What are species?

2019 ◽  
pp. 7-29
Author(s):  
Timothy G. Barraclough
Keyword(s):  
Standard Model ◽  
Alternative Models ◽  
Definition Of

This chapter looks at the ideas underpinning the definition of species. After outlining a standard model of species applicable to sexual organisms, it looks more broadly at the multiple forces that cause lineages to diversify into multiple distinct and independently evolving groups. ‘Independently evolving’ is defined and illustrated by reference to different kinds of organisms: sexuals, asexuals, prokaryotes, and hybridizing taxa. It then discusses whether forces of diversification truly act to generate discrete units, as proposed by the ‘species model’, and outlines some possible alternatives for the structure of diversity, such as a continuum of increasingly independent forms. The chapter emphasizes concrete theory that makes testable predictions to distinguish alternative models of the structure of diversity.

On finite lattices of degrees of constructibility of reals

1976 ◽  
Vol 41 (2) ◽  
pp. 313-322 ◽  
Author(s):  
Zofia Adamowicz
Keyword(s):  
Standard Model ◽  
Finite Lattice ◽  
Partial Ordering ◽  
Turing Degrees ◽  
Upper Semilattice ◽  
Finite Lattices ◽  
Definition Of ◽  
The Universe

Theorem. Assume that there exists a standard model of ZFC + V = L. Then there is a model of ZFC in which the partial ordering of the degrees of constructibility of reals is isomorphic with a given finite lattice.The proof of the theorem uses forcing. The definition of the forcing conditions and the proofs of some of the lemmas are connected with Lerman's paper on initial segments of the upper semilattice of the Turing degrees [2]. As an auxiliary notion we shall introduce the notion of a sequential representation of a lattice, which slightly differs from Lerman's representation.Let K be a given finite lattice. Assume that the universe of K is an integer l. Let ≤K be the ordering in K. A sequential representation of K is a sequence Ui ⊆ Ui+1 of finite subsets of ωi such that the following holds:(1) For any s, s′ Є Ui, i Є ω, k, m Є l, k ≤Km & s(m) = s′(m) → s(k) = s′(k).(2) For any s Є Ui, i Є ω, s(0) = 0 where 0 is the least element of K.(3) For any s, s′ Є i Є ω, k,j Є l, if k y Kj = m and s(k) = s′(k) & s(j) = s′(j) → s(m) = s′(m), where vK denotes the join in K.

scholarly journals Ways of Reading, Models for Text, and the Usefulness of Dead People

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
Yin Liu
Keyword(s):  
Test Case ◽  
Textual Information ◽  
Reading And Writing ◽  
Alternative Models ◽  
Theories Of Reading ◽  
Definition Of ◽  
Reading Models

The definition of text is still a live issue with important implications for emerging forms of digital textuality. This paper proposes that no single definition of text is sufficient to account for all manifestations of textuality. Medieval textuality is a test case: four different models for text are offered, corresponding to ways in which modern medievalists approach medieval texts. Studying medieval texts has value not only to support historically informed theories of reading and writing, but also to suggest alternative models of organizing, representing, and processing textual information.

scholarly journals Model-Theoretic Accounts of Logical Consequence - Themes from Etchemendy

2021 ◽  
Author(s):  
◽  
Kasper Højbjerg Christensen
Keyword(s):  
Standard Model ◽  
Model Theory ◽  
Logical Consequence ◽  
Kripke Semantics ◽  
Logical Necessity ◽  
Representational Model ◽  
Definition Of ◽  
In Virtue Of

<p>This thesis is a discussion and continuation of a project started by John Etchemendy with his criticism of Tarski's account of logical consequence. To this end the two central concepts of the thesis are those of an interpretational and representational model-theoretic account of logical consequence, respectively.  The first chapter introduces Etchemendy's criticism of Tarski's account of logical consequence, a criticism which turns essentially on an interpretation of Tarski according to which his proposed account gives rise to a purely interpretational model-theoretic account of logical consequence. Consequently there must be a representational aspect to our model-theoretic definition of logical consequence.  The second chapter introduces Etchemendy's notion of logical consequence: that of being truth preserving in virtue of the semantics of the involved terms. While this notion is representational, we argue that Etchemendy's notion of a categorematic treatment of terms reintroduces an interpretational aspect back into the model theory. The chapter investigates the resulting notion, compares it to other notions in the literature, and presents certain results that can be proved, under certain conditions, about this notion in relation to the notion of being truth preserving in virtue of the semantics of all terms.  Chapter three of the thesis is concerned with the question of how a standard model, seen as a domain and an interpretation function, manages to capture the different notions of model-theoretic consequence. As we explain, this question is most pressing when we want our models to both represent and interpret, and we will present a theory which allows us to see the models as both representing non-actual possibilities as well as provide interpretations for the terms.  The fourth chapter applies the lessons of the preceeding chapters to argue that Kripke Semantics can be seen as capturing the notion of being truth preserving in all possibilities under all interpretations of the non-logical terminology in the case where our language is augmented with an operator, ⃞, to represent logical necessity. We will argue this point by contrasting it with, though not necessarily disagreeing with, claims made by various authors to the effect that Kripke Semantics is not the appropriate semantics when our language contains an operator for logical necessity.</p>

scholarly journals Cosmos, Time and Creation (Remarks to the Philosophical, Theological and Physical Conceptions of Creation)

10.14311/1303 ◽  
2010 ◽  
Vol 50 (6) ◽  
Author(s):  
P. Zamarovský
Keyword(s):  
Standard Model ◽  
Theoretical Basis ◽  
Initial Singularity ◽  
Physical Processes ◽  
The Standard Model ◽  
Definition Of

The concept of the beginning of Cosmos appears to be problematic. Not only ancient theological, but also present-day physical approaches evoke many questions. They originate in the definition of time, its dimensionality and its scale. If we accept the Standard Model, all physical processes including processes utilised in clocks (chronometric processes) lose their theoretical basis in the vicinity of the initial singularity. The singularity is hidden behind horizon. Does it mean that the singularity did not exist?

A "Mind-Boggling" Implication: The Hebrew Bible, the Old Testament, and the Definition of a Work

2014 ◽  
Vol 15 (1) ◽  
pp. 1-12 ◽  
Author(s):  
David Conners
Keyword(s):  
Old Testament ◽  
Hebrew Bible ◽  
Steering Committee ◽  
Technical Solution ◽  
Alternative Models ◽  
Authority File ◽  
Rule Change ◽  
International Authority ◽  
Definition Of ◽  
Resource Description

The uniform title Bible. O.T. has long caused difficulty in Judaica libraries. The well documented problems caused by this heading are reviewed. Alternative models developed by the Hebraica Team of the Library of Congress (LC) are discussed, as is an LC proposed rule change to Resource Description and Access (RDA) that was partially approved by the Joint Steering Committee. The idea by members of the Association of Jewish Libraries to use the Virtual International Authority File as a technical solution is reviewed briefly. The author endorses a model from LC that uses different uniform titles for the Hebrew Bible and Christian Bible. Separate uniform titles are necessary because the two Bibles represent unique works; the ideational and textual differences of the Hebrew Bible and Christian Old Testament are seen in both canonical and translation differences.

scholarly journals Statistical Methodology for the Definition of Standard Model for Energy Analysis of Residential Buildings in Korea

Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5796
Author(s):  
Hye-Ryeong Nam ◽  
Seo-Hoon Kim ◽  
Seol-Yee Han ◽  
Sung-Jin Lee ◽  
Won-Hwa Hong ◽  
...  
Keyword(s):  
Standard Model ◽  
Energy Analysis ◽  
Residential Buildings ◽  
Statistical Methodology ◽  
National Scale ◽  
The Standard Model ◽  
Perform Cluster Analysis ◽  
Standard Models ◽  
Components Analysis ◽  
Definition Of

This study was conducted to propose an optimal methodology for deriving a standard model from existing residential buildings. To strategically improve existing residential buildings, it is necessary to identify standard models that can be used as quantitative standards. In this study, a total of six methods were established for different algorithms in the dimensionality reduction and clustering stage of the data preprocessing stage. In addition, a total of 22,342 households’ data were analyzed, and a total of 26 variables were used to perform cluster analysis. The process of method 6 (data pre-processing, principal components analysis, clustering [K-medoids], verification) was proposed as a way to derive the standard model from the existing Korean housing. The method proposed in this study is capable of deriving a number of standard models considering all variables (n) in a single analysis. The representative building derived in this study contains a lot of building data, so it can be effectively used for planning and research related to buildings on a regional and national scale. In addition, this process can be applied to various buildings to derive representative buildings.

scholarly journals Octonions, trace dynamics and noncommutative geometry—A case for unification in spontaneous quantum gravity

2020 ◽  
Vol 75 (12) ◽  
pp. 1051-1062
Author(s):  
Tejinder P. Singh
Keyword(s):  
Standard Model ◽  
Noncommutative Geometry ◽  
Degrees Of Freedom ◽  
Planck Scale ◽  
Space Time ◽  
Yang Mills ◽  
The Standard Model ◽  
The Matrix ◽  
Definition Of ◽  
Matrix Dynamics

AbstractWe have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics and Connes noncommutative geometry program. This is a Lagrangian dynamics in which the matrix degrees of freedom are made from Grassmann numbers, and the Lagrangian is trace of a matrix polynomial. Matrices made from even grade elements of the Grassmann algebra are called bosonic, and those made from odd grade elements are called fermionic—together they describe an ‘aikyon’. The Lagrangian of the theory is invariant under global unitary transformations and describes gravity and Yang–Mills fields coupled to fermions. In the present article, we provide a basic definition of spin angular momentum in this matrix dynamics and introduce a bosonic(fermionic) configuration variable conjugate to the spin of a boson(fermion). We then show that at energies below Planck scale, where the matrix dynamics reduces to quantum theory, fermions have half-integer spin (in multiples of Planck’s constant), and bosons have integral spin. We also show that this definition of spin agrees with the conventional understanding of spin in relativistic quantum mechanics. Consequently, we obtain an elementary proof for the spin-statistics connection. We then motivate why an octonionic space is the natural space in which an aikyon evolves. The group of automorphisms in this space is the exceptional Lie group G2 which has 14 generators [could they stand for the 12 vector bosons and two degrees of freedom of the graviton?]. The aikyon also resembles a closed string, and it has been suggested in the literature that 10-D string theory can be represented as a 2-D string in the 8-D octonionic space. From the work of Cohl Furey and others it is known that the Dixon algebra made from the four division algebras [real numbers, complex numbers, quaternions and octonions] can possibly describe the symmetries of the standard model. In the present paper we outline how in our work the Dixon algebra arises naturally and could lead to a unification of gravity with the standard model. From this matrix dynamics, local quantum field theory arises as a low energy limit of this Planck scale dynamics of aikyons, and classical general relativity arises as a consequence of spontaneous localisation of a large number of entangled aikyons. We propose that classical curved space–time and Yang–Mills fields arise from an effective gauging which results from the collection of symmetry groups of the spontaneously localised fermions. Our work suggests that we live in an eight-dimensional octonionic universe, four of these dimensions constitute space–time and the other four constitute the octonionic internal directions on which the standard model forces live.

operators and alternating sentences in arithmetic

1980 ◽  
Vol 45 (1) ◽  
pp. 144-154 ◽  
Author(s):  
Larry Manevitz ◽  
Jonathan Stavi
Keyword(s):  
Standard Model ◽  
Natural Number ◽  
Combinatorial Problem ◽  
The Other ◽  
Predicate Calculus ◽  
Completeness Proof ◽  
The Standard Model ◽  
Truth Value ◽  
The One ◽  
Definition Of

Determining the truth value of self-referential sentences is an interesting and often tricky problem. The Gödel sentence, asserting its own unprovability in P (Peano arithmetic), is clearly true in N(the standard model of P), and Löb showed that a sentence asserting its own provability in P is also true in N (see Smorynski [Sm, 4.1.1]). The problem is more difficult, and still unsolved, for sentences of the kind constructed by Kreisel [K1], which assert their own falsity in some model N* of P whose complete diagram is arithmetically defined. Such a sentence χ has the property that N ⊨ iff N* ⊭ χ (note that ¬χ has the same property).We show in §1 that the truth value in N of such a sentence χ, after a certain normalization that breaks the symmetry between it and its negation, is determined by the parity of a natural number, called the rank of N, for the particular construction of N* used. The rank is the number of times the construction can be iterated starting from N and is finite for all the usual constructions. We also show that modifications of, e.g., Henkin's construction (in his completeness proof of predicate calculus) allow arbitrary finite values for the rank of N. Thus, on the one hand the truth value of χ in N, for a given “nice” construction of N*, is independent of the particular (normalized) choice of χ, and we shall see that χ is unique up to (provable) equivalence in P. On the other hand, the truth value in question is sensitive to minor changes in the definition of N* and its determination seems to be largely a combinatorial problem.

Non-standard models for formal logics

1950 ◽  
Vol 15 (2) ◽  
pp. 113-129 ◽  
Author(s):  
J. Barkley Rosser ◽  
Hao Wang
Keyword(s):  
Number Theory ◽  
Standard Model ◽  
Formal Logic ◽  
Precise Definition ◽  
Ordinal Numbers ◽  
Equality Relation ◽  
Standard Models ◽  
Definition Of ◽  
Positive Integers

In his doctor's thesis [1], Henkin has shown that if a formal logic is consistent, and sufficiently complex (for instance, if it is adequate for number theory), then it must admit a non-standard model. In particular, he showed that there must be a model in which that portion of the model which is supposed to represent the positive integers of the formal logic is not in fact isomorphic to the positive integers; indeed it is not even well ordered by what is supposed to be the relation of ≦.For the purposes of the present paper, we do not need a precise definition of what is meant by a standard model of a formal logic. The non-standard models which we shall discuss will be flagrantly non-standard, as for instance a model of the sort whose existence is proved by Henkin. It will suffice if we and our readers are in agreement that a model of a formal logic is not a standard model if either:(a) The relation in the model which represents the equality relation in the formal logic is not the equality relation for objects of the model.(b) That portion of the model which is supposed to represent the positive integers of the formal logic is not well ordered by the relation ≦.(c) That portion of the model which is supposed to represent the ordinal numbers of the formal logic is not well ordered by the relation ≦.

scholarly journals STUECKELBERG: A FORERUNNER OF MODERN PHYSICS II

2008 ◽  
Vol 23 (08) ◽  
pp. 1105-1112 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
ORCHIDEA MARIA LECIAN
Keyword(s):  
Vector Field ◽  
Scattering Amplitudes ◽  
Standard Model ◽  
The Other ◽  
Massive Vector ◽  
Other Hand ◽  
The Standard Model ◽  
Modern Physics ◽  
The One ◽  
Definition Of

We will investigate some aspects of Stueckelberg's work, which have contributed to the development of modern physics. On the one hand, the definition of diffuse boundaries in the calculation of scattering amplitudes will be reviewed, and compared with the other proposals by physicists of that time. On the other hand, the applications of Stueckelberg's description of a massive vector field in the Standard Model will be discussed.

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