標(biāo)題: Titlebook: Essays on the Foundations of Mathematics by Moritz Pasch; Stephen Pollard Book 2010 Springer Science+Business Media B.V. 2010 Arithmetic.A [打印本頁(yè)] 作者: 歸納 時(shí)間: 2025-3-21 18:49
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作者: sleep-spindles 時(shí)間: 2025-3-21 23:27 作者: Overthrow 時(shí)間: 2025-3-22 02:28
The Decidability Requirement,ble properties have no place in mathematics. Pasch suggests that a reasonable response to this proposal is not offhand dismissal, but a searching inquiry into the logical structure and conceptual foundations of mathematics.作者: 切碎 時(shí)間: 2025-3-22 07:32 作者: Obituary 時(shí)間: 2025-3-22 12:08
Implicit Definition and the Proper Grounding of Mathematics,1), pp. 145–162. The technique Pasch calls “implicit definition” is a generalization of the more celebrated “definition by abstraction.” In an implicit definition, one introduces new vocabulary by stipulating the meaning of certain sentences in which that vocabulary is allowed to occur. Pasch uses a作者: dyspareunia 時(shí)間: 2025-3-22 13:20 作者: dyspareunia 時(shí)間: 2025-3-22 20:56 作者: 歡樂(lè)中國(guó) 時(shí)間: 2025-3-22 21:37 作者: Amylase 時(shí)間: 2025-3-23 01:47
The Concept of the Differential,mathematical theories cannot be . because close inspection shows them to be .. Since Vaihinger recognized the utility of these theories, he confronted the problem of explaining how absurd theories can be useful. Pasch insists there is no need for such an explanation because the theories Vaihinger fo作者: 晚間 時(shí)間: 2025-3-23 07:59 作者: 撫育 時(shí)間: 2025-3-23 10:44
Concepts and Proofs in Mathematics,endent essays. In “Proof and Definition in Mathematics,” Pasch analyzes the notion of direct proof. In “Equality in Mathematics,” he explains why “equals” in mathematics is best understood as “is identical to.” In “The Decidability Requirement in Mathematics,” he offers examples of decidable and und作者: 異端邪說(shuō)2 時(shí)間: 2025-3-23 15:16
Dimension and Space in Mathematics,f his “Prelude to Geometry” (Chapter 6 above) by characterizing bodies of 0, 1, 2, and 3 dimensions. He then discusses degrees (or “dimensions”) of polynomials and concludes by reviewing the fundamental structures of synthetic geometry and their counterparts in analytic geometry.作者: creditor 時(shí)間: 2025-3-23 21:06
Reflections on the Proper Grounding of Mathematics II,orrectness of his earlier paper on “The Origin of the Concept of Number,” Pasch concedes that he did not provide a foundation for number theory that was “complete in every detail.” He now undertakes to “reconsider and improve” his treatment of two topics: the distinction between restricted and unres作者: 神經(jīng) 時(shí)間: 2025-3-23 23:41
The Axiomatic Method in Modern Mathematics,iate consequence. In a direct, unabbreviated proof, each step is an immediate consequence of prior steps. Though it is not decidable whether an arbitrary conclusion follows from arbitrary premises, it is decidable whether the conclusion immediately follows. Two sentences express the same statement i作者: Preamble 時(shí)間: 2025-3-24 05:33 作者: STRIA 時(shí)間: 2025-3-24 09:00 作者: BROTH 時(shí)間: 2025-3-24 13:01
The Axiomatic Method in Modern Mathematics, from the other. Whether one sentence is an immediate consequence of another depends entirely on the structural elements (rather than the content words) occurring in those sentences. Anyone who understands those structural elements will be able to determine whether one sentence follows immediately from the other.作者: Maximizer 時(shí)間: 2025-3-24 16:45
Fundamental Questions of Geometry,athematical proofs be presented “in a purely deductive form” and suggests that “full insight into the structure of deduction” requires that proofs be “atomized”: broken up into steps linked by inferences of a certain elementary form.作者: pulse-pressure 時(shí)間: 2025-3-24 22:04
Rigid Bodies in Geometry,eduction” by identifying axioms . supplying those axioms with content. In this paper, Pasch begins the job of supplying fundamental geometric propositions with content based on experience. His two goals are “to fix the concept of rigid body and, among such bodies, to distinguish between the ‘ extended’ and ‘ unextended’ ones.”作者: 絕食 時(shí)間: 2025-3-24 23:44 作者: 無(wú)瑕疵 時(shí)間: 2025-3-25 03:56
Reflections on the Proper Grounding of Mathematics II,as “complete in every detail.” He now undertakes to “reconsider and improve” his treatment of two topics: the distinction between restricted and unrestricted common names and the related distinction between (restricted) collections and (unrestricted) sets.作者: Defiance 時(shí)間: 2025-3-25 10:04 作者: 煉油廠 時(shí)間: 2025-3-25 15:34
https://doi.org/10.1007/978-3-319-65373-0und absurd are, in fact, logically impeccable. To support this claim, Pasch offers a quick overview of the foundations of differential calculus and a more detailed analysis of Fermat’s rule for maxima and minima.作者: 倒轉(zhuǎn) 時(shí)間: 2025-3-25 17:46
1566-659X yone the familiar triad of formalism, instuitionism and logiMoritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch 作者: Adulterate 時(shí)間: 2025-3-25 23:17 作者: 拉開(kāi)這車床 時(shí)間: 2025-3-26 01:02
A Stochastic Theory of Community Food Webs,eduction” by identifying axioms . supplying those axioms with content. In this paper, Pasch begins the job of supplying fundamental geometric propositions with content based on experience. His two goals are “to fix the concept of rigid body and, among such bodies, to distinguish between the ‘ extended’ and ‘ unextended’ ones.”作者: 多樣 時(shí)間: 2025-3-26 08:02
Research and Practice in Applied Linguisticsometry. He then considers the metamathematical resources David Hilbert will need to complete his program of consistency proofs and concludes that the Hilbert school will be unable to dispense with any part of the combinatorial theory from Pasch’ s paper “The Origin of the Concept of Number,” a theory at least as strong as Peano Arithmetic.作者: 尖酸一點(diǎn) 時(shí)間: 2025-3-26 10:17 作者: 稱贊 時(shí)間: 2025-3-26 14:15
Physical and Mathematical Geometry,ions have “purely intellectual” counterparts: transformations. Because our instruments are not infinitely precise, one physical point can be represented equally well by distinct coordinates. In mathematical geometry, distinct coordinates always represent distinct points.作者: Mercurial 時(shí)間: 2025-3-26 19:04
The Concept of the Differential,und absurd are, in fact, logically impeccable. To support this claim, Pasch offers a quick overview of the foundations of differential calculus and a more detailed analysis of Fermat’s rule for maxima and minima.作者: 健談 時(shí)間: 2025-3-27 00:02
Community Identity and Political BehaviorEnglish translation of Moritz Pasch,“Die natürliche Geometrie,” . 21 (1924), pp. 151–153. The Danish mathematician Johannes Hjelmslev insisted that Pasch’ s axioms for projective geometry are incompatible with Pasch’ s empiricism. In this paper, Pasch offers a brief response.作者: euphoria 時(shí)間: 2025-3-27 04:18
Natural Geometry,English translation of Moritz Pasch,“Die natürliche Geometrie,” . 21 (1924), pp. 151–153. The Danish mathematician Johannes Hjelmslev insisted that Pasch’ s axioms for projective geometry are incompatible with Pasch’ s empiricism. In this paper, Pasch offers a brief response.作者: heterogeneous 時(shí)間: 2025-3-27 08:00
https://doi.org/10.1007/978-90-481-9416-2Arithmetic; Axiomatics; Decidability; Empiricism; Geometry; History of Mathematics; mathematics作者: Fulminate 時(shí)間: 2025-3-27 13:29
Community Energy Networks With Storagevities that had hitherto consumed much of his time. The result was a burst of scholarly productivity remarkable for a man of ever more advanced years, with nearly half his published output appearing after his 68th birthday. Mentally sharp until the end, he might have done even more had his eyesight not failed.作者: 騷動(dòng) 時(shí)間: 2025-3-27 16:19 作者: Cholagogue 時(shí)間: 2025-3-27 19:16
Government as Provider of Education Serviceser theory that, he says, “combine indispensability with the utmost simplicity.” He argues that we cannot seriously question any of these axioms without succumbing to a crippling skepticism about reason in general. He also explores “the connection between number theory and experience.”作者: Noctambulant 時(shí)間: 2025-3-27 22:25 作者: 套索 時(shí)間: 2025-3-28 03:53 作者: 迅速成長(zhǎng) 時(shí)間: 2025-3-28 06:37 作者: 欲望 時(shí)間: 2025-3-28 14:17
,Translator’s Introduction,vities that had hitherto consumed much of his time. The result was a burst of scholarly productivity remarkable for a man of ever more advanced years, with nearly half his published output appearing after his 68th birthday. Mentally sharp until the end, he might have done even more had his eyesight not failed.作者: 強(qiáng)行引入 時(shí)間: 2025-3-28 18:14
The Decidability Requirement,ble properties have no place in mathematics. Pasch suggests that a reasonable response to this proposal is not offhand dismissal, but a searching inquiry into the logical structure and conceptual foundations of mathematics.作者: TOM 時(shí)間: 2025-3-28 19:59 作者: 木質(zhì) 時(shí)間: 2025-3-28 23:52 作者: overshadow 時(shí)間: 2025-3-29 05:01
Prelude to Geometry: The Essential Ideas,ry, “does not pretend to be an axiomatic presentation of the subject.” Instead, Pasch offers a window into the mind of a mathematician struggling to identify the most fundamental principles governing bodily shapes. He guides us through a series of thought experiments involving the manipulation of physical objects.作者: 從容 時(shí)間: 2025-3-29 07:39
Dimension and Space in Mathematics,f his “Prelude to Geometry” (Chapter 6 above) by characterizing bodies of 0, 1, 2, and 3 dimensions. He then discusses degrees (or “dimensions”) of polynomials and concludes by reviewing the fundamental structures of synthetic geometry and their counterparts in analytic geometry.作者: 言行自由 時(shí)間: 2025-3-29 13:59 作者: excursion 時(shí)間: 2025-3-29 17:05
Essays on the Foundations of Mathematics by Moritz Pasch978-90-481-9416-2Series ISSN 1566-659X Series E-ISSN 2215-1974 作者: Statins 時(shí)間: 2025-3-29 19:43
Community Energy Networks With Storagevities that had hitherto consumed much of his time. The result was a burst of scholarly productivity remarkable for a man of ever more advanced years, with nearly half his published output appearing after his 68th birthday. Mentally sharp until the end, he might have done even more had his eyesight 作者: reperfusion 時(shí)間: 2025-3-30 01:23 作者: 煞費(fèi)苦心 時(shí)間: 2025-3-30 07:31 作者: 噱頭 時(shí)間: 2025-3-30 08:25 作者: 河流 時(shí)間: 2025-3-30 16:23
Linda Silka,Mario Teisl,James Settele1), pp. 145–162. The technique Pasch calls “implicit definition” is a generalization of the more celebrated “definition by abstraction.” In an implicit definition, one introduces new vocabulary by stipulating the meaning of certain sentences in which that vocabulary is allowed to occur. Pasch uses a作者: pulmonary-edema 時(shí)間: 2025-3-30 19:11
A Stochastic Theory of Community Food Webs,irement (. above), “Mathematics is a system with two parts.” While one part is “devoted entirely to deduction,” the other supplies the “material for deduction” by identifying axioms . supplying those axioms with content. In this paper, Pasch begins the job of supplying fundamental geometric proposit作者: 機(jī)密 時(shí)間: 2025-3-30 22:50 作者: Assignment 時(shí)間: 2025-3-31 01:27 作者: 凹槽 時(shí)間: 2025-3-31 06:31
https://doi.org/10.1007/978-3-319-65373-0mathematical theories cannot be . because close inspection shows them to be .. Since Vaihinger recognized the utility of these theories, he confronted the problem of explaining how absurd theories can be useful. Pasch insists there is no need for such an explanation because the theories Vaihinger fo作者: HILAR 時(shí)間: 2025-3-31 10:39
Research and Practice in Applied Linguisticsbe more “natural” than another even if the two systems yield the same theorems. He illustrates this property of naturalness with some examples from geometry. He then considers the metamathematical resources David Hilbert will need to complete his program of consistency proofs and concludes that the 作者: 燦爛 時(shí)間: 2025-3-31 15:52
