Results for 'Additive Quantities'

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  1. Properly Extensive Quantities.Zee R. Perry - 2015 - Philosophy of Science 82 (5):833-844.
    This article introduces and motivates the notion of a “properly extensive” quantity by means of a puzzle about the reliability of certain canonical length measurements. An account of these measurements’ success, I argue, requires a modally robust connection between quantitative structure and mereology that is not mediated by the dynamics and is stronger than the constraints imposed by “mere additivity.” I outline what it means to say that length is not just extensive but properly so and then briefly sketch an (...)
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  2.  48
    Intensive and Extensive Quantities.Zee Perry - manuscript
    Quantities are properties and relations which exhibit "quantitative structure". For physical quantities, this structure can impact the non-quantitative world in different ways. In this paper I introduce and motivate a novel distinction between quantities based on the way their quantitative structure constrains the possible mereological structure of their instances. Specifically, I identify a category of “properly extensive” quantities, which are a proper sub-class of the additive or extensive quantities. I present and motivate this distinction (...)
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  3.  19
    Matter Matters: Metaphysics and Methodology in the Early Modern Period.Jeremy Dunham - 2013 - Philosophical Quarterly 63 (253):849-851.
    © 2013 The Editors of The Philosophical QuarterlyWhy did matter matter for Descartes and Leibniz? The answer, Kurt Smith argues in this thought‐provoking book, is that without it mathematics would be unintelligible. A world without matter is insufficient for mathematics because the immaterial cannot be divided into discrete quantities. Without a divisible material structure, the determinate unities necessary for the additive quantities in turn necessary for mathematics are unactualisable. God needs matter to institute mathematics. However, with the (...)
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  4. Kant on Negative Quantities, Real Opposition and Inertia.Jennifer McRobert - manuscript
    Kant's obscure essay entitled An Attempt to Introduce the Concept of Negative Quantities into Philosophy has received virtually no attention in the Kant literature. The essay has been in English translation for over twenty years, though not widely available. In his original 1983 translation, Gordon Treash argues that the Negative Quantities essay should be understood as part of an ongoing response to the philosophy of Christian Wolff. Like Hoffmann and Crusius before him, the Kant of 1763 is at (...)
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  5.  14
    Conditional Random Quantities and Compounds of Conditionals.Angelo Gilio & Giuseppe Sanfilippo - 2014 - Studia Logica 102 (4):709-729.
    In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH + P(E|H)H c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give (...)
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  6.  26
    Additive Presuppositions Are Derived Through Activating Focus Alternatives.Anna Szabolcsi - 2017 - Proceedings of the 2017 Amsterdam Colloquium.
    The additive presupposition of particles like "too"/"even" is uncontested, but usually stipulated. This paper proposes to derive it based on two properties. (i) "too"/"even" is cross-linguistically focus-sensitive, and (ii) in many languages, "too"/"even" builds negative polarity items and free-choice items as well, often in concert with other particles. (i) is the source of its existential presupposition, and (ii) offers clues regarding how additivity comes about. (i)-(ii) together demand a sparse semantics for "too/even," one that can work with different kinds (...)
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  7. Ranking Multidimensional Alternatives and Uncertain Prospects.Philippe Mongin - 2015 - Journal of Economic Theory 157:146-171.
    We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically notof the Cartesian product form). We apply these representationsto (1)streams of commodity baskets through time, (...)
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  8.  74
    Numbers as Quantitative Relations and the Traditional Theory of Measurement.Joel Michell - 1994 - British Journal for the Philosophy of Science 45 (2):389-406.
    The thesis that numbers are ratios of quantities has recently been advanced by a number of philosophers. While adequate as a definition of the natural numbers, it is not clear that this view suffices for our understanding of the reals. These require continuous quantity and relative to any such quantity an infinite number of additive relations exist. Hence, for any two magnitudes of a continuous quantity there exists no unique ratio. This problem is overcome by defining ratios, and (...)
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  9.  8
    The Additive Group of the Rationals Does Not Have an Automatic Presentation.Todor Tsankov - 2011 - Journal of Symbolic Logic 76 (4):1341-1351.
    We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are p-divisible for infinitely many primes p, or groups of the form ⊕ p∈I Z(p ∞ ), where I is an infinite set of primes.
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  10.  98
    An Additive Representation on the Product of Complete, Continuous Extensive Structures.Yutaka Matsushita - 2010 - Theory and Decision 69 (1):1-16.
    This article develops an axiom system to justify an additive representation for a preference relation ${\succsim}$ on the product ${\prod_{i=1}^{n}A_{i}}$ of extensive structures. The axiom system is basically similar to the n-component (n ≥ 3) additive conjoint structure, but the independence axiom is weakened in the system. That is, the axiom exclusively requires the independence of the order for each of single factors from fixed levels of the other factors. The introduction of a concatenation operation on each factor (...)
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  11.  60
    Non-Additive Beliefs in Solvable Games.Hans Haller - 2000 - Theory and Decision 49 (4):313-338.
    This paper studies how the introduction of non-additive probabilities (capacities) affects the solvability of strategic games.
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  12.  13
    Extension of Relatively |Sigma-Additive Probabilities on Boolean Algebras of Logic.Mohamed A. Amer - 1985 - Journal of Symbolic Logic 50 (3):589 - 596.
    Contrary to what is stated in Lemma 7.1 of [8], it is shown that some Boolean algebras of finitary logic admit finitely additive probabilities that are not σ-additive. Consequences of Lemma 7.1 are reconsidered. The concept of a C-σ-additive probability on B (where B and C are Boolean algebras, and $\mathscr{B} \subseteq \mathscr{C}$ ) is introduced, and a generalization of Hahn's extension theorem is proved. This and other results are employed to show that every S̄(L)-σ-additive probability (...)
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  13.  46
    Expected Utility From Additive Utility on Semigroups.Juan C. Candeal, Juan R. de Miguel & Esteban Induráin - 2002 - Theory and Decision 53 (1):87-94.
    In the present paper we study the framework of additive utility theory, obtaining new results derived from a concurrence of algebraic and topological techniques. Such techniques lean on the concept of a connected topological totally ordered semigroup. We achieve a general result concerning the existence of continuous and additive utility functions on completely preordered sets endowed with a binary operation ``+'', not necessarily being commutative or associative. In the final part of the paper we get some applications to (...)
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  14.  23
    On the Classical Approximation in the Quantum Statistics of Equivalent Particles.Armand Siegel - 1970 - Foundations of Physics 1 (2):145-171.
    It is shown here that the microcanonical ensemble for a system of noninteracting bosons and fermions contains a subensemble of state vectors for which all particles of the system are distinguishable. This “IQC” (inner quantum-classical) subensemble is therefore fully classical, except for a rather extreme quantization of particle momentum and position, which appears as the natural price that must be paid for distinguishability. The contribution of the IQC subensemble to the entropy is readily calculated, and the criterion for this to (...)
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  15.  22
    Applications of Nonstandard Analysis in Additive Number Theory.Renling Jin - 2000 - Bulletin of Symbolic Logic 6 (3):331-341.
    This paper reports recent progress in applying nonstandard analysis to additive number theory, especially to problems involving upper Banach density.
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  16.  16
    What is Hierarchical Selection?Ben Goertzel - 1992 - Biology and Philosophy 7 (1):27-33.
    It has been proposed that natural selection occurs on a hierarchy of levels, of which the organismic level is neither the top nor the bottom. This hypothesis leads to the following practical problem: in general, how does one tell if a given phenomenon is a result of selection on level X or level Y. How does one tell what the units of selection actually are?It is convenient to assume that a unit of selection may be defined as a type of (...)
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  17.  2
    On Baire Measurable Homomorphisms of Quotients of the Additive Group of the Reals.Vladimir Kanovei & Michael Reeken - 2000 - Mathematical Logic Quarterly 46 (3):377-384.
    The quotient ℝ/G of the additive group of the reals modulo a countable subgroup G does not admit nontrivial Baire measurable automorphisms.
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  18. Armstrong on Quantities and Resemblance.M. Eddon - 2007 - Philosophical Studies 136 (3):385-404.
    Resemblances obtain not only between objects but between properties. Resemblances of the latter sort - in particular resemblances between quantitative properties - prove to be the downfall of a well-known theory of universals, namely the one presented by David Armstrong. This paper examines Armstrong's efforts to account for such resemblances within the framework of his theory and also explores several extensions of that theory. All of them fail.
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  19.  36
    A Set of Independent Axioms for Extensive Quantities.Patrick Suppes - 1951 - Portugaliae Mathematica 10 (4):163-172.
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  20.  6
    An Additive Model for Sequential Decision Making.James C. Shanteau - 1970 - Journal of Experimental Psychology 85 (2):181.
  21.  20
    A Philosophical Foundation of Non-Additive Measure and Probability.Sebastian Maaß - 2006 - Theory and Decision 60 (2-3):175-191.
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  22.  2
    Averaging of Motor Movements: Tests of an Additive Model.Irwin P. Levin, John L. Craft & Kent L. Norman - 1971 - Journal of Experimental Psychology 91 (2):287.
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  23. Additive Interference Processes in Short-Term Memory.Willi Ternes & John C. Yuille - 1973 - Journal of Experimental Psychology 100 (2):432.
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  24. Additive Theories of Rationality: A Critique.Matthew Boyle - 2016 - European Journal of Philosophy 24 (3):527-555.
    Additive theories of rationality, as I use the term, are theories that hold that an account of our capacity to reflect on perceptually-given reasons for belief and desire-based reasons for action can begin with an account of what it is to perceive and desire, in terms that do not presuppose any connection to the capacity to reflect on reasons, and then can add an account of the capacity for rational reflection, conceived as an independent capacity to ‘monitor’ and ‘regulate’ (...)
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  25. Aristotle’s Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities.Paola Cantù - 2010 - Synthese 174 (2):225-235.
    The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in (...)
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  26.  55
    Against the Additive View of Imagination.Nick Wiltsher - 2016 - Australasian Journal of Philosophy 94 (2):266-282.
    According to the additive view of sensory imagination, mental imagery often involves two elements. There is an image-like element, which gives the experiences qualitative phenomenal character akin to that of perception. There is also a non-image element, consisting of something like suppositions about the image's object. This accounts for extra- sensory features of imagined objects and situations: for example, it determines whether an image of a grey horse is an image of Desert Orchid, or of some other grey horse. (...)
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  27.  22
    Is There a Humean Account of Quantities?Phillip Bricker - 2017 - Philosophical Issues 27 (1):26-51.
    Humeans have a problem with quantities. A core principle of any Humean account of modality is that fundamental entities can freely recombine. But determinate quantities, if fundamental, seem to violate this core principle: determinate quantities belonging to the same determinable necessarily exclude one another. Call this the problem of exclusion. Prominent Humeans have responded in various ways. Wittgenstein, when he resurfaced to philosophy, gave the problem of exclusion as a reason to abandon the logical atomism of the (...)
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  28. Zero-Value Physical Quantities.Yuri Balashov - 1999 - Synthese 119 (3):253-286.
    To state an important fact about the photon, physicists use such expressions as (1) “the photon has zero (null, vanishing) mass” and (2) “the photon is (a) massless (particle)” interchangeably. Both (1) and (2) express the fact that the photon has no non-zero mass. However, statements (1) and (2) disagree about a further fact: (1) attributes to the photon the property of zero-masshood whereas (2) denies that the photon has any mass at all. But is there really a difference between (...)
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  29.  37
    Additive Particles Under Stress.Manfred Krifka - unknown
    It is customary to identify three broad classes of grading particles: additive particles like also, exclusive particles like only, and scalar particles like even (cf. König (1991); in the examples, grave accent stands for the main, falling accent).
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  30.  7
    Laue's Theorem Revisited: Energy-Momentum Tensors, Symmetries, and the Habitat of Globally Conserved Quantities.Domenico Giulini - 2018 - International Journal of Geometric Methods in Modern Physics 15 (10).
    The energy-momentum tensor for a particular matter component summarises its local energy-momentum distribution in terms of densities and current densities. We re-investigate under what conditions these local distributions can be integrated to meaningful global quantities. This leads us directly to a classic theorem by Max von Laue concerning integrals of components of the energy-momentum tensor, whose statement and proof we recall. In the first half of this paper we do this within the realm of Special Relativity and in the (...)
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  31. Infinite Value and Finitely Additive Value Theory.Peter Vallentyne & Shelly Kagan - 1997 - Journal of Philosophy 94 (1):5-26.
    000000001. Introduction Call a theory of the good—be it moral or prudential—aggregative just in case (1) it recognizes local (or location-relative) goodness, and (2) the goodness of states of affairs is based on some aggregation of local goodness. The locations for local goodness might be points or regions in time, space, or space-time; or they might be people, or states of nature.1 Any method of aggregation is allowed: totaling, averaging, measuring the equality of the distribution, measuring the minimum, etc.. Call (...)
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  32. On Subgroups of the Additive Group in Differentially Closed Fields.Sonat Süer - 2012 - Journal of Symbolic Logic 77 (2):369-391.
    In this paper we deal with the model theory of differentially closed fields of characteristic zero with finitely many commuting derivations. First we observe that the only known lower bound for the Lascar rank of types in differentially closed fields, announced in a paper of McGrail, is false. This gives us a new class of regular types which are orthogonal to fields. Then we classify the subgroups of the additive group of Lascar rank omega with differential-type 1 which are (...)
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  33. On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics.Hans Halvorson - 2000 - Journal of Philosophical Logic 30 (1):27-50.
    Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No - that the status of individual continuous quantities is very different in quantum mechanics than in (...)
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  34.  11
    Additive Particles and Polarity.H. Rullmann - 2003 - Journal of Semantics 20 (4):329-401.
    This article discusses the semantics of the additive focus particles too and either and the factors governing the alternation between the two. It is argued that too and either are not synonymous, and that this alternation is therefore not a case of morphological suppletion conditioned by polarity. Either must appear in the scope of a downward entailing licensor, just like all negative polarity items (NPIs). Naturally occurring data demonstrate that the licensors of either include not only negation and n‐words, (...)
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  35. Finite Quantities.Daniel Nolan - 2008 - Proceedings of the Aristotelian Society 108 (1pt1):23-42.
    Quantum Mechanics, and apparently its successors, claim that there are minimum quantities by which objects can differ, at least in some situations: electrons can have various “energy levels” in an atom, but to move from one to another they must jump rather than move via continuous variation: and an electron in a hydrogen atom going from -13.6 eV of energy to -3.4 eV does not pass through states of -10eV or -5.1eV, let along -11.1111115637 eV or -4.89712384 eV.
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  36.  92
    On Symmetry and Conserved Quantities in Classical Mechanics.Jeremy Butterfield - unknown
    This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem's main ``ingredient'', apart from cyclic (...)
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  37.  8
    Nonconglomerability for Countably Additive Measures That Are Not Κ-Additive.Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane - 2017 - Review of Symbolic Logic 10 (2):284-300.
    Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti and Dubins, subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our result, where we established that each finite but not countably additive (...)
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  38.  60
    What Are Quantities?Joongol Kim - 2016 - Australasian Journal of Philosophy 94 (4):792-807.
    ABSTRACTThis paper presents a view of quantities as ‘adverbial’ entities of a certain kind—more specifically, determinate ways, or modes, of having length, mass, speed, and the like. In doing so, it will be argued that quantities as such should be distinguished from quantitative properties or relations, and are not universals but are particulars, although they are not objects, either. A main advantage of the adverbial view over its rivals will be found in its superior explanatory power with respect (...)
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  39.  5
    On Phase Semantics and Denotational Semantics in Multiplicative–Additive Linear Logic.Antonio Bucciarelli & Thomas Ehrhard - 2000 - Annals of Pure and Applied Logic 102 (3):247-282.
    We study the notion of logical relation in the coherence space semantics of multiplicative-additive linear logic . We show that, when the ground-type logical relation is “closed under restrictions”, the logical relation associated to any type can be seen as a map associating facts of a phase space to families of points of the web of the corresponding coherence space. We introduce a sequent calculus extension of whose formulae denote these families of points. This logic admits a truth-value semantics (...)
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  40.  8
    Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics.Leon Loveridge, Takayuki Miyadera & Paul Busch - 2018 - Foundations of Physics 48 (2):135-198.
    We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox “absolute” quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection (...)
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  41.  55
    Quantities, Magnitudes, and Numbers.Henry E. Kyburg Jr - 1997 - Philosophy of Science 64 (3):377-410.
    Quantities are naturally viewed as functions, whose arguments may be construed as situations, events, objects, etc. We explore the question of the range of these functions: should it be construed as the real numbers (or some subset thereof)? This is Carnap's view. It has attractive features, specifically, what Carnap views as ontological economy. Or should the range of a quantity be a set of magnitudes? This may have been Helmholtz's view, and it, too, has attractive features. It reveals the (...)
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  42.  60
    Real Numbers, Quantities, and Measurement.Bob Hale - 2002 - Philosophia Mathematica 10 (3):304-323.
    Defining the real numbers by abstraction as ratios of quantities gives prominence to then- applications in just the way that Frege thought we should. But if all the reals are to be obtained in this way, it is necessary to presuppose a rich domain of quantities of a land we cannot reasonably assume to be exemplified by any physical or other empirically measurable quantities. In consequence, an explanation of the applications of the reals, defined in this way, (...)
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  43.  56
    Probability Logic of Finitely Additive Beliefs.Chunlai Zhou - 2010 - Journal of Logic, Language and Information 19 (3):247-282.
    Probability logics have been an active topic of investigation of beliefs in type spaces in game theoretical economics. Beliefs are expressed as subjective probability measures. Savage’s postulates in decision theory imply that subjective probability measures are not necessarily countably additive but finitely additive. In this paper, we formulate a probability logic Σ + that is strongly complete with respect to this class of type spaces with finitely additive probability measures, i.e. a set of formulas is consistent in (...)
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  44. Generalizing the Algebra of Physical Quantities.Mark Sharlow - manuscript
    In this paper, I define and study an abstract algebraic structure, the dimensive algebra, which embodies the most general features of the algebra of dimensional physical quantities. I prove some elementary results about dimensive algebras and suggest some directions for future work.
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  45.  2
    Against Reducing Newtonian Mass to Kinematical Quantities.Niels C. M. Martens - unknown
    It is argued that Newtonian mass cannot be reduced to kinematical quantities---distance, velocity and acceleration---without losing the explanatory and predictive power of Newtonian Gravity.
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  46.  16
    Conversational Contrast and Conventional Parallel: Topic Implicatures and Additive Presuppositions.K. J. Saebo - 2004 - Journal of Semantics 21 (2):199-217.
    Additive particles or adverbs like too or again are sometimes obligatory. This does not follow from the meaning commonly ascribed to them. I argue that the text without the additive is incoherent because the context contradicts a contrast implicature stemming from the additive's associate, and that the text with the additive is coherent because the presupposed alternative is added to the associate, so that the implicature does not concern that alternative. I show that this analysis is (...)
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  47. On Symmetry and Conserved Quantities in Classical Mechanics.I. Pitowsky - unknown
    This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether’s “first theorem”, in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics’ grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem’s main “ingredient”, apart from cyclic (...)
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  48.  1
    The Additive Multiboxes.Lorenzo Tortora de Falco - 2003 - Annals of Pure and Applied Logic 120 (1-3):65-102.
    We introduce the new notion of additive “multibox” for linear logic proof-nets. Thanks to this notion, we define a cut-elimination procedure which associates with every proof-net of multiplicative and additive linear logic a unique cut-free one.
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  49.  81
    A Representation of Preferences by the Choquet Integral with Respect to a 2-Additive Capacity.Brice Mayag, Michel Grabisch & Christophe Labreuche - 2011 - Theory and Decision 71 (3):297-324.
    In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.
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  50.  32
    Theorems as Meaningful Cultural Artifacts: Making the World Additive.Martin H. Krieger - 1991 - Synthese 88 (2):135 - 154.
    Mathematical theorems are cultural artifacts and may be interpreted much as works of art, literature, and tool-and-craft are interpreted. The Fundamental Theorem of the Calculus, the Central Limit Theorem of Statistics, and the Statistical Continuum Limit of field theories, all show how the world may be put together through the arithmetic addition of suitably prescribed parts (velocities, variances, and renormalizations and scaled blocks, respectively). In the limit — of smoothness, statistical independence, and large N — higher-order parts, such as accelerations, (...)
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