António de Freitas | Universidade do Minho (original) (raw)

Papers by António de Freitas

Revista Agustiniana-La Ciudad de Dios, 2021

Yo soy la verdad. Alhdɛia en el evangelio de San Juan RESUMEN El presente trabajo analizará el co... more Yo soy la verdad. Alhdɛia en el evangelio de San Juan RESUMEN El presente trabajo analizará el concepto de verdad en el evangelio de San Juan. El análisis se basa en los texto donde la palabra griega ààń0ɛa es usada. Basándonos en su etimología iremos explorando lo que Juan nos quiere decir en cada texto del evangelio. Este artículo no pretende ser exhaustivo desde el punto de vista filosófico-teológico, sólo pretende comentar y extraer una concepción coherente de la verdad en el evangelio de San Juan.

Transcultural Mobilities and Memories/Mobilidades e Memórias Transculturais, 2023

It is well known that Sumerians and Babylonians used a numeration system of base 12 and 60. We st... more It is well known that Sumerians and Babylonians used a numeration system of base 12 and 60. We still have influence of that system in our nowadays counting of the hours of a day, twelve plus twelve, each hour has 60 minute and each minute 60 seconds. Also the circle has 360 degrees. What is not so well known is that the Sumerians in an earlier period used a ternary system of numeration; the first notice about that system is in Thureau-Dangin (1928). Later Diakonoff (1983) described it in good details and recently, Balke (2010) studied the system and described it with more precision. Still the use of this system and the concept of number involved are open questions. I will answer to those problems making a formalization of the system and showing how it could be related to a cosmogonic design.

A lógica aristotélica sofreu grandes desenvolvimentos com a escola estóica e outras, incluindo Po... more A lógica aristotélica sofreu grandes desenvolvimentos com a escola estóica e outras, incluindo Porfírio com a sua Isagoge. Logo, no século XII, Pedro Abelardo e outros desenvolveram uma grande discussão arredor do problema dos objectos e do verbo ser. No entanto, podemos afirmar que o maior avance que teve a lógica depois de Aristóteles foi com a eclosão de um grupo de filósofos nos séculos XIII-XIV.

Revista Venezolana De Filosofia, 1999

Boletín de la Asociación Matemática Venezolana, 2006

Circulation and Exchange of goods and technology: signs of dominant ideologies, 2018

The excavations at Tel Burna (southern Israel) have exposed a large public building where cultic ... more The excavations at Tel Burna (southern Israel) have exposed a large public building where cultic activity took place. The finds that were recovered in this complex include imported artifcats from the eastern Mediterranean. In this paper, we will present these finds and discuss how they reflect trade and foreign connections with the eastern Mediterranean to the Southern Levant in the 13th century BCE, as well as their importance for understanding the local material culture and ritual activity.

The 20th century has witnessed a vertiginous development of logic: a discipline that traditionall... more The 20th century has witnessed a vertiginous development of logic: a discipline that traditionally belonged to the domain of philosophy, but whose recent development is due to the use of mathematics as its metalanguage. Considered as one of the greatest of Greek gifts to humanity, logic is now essential as the foundational model for Computer Science. Some scholars assimilate Mathematics and Logic, some think of Logic as part of Mathematics, others include it in Philosophy, and so on. When we were planning this special volume of the Boletín de la Asociación Matemática Venezolana, an article on Mediaeval Logic seemed to be appropriate. This paper is an outline of that field. We follow tradition in starting this history with Aristotle, although pre-Aristotelian logic is of considerable interest, if somewhat controversial. Following Aristotle, we take a brief excursion through Roman and Early Mediaeval logic. We stop in the 13th century AD because of the influence of the work of this period on the 20th century. The natural continuation of Mediaeval Logic occurred in the 1960's when logicians started to base new developments on translated Mediaeval texts. Two further articles dedicated to History of logic will be needed to trace these developments. This paper, then, is an outline of Mediaeval Logic, its origins and its future. 2 Aristotle The main works of philosophical logic in Greek times are due to Aristotle and are collected under the title Organon. Organon means "instrument", the instrument for science, thought of as the way the human being thinks. This collection of Aristotelian works comprises: a) The Categories. b) The Peri Hermeneias (or On the interpretation).

The 20th century has witnessed a vertiginous development of logic: a discipline that traditionall... more The 20th century has witnessed a vertiginous development of logic: a discipline that traditionally belonged to the domain of philosophy, but whose recent development is due to the use of mathematics as its metalanguage. Considered as one of the greatest of Greek gifts to humanity, logic is now essential as the foundational model for Computer Science. Some scholars assimilate Mathematics and Logic, some think of Logic as part of Mathematics, others include it in Philosophy, and so on. When we were planning this special volume of the Boletín de la Asociación Matemática Venezolana, an article on Mediaeval Logic seemed to be appropriate. This paper is an outline of that field. We follow tradition in starting this history with Aristotle, although pre-Aristotelian logic is of considerable interest, if somewhat controversial. Following Aristotle, we take a brief excursion through Roman and Early Mediaeval logic. We stop in the 13th century AD because of the influence of the work of this period on the 20th century. The natural continuation of Mediaeval Logic occurred in the 1960's when logicians started to base new developments on translated Mediaeval texts. Two further articles dedicated to History of logic will be needed to trace these developments. This paper, then, is an outline of Mediaeval Logic, its origins and its future. 2 Aristotle The main works of philosophical logic in Greek times are due to Aristotle and are collected under the title Organon. Organon means "instrument", the instrument for science, thought of as the way the human being thinks. This collection of Aristotelian works comprises: a) The Categories. b) The Peri Hermeneias (or On the interpretation).

Disputatio, 2002

Este apontamento sobre a lógica de Pedro Hispano pretende mostrar alguns dados da sua obra que po... more Este apontamento sobre a lógica de Pedro Hispano pretende mostrar alguns dados da sua obra que podem ser de interesse para um lógico contemporâneo. Não é sem surpresa que um lógico com uma formação matemática olha para o trabalho dos lógicos medievais. Este parece ter uma maior relação com a filosofia da linguagem dos nossos dias do que com as supostas teorias "escuras" e bizantinas com as quais, é dito, perdiam o seu tempo. Comecemos por dizer que a lógica medieval se desenvolveu em diferentes etapas. Uma primeira etapa, denominada de lógica velha (logica vetus), abrange de Boécio a Abelardo e baseia-se fundamentalmente nos comentários e desenvolvimentos das Categorias e dos Tópicos de Aristóteles. Uma segunda etapa da lógica medieval começa com a descoberta e estudo doutras partes do Organon, nomeadamente os Elencos Sofísticos, com o qual se avança para a Lógica Moderna-assim mesmo denominada pelos próprios lógicos medievais. Esta lógica moderna medieval caracteriza-se principalmente pela análise dos termos que conformam a linguagem e não tanto pela análise silogística das proposições. Assim, a lógica passa a ser uma filosofia da linguagem, onde os termos que conformam as proposições são fundamentais para a análise do valor lógico das mesmas. Pretendemos fazer uma breve apresentação das duas obras lógicas de Pedro Hispano que se conhecem e dar alguns elementos que caracterizam a lógica medieval. Damos também uma lista bibliográfica onde se podem encontrar os elementos apresentados aqui.

La Ciudad De Dios-Revista Agustiniana , 2021

de um dos mais relevantes documentos religiosos do Antigo Egipto, a inscrição da Pedra de Chabaka... more de um dos mais relevantes documentos religiosos do Antigo Egipto, a inscrição da Pedra de Chabaka (PCh). Este documento apresenta-se como fundamental no estudo das cosmogonias antigas em geral, e em particular do Antigo Egipto. Como o autor nos diz, o ‘Livro das origens’ foi mandado inscrever em pedra pelo faraó Chabaka (716 -702 a. C.) da XXV dinastia (747 656 a. C.) e colocado no templo de Ptah em Mên* s (p. 15), embora o texto pareça ter sido composto entre o século XIII a XI (p. 16). O autor continua, mostrando a importância não só mitológica e cosmogónica da obra, mas também a relevância politica da mesma, uma vez que evoca a uni* cação do Alto e Baixo Nilo, representado na cosmovisão da obra. Esta edição da Pedra de Chabaka, contém duas partes fundamentais. Na primeira parte, inclui a versão hieroglí* ca e tradução. Segue -se um comentário do ponto de vista da narrativa e dos géneros literários utilizados. Neste comentário discorre o autor sobre a composição e datação da obra....

El agua ha sido un elemento presente en muchas cosmogonías. El agua es necesaria a la vida, sin e... more El agua ha sido un elemento presente en muchas cosmogonías. El agua es necesaria a la vida, sin ella no existiría la vida como la conocemos. Esta percepción sobre el agua es tan antigua como la misma humanidad, haciéndose particularmente importante en pueblos donde ella no abunda, pueblos donde la orografía es desértica o pueblos donde el agua en forma de ríos se hace fundamental a la cosecha y por consiguiente a la vida, como los pueblos del cercano oriente, en particular los pueblos de la región del levante. Siendo esto así, pareciera peculiar la importancia dada por los primeros pensadores griegos, llamados filósofos presocráticos, al elemento agua en su filosofía. Argumentaré que el elemento agua es extraño al pensamiento griego, como elemento primigenio. Para ello discutiré algunos de los textos cosmogónicos griegos y del cercano oriente.

Cadmo: Revista de História Antiga, 2011

A navegação consulta e descarregamento dos títulos inseridos nas Bibliotecas Digitais UC Digitali... more A navegação consulta e descarregamento dos títulos inseridos nas Bibliotecas Digitais UC Digitalis, UC Pombalina e UC Impactum, pressupõem a aceitação plena e sem reservas dos Termos e Condições de Uso destas Bibliotecas Digitais, disponíveis em https://digitalis.uc.pt/pt-pt/termos. Conforme exposto nos referidos Termos e Condições de Uso, o descarregamento de títulos de acesso restrito requer uma licença válida de autorização devendo o utilizador aceder ao(s) documento(s) a partir de um endereço de IP da instituição detentora da supramencionada licença. Ao utilizador é apenas permitido o descarregamento para uso pessoal, pelo que o emprego do(s) título(s) descarregado(s) para outro fim, designadamente comercial, carece de autorização do respetivo autor ou editor da obra. Na medida em que todas as obras da UC Digitalis se encontram protegidas pelo Código do Direito de Autor e Direitos Conexos e demais legislação aplicável, toda a cópia, parcial ou total, deste documento, nos casos em que é legalmente admitida, deverá conter ou fazer-se acompanhar por este aviso. Foram os Hititas Henoteístas? A palavra Siu no contexto do Hitita do Antigo Reino

Interchange in Pre- and Protohistory, BAR S2891, edited by Ana Cruz and Juan F. Gibaja, published by BAR Publishing (Oxford, 2018)., 2018

The excavations at Tel Burna (southern Israel) have exposed a large public building where cultic ... more The excavations at Tel Burna (southern Israel) have exposed a large public building where cultic activity took place. The finds that were recovered in this complex include imported artifcats from the eastern Mediterranean. In this paper, we will present these finds and discuss how they reflect trade and foreign connections with the eastern Mediterranean to the Southern Levant in the 13th century BCE, as well as their importance for understanding the local material culture and ritual activity.

The Assyrian bas-relief in the Gulbenkian ́s Museum is one of its ex-libris. That is one of the 2... more The Assyrian bas-relief in the Gulbenkian ́s Museum is one of its ex-libris. That is one of the 200 bas-relief that covered the walls of Aššurnasirpal II palace in Nimrud. He was King of Assyria in the 9th century BC. This bas-relief like most of those covering the palace walls, displays a cuneiform inscription called The Standard Inscription of Aššurnasirpal II. This paper presents a direct translation from the Gulbenkian’s bas-relief. We include the cuneiform transcription and transliteration as well as English and Portuguese translations. This is not a critical edition, but we compared with other editions of the Standard Inscription. mind other editions.

Any enterprise that encounters multi-sided demands from its customers must develop an agile infra... more Any enterprise that encounters multi-sided demands from its customers must develop an agile infrastructure that enables it to identify and mitigate new kinds of risk to its sustainability. We propose an approach to the modelling and analysis of such organisations that distinguishes two aspects of time: the chronos of objects and processes and the kairos experienced by its customers as subjects. In this approach, the structure of the enterprise is elicited in the form of three articulations, existential, deontic and referential. The composition of these articulations accommodates the structural differences between chronos and kairos by applying two normalisations known as twists. These models and operations instantiate an abstract algebra of considerable theoretical interest, while their computational implementation provides a set of powerful tools for strategic intervention.

Revista Agustiniana-La Ciudad de Dios, 2021

Yo soy la verdad. Alhdɛia en el evangelio de San Juan RESUMEN El presente trabajo analizará el co... more Yo soy la verdad. Alhdɛia en el evangelio de San Juan RESUMEN El presente trabajo analizará el concepto de verdad en el evangelio de San Juan. El análisis se basa en los texto donde la palabra griega ààń0ɛa es usada. Basándonos en su etimología iremos explorando lo que Juan nos quiere decir en cada texto del evangelio. Este artículo no pretende ser exhaustivo desde el punto de vista filosófico-teológico, sólo pretende comentar y extraer una concepción coherente de la verdad en el evangelio de San Juan.

Transcultural Mobilities and Memories/Mobilidades e Memórias Transculturais, 2023

It is well known that Sumerians and Babylonians used a numeration system of base 12 and 60. We st... more It is well known that Sumerians and Babylonians used a numeration system of base 12 and 60. We still have influence of that system in our nowadays counting of the hours of a day, twelve plus twelve, each hour has 60 minute and each minute 60 seconds. Also the circle has 360 degrees. What is not so well known is that the Sumerians in an earlier period used a ternary system of numeration; the first notice about that system is in Thureau-Dangin (1928). Later Diakonoff (1983) described it in good details and recently, Balke (2010) studied the system and described it with more precision. Still the use of this system and the concept of number involved are open questions. I will answer to those problems making a formalization of the system and showing how it could be related to a cosmogonic design.

A lógica aristotélica sofreu grandes desenvolvimentos com a escola estóica e outras, incluindo Po... more A lógica aristotélica sofreu grandes desenvolvimentos com a escola estóica e outras, incluindo Porfírio com a sua Isagoge. Logo, no século XII, Pedro Abelardo e outros desenvolveram uma grande discussão arredor do problema dos objectos e do verbo ser. No entanto, podemos afirmar que o maior avance que teve a lógica depois de Aristóteles foi com a eclosão de um grupo de filósofos nos séculos XIII-XIV.

Revista Venezolana De Filosofia, 1999

Boletín de la Asociación Matemática Venezolana, 2006

Circulation and Exchange of goods and technology: signs of dominant ideologies, 2018

The excavations at Tel Burna (southern Israel) have exposed a large public building where cultic ... more The excavations at Tel Burna (southern Israel) have exposed a large public building where cultic activity took place. The finds that were recovered in this complex include imported artifcats from the eastern Mediterranean. In this paper, we will present these finds and discuss how they reflect trade and foreign connections with the eastern Mediterranean to the Southern Levant in the 13th century BCE, as well as their importance for understanding the local material culture and ritual activity.

The 20th century has witnessed a vertiginous development of logic: a discipline that traditionall... more The 20th century has witnessed a vertiginous development of logic: a discipline that traditionally belonged to the domain of philosophy, but whose recent development is due to the use of mathematics as its metalanguage. Considered as one of the greatest of Greek gifts to humanity, logic is now essential as the foundational model for Computer Science. Some scholars assimilate Mathematics and Logic, some think of Logic as part of Mathematics, others include it in Philosophy, and so on. When we were planning this special volume of the Boletín de la Asociación Matemática Venezolana, an article on Mediaeval Logic seemed to be appropriate. This paper is an outline of that field. We follow tradition in starting this history with Aristotle, although pre-Aristotelian logic is of considerable interest, if somewhat controversial. Following Aristotle, we take a brief excursion through Roman and Early Mediaeval logic. We stop in the 13th century AD because of the influence of the work of this period on the 20th century. The natural continuation of Mediaeval Logic occurred in the 1960's when logicians started to base new developments on translated Mediaeval texts. Two further articles dedicated to History of logic will be needed to trace these developments. This paper, then, is an outline of Mediaeval Logic, its origins and its future. 2 Aristotle The main works of philosophical logic in Greek times are due to Aristotle and are collected under the title Organon. Organon means "instrument", the instrument for science, thought of as the way the human being thinks. This collection of Aristotelian works comprises: a) The Categories. b) The Peri Hermeneias (or On the interpretation).

The 20th century has witnessed a vertiginous development of logic: a discipline that traditionall... more The 20th century has witnessed a vertiginous development of logic: a discipline that traditionally belonged to the domain of philosophy, but whose recent development is due to the use of mathematics as its metalanguage. Considered as one of the greatest of Greek gifts to humanity, logic is now essential as the foundational model for Computer Science. Some scholars assimilate Mathematics and Logic, some think of Logic as part of Mathematics, others include it in Philosophy, and so on. When we were planning this special volume of the Boletín de la Asociación Matemática Venezolana, an article on Mediaeval Logic seemed to be appropriate. This paper is an outline of that field. We follow tradition in starting this history with Aristotle, although pre-Aristotelian logic is of considerable interest, if somewhat controversial. Following Aristotle, we take a brief excursion through Roman and Early Mediaeval logic. We stop in the 13th century AD because of the influence of the work of this period on the 20th century. The natural continuation of Mediaeval Logic occurred in the 1960's when logicians started to base new developments on translated Mediaeval texts. Two further articles dedicated to History of logic will be needed to trace these developments. This paper, then, is an outline of Mediaeval Logic, its origins and its future. 2 Aristotle The main works of philosophical logic in Greek times are due to Aristotle and are collected under the title Organon. Organon means "instrument", the instrument for science, thought of as the way the human being thinks. This collection of Aristotelian works comprises: a) The Categories. b) The Peri Hermeneias (or On the interpretation).

Disputatio, 2002

Este apontamento sobre a lógica de Pedro Hispano pretende mostrar alguns dados da sua obra que po... more Este apontamento sobre a lógica de Pedro Hispano pretende mostrar alguns dados da sua obra que podem ser de interesse para um lógico contemporâneo. Não é sem surpresa que um lógico com uma formação matemática olha para o trabalho dos lógicos medievais. Este parece ter uma maior relação com a filosofia da linguagem dos nossos dias do que com as supostas teorias "escuras" e bizantinas com as quais, é dito, perdiam o seu tempo. Comecemos por dizer que a lógica medieval se desenvolveu em diferentes etapas. Uma primeira etapa, denominada de lógica velha (logica vetus), abrange de Boécio a Abelardo e baseia-se fundamentalmente nos comentários e desenvolvimentos das Categorias e dos Tópicos de Aristóteles. Uma segunda etapa da lógica medieval começa com a descoberta e estudo doutras partes do Organon, nomeadamente os Elencos Sofísticos, com o qual se avança para a Lógica Moderna-assim mesmo denominada pelos próprios lógicos medievais. Esta lógica moderna medieval caracteriza-se principalmente pela análise dos termos que conformam a linguagem e não tanto pela análise silogística das proposições. Assim, a lógica passa a ser uma filosofia da linguagem, onde os termos que conformam as proposições são fundamentais para a análise do valor lógico das mesmas. Pretendemos fazer uma breve apresentação das duas obras lógicas de Pedro Hispano que se conhecem e dar alguns elementos que caracterizam a lógica medieval. Damos também uma lista bibliográfica onde se podem encontrar os elementos apresentados aqui.

La Ciudad De Dios-Revista Agustiniana , 2021

de um dos mais relevantes documentos religiosos do Antigo Egipto, a inscrição da Pedra de Chabaka... more de um dos mais relevantes documentos religiosos do Antigo Egipto, a inscrição da Pedra de Chabaka (PCh). Este documento apresenta-se como fundamental no estudo das cosmogonias antigas em geral, e em particular do Antigo Egipto. Como o autor nos diz, o ‘Livro das origens’ foi mandado inscrever em pedra pelo faraó Chabaka (716 -702 a. C.) da XXV dinastia (747 656 a. C.) e colocado no templo de Ptah em Mên* s (p. 15), embora o texto pareça ter sido composto entre o século XIII a XI (p. 16). O autor continua, mostrando a importância não só mitológica e cosmogónica da obra, mas também a relevância politica da mesma, uma vez que evoca a uni* cação do Alto e Baixo Nilo, representado na cosmovisão da obra. Esta edição da Pedra de Chabaka, contém duas partes fundamentais. Na primeira parte, inclui a versão hieroglí* ca e tradução. Segue -se um comentário do ponto de vista da narrativa e dos géneros literários utilizados. Neste comentário discorre o autor sobre a composição e datação da obra....

El agua ha sido un elemento presente en muchas cosmogonías. El agua es necesaria a la vida, sin e... more El agua ha sido un elemento presente en muchas cosmogonías. El agua es necesaria a la vida, sin ella no existiría la vida como la conocemos. Esta percepción sobre el agua es tan antigua como la misma humanidad, haciéndose particularmente importante en pueblos donde ella no abunda, pueblos donde la orografía es desértica o pueblos donde el agua en forma de ríos se hace fundamental a la cosecha y por consiguiente a la vida, como los pueblos del cercano oriente, en particular los pueblos de la región del levante. Siendo esto así, pareciera peculiar la importancia dada por los primeros pensadores griegos, llamados filósofos presocráticos, al elemento agua en su filosofía. Argumentaré que el elemento agua es extraño al pensamiento griego, como elemento primigenio. Para ello discutiré algunos de los textos cosmogónicos griegos y del cercano oriente.

Cadmo: Revista de História Antiga, 2011

A navegação consulta e descarregamento dos títulos inseridos nas Bibliotecas Digitais UC Digitali... more A navegação consulta e descarregamento dos títulos inseridos nas Bibliotecas Digitais UC Digitalis, UC Pombalina e UC Impactum, pressupõem a aceitação plena e sem reservas dos Termos e Condições de Uso destas Bibliotecas Digitais, disponíveis em https://digitalis.uc.pt/pt-pt/termos. Conforme exposto nos referidos Termos e Condições de Uso, o descarregamento de títulos de acesso restrito requer uma licença válida de autorização devendo o utilizador aceder ao(s) documento(s) a partir de um endereço de IP da instituição detentora da supramencionada licença. Ao utilizador é apenas permitido o descarregamento para uso pessoal, pelo que o emprego do(s) título(s) descarregado(s) para outro fim, designadamente comercial, carece de autorização do respetivo autor ou editor da obra. Na medida em que todas as obras da UC Digitalis se encontram protegidas pelo Código do Direito de Autor e Direitos Conexos e demais legislação aplicável, toda a cópia, parcial ou total, deste documento, nos casos em que é legalmente admitida, deverá conter ou fazer-se acompanhar por este aviso. Foram os Hititas Henoteístas? A palavra Siu no contexto do Hitita do Antigo Reino

Interchange in Pre- and Protohistory, BAR S2891, edited by Ana Cruz and Juan F. Gibaja, published by BAR Publishing (Oxford, 2018)., 2018

The excavations at Tel Burna (southern Israel) have exposed a large public building where cultic ... more The excavations at Tel Burna (southern Israel) have exposed a large public building where cultic activity took place. The finds that were recovered in this complex include imported artifcats from the eastern Mediterranean. In this paper, we will present these finds and discuss how they reflect trade and foreign connections with the eastern Mediterranean to the Southern Levant in the 13th century BCE, as well as their importance for understanding the local material culture and ritual activity.

The Assyrian bas-relief in the Gulbenkian ́s Museum is one of its ex-libris. That is one of the 2... more The Assyrian bas-relief in the Gulbenkian ́s Museum is one of its ex-libris. That is one of the 200 bas-relief that covered the walls of Aššurnasirpal II palace in Nimrud. He was King of Assyria in the 9th century BC. This bas-relief like most of those covering the palace walls, displays a cuneiform inscription called The Standard Inscription of Aššurnasirpal II. This paper presents a direct translation from the Gulbenkian’s bas-relief. We include the cuneiform transcription and transliteration as well as English and Portuguese translations. This is not a critical edition, but we compared with other editions of the Standard Inscription. mind other editions.

Any enterprise that encounters multi-sided demands from its customers must develop an agile infra... more Any enterprise that encounters multi-sided demands from its customers must develop an agile infrastructure that enables it to identify and mitigate new kinds of risk to its sustainability. We propose an approach to the modelling and analysis of such organisations that distinguishes two aspects of time: the chronos of objects and processes and the kairos experienced by its customers as subjects. In this approach, the structure of the enterprise is elicited in the form of three articulations, existential, deontic and referential. The composition of these articulations accommodates the structural differences between chronos and kairos by applying two normalisations known as twists. These models and operations instantiate an abstract algebra of considerable theoretical interest, while their computational implementation provides a set of powerful tools for strategic intervention.

In former research papers I proposed a stative semantic for the non-augmented epic aorist, specif... more In former research papers I proposed a stative semantic for the non-augmented epic aorist, specifically for the verb γίγνομαι. My proposal was centred on evidences from Hesiod’s Theogony. Those evidences were supported by the research done by other scholar on the existence of preterite forms with stative value in Hittite texts. I showed, also, the parallelism of use of stative verbal forms in different cosmogonies, particularly in the Vedic Hymns, the Babylonian First Tablet of the Creation and the Genesis. In a natural way, it is valid to question on the semantic attributed to the aorist forms found in the cosmogony described in the first chapter of St. John’s Gospel. Some critical apparatus propose the need for a correction of some non-augmented aorist forms into augmented ones or even into present forms. Those suggestions are proposed in order to explain some ‘abnormal’ consecutio temporum in the text. Nevertheless, if we accept that there is a semantic continuity between the ancient non-augmented stative aorist and the augmented form, it is possible to explain that ‘abnormality’. In this paper I will elucidate and discuss possible answers to those problems.

The Hittite text CTH 324, known as the Telepinu's Myth, tells the story of the disappeared god Te... more The Hittite text CTH 324, known as the Telepinu's Myth, tells the story of the disappeared god Telepinu. This myth is related to the myths of katabasis describing the visit of a god to the netherworld, like the Sumerian visit of Innana to the netherworld. The difference is that in the Telepinu case, the god himself hides in a swamp that can be part of the netherworld. The purpose of Telepinu's action is not clear, but there are many cosmic consequences to his action. The nature has no way to procreate, the mothers reject their babychild, and the cosmos seems to be mal-functioning. We know that Telepinu was anger when decided to hide. The assembly of the gods needs to find Telepinu in order to re-establish the order. A final resource used by the assembly of the gods to solve this almost eschatological phenomenon is to summon the primeval deity Hanna-hanna. After her intervention Telepinu is found and the cosmos heals. I argue that in the Hittite culture, the illness of a god implies the illness of the cosmos and his healing shows up as normal cosmic order.

It is well known that Sumerians and Babylonians used a numeration system of base 12 and 60. We st... more It is well known that Sumerians and Babylonians used a numeration system of base 12 and 60. We still have influence of that system in our nowadays counting of the hours of a day, twelve plus twelve, each hour has 60 minute and each minute 60 seconds. Also the circle has 360 degrees. What is not so well known is that the Sumerians in an earlier period used a ternary system of numeration; the first notice about that system is in Thureau-Dangin (1928). Later Diakonoff (1983) described it in good details and recently, Balke (2010) studied the system and described it with more precision. Still the use of this system and the concept of number involved are open questions. I will answer to those problems making a formalization of the system and showing how it could be related to a cosmogonic design.

Um dos rituais mais antigos da literatura hitita é aquele que realiza o sacerdote do deus da torm... more Um dos rituais mais antigos da literatura hitita é aquele que realiza o sacerdote do deus da tormenta para conter as águas e evitar o fim-do-mundo. Este ritual encontra-se descrito em tabuinhas com versão bilingue, hatiano-hitita. O original é da mitologia hatiana e a versão hitita, sendo uma tradução livre deve ter sido realizada em época em que o hatiano era já uma lingua de pouco uso e quase que incompreensível para os hititas, provavelmente no império médio.

Os versos 116-126 da Teogonia de Hesíodo lidos com olhos matemáticos. Hesíodo é considerado junto... more Os versos 116-126 da Teogonia de Hesíodo lidos com olhos matemáticos. Hesíodo é considerado junto com Homero os mais antigos poetas gregos. Ao menos três obras são consideradas como pertencentes à Hesíodo, Teogonia, Trabalhos e dias e O escudo de Heracles. A Teogonia para além de conter a genealogia dos deuses gregos, também contém uma cosmogonia ou explicação da origem do mundo. Esta cosmogonia apresenta certas particularidades, como a menção a um objecto denominado chaos, sobre o qual muito se tem escrito. Ferécides de Siro identifica o chaos com a água, Aristóteles identifica-o com o espaço criado na separação do céu e a terra e posteriormente vai adquirir o significado oposto a 'ordem', significado que mantém-se comummente. Investigadores actuais como M. L. West seguem Aristóteles ou alguma variação da sua posição. Para interpretar o significado de chaos proponho uma leitura a pensar na teoria dos conjuntos, e usando essa mesma leitura continuarei a reler os outros pontos da cosmogonia.

The main purpose of this book is to show that the structure of Hesiod’s Cosmos stands on a philos... more The main purpose of this book is to show that the
structure of Hesiod’s Cosmos stands on a philosophical
reflection. The author made this analysis from a linguistic and
mathematic point of view, offering models that explain
concepts like Chaos or Moira and proposing a new reading
for specific verbal forms. The author uses a set theoretical
approach, logical and linguistic analysis of texts in a
comparative way, ending with a brief comparison between
Hesiod and some of the pre-Socratics. This makes this work
a book unique for philosophers, mathematicians, linguists,
classicists and any one interested in such topics.

“Mobilidades e Memórias Transculturais / Transcultural Mobilities and Memories”, 2023

H2D: digital humanities journal 3/1, 2021