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Ian Bisset Mueller (February 5, 1938 - August 6, 2010) was an American philosopher. He studied ancient Greek philosophy of science and focused on the reception of Plato and Aristotle in late antiquity. [1]
Ian Mueller authored Philosophy of Mathematics and Deductive Structure in Euclid's "Elements" (1981), which is considered standard work in this field; he was also the editor, translator and annotator of 10 volumes in the series Ancient Commentators on Aristotle. Mueller also wrote more than 70 articles on ancient Greek mathematics, cosmology and astronomy. [2]
Mueller was well-respected among his colleagues, not least because he outperformed them in mathematics. [3]
Ian Mueller received his B.A. summa cum laude in 1959 from the Princeton University, and his M.A. (1961) and Ph.D. (1964) from Harvard University. He taught at the University of Illinois, Urbana, and later joined the University of Chicago faculty in 1967. Mueller served there as chair of the Philosophy Department from 1980 to 1981.
Mueller died in 2010 and was survived by his wife Janel and two daughters.
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Aristotle was an Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology and the arts. As the founder of the Peripatetic school of philosophy in the Lyceum in Athens, he began the wider Aristotelian tradition that followed, which set the groundwork for the development of modern science.
Ammonius Saccas was a Hellenistic Platonist self-taught philosopher from Alexandria, generally regarded as the precursor of Neoplatonism and/or one of its founders. He is mainly known as the teacher of Plotinus, whom he taught from 232 to 242. He was undoubtedly the biggest influence on Plotinus in his development of Neoplatonism, although little is known about his own philosophical views. Later Christian writers stated that Ammonius was a Christian, but it is now generally assumed that there was a different Ammonius of Alexandria who wrote biblical texts.
Euclid was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.
The history of science covers the development of science from ancient times to the present. It encompasses all three major branches of science: natural, social, and formal.
Pythagoras of Samos was an ancient Ionian Greek philosopher, polymath and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos or the city of Tyre. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he ever advocated complete vegetarianism; he was said to have advised athletes to "feast on flesh" exclusively.
Proclus Lycius, called Proclus the Successor, was a Greek Neoplatonist philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully developed systems of Neoplatonism and, through later interpreters and translators, exerted an influence on Byzantine philosophy, Early Islamic philosophy, and Scholastic philosophy.
Thales of Miletus was an Ancient Greek pre-Socratic philosopher from Miletus in Ionia, Asia Minor. Thales was one of the Seven Sages, founding figures of Ancient Greece, and credited with the saying "know thyself" which was inscribed on the Temple of Apollo at Delphi.
Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and repeatability of findings are used to try to ensure the validity of scientific advances.
Simplicius of Cilicia was a disciple of Ammonius Hermiae and Damascius, and was one of the last of the Neoplatonists. He was among the pagan philosophers persecuted by Justinian in the early 6th century, and was forced for a time to seek refuge in the Persian court, before being allowed back into the empire. He wrote extensively on the works of Aristotle. Although his writings are all commentaries on Aristotle and other authors, rather than original compositions, his intelligent and prodigious learning makes him the last great philosopher of pagan antiquity. His works have preserved much information about earlier philosophers which would have otherwise been lost.
Ancient Greek philosophy arose in the 6th century BC, marking the end of the Greek Dark Ages, a period lasting more than 1,800 years. Greek philosophy continued throughout the Hellenistic period and the period in which Greece and most Greek-inhabited lands were part of the Roman Empire. Philosophy was used to make sense of the world using reason. It dealt with a wide variety of subjects, including astronomy, epistemology, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics.
Sir Thomas Little Heath was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. He was educated at Clifton College. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes of Syracuse into English.
Aristotelianism is a philosophical tradition inspired by the work of Aristotle, usually characterized by deductive logic and an analytic inductive method in the study of natural philosophy and metaphysics. It covers the treatment of the social sciences under a system of natural law. It answers why-questions by a scheme of four causes, including purpose or teleology, and emphasizes virtue ethics. Aristotle and his school wrote tractates on physics, biology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, and government. Any school of thought that takes one of Aristotle's distinctive positions as its starting point can be considered "Aristotelian" in the widest sense. This means that different Aristotelian theories may not have much in common as far as their actual content is concerned besides their shared reference to Aristotle.
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly attested from the late 7th century BC to the 6th century AD, around the shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire region, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of proofs is an important difference between Greek mathematics and those of preceding civilizations.
Science in classical antiquity encompasses inquiries into the workings of the world or universe aimed at both practical goals as well as more abstract investigations belonging to natural philosophy. Classical antiquity is traditionally defined as the period between 8th century BC and the 6th century AD, and the ideas regarding nature that were theorized during this period were not limited to science but included myths as well as religion. Those who are now considered as the first scientists may have thought of themselves as natural philosophers, as practitioners of a skilled profession, or as followers of a religious tradition. Some of the more widely known figures active in this period include Hippocrates, Aristotle, Euclid, Archimedes, Hipparchus, Galen, and Ptolemy. Their contributions and commentaries spread throughout the Eastern, Islamic, and Latin worlds and contributed to the birth of modern science. Their works covered many different categories including mathematics, cosmology, medicine, and physics.
William Keith Chambers Guthrie, usually cited as W. K. C. Guthrie, was a Scottish classical scholar, best known for his History of Greek Philosophy, published in six volumes between 1962 and his death. He served as Laurence Professor of Ancient Philosophy at the University of Cambridge from 1952 to 1973 and as master of Downing College, Cambridge from 1957 to 1972.
John Corcoran was an American logician, philosopher, mathematician, and historian of logic. He is best known for his philosophical work on concepts such as the nature of inference, relations between conditions, argument-deduction-proof distinctions, the relationship between logic and epistemology, and the place of proof theory and model theory in logic. Nine of Corcoran's papers have been translated into Spanish, Portuguese, Persian, and Arabic; his 1989 "signature" essay was translated into three languages. Fourteen of his papers have been reprinted; one was reprinted twice.
Medieval philosophy is the philosophy that existed through the Middle Ages, the period roughly extending from the fall of the Western Roman Empire in the 5th century until after the Renaissance in the 13th and 14th centuries. Medieval philosophy, understood as a project of independent philosophical inquiry, began in Baghdad, in the middle of the 8th century, and in France, in the itinerant court of Charlemagne, in the last quarter of the 8th century. It is defined partly by the process of rediscovering the ancient culture developed in Greece and Rome during the Classical period, and partly by the need to address theological problems and to integrate sacred doctrine with secular learning.
The Italian School of Pre-Socratic philosophy refers to Ancient Greek philosophers in Italy or Magna Graecia in the 6th and 5th century BC. The doxographer Diogenes Laërtius divides pre Socratic philosophy into the Ionian and Italian School. According to classicist Jonathan Barnes, "Although the Italian 'school' was founded by émigrés from Ionia, it quickly took on a character of its own." According to classicist W. K. C. Guthrie, it contrasted with the "materialistic and purely rational Milesians."