INTERVIEW WITH JOHN CORCORAN

INTERVIEW WITH JOHN CORCORAN DRAFT 9 092417 ATHANASIOS CHRISTACOPOULOS: First of all I must say that it is an honour to have an interview with one of the leading personalities in logic, both ancient and modern. I would like to begin our conversation with your first scientific interests that shaped your way to research on logic—mathematical, historical, and philosophical—till the moment you said to yourself “I have something new to say”. JOHN CORCORAN: The honour is mine, especially since the interviewer is such a master himself. Your wonderful question would get different answers—all tentative—at different times. Now, I think back to the late 1960s. My first published paper “Three logical theories”, offers rationales for logical-system properties such as weak completeness, strong completeness, deductive completeness, various forms of compactness, consistency, and soundness, and the like. We start with an interpreted language that we use to communicate: (1) to formulate hypotheses to be settled true or false, (2) to formulate premise-conclusion arguments to be settled valid or invalid, and (3) to formulate argumentations to be settled cogent or fallacious. Some of us pursuing the first stage become interested in tautologies in the broad sense. We construct a logical system to codify the language’s tautologies. Our goal would be weak completeness: a codification of all the language’s tautologies. Frege, Russell, and Quine were here. Some of us pursuing the second stage, which is still logic in a narrow sense, become interested in valid arguments. We construct a logical system to codify the language’s valid arguments. Our goal would be strong completeness: a codification of all the language’s valid arguments. Hilbert, Gödel, and Tarski could be here. Now pursuing the third stage, which is logic in a broader sense that includes epistemic and pragmatic aspects, some of us become interested in argumentations in my recommended sense. We construct a logical system to codify the language’s cogent argumentations: those that produce knowledge that their conclusions follow from their respective premises. Our goal would be deductive completeness: a codification of all ways to deduce a given conclusion from given premises. Jaskowski, Gentzen, and Bourbaki could be here. I wrote early drafts for my graduate logic courses. One goal was to take the alienating and mystifying mumbo-jumbo hocus-pocus out of logic. I wanted to begin the process of demystifying logic. I tried to connect my students to the reality logic was about so they could get traction and be able to unmask the authoritarian charlatans hiding behind pompous jargon. I wanted to help them see logic as a dynamic, growing field answering to felt human needs. To overcome alienation students must see themselves as creating logic for their own individually felt purposes. Other things that gave me confidence that there were important projects for me in logic were my observations (1) that Russell-type logicism was based on misunderstanding and rationalization and (2) that Łukasiewicz-type interpretations of Aristotle overlooked (and kept readers from seeing) central points such as that logic, specifically Aristotle’s logic, is about proof. I saw very clearly that Russell and Łukasiewicz were more concerned to gain converts by intimidation and obfuscation than they were in seeking clarity and truth. Why should they seek what they thought they already had? The more I realized that my views were in the minority the more confidence I had in my vocation. 1 Needless to say, the fact that I had studied and conferred with some the most competent and accomplished logicians in the world did not hurt. ATHANASIOS CHRISTACOPOULOS: Do you believe that truth or proof sets one free? JOHN CORCORAN: The wisdom and the clever ambiguity of your wording did not escape my notice or admiration. There are several points of resonance with my writings here. You already know that Tarski and I discussed the slogan “Truth will set you free”. We passed over the point that the slogan is addressed to people who are not free. Tarski’s view was that it was misleading and misguided if not plain false: he thought that freedom was a prerequisite for being able to gain knowledge of truth. From his perspective the slogan has things backward. Tarski’s slogan would be more like “Freedom will bring you truth”. With full appreciation and agreement, I took a complementary tack. My view was that the slogan was misleading and misguided for another reason too. It implies that possession of (belief in) truth can somehow break the chains of intellectual bondage. My view is that belief can be bondage and that doubt is essential for intellectual freedom. This might have been the downfall of Russell and Łukasiewicz. As you know I touched on these points in several places including my “Farewell”, my “Inseparability”, and my “Investigation of knowledge and opinion” written with my friend and former student Professor Idris Samawi Hamid, the Islamic scholar. Further resonances with my epistemological writings arise from considering the expression, not as a slogan, but in its historical context as a philosophical statement: “You will know the truth and the truth will set you free”. The first clause presupposes some of the most basic premises of my epistemology: e.g., that truth is distinct from knowledge, that truth is prior to knowledge, that knowledge requires knowers whereas truth doesn’t—to mention three. Given the first clause, the second could be taken to mean “knowledge will set you free”, which is close to the enlightenment motto “knowledge is power”. It is ironic, to say the least, given the broader religious context, that the first clause is “You will know the truth” and not “You will believe the truth”. The latter is how it is often taken. In fact, for many religious people belief is superior to knowledge: belief carries rewards that knowledge lacks. Some accept bribes to believe, or to pretend to believe. Here we see the conflict between the anti-scientific religious and the anti-religious scientists who take knowledge to be superior to belief. Although I don’t read historical linguistics, my guess is that there is a mountain of literature on the passage being discussed: “You will know the truth and the truth will set you free”. Your own insightful expansion of “truth will set you free” to “truth or proof will set you free” resonates with Tarski’s classic essay “Truth and proof”, which I have cited several times. It also calls to mind the Peter Andrews book Truth through proof, which I reviewed. The lessons of the Tarski essay, well learned by Andrews, who probably did not need Tarski’s instruction, is that knowledge of truth is gained though proof: proof is not manipulation of meaningless syntactic symbols—as the manipulists, or strict formalists, would have it. Beyond that is Tarski’s technical point that some arithmetic truths are unprovable: because arithmetic provability is arithmetically definable whereas arithmetic truth, although intuitively clear, is not arithmetically definable. 2 Before wrapping up my answer, I would like to remind myself and your readers of three points I have made several times. First, belief can be an obstacle to finding a proof because one of the marks of proof is its ability to resolve doubt. Second, we usually don’t try to prove propositions we don’t believe or at least suspect to be true. Third, the attempt to find proof often leads to doubts we never would have had. If you have a treasured belief you would hate to be without, do not try to prove it. There are many other rich veins in this goldmine of a question. ATHANASIOS CHRISTACOPOULOS: How did you get interested in Aristotle’s logic? And what led you to master the daunting and forbidding Łukasiewicz treatise? And why were you so suspicious of the Łukasiewicz approach? JOHN CORCORAN: When I was an undergraduate engineering-science student at Johns Hopkins University in the late 1950s, my first logic teacher had high praise for Aristotle and Boole. I had a scholarship that covered my undergraduate tuition and gave me credit in the Bookstore to pay for my books, instruments, and supplies. At the end of one semester there was enough money left in the account for me to buy inexpensive editions of Aristotle’s Prior Analytics and Boole’s Laws of Thought. I found these books fascinating but virtually impenetrable, except in broad outline. In the late 1950s and early 1960s, I took several symbolic and mathematical logic courses. I never took a course in history of logic. Without realizing it, I formulated my own philosophy of logic, with no intention to become a historian of logic: I was a mainstream contemporary mathematical and philosophical logician. Nevertheless, over the years I would come back again and again to one or the other of these tantalizingly obscure masterpieces. I came to notice that Aristotle had a theory of demonstrations as logical deductions from experientially known axioms and that Boole had an interpretation of Aristotle’s theory of deduction that made perfect sense to me—at least in broad outline. When he read Aristotle, Boole was a celebrated mathematician: self-taught and totally innocent of the corrupting influence of professional logicians and scholars. He was a sincere and gifted person with unusual maturity, independence, and common sense—not to mention his thirst for knowledge. In answering your question I see for the first time that in broad outline Boole’s interpretation of Aristotle was amazingly close to mine. Boole had Aristotle using rules of deduction to deduce categorical conclusions from categorical premises—no truth-functional combinations of categoricals and no propositional logic. What kept me from seeing this before was that Boole had no interest in explaining what Aristotle had done: Boole was obsessed with remaking Aristotle as an English algebraist—much as Łukasiewicz was obsessed with remaking Aristotle as a Russellian logicist. One thing that kept me moving more or less in the right direction was my dedication to letting Aristotle speak for himself to me. I followed this rule in studying other logicians including Boole and Łukasiewicz—two dedicated geniuses whose real work is still undervalued and not understood. Although I had spent many hours with Aristotle and Boole, and although I found Łukasiewicz unconvincing and untrustworthy, it did not occur to me that I had anything to say about Aristotle until 1970 when I discovered Aristotle’s natural-deduction system. 3 This brings me to the last part of your three-part question: why were you so suspicious of the Łukasiewicz approach? I could write an essay on this. But I will limit myself to two points. First, his treatise did not engage with the readers respecting their autonymy as Boole’s did. Łukasiewicz wanted to browbeat his readers into accepting his views. Second, Łukasiewicz said that Aristotle never revealed the purpose of the Analytics. Aristotle’s first sentence says that his work concerns proof. Łukasiewicz was so blinded by his own convictions that he could not see what was there in plain sight. ATHANASIOS CHRISTACOPOULOS: With regard to reception of your work, what were your biggest disappointments and what were your most pleasant surprises? JOHN CORCORAN: Every scholar should be asked this question. Of my many disappointments, two stand out: the delayed acceptance my discovery of Aristotle’s natural-deduction system and almost total ignoring of my work on string theory. Of course I am talking about acceptance by the community of scholars, not by journals. The editor of the journal to which “Aristotle’s natural-deduction system” was sent promptly rejected it with a short note saying there is no such thing as natural deduction. In contrast “String theory” was promptly accepted in a long letter that said, among other things, that the footnotes alone gave a useful survey of the history and philosophy of the subject. When I started publishing on Aristotle in the early 1970s, I naively thought the CorcoranSmiley approach would be quickly accepted—after a short period in which Łukasiewicz supporters would argue vigorously against it, only making its merits and Łukasiewicz’s flaws more evident. But over fifteen years passed before Aristotle’s natural-deduction system got significant recognition, largely due to Robin Smith’s acceptance of it for his 1989 translation of Prior Analytics. As far as string theory is concerned the sad story still lacks a belated but happy ending. I now see this work began in the late 1950s long before I joined the Department of Linguistics and the Department of Computer and Information Science at the University of Pennsylvania in the mid-1960s. String theory is the mathematics underlying human and machine manipulation of symbols, uninterpreted syntactic characters. Philosophically, it undermines the philosophy called “manipulism”, or “strict formalism”, by exhibiting the contentual mathematics formalism presupposes. Students and colleagues in both departments realized the foundational importance of the subject and joined me in working on it. My 1974 paper “String theory” is co-written with two of my University of Pennsylvania PhDs, one from Linguistics, William Frank, and one from Computer and Information Science, Michael Maloney. This paper is the first to treat this subject since the two ground-breaking works in the 1930s: one by Tarski and one by Hermes. This paper builds on, combines, and unifies the Tarski and Hermes approaches. In fact, it shows that the two approaches, though conceptually distinct, lead to definitionally equivalent theories. Unfortunately, it is still almost without readers as is the case with the passages on string theory by Tarski and Hermes. Of my many pleasant surprises, one stands out far above all others: my paper 2015 “Existential import today”, co-written with the young Iranian logician Hassan Masoud. Shortly after it was published, it gained first place on its journal’s “most-read list” with over 1500 readers. At the moment it is still first with over 5500 readers, the second place paper has yet to reach 1500. With all appropriate modesty and giving much credit to the energy, dedication, and 4 creativity of my co-author, I am very happy with the paper and I think it has a lot to teach logic students and their professors. Thank you, Athanasios, for your energy and initiative. ATHANASIOS CHRISTACOPOULOS: Thank you very much John, from the depths of our heart and our logic. Corcoran’s Acknowledgements: As usual, I consulted several friends before submitting my answers. Especially useful responses came from Lynn Corcoran, Calvin Jongsma, Sergej Korchevoj, Fernando Leal, Joaquin Miller, Frango Nabrasa, and others. END OF INTERVIEW DRAFT 9 092417 WORD COUNT 2350 WORD LIMIT 2000 REFERENCES IN ORDER OF MENTION 1969. Three Logical Theories, Philosophy of Science 36, 153–77. https://www.academia.edu/9855795/Three_logical_theories 2011. Farewell letter from John Corcoran. Philosophy Nousletter. Number 19, Winter 2011. 10–12. https://www.academia.edu/32207251/CORCORAN_SAYS_FAREWELL_TO_HIS_STUDENTS 1989. The Inseparability of Logic and Ethics, Free Inquiry, Spring, 37–40. AC PP RG Translations: Arabic, Greek, Italian, Persian, Portuguese, and Russian. https://www.academia.edu/9413409/INSEPARABILITY_OF_LOGIC_AND_ETHICS 2015. Investigating knowledge and opinion. The Road to Universal Logic. Vol. I. Arthur Buchsbaum and Arnold Koslow, Editors. Springer. Pp. 95-126. (Co-author Idris Samawi Hamid) https://www.academia.edu/8994046/John_Corcoran_and_Idris_Samawi_Hamid._2014._Investigating_knowledge _and_opinion._The_Road_to_Universal_Logic._Vol._I._A._Buchsbaum_and_A._Koslow_Editors._Springer._PP._95126._ 1988. Andrews, P. An Introduction to Mathematical Logic and Type Theory (1986) in Mathematical Reviews. MR0859866. https://www.academia.edu/32892480/CORCORAN_RECOMMENDS_ANDREWS_ON_TYPE_THEORY 5 2003. Aristotle's Prior Analytics and Boole's Laws of Thought. History and Philosophy of Logic. 24, 261–288. MR2033867 (2004m: 03006). Reviewed by R. Vilkko. The Bulletin of Symbolic Logic. 11(2005) 89–91. PDF AC https://www.academia.edu/8840970/Aristotle_s_Prior_Analytics_and_Boole_s_Laws_of_Thought 1974. Aristotle's Natural Deduction System, in Ancient Logic and Its Modern Interpretations, ed. John Corcoran, Reidel, Dordrecht, 85–132. MR0497848 (58 #16077). PDF AC https://www.academia.edu/9965562/Ancient_Logic_and_Its_Modern_Interpretations_ 1974. String Theory (Co-authors: William Frank, Michael Maloney), Journal of Symbolic Logic 39: 625–37. MR0398771 (53 #2622). https://www.academia.edu/13846218/String_theory_the_foundation_of_proof_theory_grammar_meta mathematics_and_word_processing END REFERENCES 6