Explicit Definition of an Observable Event in the Framework of Generalized Madelung Equations

1999 ◽  
Vol 276 (1) ◽  
pp. 12-38 ◽  
Author(s):  
Christophe Tzara
Keyword(s):  
Explicit Definition ◽  
Observable Event ◽  
Definition Of ◽  
Madelung Equations

New Views on the Fremont: The Fremont and the Sevier: Defining Prehistoric Agriculturalists North of the Anasazi

1979 ◽  
Vol 44 (4) ◽  
pp. 711-722 ◽  
Author(s):  
David B. Madsen
Keyword(s):  
Great Basin ◽  
Settlement Patterns ◽  
Colorado Plateau ◽  
Explicit Definition ◽  
Taxonomic Level ◽  
The North ◽  
Subsistence Economies ◽  
Definition Of

A satisfactory and explicit definition of the Fremont has not been produced in over 50 years of research—a failure which suggests that no comprehensive entity exists. Attempts to define a Fremont through the use of trait lists have failed, although such lists have provided the basis for three apparently conflicting theories of origin. Analyses of subsistence economies and settlement patterns suggest that no comprehensive entity exists and that all three origin theories may possibly be valid. A Sevier "culture," based on marsh collecting and supplemented by corn agriculture, can be defined in the eastern Great Basin. A Fremont "culture," based on corn agriculture and supplemented by hunting, can be defined on the Colorado Plateau. A third unnamed, but possibly Plains-related, culture may be defined to the north of these. These "cultures" are distinctive enough to be separated on the same taxonomic level as are the Anasazi and the Sinagua.

Reconsidering Ordered Pairs

2008 ◽  
Vol 14 (3) ◽  
pp. 379-397 ◽  
Author(s):  
Dana Scott ◽  
Dominic McCarty
Keyword(s):  
Explicit Definition ◽  
Wide Range ◽  
Infinite Sets ◽  
Definition Of ◽  
Ordered Pairs

AbstractThe well known Wiener-Kuratowski explicit definition of the ordered pair, which sets (x,y) = {{x}, {x,y}}, works well in many set theories but fails for those with classes which cannot be members of singletons. With the aid of the Axiom of Foundation, we propose a recursive definition of ordered pair which addresses this shortcoming and also naturally generalizes to ordered tuples of greater length. There are many advantages to the new definition, for it allows for uniform definitions working equally well in a wide range of models for set theories. In ZFC and closely related theories, the rank of an ordered pair of two infinite sets under the new definition turns out to be equal to the maximum of the ranks of the sets.

The best available science for the management of anadromous salmonids in the Columbia River Basin

2002 ◽  
Vol 59 (12) ◽  
pp. 1952-1959 ◽  
Author(s):  
Gustavo A Bisbal
Keyword(s):  
River Basin ◽  
Scientific Information ◽  
Columbia River ◽  
Columbia River Basin ◽  
Explicit Definition ◽  
Refinement Process ◽  
Best Available Science ◽  
Definition Of

Reference to the "best available science" is popular among administrators and scientists responsible for the management of anadromous salmonids in the Columbia River Basin. Regional recovery documents explicitly call for the consideration of the best available science during the formulation of policies, but they fail to elaborate on what this phrase means. In the absence of such clarification, the definition of what counts as science, how to recognize the best science from the rest, and a determination of how much of it is available invites a wide array of interpretations. Two possible remedies are proposed to alleviate this ambiguity. The first is to leave this phrase intact, but also to append an explicit definition of what each term means. This should establish sideboards for what is acceptable when compiling scientific information. The second remedy is to discontinue the impulsive use of the phrase best available science and select alternative language that more accurately reflects legislative intent. This refinement process will naturally result in other phrases tailored to the specific preferences and requirements of each situation. A decision to accept any of these alternatives may profoundly affect how science influences the management of anadromous salmonids in the Columbia River Basin.

scholarly journals Defining ethical challenge(s) in healthcare research: a rapid review

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Guy Schofield ◽  
Mariana Dittborn ◽  
Lucy Ellen Selman ◽  
Richard Huxtable
Keyword(s):  
Empirical Studies ◽  
Academic Research ◽  
Healthcare Research ◽  
Research Literature ◽  
Rapid Review ◽  
Ethical Challenge ◽  
Explicit Definition ◽  
Conceptual Clarity ◽  
Manuscript Text ◽  
Definition Of

Abstract Background Despite its ubiquity in academic research, the phrase ‘ethical challenge(s)’ appears to lack an agreed definition. A lack of a definition risks introducing confusion or avoidable bias. Conceptual clarity is a key component of research, both theoretical and empirical. Using a rapid review methodology, we sought to review definitions of ‘ethical challenge(s)’ and closely related terms as used in current healthcare research literature. Methods Rapid review to identify peer-reviewed reports examining ‘ethical challenge(s)’ in any context, extracting data on definitions of ‘ethical challenge(s)’ in use, and synonymous use of closely related terms in the general manuscript text. Data were analysed using content analysis. Four databases (MEDLINE, Philosopher’s Index, EMBASE, CINAHL) were searched from April 2016 to April 2021. Results 393 records were screened, with 72 studies eligible and included: 53 empirical studies, 17 structured reviews and 2 review protocols. 12/72 (17%) contained an explicit definition of ‘ethical challenge(s), two of which were shared, resulting in 11 unique definitions. Within these 11 definitions, four approaches were identified: definition through concepts; reference to moral conflict, moral uncertainty or difficult choices; definition by participants; and challenges linked to emotional or moral distress. Each definition contained one or more of these approaches, but none contained all four. 68/72 (94%) included studies used terms closely related to synonymously refer to ‘ethical challenge(s)’ within their manuscript text, with 32 different terms identified and between one and eight different terms mentioned per study. Conclusions Only 12/72 studies contained an explicit definition of ‘ethical challenge(s)’, with significant variety in scope and complexity. This variation risks confusion and biasing data analysis and results, reducing confidence in research findings. Further work on establishing acceptable definitional content is needed to inform future bioethics research.

CARNAP’S DEFENSE OF IMPREDICATIVE DEFINITIONS

2018 ◽  
Vol 12 (2) ◽  
pp. 372-404
Author(s):  
VERA FLOCKE
Keyword(s):  
Historical Context ◽  
Foundations Of Mathematics ◽  
Intended Meaning ◽  
Explicit Definition ◽  
Abstract Entities ◽  
Definition Of ◽  
Linguistic Framework

AbstractA definition of a property P is impredicative if it quantifies over a domain to which P belongs. Due to influential arguments by Ramsey and Gödel, impredicative mathematics is often thought to possess special metaphysical commitments. The reason is that an impredicative definition of a property P does not have its intended meaning unless P exists, suggesting that the existence of P cannot depend on its explicit definition. Carnap (1937 [1934], p. 164) argues, however, that accepting impredicative definitions amounts to choosing a “form of language” and is free from metaphysical implications. This article explains this view in its historical context. I discuss the development of Carnap’s thought on the foundations of mathematics from the mid-1920s to the mid-1930s, concluding with an account of Carnap’s (1937 [1934]) non-Platonistic defense of impredicativity. This discussion is also important for understanding Carnap’s influential views on ontology more generally, since Carnap’s (1937 [1934]) view, according to which accepting impredicative definitions amounts to choosing a “form of language”, is an early precursor of the view that Carnap presents in “Empiricism, Semantics and Ontology” (1956 [1950]), according to which referring to abstract entities amounts to accepting a “linguistic framework”.

Automated tableau generation using SPOT (Syntax Prosody in Optimality Theory)

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Jennifer Bellik ◽  
Nick Kalivoda
Keyword(s):  
Recent Work ◽  
Optimality Theory ◽  
Regular Expressions ◽  
Computational Tool ◽  
Arbitrary Size ◽  
Automated Generation ◽  
Chomsky Hierarchy ◽  
Explicit Definition ◽  
Definition Of

AbstractMuch recent work on the syntax-prosody interface has been based in Optimality Theory. The typical analysis explicitly considers only a small number of candidates that could reasonably be expected to be optimal under some ranking, often without an explicit definition of GEN. Manually generating all the possible candidates, however, is prohibitively time-consuming for most input structures – the Too Many Candidates Problem. Existing software for OT uses regular expressions for automated generation and evaluation of candidates. However, regular expressions are too low in the Chomsky Hierarchy of language types to represent trees of arbitrary size, which are needed for syntax-prosody work. This paper presents a new computational tool for research in this area: Syntax-Prosody in Optimality Theory (SPOT). For a given input, SPOT generates all prosodic parses under certain assumptions about GEN, and evaluates them against all constraints in CON. This allows for in-depth comparison of the typological predictions made by different theories of GEN and CON at the syntax-prosody interface.

Beth’s theorem and Craig’s theorem

2018 ◽  
Author(s):  
Zeno Swijtink
Keyword(s):  
Sufficient Conditions ◽  
Predicate Symbol ◽  
Expressive Power ◽  
Order Logic ◽  
First Order Logic ◽  
Infinite Length ◽  
First Order ◽  
Explicit Definition ◽  
Central Result ◽  
Definition Of

Beth’s theorem is a central result about definability of non-logical symbols in classical first-order theories. It states that a symbol P is implicitly defined by a theory T if and only if an explicit definition of P in terms of some other expressions of the theory T can be deduced from the theory T. Intuitively, the symbol P is implicitly defined by T if, given the extension of these other symbols, T fixes the extension of the symbol P uniquely. In a precise statement of Beth’s theorem this will be replaced by a condition on the models of T. An explicit definition of a predicate symbol states necessary and sufficient conditions: for example, if P is a one-place predicate symbol, an explicit definition is a sentence of the form (x) (Px ≡φ(x)), where φ(x) is a formula with free variable x in which P does not occur. Thus, Beth’s theorem says something about the expressive power of first-order logic: there is a balance between the syntax (the deducibility of an explicit definition) and the semantics (across models of T the extension of P is uniquely determined by the extension of other symbols). Beth’s definability theorem follows immediately from Craig’s interpolation theorem. For first-order logic with identity, Craig’s theorem says that if φ is deducible from ψ, there is an interpolant θ, a sentence whose non-logical symbols are common to φ and ψ, such that θ is deducible from ψ, while φ is deducible from θ. Craig’s theorem and Beth’s theorem also hold for a number of non-classical logics, such as intuitionistic first-order logic and classical second-order logic, but fail for other logics, such as logics with expressions of infinite length.

Towards a Clarification of Spatial Processing

1994 ◽  
Vol 47 (2) ◽  
pp. 465-480 ◽  
Author(s):  
J.G. Quinn
Keyword(s):  
Interference Effect ◽  
Passive Movement ◽  
Spatial Processing ◽  
Explicit Definition ◽  
Movement Characteristics ◽  
Definition Of

Three experiments that adopt an interference paradigm to investigate characteristics of a type of movement causing interference with spatial processing are reported. Experiment 1 illustrates the importance of distinguishing between movement and attention to movement when investigating the movement characteristics of spatial processing. The technique of passive movement is used to minimize attention in the subsequent experiments. Experiment 2 confirms earlier experiments showing that passive movement causes interference in spatial processing. However, it extends the previous findings by demonstrating that passive movement is detrimental to spatial processing only when the movement is to a sequence of locations known in advance by the subjects. Experiment 3 demonstrates that the movement interference cannot be interpreted as a general interference effect but that it is selective for spatial processing. The results of these experiments permit a more precise delineation of the disruptive effects of movement in spatial processing and allow an explicit definition of spatial processing to be put forward.

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