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Adonai Sant'anna [6]Adonai S. Sant'Anna [5]
  1. Time in Thermodynamics.Newton C. A. Da Costa & Adonai S. Sant'Anna - 2002 - Foundations of Physics 32 (11):1785-1796.
    We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to show that time is dispensable in continuum thermodynamics, according to the axiomatic formulation of Gurtin and Williams. We also show how to define time by means of the remaining primitive concepts of Gurtin and Williams system. Finally, we introduce thermodynamics without time as a primitive concept.
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  2.  94
    Quasi-Set-Theoretical Foundations of Statistical Mechanics: A Research Program. [REVIEW]Adonai S. Sant'Anna & Alexandre M. S. Santos - 2000 - Foundations of Physics 30 (1):101-120.
    Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell–Boltzmann statistics, it is not necessary to assume that the particles are distinguishable or individuals. In other words, Maxwell–Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. (...)
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  3.  63
    Elementary Particles, Hidden Variables, and Hidden Predicates.Adonai S. Sant'anna - 2000 - Synthese 125 (1-2):233 - 245.
    We recently showed that it is possible to deal withcollections of indistinguishable elementary particles (in thecontext of quantum mechanics) in a set-theoretical framework, byusing hidden variables. We propose in the presentpaper another axiomatics for collections of indiscernibleswithout hidden variables, where hidden predicates are implicitlyassumed. We also discuss the possibility of a quasi-settheoretical picture for quantum theory. Quasi-set theory, basedon Zermelo-Fraenkel set theory, was developed for dealing withcollections of indistinguishable, but, not identical objects.
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    Elementary Particles, Hidden Variables, And Hidden Predicates.Adonai S. Sant'anna - 2000 - Synthese 125 (1):233-245.
    We recently showed that it is possible to deal with collections of indistinguishable elementary particles in a set-theoretical framework, by using hidden variables. We propose in the present paper another axiomatics for collections of indiscernibles without hidden variables, where hidden predicates are implicitly assumed. We also discuss the possibility of a quasi-set theoretical picture for quantum theory. Quasi-set theory, based on Zermelo-Fraenkel set theory, was developed for dealing with collections of indistinguishable, but, not identical objects.
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  5. An Axiomatic Framework for Classical Particlemechanics Without Space-Time.Adonai Sant'anna - 1999 - Philosophia Naturalis 36:307.
     
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  6. An Axiomatic Framework for Classical Particle Mechanics Without Force.Adonai Sant'anna - 1996 - Philosophia Naturalis 33:187-204.
  7.  14
    A Non-Realistic Approach for Natural Languages.Adonai Sant'Anna, Otávio Bueno & Newton C. A. da Costa - unknown
    The structure of natural languages is usually studied from three major different but interconnected points of view: syntax, semantics, and pragmatics. If we consider that the main purpose of natural languages is communication, we should consider another dimension for languages, which deals with the influence of internal states of communicating individuals on meanings. Such a dimension we refer to as internalism. Within this context, internalism cannot be confused with psycholinguistics, in the same way pragmatics cannot be confused with sociolinguistics. In (...)
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  8. Individuality, Quasi-Sets and the Double-Slit Experiment.Adonai S. Sant'Anna - forthcoming - Quantum Studies: Mathematics and Foundations.
    Quasi-set theory $\cal Q$ allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. $\cal Q$ was partially motivated by the problem of non-individuality in quantum mechanics. In this paper I discuss the range of explanatory power of $\cal Q$ for quantum phenomena which demand some notion of indistinguishability among quantum objects. My main focus is (...)
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  9.  25
    A Set-Theoretic Predicate for Semantics in Natural and Formal Languages.Adonai Sant'Anna, Otavio Bueno & Newton da Costa - unknown
    We present an axiomatic framework for semantics that can be applied to natural and formal languages. Our main goal is to suggest a very simple mathematical model that describes fundamental cognitive aspects of the human brain and that can still be applied to artificial intelligence. One of our main results is a theorem that allows us to infer syntactical properties of a language out of its corresponding semantics. The role of pragmatics in semantics in our mathematical framework is also discussed.
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  10.  9
    Epistemology of Quasi-Sets.Adonai Sant'Anna - unknown
    I briefly discuss the epistemological role of quasi-set theory in mathematics and theoretical physics. Quasi-set theory is a first order theory, based on Zermelo-Fraenkel set theory with Urelemente. Nevertheless, quasi-set theory allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. Basically, quasi-set theory offers us some sort of logical apparatus for questioning the need for (...)
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  11. The Definability of Physical Concepts.Adonai Sant'Anna - unknown
    Our main purpose here is to make some considerations about the definability of physical concepts like mass, force, time, space, spacetime, and so on. Our starting motivation is a collection of supposed definitions of closed system in the literature of physics and philosophy of physics. So, we discuss the problem of definitions in theoretical physics from the point of view of modern theories of definition. One of our main conclusions is that there are different kinds of definitions in physics that (...)
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