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第96行： − In [[mathematical biology]] he is known as the originator of a class of relational models of living [[organism]]s, called <math>(M{,}R)</math>systems that he devised to capture the minimal capabilities that a material [[system]] would need in order to be one of the simplest ''functional organisms'' that are commonly said to be "alive". In this kind of system, <math>M</math> stands for the metabolic and <math>R</math> stands for the 'repair' subsystems of a simple organism, for example active 'repair' RNA molecules. Thus, his mode for determining or "defining" life in any given system is a functional, not material, mode; although he did consider in his 1970s published reports specific ''dynamic realizations'' of the simplest <math>(M{,}R)</math>systems in terms of enzymes (<math>M</math>), [[RNA]] (<math>R</math>), and functional, duplicating [[DNA]] (his <math>\beta</math>-mapping). − − In mathematical biology he is known as the originator of a class of relational models of living organisms, called (M{,}R)systems that he devised to capture the minimal capabilities that a material system would need in order to be one of the simplest functional organisms that are commonly said to be "alive". In this kind of system, M stands for the metabolic and R stands for the 'repair' subsystems of a simple organism, for example active 'repair' RNA molecules. Thus, his mode for determining or "defining" life in any given system is a functional, not material, mode; although he did consider in his 1970s published reports specific dynamic realizations of the simplest (M{,}R)systems in terms of enzymes (M), RNA (R), and functional, duplicating DNA (his \beta-mapping). − − 在数学生物学中，他被认为是一类生物有机体关系模型的创始人，这类关系模型被称为 (M{,}R)系统，他设计这类系统是为了捕捉物质系统成为通常被称为“活的”的最简单的功能有机体所需要的最低能力。在这种系统中，m 代表新陈代谢，r 代表简单有机体的修复子系统，例如活跃的修复 RNA 分子。因此，他在任何给定系统中确定或“定义”生命的模式是功能性的，而不是物质性的; 尽管他在20世纪70年代发表的报告中考虑了最简单 (M{,}R)系统在酶(m)、 RNA (r)和功能性复制 DNA (他的β模型)方面的具体动态实现。 − He went, however, even further in this direction by claiming that when studying a [[complex system]], one ''"can throw away the matter and study the organization"'' to learn those things that are essential to defining in general an entire class of systems. This has been, however, taken too literally by a few of his former students who have not completely assimilated Robert Rosen's injunction of the need for a theory of ''dynamic realizations'' of such abstract components in specific molecular form in order to close the modeling loop {{clarify|date=September 2013}} for the simplest functional organisms (such as, for example, single-cell algae or [[microorganisms]]).<ref>Robert Rosen. 1970. ''Dynamical Systems Theory in Biology'', New York: Wiley Interscience.</ref> He supported this claim (that he actually attributed to [[Nicolas Rashevsky]]) based on the fact that living organisms are a class of systems with an extremely wide range of material "ingredients", different structures, different habitats, different modes of living and [[reproduction]], and yet we are somehow able to recognize them all as ''living'', or functional organisms, without being however ''[[vitalism|vitalist]]s''. − − He went, however, even further in this direction by claiming that when studying a complex system, one "can throw away the matter and study the organization" to learn those things that are essential to defining in general an entire class of systems. This has been, however, taken too literally by a few of his former students who have not completely assimilated Robert Rosen's injunction of the need for a theory of dynamic realizations of such abstract components in specific molecular form in order to close the modeling loop for the simplest functional organisms (such as, for example, single-cell algae or microorganisms).Robert Rosen. 1970. Dynamical Systems Theory in Biology, New York: Wiley Interscience. He supported this claim (that he actually attributed to Nicolas Rashevsky) based on the fact that living organisms are a class of systems with an extremely wide range of material "ingredients", different structures, different habitats, different modes of living and reproduction, and yet we are somehow able to recognize them all as living, or functional organisms, without being however vitalists. − − 然而，他在这个方向上走得更远，声称在研究一个复杂系统时，人们“可以抛开物质并且只研究组织”，去学习那些对于一般地定义一整类系统至关重要的东西。然而，罗伯特 · 罗森以前的一些学生对此过于字面化，他们没有完全吸收罗伯特 · 罗森的观点，即需要一种动态实现特定分子形式的抽象组分的理论，以便为最简单的功能有机体(例如单细胞藻类或微生物)闭合建模循环。罗伯特·罗森.1970.生物学的动力系统理论，纽约:威利交叉科学。他支持这种说法(他实际上将其归因于尼古拉斯 · 拉舍夫斯基) ，因为生命有机体是一类系统，具有极其广泛的物质“成分”、不同的结构、不同的栖息地、不同的生存和繁殖方式，然而我们却能够以某种方式将它们全部识别为活的或功能性的有机体，而不管它们多么有生命力。 − − 【最终篇】然而，他在这个方向上更进一步，声称当研究一个复杂的系统时，人们“可以抛开物质并且只研究组织”来学习那些对定义整个系统类至关重要的东西。然而，罗伯特罗森以前的一些学生对此过于字面化，他们没有完全吸收罗伯特罗森的观点，即需要一种动态实现特定分子形式的抽象组分的理论，以便为最简单的功能有机体(例如单细胞藻类或微生物)闭合建模循环。罗伯罗森，1970。生物学的动力系统理论，纽约:威利交叉科学。他支持这一说法(实际上他归因于尼古拉斯·拉舍夫斯基)，因为生命有机体是一类系统，具有极其广泛的物质“成分”、不同的结构、不同的栖息地、不同的生存和繁殖方式，然而我们却能够以某种方式将它们全部识别为活的或功能性的有机体，而不管它们多么有生命力。 − − His approach, just like Rashevsky's latest theories of organismic sets,<ref>{{cite journal | last1 = Rashevsky | first1 = N | year = 1965 | title = The Representation of Organisms in Terms of (logical) Predicates | journal = Bulletin of Mathematical Biophysics | volume = 27 | issue = 4| pages = 477–491 | doi=10.1007/bf02476851| pmid = 4160663 }}</ref><ref>{{cite journal | last1 = Rashevsky | first1 = N | year = 1969 | title = Outline of a Unified Approach to Physics, Biology and Sociology | journal = Bulletin of Mathematical Biophysics | volume = 31 | issue = 1| pages = 159–198 | doi=10.1007/bf02478215| pmid = 5779774 }}</ref> emphasizes [[biological organization]] over [[molecular structure]] in an attempt to bypass the ''structure-functionality relationships'' that are important to all experimental biologists, including [[physiology|physiologists]]. In contrast, a study of the specific material details of any given organism, or even of a type of organisms, will only tell us about how that type of organism "does it". Such a study doesn't approach what is common to all functional organisms, i.e. "life". Relational approaches to theoretical biology would therefore allow us to study organisms in ways that preserve those essential qualities that we are trying to learn about, and that are common only to ''functional'' organisms. − − His approach, just like Rashevsky's latest theories of organismic sets, emphasizes biological organization over molecular structure in an attempt to bypass the structure-functionality relationships that are important to all experimental biologists, including physiologists. In contrast, a study of the specific material details of any given organism, or even of a type of organisms, will only tell us about how that type of organism "does it". Such a study doesn't approach what is common to all functional organisms, i.e. "life". Relational approaches to theoretical biology would therefore allow us to study organisms in ways that preserve those essential qualities that we are trying to learn about, and that are common only to functional organisms. − − 他的方法，就像Rashevsky最新的有机体集合理论一样，强调生物组织而不是分子结构，试图绕过对所有实验生物学家(包括生理学家)都很重要的结构-功能关系。相比之下，对任何特定生物体，甚至某种生物体的具体物质细节的研究，只能告诉我们这种生物体是如何“做到这一点”的。这样的一项研究并没有涉及到所有功能性生物体的共同特征，即。“生活”。因此，与理论生物学相关的方法将使我们能够以一种方式来研究生物，这种方式能够保持我们试图了解的、只有功能性生物才具有的那些基本特性。 − 【最终篇】他的方法，就像拉舍夫斯基（Rashevsky）最新的有机组合理论一样，强调生物组织多于分子结构，试图绕过对包括生理学家在内的所有实验生物学家都很重要的结构-功能关系。相比之下，对任何特定有机体，甚至是某种有机体的特定物质细节的研究，只会告诉我们这种有机体是如何“做到这一点的”。这样的一项研究并没有涉及到所有功能性生物体的共同特征，即“生命”。因此，与理论生物学相关的方法将使我们能够以这种方式来研究生物，这种方式能够保持我们试图了解的、只有功能性生物才具有的那些基本特性。+ − Robert Rosen's approach belongs conceptually to what is now known as [[Functional genomics|Functional Biology]], as well as [[Systems biology|Complex Systems Biology]], ''albeit'' in a highly abstract, mathematical form. − Robert Rosen's approach belongs conceptually to what is now known as Functional Biology, as well as Complex Systems Biology, albeit in a highly abstract, mathematical form.+ − 罗伯特 · 罗森的方法在概念上属于现在已知的功能生物学，以及复杂系统生物学，尽管是以一种高度抽象的数学形式。 − == Quantum Biochemistry and Quantum Genetics == − Rosen also questioned what he believed to be many aspects of mainstream interpretations of [[biochemistry]] and [[genetics]]. He objects to the idea that functional aspects in biological systems can be investigated via a material focus. One example: Rosen disputes that the functional capability of a biologically active [[protein]] can be investigated purely using the genetically encoded sequence of [[amino acid]]s. This is because, he said, a protein must undergo a process of folding to attain its characteristic three-dimensional shape before it can become functionally active in the system. Yet, only the [[amino acid sequence]] is genetically coded. The mechanisms by which proteins fold are not completely known. He concluded, based on examples such as this, that [[phenotype]] cannot always be directly attributed to [[genotype]] and that the chemically active aspect of a biologically active protein relies on more than the sequence of amino acids, from which it was constructed: there must be some other important factors at work, that he did not however attempt to specify or pin down. − − Rosen also questioned what he believed to be many aspects of mainstream interpretations of biochemistry and genetics. He objects to the idea that functional aspects in biological systems can be investigated via a material focus. One example: Rosen disputes that the functional capability of a biologically active protein can be investigated purely using the genetically encoded sequence of amino acids. This is because, he said, a protein must undergo a process of folding to attain its characteristic three-dimensional shape before it can become functionally active in the system. Yet, only the amino acid sequence is genetically coded. The mechanisms by which proteins fold are not completely known. He concluded, based on examples such as this, that phenotype cannot always be directly attributed to genotype and that the chemically active aspect of a biologically active protein relies on more than the sequence of amino acids, from which it was constructed: there must be some other important factors at work, that he did not however attempt to specify or pin down. − − Rosen也质疑他认为的生物化学和遗传学的主流解释的许多方面。他反对生物系统的功能方面可以通过材料焦点来研究的观点。举个例子:Rosen质疑生物活性蛋白的功能能力可以单纯地用氨基酸的基因编码序列来研究。他说，这是因为蛋白质必须经过一个折叠过程，才能获得其特有的三维形状，然后才能在系统中发挥功能。然而，只有氨基酸序列是遗传编码的。蛋白质折叠的机制还不完全清楚。基于这样的例子，他得出结论，表型并不总是直接归因于基因型，生物活性蛋白的化学活性方面依赖于氨基酸序列，而氨基酸序列是其构建的基础:一定还有其他一些重要因素在起作用，但他并没有试图具体说明或确定。 第154行：
第128行： − Certain questions about Rosen's mathematical arguments were raised in a paper authored by Christopher Landauer and Kirstie L. Bellman which claimed that some of the mathematical formulations used by Rosen are problematic from a logical viewpoint. It is perhaps worth noting, however, that such issues were also raised long time ago by Bertrand Russell and Alfred North Whitehead in their famous Principia Mathematica in relation to antinomies of set theory. As Rosen's mathematical formulation in his earlier papers was also based on set theory and the category of sets such issues have naturally re-surfaced. However, these issues have now been addressed by Robert Rosen in his recent book Essays on Life Itself, published posthumously in 2000. Furthermore, such basic problems of mathematical formulations of (M{,}R)--systems had already been resolved by other authors as early as 1973 by utilizing the Yoneda lemma in category theory, and the associated functorial construction in categories with (mathematical) structure.I.C. Baianu: 1973, Some Algebraic Properties of (M{,}R) - Systems. Bulletin of Mathematical Biophysics 35, 213-217.I.C. Baianu and M. Marinescu: 1974, A Functorial Construction of (M{,}R)- Systems. Revue Roumaine de Mathematiques Pures et Appliquees 19: 388-391. Such general category-theoretic extensions of (M{,}R)-systems that avoid set theory paradoxes are based on William Lawvere's categorical approach and its extensions to higher-dimensional algebra. The mathematical and logical extension of metabolic-replication systems to generalized (M{,}R)-systems, or G-MR, also involved a series of acknowledged letters exchanged between Robert Rosen and the latter authors during 1967—1980s, as well as letters exchanged with Nicolas Rashevsky up to 1972. − 在Christopher Landauer和Kirstie L. Bellman合著的一篇论文中，罗森的数学论证提出了一些问题，他们声称罗森使用的一些数学公式从逻辑角度来看是有问题的。然而，也许值得注意的是，很久以前，伯特兰德·罗素和阿尔弗雷德·诺斯·怀特黑德在他们著名的《数学原理》中就集合论的二律背反提出了这些问题。由于Rosen在他早期的论文中提出的数学公式也是基于集合理论的，集合的类别问题自然地重新浮出水面。然而，罗伯特·罗森在他死后于2000年出版的新书《生命本身》(Essays on Life Itself)中阐述了这些问题。此外，早在1973年，其他作者就利用范畴理论中的Yoneda引理，以及范畴中与(数学)结构相关的函数构造，解决了(M{，}R)系统的数学表述的基本问题。(M{，}R) -系统的若干代数性质。数学生物物理学通报35,213-217. c。Baianu和M. Marinescu: 1974， (M{，}R)系统的函数构造。纯粹数学和appliqueques 19: 388-391。这种避免集合理论悖论的(M{，}R)系统的一般范畴理论扩展是基于William Lawvere的范畴方法及其对高维代数的扩展。新陈代谢-复制系统的数学和逻辑扩展到广义(M{，}R)-系统，或G-MR，也涉及到1967 - 1980年期间Robert Rosen和后者的作者之间交换的一系列确认信件，以及到1972年与Nicolas Rashevsky交换的信件。+ − 【最终篇】克里斯托弗 · 兰道尔（Christopher Landauer）和克里斯蒂 · 贝尔曼（Kirstie L. Bellman）在一篇论文中提出了一些关于罗森数学论证的问题，这篇论文声称罗森使用的一些数学公式从逻辑观点来看是有问题的。然而，也许值得注意的是，这些问题很久以前也被伯特兰·罗素和阿尔弗雷德·诺思·怀特黑德在他们著名的关于集合论悖论的数学原理中提出过。正如罗森在他的早期论文中的数学公式也是基于集合论的，这类问题的集合范畴自然重新浮出水面。然而，罗伯特 · 罗森在他2000年去世后出版的新书《论生命本身》中提到了这些问题。此外，(M{,}R)系统的数学公式的这些基本问题早在1973年就已经被其他作者利用范畴论中的 Yoneda 引理和范畴中的(数学)结构中的相关函子结构解决了。数学生物物理学通报35,213-217. c.Baianu和M. Marinescu: 1974，(M{,}R)系统的函数构造。这种避免集合论悖论的(M{,}R)系统的一般范畴论扩张是基于 William Lawvere 的范畴方法及其对高维代数的扩张。新陈代谢复制系统在数学和逻辑上扩展到广义(M{,}R)系统，或 G-MR，也包括罗伯特 · 罗森和后者在1967ー1980年间的一系列公认的书信往来，以及直到1972年与尼古拉斯 · 拉舍夫斯基的书信往来。 − Rosen's ideas are becoming increasingly accepted in theoretical biology, and there are several current discussions+ − 第224行：
第195行： − − Rosen's ideas are becoming increasingly accepted in theoretical biology, and there are several current discussionsRosen的观点在理论生物学中越来越被接受，目前有一些讨论 − − 【最终篇】罗森的观点越来越被理论生物学所接受，目前有几种讨论
无编辑摘要
【最终篇】澄清简单科学模型和复杂科学模型之间的区别成为罗森后来发表报告的主要目标。罗森认为建模是科学和思想的本质。他的著作《预防系统》<ref>''Anticipatory Systems: Philosophical, Mathematical, and Methodological Foundations'', Robert Rosen, 2nd edition, with contributions by Judith Rosen, John J. Klineman and Mihai Nadin, 2012, lx + 472 pp., Springer, New York {{ISBN|978-1-4614-1268-7}}</ref>详细描述了他所说的建模关系。他展示了真实的建模关系和仿真之间的深刻区别，后者不是基于这样的建模关系。
【最终篇】澄清简单科学模型和复杂科学模型之间的区别成为罗森后来发表报告的主要目标。罗森认为建模是科学和思想的本质。他的著作《预防系统》<ref>''Anticipatory Systems: Philosophical, Mathematical, and Methodological Foundations'', Robert Rosen, 2nd edition, with contributions by Judith Rosen, John J. Klineman and Mihai Nadin, 2012, lx + 472 pp., Springer, New York {{ISBN|978-1-4614-1268-7}}</ref>详细描述了他所说的建模关系。他展示了真实的建模关系和仿真之间的深刻区别，后者不是基于这样的建模关系。
【最终篇】在数学生物学中，他被认为是一类生物有机体关系模型的创始人，这类关系模型被称为 (M{,}R)系统，他设计这类系统是为了捕捉物质系统成为通常被称为“活的”的最简单的功能有机体所需要的最低能力。在这种系统中，M代表新陈代谢，R代表简单生物体的“修复”子系统，例如活性的“修复”RNA分子。因此，他在任何给定系统中决定或“定义”生命的模式是一种功能模式，而不是物质模式;尽管他在20世纪70年代发表的报告中考虑了最简单的(M{，}R)系统在酶(M)、RNA (R)和功能复制DNA(他的beta图谱)方面的具体动态实现。
【最终篇】在数学生物学中，他被认为是一类生物有机体关系模型的创始人，这类关系模型被称为 (M{,}R)系统，他设计这类系统是为了捕捉物质系统成为通常被称为“活的”的最简单的功能有机体所需要的最低能力。在这种系统中，M代表新陈代谢，R代表简单生物体的“修复”子系统，例如活性的“修复”RNA分子。因此，他在任何给定系统中决定或“定义”生命的模式是一种功能模式，而不是物质模式;尽管他在20世纪70年代发表的报告中考虑了最简单的(M{，}R)系统在酶(M)、RNA (R)和功能复制DNA(他的beta图谱)方面的具体动态实现。
【最终篇】然而，他在这个方向上更进一步，声称当研究一个复杂的系统时，人们“可以抛开物质并且只研究组织”来学习那些对定义整个系统类至关重要的东西。然而，罗伯特罗森以前的一些学生对此过于字面化，他们没有完全吸收罗伯特罗森的观点，即需要一种动态实现特定分子形式的抽象组分的理论，以便为最简单的功能有机体(例如单细胞藻类或微生物)闭合建模循环。罗伯罗森，1970。生物学的动力系统理论，纽约:威利交叉科学。<ref>Robert Rosen. 1970. ''Dynamical Systems Theory in Biology'', New York: Wiley Interscience.</ref>他支持这一说法(实际上他归因于尼古拉斯·拉舍夫斯基)，因为生命有机体是一类系统，具有极其广泛的物质“成分”、不同的结构、不同的栖息地、不同的生存和繁殖方式，然而我们却能够以某种方式将它们全部识别为活的或功能性的有机体，而不管它们多么有生命力。
【最终篇】他的方法，就像拉舍夫斯基（Rashevsky）最新的有机组合理论一样<ref>{{cite journal | last1 = Rashevsky | first1 = N | year = 1965 | title = The Representation of Organisms in Terms of (logical) Predicates | journal = Bulletin of Mathematical Biophysics | volume = 27 | issue = 4| pages = 477–491 | doi=10.1007/bf02476851| pmid = 4160663 }}</ref><ref>{{cite journal | last1 = Rashevsky | first1 = N | year = 1969 | title = Outline of a Unified Approach to Physics, Biology and Sociology | journal = Bulletin of Mathematical Biophysics | volume = 31 | issue = 1| pages = 159–198 | doi=10.1007/bf02478215| pmid = 5779774 }}</ref>，强调生物组织多于分子结构，试图绕过对包括生理学家在内的所有实验生物学家都很重要的结构-功能关系。相比之下，对任何特定有机体，甚至是某种有机体的特定物质细节的研究，只会告诉我们这种有机体是如何“做到这一点的”。这样的一项研究并没有涉及到所有功能性生物体的共同特征，即“生命”。因此，与理论生物学相关的方法将使我们能够以这种方式来研究生物，这种方式能够保持我们试图了解的、只有功能性生物才具有的那些基本特性。
【最终篇】罗伯特罗森的方法在概念上属于现在所知的功能生物学，以及复杂系统生物学，尽管是一种高度抽象的数学形式。
【最终篇】罗伯特罗森的方法在概念上属于现在所知的功能生物学，以及复杂系统生物学，尽管是一种高度抽象的数学形式。
== 量子生物化学与量子遗传学 ==
== 量子生物化学与量子遗传学 ==
【最终篇】罗森还质疑他所认为的生物化学和遗传学的主流解释的许多方面。他反对这样一种观点，即生物系统的功能方面可以通过聚焦物质方面来调查。举个例子: 罗森质疑生物活性蛋白质的功能能力可以仅仅通过基因编码的氨基酸序列来研究。他说，这是因为蛋白质必须经过一个折叠过程才能获得其特有的三维形状，然后才能在系统中发挥功能。然而，只有氨基酸序列是基因编码的。蛋白质折叠的机制尚不完全清楚。基于这样的例子，他得出结论，表型不能总是直接归因于基因型，生物活性蛋白质的化学活性方面不仅仅依赖于构成它的氨基酸序列: 一定还有其他一些重要因素在起作用，然而他并没有试图指明或确定。
【最终篇】罗森还质疑他所认为的生物化学和遗传学的主流解释的许多方面。他反对这样一种观点，即生物系统的功能方面可以通过聚焦物质方面来调查。举个例子: 罗森质疑生物活性蛋白质的功能能力可以仅仅通过基因编码的氨基酸序列来研究。他说，这是因为蛋白质必须经过一个折叠过程才能获得其特有的三维形状，然后才能在系统中发挥功能。然而，只有氨基酸序列是基因编码的。蛋白质折叠的机制尚不完全清楚。基于这样的例子，他得出结论，表型不能总是直接归因于基因型，生物活性蛋白质的化学活性方面不仅仅依赖于构成它的氨基酸序列: 一定还有其他一些重要因素在起作用，然而他并没有试图指明或确定。
}}</ref> which claimed that some of the mathematical formulations used by Rosen are problematic from a logical viewpoint. It is perhaps worth noting, however, that such issues were also raised long time ago by [[Bertrand Russell]] and [[Alfred North Whitehead]] in their famous ''[[Principia Mathematica]]'' in relation to [[Antinomy|antinomies]] of [[set theory]]. As Rosen's mathematical formulation in his earlier papers was also based on [[set theory]] and the [[category of sets]] such issues have naturally re-surfaced. However, these issues have now been addressed by Robert Rosen in his recent book ''Essays on Life Itself'', published posthumously in 2000. Furthermore, such basic problems of mathematical formulations of '''<math>(M{,}R)</math>'''--systems had already been resolved by other authors as early as 1973 by utilizing the [[Yoneda lemma]] in [[category theory]], and the associated [[functor]]ial construction in categories with (mathematical) structure.<ref>I.C. Baianu: 1973, Some Algebraic Properties of '''<math>(M{,}R)</math>''' - Systems. ''Bulletin of Mathematical Biophysics'' '''35''', 213-217.</ref><ref>I.C. Baianu and M. Marinescu: 1974, A Functorial Construction of '''<math>(M{,}R)</math>'''- Systems. ''Revue Roumaine de Mathematiques Pures et Appliquees'' '''19''': 388-391.</ref> Such general [[category theory|category-theoretic]] extensions of '''<math>(M{,}R)</math>'''-systems that avoid [[Paradoxes of set theory|set theory paradox]]es are based on [[William Lawvere]]'s categorical approach and its extensions to [[higher-dimensional algebra]]. The mathematical and logical extension of '' metabolic-replication systems'' to generalized '''<math>(M{,}R)</math>'''-systems, or ''G-MR'', also involved a series of acknowledged letters exchanged between Robert Rosen and the latter authors during 1967—1980s, as well as letters exchanged with Nicolas Rashevsky up to 1972.
}}</ref> which claimed that some of the mathematical formulations used by Rosen are problematic from a logical viewpoint. It is perhaps worth noting, however, that such issues were also raised long time ago by [[Bertrand Russell]] and [[Alfred North Whitehead]] in their famous ''[[Principia Mathematica]]'' in relation to [[Antinomy|antinomies]] of [[set theory]]. As Rosen's mathematical formulation in his earlier papers was also based on [[set theory]] and the [[category of sets]] such issues have naturally re-surfaced. However, these issues have now been addressed by Robert Rosen in his recent book ''Essays on Life Itself'', published posthumously in 2000. Furthermore, such basic problems of mathematical formulations of '''<math>(M{,}R)</math>'''--systems had already been resolved by other authors as early as 1973 by utilizing the [[Yoneda lemma]] in [[category theory]], and the associated [[functor]]ial construction in categories with (mathematical) structure.<ref>I.C. Baianu: 1973, Some Algebraic Properties of '''<math>(M{,}R)</math>''' - Systems. ''Bulletin of Mathematical Biophysics'' '''35''', 213-217.</ref><ref>I.C. Baianu and M. Marinescu: 1974, A Functorial Construction of '''<math>(M{,}R)</math>'''- Systems. ''Revue Roumaine de Mathematiques Pures et Appliquees'' '''19''': 388-391.</ref> Such general [[category theory|category-theoretic]] extensions of '''<math>(M{,}R)</math>'''-systems that avoid [[Paradoxes of set theory|set theory paradox]]es are based on [[William Lawvere]]'s categorical approach and its extensions to [[higher-dimensional algebra]]. The mathematical and logical extension of '' metabolic-replication systems'' to generalized '''<math>(M{,}R)</math>'''-systems, or ''G-MR'', also involved a series of acknowledged letters exchanged between Robert Rosen and the latter authors during 1967—1980s, as well as letters exchanged with Nicolas Rashevsky up to 1972.
【最终篇】克里斯托弗 · 兰道尔（Christopher Landauer）和克里斯蒂 · 贝尔曼（Kirstie L. Bellman）在一篇论文中提出了一些关于罗森数学论证的问题，这篇论文声称罗森使用的一些数学公式从逻辑观点来看是有问题的。然而，也许值得注意的是，这些问题很久以前也被伯特兰·罗素和阿尔弗雷德·诺思·怀特黑德在他们著名的关于集合论悖论的数学原理中提出过。正如罗森在他的早期论文中的数学公式也是基于集合论的，这类问题的集合范畴自然重新浮出水面。然而，罗伯特 · 罗森在他2000年去世后出版的新书《论生命本身》中提到了这些问题。此外，(M{,}R)系统的数学公式的这些基本问题早在1973年就已经被其他作者利用范畴论中的 Yoneda 引理和范畴中的(数学)结构中的相关函子结构解决了。数学生物物理学通报35,213-217. c.Baianu和M. Marinescu: 1974，(M{,}R)系统的函数构造。这种避免集合论悖论的(M{,}R)系统的一般范畴论扩张是基于 William Lawvere 的范畴方法及其对高维代数的扩张。新陈代谢复制系统在数学和逻辑上扩展到广义(M{,}R)系统，或 G-MR，也包括罗伯特 · 罗森和后者在1967ー1980年间的一系列公认的书信往来，以及直到1972年与尼古拉斯 · 拉舍夫斯基的书信往来。
【最终篇】罗森的观点越来越被理论生物学所接受，目前有几种讨论<ref>{{cite journal
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[[Erwin Schrödinger]] discussed issues of quantum genetics in his famous book of 1945, ''[[What Is Life?]]'' These were critically discussed by Rosen in ''Life Itself'' and in his subsequent book ''[[Essays on Life Itself]]''.<ref>''Note, by Judith Rosen, who owns the copyrights to her father's books:'' Some confusion about Rosen's analysis is due to errata in ''Life Itself''. For example, the diagram that refers to <math>(M{,}R)</math>-Systems has more than one error; errors which do not exist in Rosen's manuscript for the book. <!--These errata were made known to Columbia University Press when the company switched from hardcover to paperback version of the book (in 2006) but the errors were not corrected and remain in the paperback version as well.--> The book ''Anticipatory Systems; Philosophical, Mathematical, and Methodological Foundations'' has the same diagram, correctly represented.</ref>
[[Erwin Schrödinger]] discussed issues of quantum genetics in his famous book of 1945, ''[[What Is Life?]]'' These were critically discussed by Rosen in ''Life Itself'' and in his subsequent book ''[[Essays on Life Itself]]''.<ref>''Note, by Judith Rosen, who owns the copyrights to her father's books:'' Some confusion about Rosen's analysis is due to errata in ''Life Itself''. For example, the diagram that refers to <math>(M{,}R)</math>-Systems has more than one error; errors which do not exist in Rosen's manuscript for the book. <!--These errata were made known to Columbia University Press when the company switched from hardcover to paperback version of the book (in 2006) but the errors were not corrected and remain in the paperback version as well.--> The book ''Anticipatory Systems; Philosophical, Mathematical, and Methodological Foundations'' has the same diagram, correctly represented.</ref>