John Corcoran Obituary | In addition to his work as a logician, philosopher, and mathematician, John Corcoran was also an American logic historian. Concepts such as the nature of inference, linkages between conditions and arguments, proof-deduction-proof differences.
the relationship between logic/epistemology, the location of proof theory/model theory in logic are among his most well-known philosophical contributions.
Nine of Corcoran’s papers have been translated into Spanish, Portuguese, Persian, and Arabic; his 1989 “signature” essay has been translated into three different languages. In total, fourteen of his works have been reprinted, with one paper being reproduced twice.
My heartfelt condolences go out to John’s family and friends. John passed away on 8 January 2021.Teaching and research were equally important in John’s academic career. He put all of his effort into both up until the point where he fell ill.
While he was working on new articles and abstracts, he was also coordinating translations of some of his papers into languages such as Turkish, Arabic and German. Former pupils from throughout the world are part of his extended family.
On the day before he became unwell, the weather in Florida was lovely. He went swimming, walked with me, worked on his laptop, and then we had a leisurely lunch in our tropical garden. It was a wonderful day. John lived a long and fulfilling life, fully immersed in the events of this present moment.
In 1970, John Corcoran joined the staff of the University at Buffalo’s Philosophy Department (SUNY). In his work on the history of logic, Corcoran covers nearly the whole span of the field’s history.
Aristotle, the Stoics, William of Ockham, Giovanni Girolamo Saccheri, George Boole, and the American Postulate Theorists are some of the philosophers he has discussed in the past.
An crucial part of all of his mathematical work is mathematics’ foundational theory of the theory of strings, which is the subject of much of his work in mathematical logic and provides the necessary framework for all of his other mathematical work.
Corcoran’s philosophy of mathematics is influenced by a subtle and inclusive Platonism that attempts to account for all aspects of mathematical and logical experience. “
His work on Aristotle’s logic of the Prior Analytics is recognised as remarkably accurate both to the Greek text and to the historical setting of the time.Numerous further investigations have been built on top of it.
There are many applications of his mathematical conclusions on character-string theories, which are sciences of strings of characters over finite alphabets, in logic and formal linguistics as well as in computer science. “
In 1956, Corcoran received a degree in Advanced Curriculum Engineering from the Baltimore Polytechnic Institute, and in 1959, he received a BES in Mechanical Engineering from Johns Hopkins University.
In 1963, he received a PhD in philosophy from John Hopkins University after completing a brief stint as an engineer.
For his post-doctoral studies in mathematics, he attended the University of California, Berkeley, in 1964 and the Yeshiva University in 1964, respectively Generic Structure of Two-Valued logics was the subject of his dissertation.
He was taught logic by Albert Hammond, who was also his first teacher. Aristotle and Plato were taught to Corcoran by Ludwig Edelstein. Joseph Ullian and Richard Wiebe were his second and third logic teachers, respectively.
Dr. Robert McNaughton served as Corcoran’s dissertation advisor. Raymond Smullyan and Martin Davis taught Corcoran at Yeshiva University in New York City.
At the University of Pennsylvania, Corcoran’s dissertation was supervised by a Professor of Computer and Information Science, who hired him into a tenure-track job.
In his work on the history of logic, Corcoran covers nearly the whole span of the field’s history. There have been several topics that he has touched on, including Aristotle, the Stoics, William of Ockham and Giovanni Girolamo Saccheri.
He has also discussed Richard Dedekind and Gottlob Frege as well as Charles Sanders Peirce and Clarence Irving Lewis as well as the American Postulate Theorists.
Aristotle’s Prior Analytics, interpreted by Timothy Smiley in 1972, has been judged to be more accurate to the Greek text and the historical context than prior readings.
Edgar Andrade, George Boger, Manuel Correia, Paolo Crivelli, Newton da Costa, Catarina Dutilh, Paolo Fait, Nicolas Fillion, James Gasser, Klaus Glashoff, John Martin, Mary Mulhern, Michael Scanlan, Robin Smith.
Neil Tennant, and others have used it as a starting point for further research. Prior Analytics Book A by Gisela Striker and Robin Smith’s 1989 translation of the Prior Analytics used this term.
It was his 1980 reconstruction of Boole’s original 1847 system that uncovered previously undiscovered gaps and mistakes in Boole’s work, and confirmed Boole’s reasoning as essentially Aristotelian.
Boolean logic is revealed to be important to Boole’s theory of logic by a 2003 article that compares and critiques Aristotelian logic and Boolean logic systematically.
According to Corcoran, Boole endorsed Aristotle’s reasoning to the fullest extent possible. In his work, Boole did not dispute a single point made by Aristotle.
but he did “go under, over, and beyond” Aristotle’s logic by providing it with a mathematical foundation involving equations, expanding the class of problems it could treat to validity assessment.
he added solving equations and expanding the range of applications it could handle, for example, going from propositions having only two terms to those having arbitrarily many.
Boole’s ‘disagreements,’ if one can call them that, are about what Aristotle did not say, rather than what Aristotle had stated.
Aristotle’s four propositional forms were reduced by Boole in the realm of foundations to one single form, that of equations, which was a novel idea in and of itself.
As a second example, Boole’s theory that Aristotle’s rules of inference must be supplemented with rules for solving equations was a breakthrough idea in the field of logic.
Aristotle could only deal with two-term subject-predicate arguments, whereas Boole’s approach could deal with multi-term propositions and arguments.
No square that is a quadrangle is a rhombus that is a rectangle, for example, could be deduced using Aristotle’s approach, nor could “No rhombus that is a rectangle” be deduced using Aristotle’s system.
During the late 1970s and early 1980s, he collaborated with Alfred Tarski to produce publications on Tarski’s work and to the 2007 article Notes on the Foundation of Logics and Metalogic:
Aristotle, Boole and Tarski, which traces Aristotelian and Boolean ideas in Tarski’s work and substantiates his status as a founding figure in logic on the same level as Aristotle and Boole.
It is not uncommon for Corcoran’s articles and reviews to have been co-authored with colleagues and students. For Corcoran, all information, including logical knowledge, is deeply and fundamentally personal.
However, he also emphasises the value of communities of knowers and how much each individual may profit from critical cooperation with other objective researchers in their personal search for truth.
A society of philosophers, historians, linguists, logicians, and mathematicians dedicated to the study of the origin of logic has been led by him for more than 40 years.
“Aristotle’s Logic in the University of Buffalo’s Department of Philosophy,” Ideas y Valores: Revista Colombiana de Filosofa 140 99–117 summarises the accomplishments of this group.
In the 1999 volume of History and Philosophy of Logic, there is a complete list of John Corcoran’s writings up to 2000, as well as an expository article titled “The Work of John Corcoran: An Appreciation.”
Additionally, there are essays about his work in a 2007 volume released by the University of Santiago de Compostela Press titled “Corcoran in Spanish,” “Corcoran the Mathematician,” “Corcoran the Philosopher,” and “Corcoran in Spanish.”
In the article “Methodological Practice and Complementary Concepts of Logical Consequence: Tarski’s Model-Theoretic Consequence and Corcoran’s Information-Theoretic Consequence”, which won the 2009 Ivor Grattan-Guinness Award for the History and Philosophy of Logic, José M. Sagüillo discusses Corcoran’s 1990s work on information.