A note on the axiomatization of the Nash equilibrium correspondence

A new axiomatization of the Nash equilibrium correspondence for n-person games based on independence of irrelevant strategies is given. Using a flexible general model, it is proved that the Nash equilibrium correspondence is the only solution to satisfy the axioms of non-emptiness, weak one-person rationality, independence of irrelevant strategies and converse independence of irrelevant strategies on the class of subgames of a fixed finite n-person game which admit at least one Nash equilibrium. It is also shown that these axioms are logically independent.

The logo is not flat: evolving picture marks

From the boom of corporate identity in the 50s, 60 years have passed, and we now see picture marks become more complex and question axioms of identity design, like simplicity or bidimensionality. In these changing times, where access to technology and to information makes it possible for one to see the world as a ‘flat’ place [1], where virtually anyone with a computer can create, it is worth considering how much has changed and how much remains the same in picture marks design. Are the silent designers [2] — the technology and software — growing louder? Are picture marks mimicking each other? Are graphic marks following trendy solutions? It is clear the change of paradigms the new technologies have over the graphic zeitgeist. However, what are the consequences of the transformation in the modus operandi and its result in picture marks evolving solutions? And what does this evolution say about us? Being both a condensation of meaning about a corporation or institution and a rhetorical instrument by which to persuade an audience that a product or entity has distinctive and desirable qualities, picture marks are, therefore, a condensed representation of social identity. They are signs full of signification beyond themselves, representing ourselves and our world and by means of its analysis we can learn a bit more about our role as designers, our relation towards new technologies and foresee our role as designers in the future.

Characterizing Behavioral Decisions with Choice Datas

A number of different models with behavioral economics have a reduced form representation where potentially boundedly rational decision-makers do not necessarily internalize all the consequences of their actions on payoff relevant features (which we label as psychological states) of the choice environment. This paper studies the restrictions that such behavioral models impose on choice data and the implications they have for welfare analysis. First, we propose a welfare benchmark that is justified using standard axioms of rational choice and can be applied to a number of existing seminal behavioral economics models. Second, we show that Sen's axioms and fully characterize choice data consistent with behavioral decision-makers. Third, we show how choice data to infer information about the normative signi.cance of psychological states and establish the possibility of identifying welfare dominated choices.

Additive utility with intransitive indifference and without independence: A homogeneous case

In the homogeneous case of one type of goods or objects, we prove theexistence of an additive utility function without assuming transitivityof indifference and independence. The representation reveals a positivefactor smaller than 1 that infuences rational choice beyond the utilityfunction and explains departures from these standard axioms of utilitytheory (factor equals to 1).

Conditional Expected Utility

Let 'epsilon' be a class of event. Conditionally Expected Utility decision makers are decision makers whose conditional preferences ≿E, E є 'epsilon', satisfy the axioms of Subjective Expected Utility theory (SEU). We extend the notion of unconditional preference that is conditionally EU to unconditional preferences that are not necessarily SEU. We give a representation theorem for a class of such preferences, and show that they are Invariant Bi-separable in the sense of Ghirardato et al.[7]. Then, we consider the special case where the unconditional preference is itself SEU, and compare our results with those of Fishburn [6].

Bayesian inference and model comparison for random choice structures

We complete the development of a testing ground for axioms of discrete stochastic choice. Our contribution here is to develop new posterior simulation methods for Bayesian inference, suitable for a class of prior distributions introduced by McCausland and Marley (2013). These prior distributions are joint distributions over various choice distributions over choice sets of di fferent sizes. Since choice distributions over di fferent choice sets can be mutually dependent, previous methods relying on conjugate prior distributions do not apply. We demonstrate by analyzing data from a previously reported experiment and report evidence for and against various axioms.

ONTIC: A Knowledge Representation System for Mathematics

Ontic is an interactive system for developing and verifying mathematics. Ontic's verification mechanism is capable of automatically finding and applying information from a library containing hundreds of mathematical facts. Starting with only the axioms of Zermelo-Fraenkel set theory, the Ontic system has been used to build a data base of definitions and lemmas leading to a proof of the Stone representation theorem for Boolean lattices. The Ontic system has been used to explore issues in knowledge representation, automated deduction, and the automatic use of large data bases.

Truth in complex adaptive systems models should be based on truth by constructive verification

It is argued that the truth status of emergent properties of complex adaptive systems models should be based on an epistemology of proof by constructive verification and therefore on the ontological axioms of a non-realist logical system such as constructivism or intuitionism. ‘Emergent’ properties of complex adaptive systems (CAS) models create particular epistemological and ontological challenges. These challenges bear directly on current debates in the philosophy of mathematics and in theoretical computer science. CAS research, with its emphasis on computer simulation, is heavily reliant on models which explore the entailments of Formal Axiomatic Systems (FAS). The incompleteness results of Gödel, the incomputability results of Turing, and the Algorithmic Information Theory results of Chaitin, undermine a realist (platonic) truth model of emergent properties. These same findings support the hegemony of epistemology over ontology and point to alternative truth models such as intuitionism, constructivism and quasi-empiricism.

Racionalidade e pesquisa comportamental no direito: avanço científico ou retórica?

Esse é um trabalho sobre estudos comportamentais que questionam a confiabilidade empírica das premissas de racionalidade das ciências sociais. Décadas de pesquisa comportamental vêm nos ensinando é que a grande maioria das tendências cognitivas identificadas e comprovadas, que se afastam dos pressupostos da Teoria da Escolha Racional não são de forma alguma aleatórias, mas ao invés, são sistemáticas e previsíveis. A ideia unificando esse trabalho é de que a literatura de pesquisa comportamental pode nos permitir modelar e prever comportamentos relevantes para o direito, com pressupostos mais realistas sobre o comportamento humano. No entanto, alguns pesquisadores pintam uma figura entusiástica sobre o potencial que tal pesquisa possui para informar a análise jurídica e, assim, cometem algumas desatenções ao defender generalizações não embasadas por evidências científicas, quase aproximando-se do uso de uma mera retórica. Dado esse cenário, devemos procurar garantir que a incorporação das evidências da pesquisa comportamental no discurso jurídico seja acompanhada de maior ênfase na pesquisa empírica em ambientes específicos. Esse trabalho possui três objetivos. O primeiro é analisar as diferentes concepções de racionalidade e caso elas devem manter sua posição privilegiada nas ciências sociais. O segundo é tentar entender melhor a literatura de pesquisa comportamental que questionam a validade empírica dos axiomas da Teoria da Escolha Racional. O terceiro é identificar problemas na forma pela qual a pesquisa comportamental tem sido incorporada no discurso jurídico.

La influencia argentina en la configuración de la historiografía uruguaya. Estudio de caso: Francisco Bauzá

En la segunda mitad del siglo XIX se crearon en el Río de la Plata las condiciones necesarias para el surgimiento y desarrollo de las historiografías nacionales, humus primordial del cual emergieron proposiciones fácticas y axiomas historiográficos de cuño patriótico. La historiografía argentina, por diversidad de motivos -disponibilidad de insumos heurísticos y repertorios bibliográficos, número de intelectuales (historiadores, poetas, novelistas, ensayistas) consagrados al estudio y exaltación del pasado nacional, instituciones dedicadas al desarrollo de la investigación, recursos aportados por el Estado- tuvo un temprano e importante desarrollo e influyó de forma determinante en la historiografía uruguaya. El objeto de este artículo es conocer las modalidades, el carácter y significación de esta influencia en un autor concreto, Francisco Bauzá, a efectos de dilucidar los cimientos sobre los cuales se definieron las estructuras teóricas y la preceptivas técnico-metodológicas fundantes de la disciplina en Uruguay.

La influencia argentina en la configuración de la historiografía uruguaya. Estudio de caso: Francisco Bauzá

En la segunda mitad del siglo XIX se crearon en el Río de la Plata las condiciones necesarias para el surgimiento y desarrollo de las historiografías nacionales, humus primordial del cual emergieron proposiciones fácticas y axiomas historiográficos de cuño patriótico. La historiografía argentina, por diversidad de motivos -disponibilidad de insumos heurísticos y repertorios bibliográficos, número de intelectuales (historiadores, poetas, novelistas, ensayistas) consagrados al estudio y exaltación del pasado nacional, instituciones dedicadas al desarrollo de la investigación, recursos aportados por el Estado- tuvo un temprano e importante desarrollo e influyó de forma determinante en la historiografía uruguaya. El objeto de este artículo es conocer las modalidades, el carácter y significación de esta influencia en un autor concreto, Francisco Bauzá, a efectos de dilucidar los cimientos sobre los cuales se definieron las estructuras teóricas y la preceptivas técnico-metodológicas fundantes de la disciplina en Uruguay.

La influencia argentina en la configuración de la historiografía uruguaya. Estudio de caso: Francisco Bauzá

En la segunda mitad del siglo XIX se crearon en el Río de la Plata las condiciones necesarias para el surgimiento y desarrollo de las historiografías nacionales, humus primordial del cual emergieron proposiciones fácticas y axiomas historiográficos de cuño patriótico. La historiografía argentina, por diversidad de motivos -disponibilidad de insumos heurísticos y repertorios bibliográficos, número de intelectuales (historiadores, poetas, novelistas, ensayistas) consagrados al estudio y exaltación del pasado nacional, instituciones dedicadas al desarrollo de la investigación, recursos aportados por el Estado- tuvo un temprano e importante desarrollo e influyó de forma determinante en la historiografía uruguaya. El objeto de este artículo es conocer las modalidades, el carácter y significación de esta influencia en un autor concreto, Francisco Bauzá, a efectos de dilucidar los cimientos sobre los cuales se definieron las estructuras teóricas y la preceptivas técnico-metodológicas fundantes de la disciplina en Uruguay.

Contribución al estudio de las negaciones, autocontradicción, t-normas y t-conormas en los conjuntos borrosos de tipo 2

Los conjuntos borrosos de tipo 2 (T2FSs) fueron introducidos por L.A. Zadeh en 1975 [65], como una extensión de los conjuntos borrosos de tipo 1 (FSs). Mientras que en estos últimos el grado de pertenencia de un elemento al conjunto viene determinado por un valor en el intervalo [0, 1], en el caso de los T2FSs el grado de pertenencia de un elemento es un conjunto borroso en [0,1], es decir, un T2FS queda determinado por una función de pertenencia μ : X → M, donde M = [0, 1][0,1] = Map([0, 1], [0, 1]), es el conjunto de las funciones de [0,1] en [0,1] (ver [39], [42], [43], [61]). Desde que los T2FSs fueron introducidos, se han generalizado a dicho conjunto (ver [39], [42], [43], [61], por ejemplo), a partir del “Principio de Extensión” de Zadeh [65] (ver Teorema 1.1), muchas de las definiciones, operaciones, propiedades y resultados obtenidos en los FSs. Sin embargo, como sucede en cualquier área de investigación, quedan muchas lagunas y problemas abiertos que suponen un reto para cualquiera que quiera hacer un estudio profundo en este campo. A este reto se ha dedicado el presente trabajo, logrando avances importantes en este sentido de “rellenar huecos” existentes en la teoría de los conjuntos borrosos de tipo 2, especialmente en las propiedades de autocontradicción y N-autocontradicción, y en las operaciones de negación, t-norma y t-conorma sobre los T2FSs. Cabe destacar que en [61] se justifica que las operaciones sobre los T2FSs (Map(X,M)) se pueden definir de forma natural a partir de las operaciones sobre M, verificando las mismas propiedades. Por tanto, por ser más fácil, en el presente trabajo se toma como objeto de estudio a M, y algunos de sus subconjuntos, en vez de Map(X,M). En cuanto a la operación de negación, en el marco de los conjuntos borrosos de tipo 2 (T2FSs), usualmente se emplea para representar la negación en M, una operación asociada a la negación estándar en [0,1]. Sin embargo, dicha operación no verifica los axiomas que, intuitivamente, debe verificar cualquier operación para ser considerada negación en el conjunto M. En este trabajo se presentan los axiomas de negación y negación fuerte en los T2FSs. También se define una operación asociada a cualquier negación suprayectiva en [0,1], incluyendo la negación estándar, y se estudia, junto con otras propiedades, si es negación y negación fuerte en L (conjunto de las funciones de M normales y convexas). Además, se comprueba en qué condiciones se cumplen las leyes de De Morgan para un extenso conjunto de pares de operaciones binarias en M. Por otra parte, las propiedades de N-autocontradicción y autocontradicción, han sido suficientemente estudiadas en los conjuntos borrosos de tipo 1 (FSs) y en los conjuntos borrosos intuicionistas de Atanassov (AIFSs). En el presente trabajo se inicia el estudio de las mencionadas propiedades, dentro del marco de los T2FSs cuyos grados de pertenencia están en L. En este sentido, aquí se extienden los conceptos de N-autocontradicción y autocontradicción al conjunto L, y se determinan algunos criterios para verificar tales propiedades. En cuanto a otras operaciones, Walker et al. ([61], [63]) definieron dos familias de operaciones binarias sobre M, y determinaron que, bajo ciertas condiciones, estas operaciones son t-normas (normas triangulares) o t-conormas sobre L. En este trabajo se introducen operaciones binarias sobre M, unas más generales y otras diferentes a las dadas por Walker et al., y se estudian varias propiedades de las mismas, con el objeto de deducir nuevas t-normas y t-conormas sobre L. ABSTRACT Type-2 fuzzy sets (T2FSs) were introduced by L.A. Zadeh in 1975 [65] as an extension of type-1 fuzzy sets (FSs). Whereas for FSs the degree of membership of an element of a set is determined by a value in the interval [0, 1] , the degree of membership of an element for T2FSs is a fuzzy set in [0,1], that is, a T2FS is determined by a membership function μ : X → M, where M = [0, 1][0,1] is the set of functions from [0,1] to [0,1] (see [39], [42], [43], [61]). Later, many definitions, operations, properties and results known on FSs, have been generalized to T2FSs (e.g. see [39], [42], [43], [61]) by employing Zadeh’s Extension Principle [65] (see Theorem 1.1). However, as in any area of research, there are still many open problems which represent a challenge for anyone who wants to make a deep study in this field. Then, we have been dedicated to such challenge, making significant progress in this direction to “fill gaps” (close open problems) in the theory of T2FSs, especially on the properties of self-contradiction and N-self-contradiction, and on the operations of negations, t-norms (triangular norms) and t-conorms on T2FSs. Walker and Walker justify in [61] that the operations on Map(X,M) can be defined naturally from the operations onMand have the same properties. Therefore, we will work onM(study subject), and some subsets of M, as all the results are easily and directly extensible to Map(X,M). About the operation of negation, usually has been employed in the framework of T2FSs, a operation associated to standard negation on [0,1], but such operation does not satisfy the negation axioms on M. In this work, we introduce the axioms that a function inMshould satisfy to qualify as a type-2 negation and strong type-2 negation. Also, we define a operation on M associated to any suprajective negation on [0,1], and analyse, among others properties, if such operation is negation or strong negation on L (all normal and convex functions of M). Besides, we study the De Morgan’s laws, with respect to some binary operations on M. On the other hand, The properties of self-contradiction and N-self-contradiction have been extensively studied on FSs and on the Atanassov’s intuitionistic fuzzy sets (AIFSs). Thereon, in this research we begin the study of the mentioned properties on the framework of T2FSs. In this sense, we give the definitions about self-contradiction and N-self-contradiction on L, and establish the criteria to verify these properties on L. Respect to the t-norms and t-conorms, Walker et al. ([61], [63]) defined two families of binary operations on M and found that, under some conditions, these operations are t-norms or t-conorms on L. In this work we introduce more general binary operations on M than those given by Walker et al. and study which are the minimum conditions necessary for these operations satisfy each of the axioms of the t-norm and t-conorm.

Sostenibilidad en el sector de la construcción. Sostenibilidad en estructuras y puentes ferroviarios

La escasez de recursos, el cambio climático, la pobreza y el subdesarrollo, los desastres naturales, son solo algunos de los grandes retos a que se enfrenta la humanidad y a los que la economía verde y el desarrollo sostenible tienen que dar respuesta. El concepto sostenible surge a raíz de la necesidad de lograr en todas las actividades humanas un nuevo equilibrio con el medioambiente, la sociedad y la economía, es decir un desarrollo más sostenible. La construcción supone en este nuevo concepto un sector básico, con grandes impactos en los recursos, los residuos, las emisiones, la biodiversidad, el paisaje, las necesidades sociales, la integración, el desarrollo económico del entorno, etc. Es por ello, que la construcción sostenible tiene una importancia esencial como demuestra su amplia aplicación teórica y práctica ya en proyectos de planificación urbana y de edificación. En la ingeniería civil estas aproximaciones son todavía mínimas, aunque ya se están considerando ciertos criterios de sostenibilidad en proyectos de construcción. La construcción consume muchos recursos naturales, económicos y tiene gran incidencia social. En la actualidad su actividad consume un 30% de los recursos extraídos de la tierra y la energía, y en consecuencia genera el 30% de los gases de efecto invernadero y residuos sólidos del mundo (EEA, 2014). Este impacto debería suponer una gran responsabilidad para los profesionales y gobiernos que toman cada día las decisiones de diseño e inversión en la construcción, y su máxima eficiencia debería estar muy presente entre los objetivos. En esta tesis doctoral se plantea un nuevo modelo para la evaluación de la sostenibilidad en los proyectos mediante un sistema de indicadores, basados en las áreas de estudio de las certificaciones de sostenibilidad existentes y en un análisis multi-criterio de cada uno de los axiomas de la sostenibilidad. Como reto principal se marca la propuesta de una metodología que permita identificar, priorizar y seleccionar los indicadores y las variables más importantes de lo que es considerado como una construcción sostenible en el caso de infraestructuras ferroviarias, más concretamente en puentes ferroviarios, y que además sirva para priorizar nuevos proyectos que se adapten a los nuevos objetivos del desarrollo sostenible: el respeto al medioambiente, la integración social y la económica. El objetivo es la aplicación de estos indicadores desde las etapas más tempranas del proyecto: planificación, diseño de alternativas y selección de alternativas. Para ello, en primer lugar, se ha realizado un análisis en profundidad de los distintas organizaciones de certificación de la sostenibilidad mundiales y se ha desarrollado una comparativa entre ellas, detallando el funcionamiento de las más extendidas (BREEAM, LEED, VERDE, DGNB). Tras esto, se ha analizado la herramienta matemática MIVES de análisis multi-criterio para su aplicación, en la tesis, a las infraestructuras ferroviarias. En la segunda parte se desarrolla para las estructuras ferroviarias un nuevo modelo de indicadores, un sistema de ayuda a la decisión multi-criterio basado en los tres axiomas de las sostenibilidad (sociedad, medioambiente y economía), articulados en un árbol de requerimientos inspirado en el método MIVES, que propone una metodología para el caso de las infraestructuras ferroviarias. La metodología MIVES estructura el proceso de decisión en tres ramas: Requisitos, componentes y ciclo de vida. Estas ramas definen los límites de los sistemas. El eje de los requisitos del árbol de los requisitos o se estructura en tres niveles que corresponden al requisito específico: criterios e indicadores. Además, es necesario definen la función del valor para cada indicador, definen el peso de importancia de cada elemento del árbol y finalmente con el calcular el valor de cada alternativa selecciona el mejor de él. La generación de este árbol de requerimientos en estructuras ferroviarias y la medición de los parámetro es original para este tipo de estructuras. Por último, tras el desarrollo de la metodología, se ha aplicado la propuesta metodológica mediante la implementación práctica, utilizando el método propuesto con 2 puentes ferroviarios existentes. Los resultados han mostrado que la herramienta es capaz de establecer una ordenación de las actuaciones coherente y suficientemente discriminante como para que el decisor no tenga dudas cuando deba tomar la decisión. Esta fase, es una de las grandes aportaciones de la tesis, ya que permite diferenciar los pesos obtenidos en cada una de las áreas de estudio y donde la toma de decisión puede variar dependiendo de las necesidades del decisor, la ubicación del puente de estudio etc. ABSTRACT Scarce resources, climate change, poverty and underdevelopment, natural disasters are just some of the great challenges facing humanity and to which the green economy will have to respond. The sustainable concept arises from the need for all human activities in a new equilibrium with the environment, society and the economy, which is known as sustainable development. The construction industry is part of this concept, because of its major impacts on resources, waste, emissions, biodiversity, landscape, social needs, integration, economical development, environment, etc. Therefore, sustainable construction has a critical importance as already demonstrated by its wide application and theoretical practice in urban planning and building projects. In civil engineering, these approaches are still minimal, although some criteria are already taken into account for sustainability in infrastructure projects. The construction industry requires a lot of natural resources, has a real economic relevance and a huge social impact. Currently, it consumes 40% of produced power as well as natural resources extracted from the earth and thus leads to an environmental impact of 40% regarding greenhouse gas emissions and solid wastes (EEA 2014). These repercussions should highly concern our governments and professional of this industry on the decisions they take regarding investments and designs. They must be inflexible in order to ensure that the main concern has to be a maximum efficiency. Major events like the COP21 held in Paris in December 2015 are a concrete signal of the worldwide awareness of the huge impact of each industry on climate. In this doctoral thesis a new model for the evaluation of the sustainability in the projects by means of a system of indicators, based on the areas of study of the existing certifications of sustainability and on an analysis considers multi-criterion of each one of the axioms of the sustainability. The primary aim of this thesis is to study the mode of application of sustainability in projects through a system of indicators. . The main challenge consists of create a methodology suitable to identify, prioritize and select the most important indicators which define if a building is sustainable in the specific case of railway infrastructures. The methodology will help to adapt future projects to the new goals of sustainable development which are respect of nature, social integration and economic relevance. A crucial point is the consideration of these indicators from the very beginning steps of the projects: planning, design and alternatives reflections. First of all, a complete inventory of all world energy certification organizations has been made in order to compare the most representative ones regarding their way of functioning (BREEAM, LEED, VERDE, DGNB). After this, mathematical tool MIVES of analysis has been analyzed multi-criterion for its application, in the thesis, to railway infrastructures. The second part of the thesis is aimed to develop a new model of indicators, inspired by the MIVES method, consisting in a decision-making system based on the 3 foundations of sustainability: nature impact, social concerns, and economic relevance. The methodology MIVES structures the decision process in three axes: Requirements, components and life cycle. These axes define the boundaries of the systems. The axis of requirements o tree requirements is structured in three levels corresponding to specific requirement: criteria and indicators. In addition, is necessary define the value function for each indicator, define the weight of importance of each element of the tree and finally with the calculate the value of each alternative select the best of them. The generation of this tree requirements in railway structures and measuring the parameter is original for this type of structures. Finally, after the development of the methodology, it has validated the methodology through practical implementation, applying the proposed method 2 existing railway bridges. The results showed that the tool is able to establish a coherent management of performances and discriminating enough so that the decision maker should not have doubts when making the decision. This phase, is one of the great contributions of the thesis, since it allows to differentiate the weights obtained in each one from the study areas and where the decision making can vary depending on the necessities of the decisor, the location of the bridge of study etc.

'That Puissant City': John Milton's Roman Sojourns 1638-1639

John Milton’s sojourns in Rome (1638-9) are attested by his comments in Defensio Secunda, by the minutes of the English College, by Latin encomia which he received from Roman academicians, and, not least, by his Latin letter to Lucas Holstenius (19/29 March 1639), and several Latin poems which he composed in the course of his residency in the capital city: Ad Salsillum, and three Latin epigrams extolling the praises of the virtuosa soprano, Leonora Baroni. Read together, these texts serve to reveal much about Milton’s participation in, and reaction to, the ‘Puissant City’, (History of Britain, Bk 2).

The present monograph presents fresh evidence of Milton's integration into the academic and cultural life of seventeenth-century Rome. It argues that his links with two Roman academies: the Accademia dei Fantastici and Accademia degli Umoristi constitute a sustained participation in an academic community paralleling that of his independently attested performance in Florentine academies (on which I have published extensively). It also investigates his links with Alessandro Cherubini, David Codner, Giovanni Batista Doni, and the Baroni circle hymned in three published anthologies.

Chapter 1: Milton and the Accademia dei Fantastici investigates the cultural climate surrounding Milton's Ad Salsillum by examining two of that academy's publications: the Poesie dei Signori Accademici Fantastici di Roma (Rome, 1637) and the Academia Tenuta da Fantastici a. 12 di Maggio 1655 (Rome, 1655), the latter celebrating the creation of Fabio Chigi as Pope Alexander VII on 5 April 1655. Read in a new light, Milton’s self-fashioning, it is argued, takes its place not only alongside Salzilli’s encomium in Milton's honour, and his Italian sonnets in the 1637 Poesie, but also in relation to other poems in that collection, and the academy's essentially Catholic eulogistic trend. The chapter also provides fresh evidence of Salzilli’s survival of the illness described in Milton’s poem by his epistolary correspondence with Tomaso Stigliani.

Chapter 2: Milton and the Vatican argues for links between Milton’s Latin letter to Holstenius and a range of Holstenius’ published works: his edition of the axioms of the later Pythagoreans gifted by him to Milton, and his published neo-Platonic works. This is achieved by mutual appropriation of Similitudes in a series of Miltonic similes, the anabasis/katabasis motifs in a reworking of the Platonic theory of the transmigration of souls, and allusion to etymological details highlighted in Holstenius’ published editions. The chapter also reveals Milton’s alertness to typographical procedures and, by association, to Holstenius’ recent role (1638) as Director of the press of the Biblioteca Vaticana.

Chapter 3: Milton and the Accademia degli Umoristi argues for Milton’s likely participation in this Roman academy, as suggested by his links with its members. His three Latin epigrams in praise of Leonora Baroni, the only female member of the Umoristi, have hitherto been studied in relation to the 1639 Applausi in her honour. In a new reading, Milton, it is suggested, invokes and interrogates Catholic doctrine before a Catholic audience only to view the whole through the lens of a neo-Platonic Hermeticism (by echoing the phraseology of the sixteenth-century Franciscan Hannibal Rosselli) that refreshingly transcends religious difference. Crucially, the hitherto neglected L’Idea della Veglia (Rome, 1640) includes further encomiastic verse, sonnets to, and by Leonora, and details of the conversazioni hosted by her family at the precise time of Milton’s Roman sojourns. Milton may well have been a participant. The chapter concludes in an assessment of his links with the youthful prodigy Alessandro Cherubini, and of his audience with Francesco Barberini.

Chapter 4: Milton at a Roman Opera analyses the potential impact of ‘Chi Soffre, Speri’, which he attended on 18/28 February 1639, mounted by Francesco Barberini to inaugurate the recently completed theatre of the Palazzo Barberini. A detailed analysis of the opera's libretto, music, and theatricality casts a backward glance to Milton's Comus, and a forward glance to Paradise Lost. It also assesses Milton’s musical interests at this time, as attested by his links with Doni, and his purchase of works by Monteverdi and others.

Chapter 5: Milton’s English Connections in Rome develops the work of Miller and Chaney by investigating Milton’s co-diners at the English College in Rome on 30 October 1638, and by analysing his links between David Codner (alias Matteo Selvaggio), and the family of Jane Savage, Marchioness of Winchester, lamented by Milton in 1631. It also assesses his potential relations with the Englishman Thomas Gawen, who ‘accidentally sometimes fell into the company of John Milton’ (Antony Wood).