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W.J. Zhu, X.A. Xiao
An Introduction to Set Theory
Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
The inconsistency of countable infinite setsKybernetes, 37
H. Hendrix (1988)
Getting the Love You Want: A Guide for Couples
P. Fletcher (1989)
Nonstandard set theoryJournal of Symbolic Logic, 54
Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Modern system of mathematics and special Cauchy theater in its theoretical foundationKybernetes, 37
(1935)
Mengenlehve, Watter ac., Hruyler
Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Mathematical system of potential infinities (I) - preparationKybernetes, 37
E. Wigner (1960)
The Unreasonable Effectiveness of Mathematics in the Natural Sciences (reprint)
R. Hide (1953)
Some experiments on thermal convection in a rotating liquidQuarterly Journal of the Royal Meteorological Society, 79
Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Mathematical system of potential infinities (IV) - set theoretic foundationKybernetes, 37
H. Eves, J. Eves (1990)
An introduction to the history of mathematics :with culturalconnections
Theodore Hailperin (2001)
Potential Infinite Models and Ontologically Neutral LogicJournal of Philosophical Logic, 30
J. Engelfriet, T. Gelsema (2004)
A new natural structural congruence in the pi-calculus with replicationActa Informatica, 40
Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Modern system of mathematics and general Cauchy theater in its theoretical foundationKybernetes, 37
R. Hodel (1995)
An Introduction to Mathematical Logic
Yi Lin, T. Fan (1997)
Fundamental structure of general systems and its relation to knowability of the physical worldKybernetes, 26
Yi Lin, Yonghoa Ma (1987)
REMARKS ON ANALOGY BETWEEN SYSTEMSInternational Journal of General Systems, 13
Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Descriptive definitions of potential and actual infinitiesKybernetes, 37
A. Rapoport
Paradoxes: The Limit of Science and the Science of Limits
(2008)
2008j), “Modern system of mathematics and a pair
Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Inconsistency of uncountable infinite sets under ZFC frameworkKybernetes, 37
J. Hoffman, Claes Johnson, A. Logg (2004)
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Frank DeSua (1956)
Consistency and Completeness—A RésuméAmerican Mathematical Monthly, 63
G. Becker (1974)
A Theory of Social InteractionsJournal of Political Economy, 82
Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Modern system of mathematics and a pair of hidden contradictions in its foundationKybernetes, 37
K. Hrbacek (1978)
Axiomatic foundations for Nonstandard AnalysisFundamenta Mathematicae, 98
Yi Lin (2007)
Systemic yoyo model and applications in Newton's, Kepler's laws, and othersKybernetes, 36
Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Mathematical system of potential infinities (III) - meta theory of logical basisKybernetes, 37
Theodore Hailperin (1997)
Ontologically neutral logicHistory and Philosophy of Logic, 18
Yi Lin, D. Forrest (2008)
Economic yoyos and Becker's Rotten Kid theoremKybernetes, 37
F. Hausdorff
Mengenlehve
T. Kawai (1981)
Axiom systems of nonstandard set theory
Yong Wu, Yi Lin (2002)
Beyond Nonstructural Quantitative Analysis: Blown-Ups, Spinning Currents and Modern Science
(1964)
Formalism 64, logic, methodology, and philosophy of science
Zhenqiu Ren, Yi Lin, S. Ouyang (1998)
Conjecture on law of conservation of informational infrastructureKybernetes, 27
Yi Lin (1990)
A Few Systems-Colored Views of the World
Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
New Berkeley paradox in the theory of limitsKybernetes, 37
V. Kanovei, M. Reeken (2000)
Extending Standard Models of ZFC to Models of Nonstandard Set TheoriesStudia Logica, 64
Ibrahim Garro (2001)
General Systems Theory: A Mathematical ApproachKybernetes, 30
Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Mathematical system of potential infinities (II) - formal systems of logical basisKybernetes, 37
W.J. Zhu, X.A. Xiao
An Introduction to Foundations of Mathematics
Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Intension and structure of actually infinite, rigid setsKybernetes, 37
J. Engelfriet (1993)
A Multiset Semantics for the pi-Calculus with ReplicationTheor. Comput. Sci., 153
R. Mickens (1990)
Mathematics and Science
S. Hess (1959)
Introduction to theoretical meteorology
M. Kline (1972)
Mathematical Thought from Ancient to Modern Times
Yi Lin, D. Forrest (2008)
Economic yoyos and never-perfect value systemsKybernetes, 37
D. Fultz, R.R. Long, G.V. Owens, W. Bohan, R. Kaylor, J. Weil
Studies of thermal convection in a rotating cylinder with some implications for large‐scale atmospheric motion
(1991)
An Introduction to Set Theory, Nanjing University Press, Nanjing
Yi Lin, D. Forrest (2008)
Economic yoyos, parasites and child laborKybernetes, 37
IFHP
The Philosophy of Ancient Greeks (in Chinese)
C. Mann (2003)
Beyond Nonstructural Quantitative Analysis – Blown-Ups, Spinning Currents and Modern ScienceKybernetes, 32
R. Milner (1990)
Functions as processesMathematical Structures in Computer Science, 2
Edward Nelson (1977)
Internal set theory: A new approach to nonstandard analysisBulletin of the American Mathematical Society, 83
(2000)
Paradoxes: The Limit of Science and the Science of Limits, Shanghai Press of Science and Technology, Shanghai (in Chinese, translated by X.Z. Li)
Yi Lin, Qingping Hu, Dan Li (1997)
Some Unsolved Problems in General Systems Theory (i)Cybern. Syst., 28
Theodore Hailperin (1992)
Herbrand semantics, the potential infinite, and ontology-free logicHistory and Philosophy of Logic, 13
Y. Lin
Systemic yoyo model and applications in Newton's, Kepler's laws, etc.
Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Problem of infinity between predicates and infinite setsKybernetes, 37
(1998)
Blown-ups and the concept of whole evolution in systems science
Purpose – The paper aims to show the existence of the systemic yoyo structure in human thoughts so that the human way of thinking is proven to have the same structure as that of the material world. Design/methodology/approach – Parallel comparison is used to reveal the underlying structure existing in human thoughts. Findings – After highlighting all the relevant ideas and concepts, which are behind each and every crisis in the foundations of mathematics, it becomes clear that some difficulties in the authors' understanding of nature are originated from confusing actual infinities with potential infinities, and vice versa. By pointing out the similarities and differences between these two kinds of infinities, then some hidden contradictions existing in the system of modern mathematics are handily picked out. Then, theoretically, using the authors' yoyo model, it is predicted that the fourth crisis in the foundations of mathematics has appeared. And, a plan of resolution of this new crisis is provided. Originality/value – This paper shows the first time in history that human thought, the material world, and each economic entity, share a common structure – the systemic yoyo structure. And it proves the arrival of the fourth crisis in mathematics by using systems modeling and listing several; contradictions hidden deeply in the foundations of mathematics.
Kybernetes – Emerald Publishing
Published: Apr 11, 2008
Keywords: Cybernetics; Critical thinking; Set theory; Mathematics
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