Search results for 'Primitive Terms' (try it on Scholar)

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  1.  21
    Wolfgang Lenzen (1991). Leibniz on Privative and Primitive Terms. Theoria 6 (1/2):83-96.
    We first present an edition of the manuscript LH VII, B 2, 39 in which Leibniz develops a new formalism in order to give rigorous definitions of positive, of privative, and of primitive terms.This formalism involves a symbolic treatment of conceptual quantification which differs quite considerably from Leibniz’s “standard” theory of “indefinite concepts” as developed, e.g., in the “General Inquirles” In the subsequent commentary we give an interpretation and a critical evaluation of Leibniz’s symbolic apparatus. It turns out (...)
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  2.  16
    Wolfgang Lenzen (1991). Leibniz on Privative and Primitive Terms. Theoria 6 (1):83-96.
    We first present an edition of the manuscript LH VII, B 2, 39 in which Leibniz develops a new formalism in order to give rigorous definitions of positive, of privative, and of primitive terms.This formalism involves a symbolic treatment of conceptual quantification which differs quite considerably from Leibniz’s “standard” theory of “indefinite concepts” as developed, e.g., in the “General Inquirles” In the subsequent commentary we give an interpretation and a critical evaluation of Leibniz’s symbolic apparatus. It turns out (...)
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  3.  5
    Danie Strauss (2013). Primitive Terms and the Limits of Conceptual Understanding. South African Journal of Philosophy 32 (2):173-185.
    Ignoring primitive terms leads to an infinite regress. The alternative is to account for an intuitive understanding into the meaning of such terms. The current investigation proceeds on the basis of an idea of the structure of the various modes of being within which concrete entities function. Examples of primtive terms are given from disciplines such as mathematics, physics and logic and they are related to the general idea of a modal aspect. It is argued that (...)
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  4.  16
    Czesław Lejewski (1968). A Propositional Calculus in Which Three Mutually Undefinable Functors Are Used as Primitive Terms. Studia Logica 22 (1):17 - 50.
  5.  26
    Lucas Dunlap (2015). On the Common Structure of the Primitive Ontology Approach and the Information-Theoretic Interpretation of Quantum Theory. Topoi 34 (2):359-367.
    We use the primitive ontology framework of Allori et al. to analyze the quantum information-theoretic interpretation of Bub and Pitowsky. There are interesting parallels between the two approaches, which differentiate them both from the more standard realist interpretations of quantum theory. Where they differ, however, is in terms of their commitments to an underlying ontology on which the manifest image of the world supervenes. Employing the primitive ontology framework in this way makes perspicuous the differences (...)
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  6.  20
    Valia Allori (2007). Fundamental Physical Theories: Mathematical Structures Grounded on a Primitive Ontology. Dissertation, Rutgers
    In my dissertation I analyze the structure of fundamental physical theories. I start with an analysis of what an adequate primitive ontology is, discussing the measurement problem in quantum mechanics and theirs solutions. It is commonly said that these theories have little in common. I argue instead that the moral of the measurement problem is that the wave function cannot represent physical objects and a common structure between these solutions can be recognized: each of them is about a clear (...)
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  7. David Steiner & Thomas Strahm (2006). On the Proof Theory of Type Two Functionals Based on Primitive Recursive Operations. Mathematical Logic Quarterly 52 (3):237-252.
    This paper is a companion to work of Feferman, Jäger, Glaß, and Strahm on the proof theory of the type two functionals μ and E1 in the context of Feferman-style applicative theories. In contrast to the previous work, we analyze these two functionals in the context of Schlüter's weakened applicative basis PRON which allows for an interpretation in the primitive recursive indices. The proof-theoretic strength of PRON augmented by μ and E1 is measured in terms of the (...)
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  8.  87
    T. Parent (2013). In the Mental Fiction, Mental Fictionalism is Fictitious. The Monist 96 (4):605-621.
    Here I explore the prospects for fictionalism about the mental, modeled after fictionalism about possible worlds. Mental fictionalism holds that the mental states posited by folk psychology do not exist, yet that some sentences of folk psychological discourse are true. This is accomplished by construing truths of folk psychology as “truths according to the mentalistic fiction.” After formulating the view, I identify five ways that the view appears self-refuting. Moreover, I argue that this cannot be fixed by semantic ascent or (...)
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  9.  35
    John T. Roberts, The Semantic Novelty of Theoretical Terms.
    Often when a new scientific theory is introduced, new terms are introduced along with it. Some of these new terms might be given explicit definitions using only terms that were in currency prior to the introduction of the theory. Some of them might be defined using other new terms introduced with the theory. But it frequently happens that the standard formulations of a theory do not define some of the new terms at all; these (...) are adopted as primitives. The audience is expected to come to grasp the meanings of the primitive terms by learning the role they play in the theory and its applications. I shall call such new and undefined terms, as well as new terms that are defined using them, theoretical terms. 1 If T is a theory, the T-terms are the theoretical terms introduced by T. A theoretical term need not be a word new to human language; it might be an old term that is employed in a new and specialized sense, not equivalent to any of its familiar senses; e.g. “color” in quantum chromodynamics. (shrink)
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  10.  37
    D. F. M. Strauss (2010). The Significance of a Non-Reductionist Ontology for the Discipline of Mathematics: A Historical and Systematic Analysis. [REVIEW] Axiomathes 20 (1):19-52.
    A Christian approach to scholarship, directed by the central biblical motive of creation, fall and redemption and guided by the theoretical idea that God subjected all of creation to His Law-Word, delimiting and determining the cohering diversity we experience within reality, in principle safe-guards those in the grip of this ultimate commitment and theoretical orientation from absolutizing or deifying anything within creation. In this article my over-all approach is focused on the one-sided legacy of mathematics, starting with Pythagorean arithmeticism (“everything (...)
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  11.  14
    K. Hałkowska (1967). A Note on the System of Propositional Calculus with Primitive Rule of Extensionality. Studia Logica 20 (1):150-150.
    The present paper deals with a systemS of propositional calculus, conjunction, equivalence and falsum being its primitive terms.The only primitive rule inS is the rule of extensionality defined by the scheme: $\frac{{E\alpha \beta ,\Phi (\alpha )}}{{\Phi (\beta )}}$.
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  12.  13
    Michael Esfeld, Dustin Lazarovici, Vincent Lam & Mario Hubert (forthcoming). The Physics and Metaphysics of Primitive Stuff. British Journal for the Philosophy of Science:axv026.
    The article sets out a primitive ontology of the natural world in terms of primitive stuff—that is, stuff that has as such no physical properties at all—but that is not a bare substratum either, being individuated by metrical relations. We focus on quantum physics and employ identity-based Bohmian mechanics to illustrate this view, but point out that it applies all over physics. Properties then enter into the picture exclusively through the role that they play for the dynamics (...)
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  13.  67
    Adrian Haddock (2012). Meaning, Justification, And'Primitive Normativity'. Aristotelian Society Supplementary Volume 86 (1):147-174.
    I critically discuss two claims which Hannah Ginsborg makes on behalf of her account of meaning in terms of ‘primitive normativity’(2011; 2012): first, that it avoids the sceptical regress articulated by Kripke's Wittgenstein; second, that it makes sense of the thought—central to Kripke's Wittgenstein—that ‘meaning is normative’, in a way which shows this thought not only to be immune from recent criticisms but also to undermine reductively naturalistic theories of content. In the course of the discussion, I consider (...)
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  14.  10
    Alexander P. Kreuzer (2012). Primitive Recursion and the Chain Antichain Principle. Notre Dame Journal of Formal Logic 53 (2):245-265.
    Let the chain antichain principle (CAC) be the statement that each partial order on $\mathbb{N}$ possesses an infinite chain or an infinite antichain. Chong, Slaman, and Yang recently proved using forcing over nonstandard models of arithmetic that CAC is $\Pi^1_1$-conservative over $\text{RCA}_0+\Pi^0_1\text{-CP}$ and so in particular that CAC does not imply $\Sigma^0_2$-induction. We provide here a different purely syntactical and constructive proof of the statement that CAC (even together with WKL) does not imply $\Sigma^0_2$-induction. In detail we show using a (...)
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  15. Susan Schneider (forthcoming). The Nature of Primitive Symbols in the Language of Thought. Mind and Language.
    This paper provides a theory of the nature of symbols in the language of thought (LOT). My discussion consists in three parts. In part one, I provide three arguments for the individuation of primitive symbols in terms of total computational role. The first of these arguments claims that Classicism requires that primitive symbols be typed in this manner; no other theory of typing will suffice. The second argument contends that without this manner of symbol individuation, there will (...)
     
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  16.  48
    Dale Jacquette (2011). Intentionality as a Conceptually Primitive Relation. Acta Analytica 26 (1):15-35.
    If conceptual analysis is possible for finite thinkers, then there must ultimately be a distinction between complex and primitive or irreducible and unanalyzable concepts, by which complex concepts are analyzed as relations among primitive concepts. This investigation considers the advantages of categorizing intentionality as a primitive rather than analyzable concept, in both a historical Brentanian context and in terms of contemporary philosophy of mind. Arguments in support of intentionality as a primitive relation are evaluated relative (...)
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  17.  23
    Alessandro Salice (2015). There Are No Primitive We-Intentions. Review of Philosophy and Psychology 6 (4):695-715.
    John Searle’s account of collective intentions in action appears to have all the theoretical pros of the non-reductivist view on collective intentionality without the metaphysical cons of committing to the existence of group minds. According to Searle, when we collectively intend to do something together, we intend to cooperate in order to reach a collective goal. Intentions in the first-person plural form therefore have a particular psychological form or mode, for the we-intender conceives of his or her intended actions as (...)
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  18.  13
    Gabriel Segal & Mark Textor (2015). Hope as a Primitive Mental State. Ratio 28 (2):207-222.
    We criticize attempts to define hope in terms of other psychological states and argue that hope is a primitive mental state whose nature can be illuminated by specifying key aspects of its functional profile.
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  19.  21
    Herbert Hochberg (1978). Nominalism, General Terms, and Predication. The Monist 61 (3):460-475.
    Platonism, in its most recent and seemingly most cogent form, has rested on (a) the supposed indispensability of descriptive predicate terms in so-called "improved," or "clarified," or "perspicuous" languages; (b) the distinction between subject and predicate terms based on the asymmetry of the predication relation; and (c) the claimed ontological significance of the different categories of terms implied by (a) and (b). Nominalism, in one of its most pervasive recent forms, has involved the denial of the criterion (...)
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  20.  3
    Helmut Schwichtenberg (1998). Finite Notations for Infinite Terms. Annals of Pure and Applied Logic 94 (1-3):201-222.
    Buchholz presented a method to build notation systems for infinite sequent-style derivations, analogous to well-known systems of notation for ordinals. The essential feature is that from a notation one can read off by a primitive recursive function its n th predecessor and, e.g. the last rule applied. Here we extend the method to the more general setting of infinite terms, in order to make it applicable in other proof-theoretic contexts as well as in recursion theory. As examples, we (...)
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  21.  14
    Calvin Normore (2010). Primitive Intentionality and Reduced Intentionality: Ockham's Legacy. Quaestio 10 (1):255-266.
    Three philosophical questions that are often confused should instead be keep distinct: First, what is a thought? Second, what is that in virtue of which a thought is a thought? Third, what is it that determines of what a thought is a thought? These questions raise very different issues within Ockham’s philosophy. Although Ockham’s views about the first question evolve, he seems to answer the second and the third questions in the same way, maintaining throughout his career that the intentionality (...)
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  22.  6
    Gyula Klima (2012). Ontological Reduction by Logical Analysis and the Primitive Vocabulary of Mentalese. American Catholic Philosophical Quarterly 86 (3):403-414.
    This paper confronts a certain modern view of the relation between semantics and ontology with that of the late-medieval nominalist philosophers, William Ockham and John Buridan. The modern view in question is characterized in terms of what is called here “the thesis of onto-semantic parallelism,” which states that the primitive categorematic concepts of our semantics mark out the primary entities in reality. The paper argues that, despite some apparently plausible misinterpretations to the contrary, the late-medieval nominalist program of (...)
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  23.  16
    Ken Warmbrōd (1992). Primitive Representation and Misrepresentation. Topoi 11 (1):89-101.
    This paper develops a statistical approach to the problem of primitive representation. Representation of the kind commonly attributed to litmus paper, fuel gauges and tree rings occurs when, so to speak, there is a sufficiently good correlation between two variables. The fundamental distinction between misrepresentation and non-representation is explained in terms of the notion of an informationally useful correlation. The paper further argues that the statistical approach satisfactorily resolves well known puzzles such as Fodor's disjunction problem.
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  24.  1
    Karl-Heinz Niggl (1995). Towards the Computational Complexity of ℘Rω-Terms. Annals of Pure and Applied Logic 75 (1-2):153-178.
    We investigate a simply typed term system ℘R ω aimed at defining partial primitive recursive functionals over arbitrary Scott domains . A hierarchy of complexity classes R n ω for functionals definable in ℘R ω is given based on a hierarchy of term classes ℘R n ωpn denoting the n th class of so-called prenormal terms . They come into play by the key observation that every term t can be transformed by what we call higher type modularization (...)
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  25.  25
    Ken Warmbrod (1992). Primitive Representation and Misrepresentation. Topoi 11 (1):89-101.
    This paper develops a statistical approach to the problem of primitive representation. Representation of the kind commonly attributed to litmus paper, fuel gauges and tree rings occurs when, so to speak, there is a sufficiently good correlation between two variables. The fundamental distinction between misrepresentation and non-representation is explained in terms of the notion of an informationally useful correlation. The paper further argues that the statistical approach satisfactorily resolves well-known puzzles such as Fodor's disjunction problem.
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  26.  22
    M. B. Kac (1997). The Proper Treatment of Singular Terms in Ordinary English. Mind 106 (424):661-696.
    A free logical analysis of singular terms couched in terms of the semantic theory of Keenan and Faltz is shown to avoid problems with both Frege's and Russell's treatments. At its heart is the proposal of Keenan and Faltz to reverse the usual mode-theoretic conception of individuals and properties, taking the latter as primitive and the former as derived therefrom. A simple extension of the notion 'property' is then shown to enable a parallel treatment of definite generics.
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  27.  16
    Timothy J. Nulty (2007). Primitive Disclosive Alethism. Metaphysica 8 (1):1-15.
    The contemporary debate about truth is polarized between deflationists and those who offer robust accounts of truth. I present a theory of truth called ‘Primitive Disclosive Alethism’ that occupies the middle ground between these two extremes. Contrary to deflationist claims, truth has a nature beyond its merely linguistic, expressive function. Truth is objective and non-epistemic, yet cannot be characterized in terms of correspondence. Primitive Disclosive Alethism offers a metaphysically satisfying explanation of our correspondence intuitions, while explaining why (...)
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  28.  11
    Raymond D. Gumb (2002). The Lazy Logic of Partial Terms. Journal of Symbolic Logic 67 (3):1065-1077.
    The Logic of Partial Terms LPT is a strict negative free logic that provides an economical framework for developing many traditional mathematical theories having partial functions. In these traditional theories, all functions and predicates are strict. For example, if a unary function (predicate) is applied to an undefined argument, the result is undefined (respectively, false). On the other hand, every practical programming language incorporates at least one nonstrict or lazy construct, such as the if-then-else, but nonstrict functions cannot be (...)
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  29. Peter Smith, Expressing and Capturing the Primitive Recursive Functions.
    The last Episode wasn’t about logic or formal theories at all: it was about common-or-garden arithmetic and the informal notion of computability. We noted that addition can be defined in terms of repeated applications of the successor function. Multiplication can be defined in terms of repeated applications of addition. The exponential and factorial functions can be defined, in different ways, in terms of repeated applications of multiplication. There’s already a pattern emerging here! The main task in the (...)
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  30.  1
    Karl-Heinz Niggl (1995). Towards the Computational Complexity of℘ Rω-Terms. Annals of Pure and Applied Logic 75 (1):153-178.
    We investigate a simply typed term system ℘R ω aimed at defining partial primitive recursive functionals over arbitrary Scott domains . A hierarchy of complexity classes R n ω for functionals definable in ℘R ω is given based on a hierarchy of term classes ℘R n ωpn denoting the n th class of so-called prenormal terms . They come into play by the key observation that every term t can be transformed by what we call higher type modularization (...)
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  31.  5
    William R. Stirton (2012). How to Assign Ordinal Numbers to Combinatory Terms with Polymorphic Types. Archive for Mathematical Logic 51 (5-6):475-501.
    The article investigates a system of polymorphically typed combinatory logic which is equivalent to Gödel’s T. A notion of (strong) reduction is defined over terms of this system and it is proved that the class of well-formed terms is closed under both bracket abstraction and reduction. The main new result is that the number of contractions needed to reduce a term to normal form is computed by an ε 0-recursive function. The ordinal assignments used to obtain this (...)
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  32. Antonio Vassallo & Michael Esfeld (2014). A Proposal for a Bohmian Ontology of Quantum Gravity. Foundations of Physics (1):1-18.
    The paper shows how the Bohmian approach to quantum physics can be applied to develop a clear and coherent ontology of non-perturbative quantum gravity. We suggest retaining discrete objects as the primitive ontology also when it comes to a quantum theory of space-time and therefore focus on loop quantum gravity. We conceive atoms of space, represented in terms of nodes linked by edges in a graph, as the primitive ontology of the theory and show how a non-local (...)
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  33. Berit Brogaard (2011). Primitive Knowledge Disjunctivism. Philosophical Issues 21 (1):45-73.
    I argue that McDowell-style disjunctivism, as the position is often cashed out, goes wrong because it takes the good epistemic standing of veridical perception to be grounded in “manifest” facts which do not necessarily satisfy any epistemic constraints. A better form of disjunctivism explains the difference between good and bad cases in terms of epistemic constraints that the states satisfy. This view allows us to preserve McDowell’s thesis that good cases make facts manifest, as long as manifest facts must (...)
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  34. Jamin Asay (2013). Primitive Truth. Dialectica 67 (4):503-519.
    Conceptual primitivism is the view that truth is among our most basic and fundamental concepts. It cannot be defined, analyzed, or reduced into concepts that are more fundamental. Primitivism is opposed to both traditional attempts at defining truth (in terms of correspondence, coherence, or utility) and deflationary theories that argue that the notion of truth is exhausted by means of the truth schema. Though primitivism might be thought of as a view of last resort, I believe that the view (...)
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  35.  59
    Richard Holton (forthcoming). Primitive Self-Ascription: Lewis on the De Se. In Barry Loewer & Jonathan Schaffer (eds.), The Blackwell Companion to David Lewis. Blackwell
    There are two parts to Lewis's account of the de se. First there is the idea that the objects of de se thought (and, by extension of de dicto thought too) are properties, not propositions. This is the idea that is center-stage in Lewis's discussion. Second there is the idea that the relation that thinkers bear to these properties is that of self-ascription. It is crucial to LewisÕs account that this is understood as a fundamental, unanalyzable, notion: self-ascription of a (...)
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  36.  32
    C. Taylor (1999). Sympathy. Journal of Ethics 3 (1):73-87.
    In this article I examine an example of sympathy -- the actions of one woman who rescued Jews during their persecution in Nazi Europe. I argue that this woman''s account of her actions here suggests that sympathy is a primitive response to the suffering of another. By primitive here I mean: first, that these responses are immediate and unthinking; and second, that these responses are explanatorily basic, that they cannot be explained in terms of some more fundamental (...)
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  37.  6
    Sören Stenlund (1972). Combinators, -Terms and Proof Theory. Dordrecht,D. Reidel.
    The main aim of Schonfinkel's paper was methodological: to reduce the primitive logical notions to as few and definite notions as possible. ...
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  38.  19
    Kordula Świętorzecka (2008). The Formalised Conception of Substantial Change in Terms of Some Modal Sentential Calculus (Logic LCG). Proceedings of the Xxii World Congress of Philosophy 13:113-120.
    The intention of the presented paper is to establish within a certain modal semantic based on the situational ontology a description of the phenomenon of substantial change, which originally had been formulated within Aristotelian metaphysics – a theory based in reistic ontology. We understand substantial changesto be such changes whose subjects are primary substances (πρωται ουσι αι ) conceived as actually existing individual essences. The analysed changeability is of an existential character - it pertains to the existence of those substances. (...)
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  39.  4
    William R. Stirton (2013). A Decidable Theory of Type Assignment. Archive for Mathematical Logic 52 (5-6):631-658.
    This article investigates a theory of type assignment (assigning types to lambda terms) called ETA which is intermediate in strength between the simple theory of type assignment and strong polymorphic theories like Girard’s F (Proofs and types. Cambridge University Press, Cambridge, 1989). It is like the simple theory and unlike F in that the typability and type-checking problems are solvable with respect to ETA. This is proved in the article along with three other main results: (1) all primitive (...)
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  40. P. A. Guil Asensio, M. C. Izurdiaga, Ph Rothmaler & B. Torrecillas (2011). Strict Mittag‐Leffler Modules. Mathematical Logic Quarterly 57 (6):566-570.
    We characterize strict Mittag-Leffler modules in terms of free realizations of positive primitive formulas, and rings over which projectives are trivial in terms of various notions of separability of strict Mittag-Leffler modules. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  41. E. A. Cichon & E. Tahhan-Bittar (2001). Strictly Orthogonal Left Linear Rewrite Systems and Primitive Recursion. Annals of Pure and Applied Logic 108 (1-3):79-101.
    Let F be a signature and R a strictly orthogonal rewrite system on ground terms of F . We give an effective proof of a bounding condition for R , based on a detailed analysis of how terms are transformed during the rewrite process, which allows us to give recursive bounds on the derivation lengths of terms. We give a syntactic characterisation of the Grzegorczyk hierarchy and a rewriting schema for calculating its functions. As a consequence of (...)
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  42. Nils Kürbis (forthcoming). Some Comments on Ian Rumfitt’s Bilateralism. Journal of Philosophical Logic:1-22.
    Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of ‘exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use’ : 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I then formalise an intuitionist (...)
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  43.  16
    Ansten Klev (2011). Dedekind and Hilbert on the Foundations of the Deductive Sciences. Review of Symbolic Logic 4 (4):645-681.
    We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert sees such beginnings in axioms. Secondly, it is argued that for Dedekind, the primitive terms of a science are substantive terms whose sense is to be conveyed (...)
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  44.  76
    J. Baird Callicott (1986). The Metaphysical Implications of Ecology. Environmental Ethics 8 (4):301-316.
    Although ecology is neither a universal nor foundational science, it has metaphysical implications because it profoundly alters traditional Western concepts of terrestrial nature and human being. I briefly sketch the received metaphysical foundations of the modem world view, set out a historical outline of an emerging ecological world view, and identify its principal metaphysical implications. Among these the most salient are a field ontology, the ontological subordination of matter to energy, internal relations, and systemic (as opposed to oceanic) holism. I (...)
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  45.  81
    James Robert Brown (1998). What is a Definition? Foundations of Science 3 (1):111-132.
    According to the standard view of definition, all defined terms are mere stipulations, based on a small set of primitive terms. After a brief review of the Hilbert-Frege debate, this paper goes on to challenge the standard view in a number of ways. Examples from graph theory, for example, suggest that some key definitions stem from the way graphs are presented diagramatically and do not fit the standard view. Lakatos's account is also discussed, since he provides further (...)
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  46.  16
    David J. Stump (2007). The Independence of the Parallel Postulate and Development of Rigorous Consistency Proofs. History and Philosophy of Logic 28 (1):19-30.
    I trace the development of arguments for the consistency of non-Euclidean geometries and for the independence of the parallel postulate, showing how the arguments become more rigorous as a formal conception of geometry is introduced. I analyze the kinds of arguments offered by Jules Hoüel in 1860-1870 for the unprovability of the parallel postulate and for the existence of non-Euclidean geometries, especially his reaction to the publication of Beltrami’s seminal papers, showing that Beltrami was much more concerned with the existence (...)
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  47.  20
    J. Baird Callicott (1986). The Metaphysical Implications of Ecology. Environmental Ethics 8 (4):301-316.
    Although ecology is neither a universal nor foundational science, it has metaphysical implications because it profoundly alters traditional Western concepts of terrestrial nature and human being. I briefly sketch the received metaphysical foundations of the modem world view, set out a historical outline of an emerging ecological world view, and identify its principal metaphysical implications. Among these the most salient are a field ontology, the ontological subordination of matter to energy, internal relations, and systemic (as opposed to oceanic) holism. I (...)
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  48.  8
    Daniël F. M. Strauss (2003). How “Rational” is “Rationality”? South African Journal of Philosophy 22 (3):247-266.
    By taking serious a remark once made by Paul Bernays, namely that an account of the nature of rationality should begin with concept-formation, this article sets out to uncover both the restrictive and the expansive boundaries of rationality. In order to do this some implications of the perennial philosophical problem of the “coherence of irreducibles” will be related to the acknowledgement of primitive terms and of their indefinability. Some critical remarks will be articulated in connection with an over-estimation (...)
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    Jim Edwards (2003). Reduction and Tarski's Definition of Logical Consequence. Notre Dame Journal of Formal Logic 44 (1):49-62.
    In his classic 1936 paper Tarski sought to motivate his definition of logical consequence by appeal to the inference form: P(0), P(1), . . ., P(n), . . . therefore ∀nP(n). This is prima facie puzzling because these inferences are seemingly first-order and Tarski knew that Gödel had shown first-order proof methods to be complete, and because ∀nP(n) is not a logical consequence of P(0), P(1), . . ., P(n), . . . by Taski's proposed definition. An attempt to resolve (...)
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    Francis Heylighen (1999). Advantages and Limitations of Formal Expression. Foundations of Science 4 (1):25-56.
    Testing the validity of knowledge requires formal expression of that knowledge. Formality of an expression is defined as the invariance, under changes of context, of the expression's meaning, i.e. the distinction which the expression represents. This encompasses both mathematical formalism and operational determination. The main advantages of formal expression are storability, universal communicability, and testability. They provide a selective edge in the Darwinian competition between ideas. However, formality can never be complete, as the context cannot be eliminated. Primitive (...), observation set-ups, and background conditions are inescapable parts of formal or operational definitions, that all refer to a context beyond the formal system. Heisenberg's Uncertainty Principle and Gödel's Theorem provide special cases of this more universal limitation principle. Context-dependent expressions, on the other hand, have the benefit of being more flexible, intuitive and direct, and putting less strain on memory. It is concluded that formality is not an absolute property, but a context-dependent one: different people will apply different amounts of formality in different situations or for different purposes. Some recent computational and empirical studies of formality and contexts illustrate the emerging scientific investigation of this dependence. (shrink)
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