thereby having proved the proposition ‘Peter denies Christ’ in a finite number of steps. It also faces a more general but (...) related problem that we dub the Problem of Guaranteed Proof . We argue that Leibniz has an answer to these problems since for him one has not proved that ‘Peter denies Christ’ unless one has also proved that ‘Peter’ is a consistent concept, an impossible task since it requires the full decomposition of the infinite concept ‘Peter’. We defend this view from objections found in the literature and maintain that for Leibniz all truths about created individual beings are contingent. (shrink)
While there is controversy over which of several naturalistic theories of the mental is most plausible, there is consensus regarding the desideratum of a naturalistically respectable theory. A naturalistic theory of the mental, it is agreed, must explicate representation in nonintentional terms. I argue that this constraint does not get at the heart of what it is to be natural. On the one hand, it fails to provide us with a meaningful distinction between the natural and the unnatural. On the (...) other hand, it unfairly suggests that we withhold judgment on those successes our sciences of the mind have already achieved until a convincing decomposition of the mental is available. I urge a new conception of naturalism that focuses less upon ontological considerations and more upon methodological ones. (shrink)
Biological atomism postulates that all life is composed of elementary and indivisible vital units. The activity of a living organism is thus conceived as the result of the activities and interactions of its elementary constituents, each of which individually already exhibits all the attributes proper to life. This paper surveys some of the key episodes in the history of biological atomism, and situates cell theory within this tradition. The atomistic foundations of cell theory are subsequently dissected and discussed, together with (...) the theory’s conceptual development and eventual consolidation. This paper then examines the major criticisms that have been waged against cell theory, and argues that these too can be interpreted through the prism of biological atomism as attempts to relocate the true biological atom away from the cell to a level of organization above or below it. Overall, biological atomism provides a useful perspective through which to examine the history and philosophy of cell theory, and it also opens up a new way of thinking about the epistemic decomposition of living organisms that significantly departs from the physicochemical reductionism of mechanistic biology. (shrink)
Marinov''s critique I argue, is vitiated by its failure to recognize the distinctive role of superposition within the distributed connectionist paradigm. The use of so-called subsymbolic distributed encodings alone is not, I agree, enough to justify treating distributed connectionism as a distinctive approach. It has always been clear that microfeatural decomposition is both possible and actual within the confines of recognizably classical approaches. When such approaches also involve statistically-driven learning algorithms — as in the case of ID3 — the (...) fundamental differences become even harder to spot. To see them, it is necessary to consider not just the nature of an acquired input-output function but the nature of the representational scheme underlying it. Differences between such schemes make themselves best felt outside the domain of immediate problem solving. It is in the more extended contexts of performance DURING learning and cognitive change as a result of SUBSEQUENT training on new tasks (or simultaneous training on several tasks) that the effects of superpositional storage techniques come to the fore. I conclude that subsymbols, distribution and statistically driven learning alone are indeed not of the essence. But connectionism is not just about subsymbols and distribution. It is about the generation of whole subsymbol SYSTEMS in which multiple distributed representations are created and superposed. (shrink)
This review evaluates pros and cons of the schema theory as a general framework for expressing what Arbib et al. call “systems neuroscience.” We discuss the software/hardware duality of the schema concept and the relative neglect of the mechanical properties of muscles. We propose a computational alternative to the functional decomposition in terms of schemas.
The question of the influence of genes on behavior raises difficult philosophical and social issues. In this paper I delineate what I call the Developmentalist Challenge (DC) to assertions of genetic influence on behavior, and then examine the DC through an indepth analysis of the behavioral genetics of the nematode, C. elegans, with some briefer references to work on Drosophila. I argue that eight "rules" relating genes and behavior through environmentally-influenced and tangled neural nets capture the results of developmental and (...) behavioral studies on the nematode. Some elements of the DC are found to be sound and others are criticized. The essay concludes by examining the relations of this study to Kitcher's antireductionist arguments and Bechtel and Richardson's decomposition and localization heuristics. Some implications for human behavioral genetics are also briefly considered. (shrink)
Theories of diagrams and diagrammatic reasoning typically seek to account for either the formal semantics of diagrams, or for the advantages which diagrammatic representations hold for the reasoner over other forms of representation. Regrettably, almost no theory exists which accounts for both of these issues together, nor how they affect one another. We do not attempt to provide such an account here. We do, however, seek to lay out larger context than is generally used for examining the processes of using (...) diagrams in reasoning or communication. A context in which detailed studies of sub-problems, such as the formal semantics or cognitive impact of specific diagrammatic systems, may be embedded.Accounts of the embedding of sentential logics in the computational processes of reasoners and communicators are relatively well developed from several decades of research in AI. Analogies between the sentential and the graphical cases are quite revealing about both similarities and differences. To provide a structure for the 'grand context' of diagrammatic representation and reasoning, and to clarify the relations between its component problems, we examine carefully these analogies and the decomposition they provide of subproblems for analysing diagrammatic reasoning. (shrink)
Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact that agents do (...) not always believe, let alone know, the consequences of what they know—a fact that raises the “problem of logical omniscience” that has been central in epistemic logic. -/- This paper, part I of II, is a study of epistemic closure from the perspective of epistemic logic. First, I introduce models for epistemic logic, based on Lewis’s models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology. Second, I give an exact characterization of the closure properties of knowledge according to these theories, as formalized. Finally, I consider the relation between closure and higher-order knowledge. The philosophical repercussions of these results and results from part II, which prompt a reassessment of the issue of closure in epistemology, are discussed further in companion papers. -/- As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. By “modal decomposition” I obtain completeness and other results for two non-normal modal logics with respect to new semantics. One of these logics, dubbed the logic of ranked relevant alternatives, appears not to have been previously identified in the modal logic literature. More broadly, the paper presents epistemology as a rich area for logical study. (shrink)
It matters to a number of projects whether monomorphemic lexical items (‘boy’, ‘cat’, ‘give’, ‘break’, etc.) have internal linguistic structure. (Call the theory that they do the Decomposition Hypothesis (DC).) The cognitive science consensus is, overwhelmingly, that DC is true; for example, that there is a level of grammar at which ‘breaktr’ has the structure ‘cause to breakint’ and so forth. We find this consensus surprising since, as far as we can tell, there is practically no evidence to support (...) it. (For example, there is no psychological evidence that you can’t have a word that expresses the concept BREAKTR unless you have the concept CAUSE. But there ought to be if CAUSE is a constituent of BREAKTR) This isn’t, of course, to say that there are no prima facie arguments at all for DC. The best one’s we’ve heard are the Impossible Word Arguments (IWA). That being so we’re very interested in whether IWAs are, in fact, sound. (shrink)
According to one of Leibniz’s theories of contingency a proposition is contingent if and only if it cannot be proved in a finite number of steps. It has been argued that this faces the Problem of Lucky Proof, namely that we could begin by analysing the concept ‘Peter’ by saying that ‘Peter is a denier of Christ and …’, thereby having proved the proposition ‘Peter denies Christ’ in a finite number of steps. It also faces a more general but related (...) problem that we dub the Problem of Guaranteed Proof. We argue that Leibniz has an answer to these problems since for him one has not proved that ‘Peter denies Christ’ unless one has also proved that ‘Peter’ is a consistent concept, an impossible task since it requires the full decomposition of the infinite concept ‘Peter’. We defend this view from objections found in the literature and maintain that for Leibniz all truths about created individual beings are contingent. (shrink)
We introduce CE- cell decomposition , a modified version of the usual o-minimal cell decomposition. We show that if an o-minimal structure $\mathcal{R}$ admits CE-cell decomposition then any definable open set in $\mathcal{R}$ may be expressed as a finite union of definable open cells. The dense linear ordering and linear o-minimal expansions of ordered abelian groups are examples of such structures.
Science is praxis relevant to the extent that it guides goal-directed action by telling us how to act in order to achieve the goals. Investigations aiming at high praxis relevance are performed in various disciplines under names such as clinical trials, evaluation research, intervention research and social experiments. In this contribution, the notion of (direct) praxis relevance is delineated, and it is distinguished from related properties of science such as those of being applied and being practically useful in a wider (...) sense. Recommendations for the achievement of praxis relevance are offered in the form of five principles: the prerogative of direct experiments, minimized theory-induced uncertainty, multiple approximations, causal chain decomposition and successive improvements. (shrink)
This paper establishes a connection between structure sensitive categorial inference and classical modal logic. The embedding theorems for non-associative Lambek Calculus and the whole class of its weak Sahlqvist extensions demonstrate that various resource sensitive regimes can be modelled within the framework of unimodal temporal logic. On the semantic side, this requires decomposition of the ternary accessibility relation to provide its correlation with standard binary Kripke frames and models.
It matters to a number of projects whether monomorphemic lexical items (‘boy’, ‘cat’, ‘give’, ‘break’, etc.) have internal linguistic structure. (Call the theory that they do the Decomposition Hypothesis (DC).) The cognitive science consensus is, overwhelmingly, that DC is true; for example, that there is a level of grammar at which ‘breaktr’ has the structure ‘cause to breakint’ and so forth. We find this consensus surprising since, as far as we can tell, there is practically no evidence to support (...) it. (For example, there is no psychological evidence that you can’t have a word that expresses the concept BREAKTR unless you have the concept CAUSE. But there ought to be if CAUSE is a constituent of BREAKTR) This isn’t, of course, to say that there are no prima facie arguments at all for DC. The best one’s we’ve heard are the Impossible Word Arguments (IWA). That being so we’re very interested in whether IWAs are, in fact, sound. (shrink)
: American society traditionally has assumed a univocal notion of "death," largely because we have only one word for it and, until recently, have not needed a more nuanced notion. The reality of death-processes does not preclude the reality of death events. Linguistically, "death" can be understood only as an event; there are other words for the process. Our death vocabulary should expand to reflect multiple events along the process from sickness to decomposition. Depending on context, some death-related events (...) may constitute a more obvious discontinuity than others and more justifiably may be considered "death" within that context. There is no reason to assume a priori that there must be an overarching, unitary concept of death from which all diagnostic criteria must derive. Regarding organ transplantation, the relevant question is not "Is the patient dead?" but rather "Can organs X, Y, Z . . . be removed without causing or hastening death or harming the patient?". (shrink)
In (Jäger and Blutner 1999), Gerhard Jäger and Reinhard Blutner (henceforth J&B) have launched a forceful attack against the account of the adverb wieder “again” I presented in (Stechow 1995) and (Stechow 1996) There I defended a classical account of the repetitive/restitutive ambiguity exhibited by the adverb wieder, which is very close to early proposals found in the Generative Semantics literature, notably (Morgan 1969) and (McCawley 1971). I argued that German surface syntax shows that something in the style of this (...) old decomposition analysis must be correct. (shrink)
A Dedekind algebra is an ordered pair (B, h), where B is a non-empty set and h is a similarity transformation on B. Among the Dedekind algebras is the sequence of the positive integers. From a contemporary perspective, Dedekind established that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. The purpose here is to show that this seemingly isolated result is a consequence of more general results in the model theory of second-order languages. (...) Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are ?0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on ? called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type that occurs in the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. The second-order theory of any countably infinite Dedekind algebra is categorical, and there are countably infinite Dedekind algebras whose second-order theories are not finitely axiomatizable. It is shown that there is a condition on configuration signatures necessary and sufficient for the second-order theory of a Dedekind algebra to be finitely axiomatizable. It follows that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. (shrink)
In the context of mechanistic explanation, reductionistic research pursues a decomposition of complex systems into their component parts and operations. Using research on the mechanisms responsible for circadian rhythms, I consider both the gains that have been made by discovering genes and proteins that figure in these intracellular oscillators and also highlight the increasingly recognized need to understand higher-level integration, both between cells in the central oscillator and between the central and peripheral oscillators. This history illustrates a common need (...) to complement reductionistic inquiry with investigations at higher-levels. Unlike most other accounts of reduction, the mechanistic framework accommodates this complementary relationship between reductionistic and systems approaches. (shrink)
In his long 1957 paper, “The Theory of the Universal Wave Function”, Hugh Everett III made some significant preliminary steps towards the application and generalization of Shannon’s information theory to quantum mechanics. In the course of doing so, he conjectured that, for a given wavefunction on a compound space, the Schmidt decomposition maximises the correlation between subsystem bases. This is proved here.
We define an R-group to be a stable group with the property that a generic element (for any definable transitive group action) can only be algebraic over a generic. We then derive some corollaries for R-groups and fields, and prove a decomposition theorem and a field theorem. As a nonsuperstable example, we prove that small stable groups are R-groups.
One of the most foundational and continually contested questions in the cognitive sciences is the degree to which the functional organization of the brain can be understood as modular. In its classic formulation, a module was defined as a cognitive sub-system with (all or most of) nine specific properties; the classic module is, among other things, domain specific, encapsulated (i.e. maintains proprietary representations to which other modules have no access), and implemented in dedicated neural substrates. Most of the examinations—and especially (...) the criticisms—of the modularity thesis have focused on these properties individually, for instance by finding counterexamples in which otherwise good candidates for cognitive modules are shown to lack domain specificity or encapsulation. The current paper goes beyond the usual approach by asking what some of the broad architectural implications of the modularity thesis might be, and attempting to test for these. The evidence does not favor a modular architecture for the cortex. Moreover, the evidence suggests that best way to approach the understanding of cognition is not by analyzing and modelling different functional domains (visual perception, attention, language, motor control, etc.) in isolation from the others, but rather by looking for points of overlap in their neural implementations, and exploiting these to guide the analysis and decomposition of the functions in question. This has significant implications for the question of how to approach the design and implementation of intelligent artifacts in general, and language-using robots in particular. (shrink)
Neural organization: Structure, function, and dynamics shows how theory and experiment can supplement each other in an integrated, evolving account of the brain's structure, function, and dynamics. (1) Structure: Studies of brain function and dynamics build on and contribute to an understanding of many brain regions, the neural circuits that constitute them, and their spatial relations. We emphasize Szentágothai's modular architectonics principle, but also stress the importance of the microcomplexes of cerebellar circuitry and the lamellae of hippocampus. (2) Function: Control (...) of eye movements, reaching and grasping, cognitive maps, and the roles of vision receive a functional decomposition in terms of schemas. Hypotheses as to how each schema is implemented through the interaction of specific brain regions provide the basis for modeling the overall function by neural networks constrained by neural data. Synthetic PET integrates modeling of primate circuitry with data from human brain imaging. (3) Dynamics: Dynamic system theory analyzes spatiotemporal neural phenomena, such as oscillatory and chaotic activity in both single neurons and (often synchronized) neural networks, the self-organizing development and plasticity of ordered neural structures, and learning and memory phenomena associated with synaptic modification. Rhythm generation involves multiple levels of analysis, from intrinsic cellular processes to loops involving multiple brain regions. A variety of rhythms are related to memory functions. The Précis presents a multifaceted case study of the hippocampus. We conclude with the claim that language and other cognitive processes can be fruitfully studied within the framework of neural organization that the authors have charted with John Szentágothai. Key Words: cognitive maps; computational neuroscience; dynamics; hippocampus; memory; modular architectonics; neural modeling; neural organization; neural plasticity; rhythmogenesis; Szentágothai. (shrink)
In the final analysis, sustainable agriculture must derive from applied ecology, especially the principle of the regulation of the abundance and distribution of species (and, secondarily, their activities) in space and time. Interspecific competition in natural ecosystems has its counterparts in agriculture, designed to divert greater amounts of energy, nutrients, and water into crops. Whereas natural ecosystems select for a diversity of species in communities, recent agriculture has minimized diversity in favour of vulnerable monocultures. Such systems show intrinsically less stability (...) and resilience to perturbations. Some kinds of crop rotation resemble ecological succession in that one crop prepares the land for successive crop production. Such rotations enhance soil organic processes such as decomposition and material cycling, build a nutrient capital to sustain later crop growth, and reduce the intensity of pest buildup. Species in natural communities occur at discrete points along the r-K continuum of reproductive maturity. Clearing forested land for agriculture, rotational burning practices, and replacing perennial grassland communities by cereal monocultures moves the agricultural community towards the r extreme. Plant breeders select for varieties which yield at an earlier age and lower plant biomass, effectively moving a variety towards the r type. Features of more natural landscapes, such as hedgerows, may act as physical and biological adjuncts to agricultural production. They should exist as networks in agricultural lands to be most effective. Soil is of major importance in agroecosystems, and maintaining, deliberately, its vitality and resilience to agricultural perturbations is the very basis of sustainable land use. (shrink)
In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the 3-ball B. i.e., a piecewise isometry from B onto two copies of B. This article answers a question of de Groot from 1958 by showing that there is a paradoxical decomposition of B in which the pieces move continuously while remaining disjoint to yield two copies of B. More generally, we show that if n ≥ 2, any two bounded sets in Rⁿ that are (...) equidecomposable with proper isometries are continuously equidecomposable in this sense. (shrink)
The distinguishing feature of ‘modal’ interpretations of quantum mechanics is their abandonment of the orthodox eigenstate–eigenvalue rule, which says that an observable possesses a definite value if and only if the system is in an eigenstate of that observable. Kochen's and Dieks' new biorthogonal decomposition rule for picking out which observables have definite values is designed specifically to overcome the chief problem generated by orthodoxy's rule, the measurement problem, while avoiding the no-hidden-variable theorems. Otherwise, their new rule seems completely (...) ad hoc. The ad hoc charge can only be laid to rest if there is some way to give Kochen's and Dieks' rule for picking out which observables have definite values some independent motivation. And there is, or so I will argue here. Specifically, I shall show that theirs is the only rule able to save Schrödinger's cat from a fate worse than death, and sidestep the Bell–Kochen–Specker no-hidden-variables theorem, once we impose four independently natural conditions on such rules. (shrink)
Visual analytics is a new interdisciplinary field of study that calls for a more structured scientific approach to understanding the effects of interaction with complex graphical displays on human cognitive processes. Its primary goal is to support the design and evaluation of graphical information systems that better support cognitive processes in areas as diverse as scientific research and emergency management. The methodologies that make up this new field are as yet ill defined. This paper proposes a pathway for development of (...) visual analytics as a translational cognitive science that bridges fundamental research in human/computer cognitive systems and design and evaluation of information systems in situ. Achieving this goal will require the development of enhanced field methods for conceptual decomposition of human/computer cognitive systems that maps onto laboratory studies, and improved methods for conducting laboratory investigations that might better map onto real-world cognitive processes in technology-rich environments. (shrink)
A formal language of two-valued logic is developed, whose terms are formulas of the language of Kleene's three-valued logic. The atomic formulas of the former language are pairs of formulas of the latter language joined by consequence operators. These operators correspond to the three sensible types of consequence (strong-strong, strong-weak and weak-weak) in Kleene's logic in analogous way as the implication connective in the classical logic corresponds to the classical consequence relation. The composed formulas of the considered language are built (...) from the atomic ones by means of the classical connectives and quantifiers.A deduction system for the developed language is given, consisting of a set of decomposition rules for sequences of formulas. It is shown that the deduction system is sound and complete. (shrink)
Using a contextual method the specific development of logic between c. 1830 and 1930 is explained. A characteristic mark of this period is the decomposition of the complex traditional philosophical omnibus discipline logic into new philosophical subdisciplines and separate disciplines such as psychology, epistemology, philosophy of science, and formal (symbolic, mathematical) logic. In the 19th century a growing foundational need in mathematics provoked the emergence of a structural view on mathematics and the reformulation of logic for mathematical means. As (...) a result formallogic was taken over by mathematics in the beginning of the 20th century as is shown by sketching the German example. (shrink)
The proponents of strong lexicalism hold the view that “words” are formed in the lexicon and are opaque for the syntax ((Dowty 1979), (DiSciullo and Williams 1987), (Jackendoff 1990) and many others). Modular morphology, on the other hand, offers the possibility that at least some words are partially formed in the syntax ((Baker 1988), (Borer 1988), (Hale and Keyser 1994), (Chomsky 1995) and many others). In (Stechow 1995) and (Stechow 1996) it has been argued that facts observed with German wieder (...) “again” cannot be accounted for within the framework of strong lexicalism and therefore favour the second position. The authors of this paper want to check these claims by investigating the behaviour of the German adverb fast “ almost”, the other classical adverb to which the method of decomposition has been applied in the linguistic literature (cf. (McCawley 1971)). Most adverbs cannot look into lexical decomposition structures, but some can. In order to have a suitable name, let us call these D-adverbs. Again and almost are the prototypical representatives of this class. The method adopted is to investigate whether fast has access to different aspects of verbal meaning depending on its position. Following (Dowty 1979), resultative verbs and prepositions are decomposed into BECOME + XP, where XP is the result state. Agentive verbs contain an additional AGENT part. Other thematic relations connecting the subject and the event are HOLDER and cause. If the syntax tells us that an adverb like wieder or fast must have wide scope with respect to BECOME, then we expect other readings than in a configuration where fast can have narrow scope with respect to BECOME. In other words, the motivation for decomposition is syntactic and semantic. The idea is that certain function projections in the classical VP have a meaning and hence scopally interact with adverbs. (shrink)
The proponents of strong lexicalism hold the view that “words” are formed in the lexicon and are opaque for the syntax ((Dowty 1979), (DiSciullo and Williams 1987), (Jackendoff 1990) and many others). Modular morphology, on the other hand, offers the possibility that at least some words are partially formed in the syntax ((Baker 1988), (Borer 1988), (Hale and Keyser 1994), (Chomsky 1995) and many others). In (Stechow 1995) and (Stechow 1996) it has been argued that facts observed with German wieder (...) “again” cannot be accounted for within the framework of strong lexicalism and therefore favour the second position. The authors of this paper want to check these claims by investigating the behaviour of the German adverb fast “ almost”, the other classical adverb to which the method of decomposition has been applied in the linguistic literature (cf. (McCawley 1971)). Most adverbs cannot look into lexical decomposition structures, but some can. In order to have a suitable name, let us call these D-adverbs. Again and almost are the prototypical representatives of this class. The method adopted is to investigate whether fast has access to different aspects of verbal meaning depending on its position. Following (Dowty 1979), resultative verbs and prepositions are decomposed into BECOME + XP, where XP is the result state. Agentive verbs contain an additional AGENT part. Other thematic relations connecting the subject and the event are HOLDER and cause. If the syntax tells us that an adverb like wieder or fast must have wide scope with respect to BECOME, then we expect other readings than in a configuration where fast can have narrow scope with respect to BECOME. In other words, the motivation for decomposition is syntactic and semantic. The idea is that certain function projections in the classical VP have a meaning and hence scopally interact with adverbs. (shrink)
