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  • Books
  • Articles  (16)
  • rationality
  • Sociology  (8)
  • Mathematics  (5)
  • Nature of Science, Research, Systems of Higher Education, Museum Science  (3)
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  • Books
  • Articles  (16)
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  • 1
    Electronic Resource
    Electronic Resource
    Kuhn'sThe Structure of Scientific Revolutions revisited (1995)
    Springer
    Journal for general philosophy of science 26 (1995), S. 75-92 
    Details
    ISSN: 1572-8587
    Keywords: Kuhn ; Wittgenstein ; paradigm ; incommensurability ; language games ; relativism ; rationality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Philosophy , Nature of Science, Research, Systems of Higher Education, Museum Science
    Notes: Summary The present paper argues that there is an affinity between Kuhn'sThe Structure of Scientific Revolutions and Wittgenstein's philosophy. It is maintained, in particular, that Kuhn's notion of paradigm draws on such Wittgensteinian concepts as language games, family resemblance, rules, forms of life. It is also claimed that Kuhn's incommensurability thesis is a sequel of the theory of meaning supplied by Wittgenstein's later philosophy. As such its assessment is not fallacious, since it is not an empirical hypothesis and it does not have the relativistic implications Kuhn's critics repeatedly indicated. Although concepts are indeed relative to a language game or paradigm, interparadigmatic intelligibility is preserved through the standard techniques of translation or praxis. The impossibility of radical translation which is captured by the claim of incommensurability lies with that which cannot be said but only shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01130927
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  • 2
    Electronic Resource
    Electronic Resource
    Integrating psychology and methodology (1990)
    Springer
    Journal for general philosophy of science 21 (1990), S. 293-308 
    Details
    ISSN: 1572-8587
    Keywords: psychology ; Külpe ; methodology ; Popper ; rationality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Philosophy , Nature of Science, Research, Systems of Higher Education, Museum Science
    Notes: Summary The importance of the problem of how to integrate psychology and methodology was rediscovered by Oswald Külpe. He noted that Wundt's psychology was inadequate and that a new methodology was needed to construct an alternative. Külpe made real progress but his program turned out to be quite difficult: he had no appropriate method for integrating the two fields. August Messer tried to fill the gap but failed. The problem was largely dropped due to poor methods at hand for studying it but remained important due to Popper's methodology and de Groot's psychology at least. We may now more effectively return to it by using a bootstrap method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01801040
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  • 3
    Electronic Resource
    Electronic Resource
    Mathematical progress: Between reason and society (1993)
    Springer
    Journal for general philosophy of science 24 (1993), S. 43-62 
    Details
    ISSN: 1572-8587
    Keywords: mathematics ; progress ; rationality ; methodology ; historiography ; cognitive and social factors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Philosophy , Nature of Science, Research, Systems of Higher Education, Museum Science
    Notes: Summary Is mathematical knowledge the product of a method fulfilling temporally and locally invariant criteria and thus manifesting a rationality which sets it entirely apart from all other cultural products? Or is it a socially constructed product, sharing in the accidental and conventional nature of all historically contingent cultural products? In order to be able to take the latter point of view at all seriously into consideration, the most sophisticated and historically informed methodological model is carefully and critically examined. This (Lakatosian) model, however liberal and history-directed it may seem, turns out to incorporate the former, (methodo)logical view of the development of mathematics. It will be demonstrated that the basic assumption underlying Lakatosian methodology is both unwarranted and superfluous for the rational explanation of the growth of mathematical knowledge. This leads to the provisional conclusion that the relevant question is not whether mathematical progress derives ultimately from irreducibly cognitive or from irreducibly social factors, but how cognitive and social factors are interrelated and together, in their indivisible unity, are constitutive of the development of mathematical knowledge. In the forthcoming second part of the article, a model of this socio-cognitive interplay, relying heavily on empirical analyses, will be presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00769514
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  • 4
    Electronic Resource
    Electronic Resource
    Rationality and the definition of consistent pairs (1998)
    Springer
    International journal of game theory 27 (1998), S. 49-59 
    Details
    ISSN: 1432-1270
    Keywords: Key words: Consistent pairs ; rationality ; lexicographic probability systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. A consistent pair specifies a set of “rational” strategies for both players such that a strategy is rational if and only if it is a best reply to a Bayesian belief that gives positive probability to every rational strategy of the opponent and probability zero otherwise. Although the idea underlying consistent pairs is quite intuitive, the original definition suffers from non-existence problems. In this article, we propose an alternative formalization of consistent pairs. According to our definition, a strategy is “rational” if and only if it is a best reply to some lexicographic probability system that satisfies certain consistency conditions. These conditions imply in particular that a player's probability system gives infinitely more weight to rational strategies than to other strategies. We show that modified consistent pairs exist for every game.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001820050057
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  • 5
    Electronic Resource
    Electronic Resource
    Rationality and the definition of consistent pairs (1998)
    Springer
    International journal of game theory 27 (1998), S. 49-59 
    Details
    ISSN: 1432-1270
    Keywords: Consistent pairs ; rationality ; lexicographic probability systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A consistent pair specifies a set of “rational” strategies for both players such that a strategy is rational if and only if it is a best reply to a Bayesian belief that gives positive probability to every rational strategy of the opponent and probability zero otherwise. Although the idea underlying consistent pairs is quite intuitive, the original definition suffers from non-existence problems. In this article, we propose an alternative formalization of consistent pairs. According to our definition, a strategy is “rational” if and only if it is a best reply to some lexicographic probability system that satisfies certain consistency conditions. These conditions imply in particular that a player's probability system gives infinitely more weight to rational strategies than to other strategies. We show that modified consistent pairs exist for every game.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01243194
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  • 6
    Electronic Resource
    Electronic Resource
    The survival value of assuming others to be rational (2000)
    Springer
    International journal of game theory 29 (2000), S. 147-163 
    Details
    ISSN: 1432-1270
    Keywords: Key words: Evolutionary psychology ; rationality ; beliefs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. I study the evolution of rationality, using an indirect evolutionary approach, in which nature selects a decision-making procedure, and the procedure chooses actions in matching-games. The main result is that in order for (knowledge of) rationality to survive, it is necessary and sufficient that the rational procedure respects the attraction principle. That is, when a rational agent eliminates a strictly dominated action A, he should only increase the choice probability of the actions actually dominating A and not change the choice probability of other undominated actions. The attraction principle sharpens gametheoretic predictions. Attraction effects have been verified in psychological experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001820070001
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  • 7
    Electronic Resource
    Electronic Resource
    Approximated solutions in rational form for systems of differential equations (1999)
    Springer
    Numerical algorithms 21 (1999), S. 185-203 
    Details
    ISSN: 1572-9265
    Keywords: systems of differential equations ; analytic solutions ; matrix Padé approximation ; rationality ; minimum degrees ; uniqueness ; partial differential equations ; 41A21 ; 34A45 ; 35A35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we present a technique to study the existence of rational solutions for systems of differential equations — for an ordinary differential equation, in particular. The method is relatively straightforward; it is based on a rationality characterisation that involves matrix Padé approximants. It is important to note that, when the solution is rational, we use formal power series “without taking into account” their circle of convergence; at the end of this paper we justify this. We expound the theory for systems of linear first-order ordinary differential equations in the general case. However, the main ideas are applied in numerical resolution of partial differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019109429882
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  • 8
    Electronic Resource
    Electronic Resource
    Matrix Padé Approximation of rational functions (1997)
    Springer
    Numerical algorithms 15 (1997), S. 167-192 
    Details
    ISSN: 1572-9265
    Keywords: Matrix Padé Approximation ; rationality ; minimum degrees ; uniqueness ; 65 ; 41 ; 15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In many applications it is of major interest to decide whether a given formal power series with matrix-valued coefficients of arbitrary dimensions results from a matrix-valued rational function. As the main result of this paper we provide an answer to this question in terms of Matrix Padé Approximants of the given power series. Furthermore, given a matrix rational function, the “smallest” degrees of the matrix polynomials which represent it are not necessarily unique. Therefore we study a certain minimality-type, that is, minimum degrees. We aim to obtain all the minimum degrees for the polynomials which represent the function as equivalents. In addition, given that the rational representation of the function for the same pair of degrees need not be unique, we have obtained conditions to study the uniqueness of said representation. All the results obtained are presented graphically in tables setting out the above information. They lead to a number of properties concerning special structures, staired blocks, in the Padé Table.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019193820428
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  • 9
    Electronic Resource
    Electronic Resource
    An axiomatic analysis of the Nash equilibrium concept (1992)
    Springer
    Theory and decision 33 (1992), S. 177-189 
    Details
    ISSN: 1573-7187
    Keywords: Axioms ; cooperation ; game theory ; Nash equilibrium ; rationality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract The purpose of this paper is to analyze axiomatically the Nash equilibrium concept. The class of games under study is a (relatively large) subclass of n-person normal form games. Solutions are correspondences which associate to each game a non empty set of strategy vectors of this game. It is shown that if a solution satisfies the axioms Independence of irrelevant alternatives (IIA) and Individual rationality (IR), then all the strategy vectors in this solution are Nash equilibria. This result holds good also if IR is replaced by Strong individual monotonicity (SIM) or Weak principle of fair compromise (WPFC).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00134095
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  • 10
    Electronic Resource
    Electronic Resource
    Instrumental rationality and cognitive rationality (1989)
    Springer
    Theory and decision 27 (1989), S. 7-36 
    Details
    ISSN: 1573-7187
    Keywords: rationality ; information ; expectations ; beliefs ; dynamic games ; game equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract Beside instrumental rationality, concerned with consistency between available means and pursued objectives, cognitive rationality, concerned with consistency between current beliefs and detained information, is nowadays bursting in economic theory. For an individual decision, the two notions are expressed structurally in similar forms, but they heavily interact in the deliberation process, especially when the agent is searching relevant information on his environment and his own determiners. In a game framework, the players' representations are formalized in a more and more sophisticated way, and are closely interwoven with their preferences in contemporary equilibrium notions as well as in selection between corresponding equilibrium points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00133986
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