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Author: Casper Storm Hansen Publisher: Springer Nature ISBN: 3030885348 Category : Mathematics Languages : en Pages : 259
Book Description
This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory. Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis. Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell’s paradox and the other mathematical paradoxes of self-reference. In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.
Author: Casper Storm Hansen Publisher: Springer Nature ISBN: 3030885348 Category : Mathematics Languages : en Pages : 259
Book Description
This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory. Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis. Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell’s paradox and the other mathematical paradoxes of self-reference. In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.
Author: Nuel Belnap Publisher: Oxford University Press ISBN: 0195350073 Category : Philosophy Languages : en Pages : 518
Book Description
Here is an important new theory of human action, a theory that assumes actions are founded on choices made by agents who face an open future. It is a theory that makes indeterminism not only intelligible but illuminating. Tools from philosophy of language and philosophical logic help generate a full-scale account of agents "seeing to it that." The authors then proceed to clarify a variety of action-related topics such as determinism vs. indeterminism, imperatives, promises, strategies, joint agency, "could have done otherwise," deontic constructions, and assertions about a not yet settled future.
Author: Kenneth Train Publisher: Cambridge University Press ISBN: 0521766559 Category : Business & Economics Languages : en Pages : 399
Book Description
This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.
Author: Norbert Schmitt Publisher: John Benjamins Publishing ISBN: 9781588115003 Category : Language Arts & Disciplines Languages : en Pages : 324
Book Description
Formulaic sequences (FS) are now recognized as an essential element of language use. However, research on FS has generally been limited to a focus on description, or on the place of FS in L1 acquisition. This volume opens new directions in FS research, concentrating on how FS are acquired and processed by the mind, both in the L1 and L2. The ten original studies in the volume illustrate the L2 acquisition of FS, the relationship between L1 and L2 FS, the relationship between corpus recurrence of FS and their psycholinguistic reality, the processes involved in reading FS, and pedagogical issues in teaching FS. The studies use a wide range of methodologies, many of them innovative, and thus the volume serves as a model for future research in the area. The volume begins with three survey chapters offering a background on the characteristics and measurement of FS.
Author: Thomas J. Jech Publisher: Courier Corporation ISBN: 0486466248 Category : Mathematics Languages : en Pages : 226
Book Description
Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Author: Stewart Shapiro Publisher: Oxford University Press ISBN: 0190287535 Category : Mathematics Languages : en Pages : 856
Book Description
Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
Author: Daniel J. Galiffa Publisher: Springer Science & Business Media ISBN: 1461459699 Category : Mathematics Languages : en Pages : 118
Book Description
On the Higher-Order Sheffer Orthogonal Polynomial Sequences sheds light on the existence/non-existence of B-Type 1 orthogonal polynomials. This book presents a template for analyzing potential orthogonal polynomial sequences including additional higher-order Sheffer classes. This text not only shows that there are no OPS for the special case the B-Type 1 class, but that there are no orthogonal polynomial sequences for the general B-Type 1 class as well. Moreover, it is quite provocative how the seemingly subtle transition from the B-Type 0 class to the B-Type 1 class leads to a drastically more difficult characterization problem. Despite this issue, a procedure is established that yields a definite answer to our current characterization problem, which can also be extended to various other characterization problems as well. Accessible to undergraduate students in the mathematical sciences and related fields, This book functions as an important reference work regarding the Sheffer sequences. The author takes advantage of Mathematica 7 to display unique detailed code and increase the reader's understanding of the implementation of Mathematica 7 and facilitate further experimentation. In addition, this book provides an excellent example of how packages like Mathematica 7 can be used to derive rigorous mathematical results.
Author: Hong Jiao Publisher: Frontiers Media SA ISBN: 2889741389 Category : Science Languages : en Pages : 383
Book Description
Publisher’s note: In this 2nd edition: The following article has been added: Jiao H, He Q and Veldkamp BP (2021) Editorial: Process Data in Educational and Psychological Measurement. Front. Psychol. 12:793399. doi: 10.3389/fpsyg.2021.793399 The following article has been added: Reis Costa D, Bolsinova M, Tijmstra J and Andersson B (2021) Improving the Precision of Ability Estimates Using Time-On-Task Variables: Insights From the PISA 2012 Computer-Based Assessment of Mathematics. Front. Psychol. 12:579128. doi: 10.3389/fpsyg.2021.579128 The following article has been removed: Minghui L, Lei H, Xiaomeng C and Potměšilc M (2018) Teacher Efficacy, Work Engagement, and Social Support Among Chinese Special Education School Teachers. Front. Psychol. 9:648. doi: 10.3389/fpsyg.2018.00648
Author: Reinhard Kahle Publisher: Springer ISBN: 331910103X Category : Mathematics Languages : en Pages : 563
Book Description
Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.
Author: Casper Storm Hansen
Author: Casper Storm Hansen
Author: Nuel Belnap
Author: Kenneth Train
Author: Norbert Schmitt
Author: Dan Gusfield
Author: Thomas J. Jech
Author: Stewart Shapiro
Author: Daniel J. Galiffa
Author: Hong Jiao
Author: Reinhard Kahle