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Introduction

Born in Baltimore, after Baltimore Polytechnic Institute, he went to Johns Hopkins U in Engineering and then graduate study in Philosophy. He did post-doctoral study in Mathematics at Yeshiva University in New York City and at UC Berkeley. He taught at Johns Hopkins, UC Berkeley, U of Pennsylvania, U of Michigan, U of Santiago de Compostela, and U of Buffalo.His publications are mostly in logic: mathematical, historical , philosophical.
http://en.wikipedia.org/wiki/John_Corcoran_(Logician)

Additional affiliations

August 1969 - August 2011

September 1965 - June 1969

## Publications

Publications (187)

This presentation includes a complete bibliography of John Corcoran’s publications relevant on Aristotle’s logic. The Sections I, II, III, and IV list respectively 23 articles, 44 abstracts, 3 books, and 11 reviews. Section I starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article—from Corcoran’s Phi...

Tarski's Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of 'every truth is a sentence'. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (de...

The �five ambiguous words--sentence, proposition, judgment, statement, and fact--each have meanings that are vague in the sense of admitting borderline cases. This paper discusses several senses of these and related words used in logic. It focuses on a constellation of recommended primary senses. A judgment is a private epistemic act that results i...

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to app...

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page Tarski consequence-definition paper is based on a monistic fixed-universe framework—like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of th...

This presentation includes a complete bibliography of John Corcoran’s publications relevant on Aristotle’s logic. The Sections I, II, III, and IV list respectively 23 articles, 44 abstracts, 3 books, and 11 reviews. Section I starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article—from Corcoran’s Phi...

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” wh...

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” wh...

Contrary to dictionaries, a non sequitur isn’t “any statement that doesn’t follow logically from previous statements”.
This lecture surveys and analyses a wide selection of uses of ‘nonsequitur’ in logic and logic-related literature.
END OF DRAFT 4
NOTE 091215: When Rick Perry was discussing possible withdrawal from the race—unfortunately not th...

John Corcoran and Gerald Rising. Expressing set-size equality. Bulletin of Symbolic Logic.21 (2015) 239.
The word ‘equality’ often requires disambiguation, which is provided by context or by an explicit modifier. For each sort of magnitude, there is at least one sense of ‘equals’ with its correlated senses of ‘is greater than’ and ‘is less than’....

Where two methods produce similar results, mixing the two sometimes creates errors we call two-method errors, TMEs: in style, syntax, semantics, pragmatics, implicature, logic, or action. This lecture analyzes examples found in technical and in non-technical contexts.
One can say “Abe knows whether Ben draws” in two other ways: ‘Abe knows whether...

Mathematical representation: playing a role. (English summary) Philos. Stud. 168 (2014), no. 3, 769–782. The article under review—hereafter MRPR—concerns recent aspects of a two-century-old development. In the last half of the twentieth century this development spawned several philosophies known as mathematical structuralisms; in philosophy-of-math...

First-order logic has limited existential import: the universalized conditional ∀ x [S( x ) → P( x )] implies its corresponding existentialized conjunction ∃ x [S( x ) & P( x )] in some but not all cases. We prove the Existential-Import Equivalence :
∀ x [S( x ) → P( x )] implies ∃ x [S( x ) & P( x )] iff ∃ x S( x ) is logically true.
The anteceden...

This presentation includes a complete bibliography of John Corcoran’s publications devoted at least in part to Aristotle’s logic. Sections I–IV list 20 articles, 43 abstracts, 3 books, and 10 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article that antedates Corcoran’s Aristotle’s stu...

Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S(x)→ P(x)] implies its corresponding existentialized conjunction ∃ x [S(x) & P(x)], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S(x) of the univers...

Abstract
This work treats the correlative concepts knowledge and opinion, in various senses. In all senses of ‘knowledge’ and ‘opinion’, a belief known to be true is knowledge; a belief not known to be true is opinion. In this sense of ‘belief’, a belief is a proposition thought to be true—perhaps, but not necessarily, known to be true. All knowled...

This work treats the correlative concepts knowledge and opinion, in various senses. In all senses of ‘knowledge’ and ‘opinion’, a belief known to be true is knowledge; a belief not known to be true is opinion. In this sense of ‘belief’, a belief is a proposition thought to be true—perhaps, but not necessarily, known to be true. All knowledge is tru...

LouxMichael J.. The ontology of William of Ockham. Ockham's theory of terms, Part I of the Summa logicae, translated and introduced by LouxMichael J., University of Notre Dame Press, Notre Dame and London1974, pp. 1–21. LouxMichael J.. Ockham on generality. Ockham's theory of terms, Part I of the Summa logicae, translated and introduced by LouxMich...

EbbinghausHeinz-Dieter. Über eine Prädikatenlogik mit partiell definierten Prädikaten und Funktionen. Archie für mathematische Logik und Grundlagenforschung, vol. 12 (1969), pp. 39–53. - Volume 37 Issue 3 - John Corcoran, John Herring

CocchiarellaNino B.. Logical investigations of predication theory and the problem of universals. Indices, no. 2. Bibliopolis, Naples1986, also distributed by Humanities Press, Atlantic Highlands, N.J., 265 pp. - Volume 53 Issue 3 - John Corcoran, Woosuk Park

Complete list of publications through August 2014: articles, abstracts, books, reviews, miscelaneous.

EXCERPT:
THE TARSKIAN TURN has been praised by distinguished philosophers of mathematical logic: on the dust jacket John Burgess calls it “clear and concise”. Vann McGee says it shows “remarkable insight and technical dexterity”; and elsewhere John and Alexis Burgess call it “indispensible, and perhaps more accessible than the seminal papers by Fe...

MendelsonElliott, Introduction to mathematical logic, Third edition of XXXIV 110 and XLV 631. The Wadsworth & Brooks/Cole mathematics series. Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, Calif., 1987, ix + 341 pp. - Volume 54 Issue 2 - John Corcoran, Woosuk Park

Newton's Principia Mathematica famously denied " making hypotheses ". His frequently-quoted Latin sentence— " Hypotheses non fingo " (" I make no hypotheses ")—puzzles modern readers and prompts consideration of various interpretations of make and hypothesis. A literature exists on how fingo (" I make ") could be taken and, in particular, what maki...

THE REVIEWER WROTE: Many of Corcoran's remarks throughout this very rich paper ... will be of interest to the reader, including his discussion of recent studies concerning the Aristotelian system, and the conclusions that he makes. Corcoran states that "the gulf between modern logic and Boole is much greater than that between modern logic and Arist...

Since 1974, the terminology in the field has changed: the well-chosen expression "definitionally equivalent" replaces the awkward and misleading term "synonymous". After all, we are talking about uninterpreted formal theories. See John Corcoran, 1980. A note concerning definitional equivalence, History and Philosophy of Logic, 1, 231–34, available...

Hence, there can never be surprises in logic.—Wittgenstein, 1922, 6.1251. Contents Abstract Introduction 1 The existential-import equivalence 2 The import-carrying-predicate lemma 3 The import-free-predicate lemma 4 Equivalence relations 5 Enthymemic implications 6 Concluding remarks Acknowledgements References

FROM: Errors in Tarski's 1983 truth-definition paper. Bull. Symb. Logic. 19 (2013) 514.
In 1935, at 34 years of age, Alfred Tarski (1901–1983) published a German translation by Leopold Blaustein of the world-shaking truth-definition paper [1, pp. 152–278] begun over six years earlier [1, p. 277]. The main results were achieved when he was 28 years...

This brief, largely expository book—hereafter TT—blends history and philosophy of logic with contemporary mathematical logic. Page 3 says it "is about the relation between formal theories of truth and deflationism about truth". It is intended "as a textbook . . . for senior undergraduate and beginning graduate students in philosophy" (p.6). It has...

This massive 500-page volume—hereafter PP—is the most comprehensive study to date of Pythagoras and his immediate followers, the early Pythagoreans. Pythagoras lived about 75 years, roughly 570–495 BCE, near the dawn of mathematics in Greece. By comparison, Thales flourished a few years before Pythagoras's birth and Euclid flourished about 300 BCE,...

A mathematical-induction proof MIP concludes " every [natural] number has property P " using the induction axiom IA and two lemmas: its zero-lemma— " zero has P " —and its successor-lemma— " P belongs to the successor of every number having P " . IA: Every property belonging to zero and to the successor of every number having it belongs to every nu...

Following Tarski's truth-definition and consequence-definition papers [3, pp. 152–278, 409– 420], we assume an interpreted formalized language: a first-order language interpreted number-theoretically. We use ordinary variable-enhanced English: for example, the English sentence schema 'every number x is such that P(x)' translates the first-order sch...

This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the th...

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný)
Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms.
Euclid’s pos...

In 1935, at 34 years of age, Alfred Tarski (1901–1983) published a German translation by Leopold Blaustein of the world-shaking truth-definition paper [1, pp. 152–278] begun over six years earlier [1, p. 277]. The main results were achieved when he was 28 years old (ibid.). The German translation was not flawless. Further errors were introduced in...

This applied-logic lecture builds on [1] arguing that character traits fostered by logic serve clarity and understanding in ethics, confirming hopeful views of Alfred Tarski [2, Preface, and personal communication]. Hypotheses in one strict usage are propositions not known to be true and not known to be false or—more loosely—propositions so conside...

ABSTRACT
This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is.
I know I am asking a lot, but I have to ask you to read the quoted passages—aloud if pos...

The premise-fact confusion in Aristotle’s PRIOR ANALYTICS.
The premise-fact fallacy is talking about premises when the facts are what matters or talking about facts when the premises are what matters. It is not useful to put too fine a point on this pencil.
In one form it is thinking that the truth-values of premises are relevant to what their co...

Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth)
Also see https://www.academia.edu/s/a6bf02aaab
This article uses ‘equals’ [‘is equal to’] and ‘is’ [‘is identical to’, ‘is one and the same as’] as they are used in ordinary exact English. In a logically perfect language the oxymoron ‘the numbers 3 and...

JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 (2013) 253.
Some people, not just beginning students, are at first surprised to learn that the proposition “If zero is odd, then zero is not odd” is not self-contradictory. Some people are surprised to find out that there are logically equivalent false universal pro...

History witnesses alternative approaches to “the proposition”. The proposition has been referred to as the object of belief, disbelief, and doubt: generally as the object of propositional attitudes, that which can be said to be believed, disbelieved, understood, etc. It has also been taken to be the object of grasping, judging, assuming, affirming,...

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework—like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range...

History witnesses alternative approaches to “the proposition”. The proposition has been referred to as the object of belief, disbelief, and doubt: generally as the object of propositional attitudes, that which can be said to be believed, disbelieved, understood, etc. It has also been taken to be the object of grasping, judging, assuming, affirming,...

mx This BULLETIN 15(2009), p. 133, discussed the Alternative Constituent Format or ACF for presenting linguistic and logical data. A string in the ACF is called an Alternative Constituent String or ACS. ACS1. (Zero * One* Two) is closer to four than (six * to six * six is). Above, nine interrelated sentences are compactly presented for easy compari...

A counterargument for a given argument is an argument having all true premises, a false conclusion, and the same form as the given argument. Consider the following one-premise argument whose premise and conclusion are about numbers in the sense of the non-negative integers, the so-called natural numbers beginning with zero. Zero is neither positive...

History witnesses alternative approaches to "the proposition". The proposition has been referred to as the object of belief, disbelief, and doubt: generally as the object of propositional attitudes. It has also been taken to be the object of grasping, judging, assuming, affirming, denying, and inquiring: generally as the object of propositional act...

The author of this translation and commentary, is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle's Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts...

Two related problem types are central to logic: consequence problems and independence problems.
Consequence problems have the form: to show that a given conclusion is a consequence of a given premise set—if it is.
Independence problems have the form: to show that a given conclusion is not a consequence of a given premise set—if it is not. Tradit...

Los primeros días de todo curso de Lógica
John Corcoran
Philosophy, University at Buffalo,
Buffalo, NY 14260-4150
E-mail: corcoran@buffalo.edu
Abstract
This short paper sketches some of the basic ideas that should be presented on the first days of any logic course. It treats the nature and goals of logic. It discusses what a student can hope to ach...

We begin with an introductory overview of contributions made by more than twenty scholars associated with the Philosophy Department at the University of Buffalo during the last half-century to our understanding and evaluation of Aristotle’s logic. More well-known developments are merely mentioned in order to make room to focus on issues at the cent...

The alternative constituent format displays linguistic or logical data in a succinct way that permits ready grasp of subtle contrasts. A grammatical constituent of a sentence is replaced by a sequence of alternatives. Consider an ambiguous question Q. (Q) Is two closer to three than four? Consider an initial sentence A as an affirmative answer. (A)...

The alternative constituent format displays linguistic or logical data in a succinct way that permits ready grasp of subtle contrasts. A grammatical constituent of a sentence is replaced by a sequence of alternatives. Consider an ambiguous question Q. (Q) Is two closer to three than four? Consider an initial sentence A as an affirmative answer. (A)...

Brady Geraldine . From Peirce to Skolem. A neglected chapter in the history of logic. Elsevier, Amsterdam, 2000, xi + 468 pp. - Volume 14 Issue 4 - John Corcoran

As noted in 1962 by Timothy Smiley, if Aristotle’s logic is FAITHFULLY translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system i...

The expressions 'form', 'structure', 'schema', 'shape', 'pattern', 'figure', 'mold', and related locutions are used in logic both as technical terms and in metaphors. This paper juxtaposes, distinguishes, and analyses uses of these expressions by logicians. No such project has been attempted previously. After establishing general terminology, we pr...

This largely expository lecture deals with aspects of traditional solid geometry suitable for applications in logic courses. A regular polygon has equal sides and equal angles. A subregular polyhedron has congruent faces and congruent [polyhedral] angles. A subregular polyhedron whose faces are all regular polygons is regular. Geometers before Eucl...

The expressions 'form', 'structure', 'schema', 'shape', 'pattern', 'figure', 'mold', and related locutions are used in logic both as technical terms and in metaphors. This paper juxtaposes, distinguishes, and analyses uses of these expressions by logicians. No such project has been attempted previously. After establishing general terminology, we pr...

This paper discusses treatments of "existential import" in the literature of standard first-order logic with identity. According to one of several usages reviewed, a universal sentence has existential import if it implies "the corresponding existential". Confusions arise from several sources including ambiguity of the expression 'the corresponding...

Apriori (or a priori) knowledge is often taken to be exemplified by logic and arithmetic, where sense experience is thought to be irrelevant. Aposteriori (or a posteriori) knowledge is often taken to be exemplified by physics and chemistry, where it is thought that self-evidence and intuition must be supplemented with experimental data based on sen...

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralis...

As noted in 1962 by Timothy Smiley, if Aristotle's logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley's method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle's system i...

This paper is more a series of notes than a scholarly treatise. It focuses on certain achievements of Aristotle, Boole, and Tarski. The notes presented here using concepts introduced or formalized by Tarski contribute toward two main goals: comparing Aristotle’s system with one Boole constructed intending to broaden and to justify Aristotle’s, and...

John Corcoran. 2005. Logically Equivalent False Universal Propositions with Different Counterexample Sets. Bulletin of Symbolic Logic. 11: 554-5.
This paper corrects a mistake I saw students make but I have yet to see in print. The mistake is thinking that logically equivalent propositions have the same counterexamples—always. Of course, it is oft...

This elementary 4-page paper is a preliminary survey of some of the most important uses of ‘condition’ and ‘consequence’ in American Philosophy. A more comprehensive treatment is being written. Your suggestions, questions, and objections are welcome. A statement of a conditional need not be a conditional statement and conditional statement need not...

Corcoran, J. 2007. Psychologism. American Philosophy: an Encyclopedia. Eds. John Lachs and Robert Talisse. New York: Routledge. Pages 628-9.
Psychologism with respect to a given branch of knowledge, in the broadest neutral sense, is the view that the branch is ultimately reducible to, or at least is essentially dependent on, psychology. The parall...

C. I. Lewis (1883-1964) was the first major figure in history and philosophy of logic – a field that now recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others. The publication of Murray Murphey’s masterful intellectual biography C. I. Lewis: the Last Great Pragmatist (Albany: SUNY Press, 2005) is occasion to ree...

This essay treats knowledge and belief, both in various senses. The focus is on propositional knowledge (knowledge-that) but it also treats both objectual knowledge (knowledge of objects in the broadest sense, or knowledge-of) and operational knowledge (abilities and skills, knowledge-how-to, or know-how). It begins with knowledge in a strict sense...

Schemata have played important roles in logic since Aristotle’s Prior Analytics. The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role...

2006. George Boole. Encyclopedia of Philosophy. 2nd edition. Detroit: Macmillan Reference USA.
George Boole (1815-1864), whose name lives among modern computer-related sciences in Boolean Algebra, Boolean Logic, Boolean Operations, and the like, is one of the most celebrated logicians of all time. Ironically, his actual writings often go unread an...

Consider the following. The first is a one-premise argument; the second has two premises. The question sign marks the conclusions as such.
Matthew, Mark, Luke, and John wrote Greek.
? Every evangelist wrote Greek.
Matthew, Mark, Luke, and John wrote Greek.
Every evangelist is Matthew, Mark, Luke, or John.
? Every evangelist wrote Greek.
The abov...

In its strongest unqualified form, the principle of wholistic reference is that in any given discourse, each proposition refers to the whole universe of that discourse, regardless of how limited the referents of its non-logical or content terms. According to this principle every proposition of number theory, even an equation such as "5 + 7 = 12", r...

Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over t...

This paper is more a series of notes than a scholarly treatise. It focuses on certain achieve‑ ments of Aristotle, Boole and Tarski. The notes presented here using concepts introduced or formalized by Tarski contribute toward two main goals: comparing Aristotle's system with one Boole constructed intending to broaden and to justify Aristotle's, and...

Alonzo Church was born in Washington, DC, on 14 June 1903, the son of Samuel Robbins Church, Justice of the Municipal Court of the District of Columbia, and Mildred Hannah Church (née Parker). The Church family was of considerable civic and academic distinc- tion; Church's great grandfather, also named Alonzo Church, was a professor of mathematics...

Corcoran, J. 2007. Syntactics, American Philosophy: an Encyclopedia. 2007. Eds. John Lachs and Robert Talisse. New York: Routledge. pp.745-6.
Syntactics, semantics, and pragmatics are the three levels of investigation into semiotics, or the comprehensive study of systems of communication, as described in 1938 by the American philosopher Charles Mo...

This expository article focuses on the fundamental differences between first-order logic and second-order logic. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and that it is not an artificial f...

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001.
Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols.
It...

Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a conseque...

Critical thinking involves deliberate application of tests and standards to beliefs per se and to methods used to arrive at beliefs. Pedagogical license is authorization accorded to teachers permitting them to use otherwise illicit means in order to achieve pedagogical goals. Pedagogical license is thus analogous to poetic license or, more generall...

## Questions

Questions (11)

This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed indirect proof. Lukasiewicz evidence is presented fully; it is irrefutable. But, instead of considering the possibility that Aristotle’s discourses were not intended to express indirect proofs of universalized conditions presupposing axiomatic premises, Lukasiewicz came to the amazing conclusion that Aristotle did not understand indirect proof.

This paper builds on the admirable Lukasiewicz scholarship to establish a conclusion diametrically opposed to the one Lukasiewicz asserted.

Does a scholar have a moral obligation to expose flawed scholarship? More generally, what should be done when seriously flawed work is discovered?

The editor of MATHEMATICAL REVIEWS asked me to review this paper. I could hardly believe my eyes when I was reading it. I considered refusing the request using some vague polite excuse.

PS Since my first review in 1970 (reference below), I have written scores of reviews in MATHEMATICAL REVIEWS, most of which were positive or even laudatory. You can get the whole lot on MathSciNet.

1970. Beth, Evert. Mathematical Thought. An Introduction to the Philosophy of Mathematics. In Mathematical Reviews, 40, 988–89.

REDUCTIO QUESTIONS

Corcoran’s 2009 ARISTOTLE’S DEMONSTRATIVE LOGIC deals decisively with several issues that had previously been handled by vague speculation and dogmatic pontification if at all. One possible example: Corcoran [2009, p. 13] proves conclusively that the imperfect syllogisms Baroco and Bocardo—which Aristotle completed indirectly [by reductio-ad-impossible]—cannot be completed directly. More generally, Corcoran shows that no valid premise-conclusion argument, regardless of the number of premises, having an existential negative [“particular negative” or “O-proposition”] as a premise can be completed using a direct deduction—assuming of course that no premises are redundant and that the conclusion is not among the premises. To be clear this means that for no such argument is it possible to deduce the conclusion from the premises without using reductio.

This result, called the EXISTENTIAL-NEGATIVE EXCLUSION [ENE], was circulated informally by Corcoran much earlier but it seems not to have been printed before 2009.

Q1: Was ENE, or a stronger result, stated in print before 2009?

Q2: Was ENE, or a stronger result, proved in print before 2009?

Q3: Are there other categorical arguments besides those having existential negative premises that are not directly deducible?

Q4: What is a necessary and sufficient condition for a categorical argument to be directly deducible?

Q5: Does Aristotle say anything about incomplete syllogisms that cannot be completed directly?

Q6: Which later logicians say anything notable about premise-conclusion arguments that cannot be shown to be valid by direct deduction?

The above presupposes the system of deductions and the definitions given in Corcoran’s 2009 ARISTOTLE’S DEMONSTRATIVE LOGIC.

Article Aristotle's Demonstrative Logic

Critical Notice: Contemporary Relevance of Ancient Logical Theory (Co-author: M. Scanlan), Philosophical Quarterly 32, 76–86.

Englebretsen 1996, p. 49 wrote: I have offered a slightly different survey of Aristotle’s logic […]. Corcoran and Scanlan 1982 is an ideal place to start. Also see the essays in Corcoran 1974.

Section II of “The fixation of belief” [2] opens dramatically with a one-premise argument—Peirce’s truth-preservation argument PTPA—concluding that truth-preservation is necessary and sufficient for validity: he uses ‘good’ interchangeably with ‘valid’. He premises an epistemic function and concludes an ontic nature.

The object of reasoning is determining from what we know something not known.

Consequently, reasoning is good if it gives true conclusions from true premises, and not otherwise.

Assuming Peirce’s premise for purposes of discussion, it becomes clear that PTPA is a formal fallacy: reasoning that concludes one of its known premises is truth-preserving without “determining” something not known. It is conceivable that Peirce’s conclusion be false with his premise true [1, pp. 19ff].

The above invalidation of PTPA overlooks epistemically important points that independently invalidate PTPA: nothing in the conclusion is about reasoning producing knowledge of the conclusion from premises known true: in fact, nothing is about premises known to be true, nothing is about conclusions known to be true, and nothing is about reasoning being knowledge-preservative.

The following is an emended form of PTPA.

One object of reasoning is determining from what we know something not known.

Consequently, reasoning is good if it gives knowledge of true conclusions not among the premises from premises known to be true, and not otherwise.

PTPA has other flaws. For example, besides being a formal non-sequitur, PTPA is also a petitio-principi [1, pp.34ff]. Peirce’s premise not only isn’t known to be true—which would be enough to establish question-begging—it’s false: reasoning also determines consequences of premises not known to be true [1, pp. 17f].

[1] JOHN CORCORAN, Argumentations and logic, Argumentation, vol. 3 (1989), pp. 17–43.

[2] CHARLES SANDERS PEIRCE, The fixation of belief, Popular Science Monthly. vol. 12 (1877), pp. 1–15.

Q1 Did Peirce ever retract PTPA?

Q2 Has PTPA been discussed in the literature?

Q3 Did Peirce ever recognize consequence-preservation as a desideratum of reasoning?

Q4 Did Peirce ever recognize knowledge-preservation as a desideratum of reasoning?

Q5 Did Peirce ever retract the premise or the conclusion of PTPA?

"True" and "false" syllogisms in Aristotle's ANALYTICS. In Aristotle's ANALYTICS, what does Aristotle mean by saying that a syllogism is true or that it is false? For example, see POSTERIOR ANALYTICS, Book I, Chapter 32. More generally, where in the corpus is 'true' or 'false' applied to syllogisms, or to anything other than a proposition, and in each case what is meant?

Proving categoricity of Gödel Arithmetic using the Hilbert interpretation and the denotation function.

In 1997 I published a sketch of one such proof. The abstract is available below on this RG profile. What is unique about such a proof is (1) the use of the Hilbert model whose universe is the set of numerals and (2) the use of an arbitrary model’s denotation function to construct an isomorphism. I do not start with two arbitrary models and show that they are isomorphic. I start with one arbitrary model and construct an isomorphism from the Hilbert model to it.

Q1. Are there other such proofs of categoricity of Gödel Arithmetic published before or since?

Q2. Is the argument sketched in the abstract correct in every detail? Are there mistakes or gaps?

Q3. In the modern sense, categoricity is a property of a set of sentences with respect to a set of interpretations of the sentences’ formalized language. What is the earliest categoricity proof in the modern sense that you know of?

According to conventional wisdom, mathematicians tend to accept platonism but find logicism wildly implausible if not ridiculous, whereas philosophers tend to find platonism wildly implausible if not ridiculous while being attracted to logicism.

Q1. Where can one find versions or variants of this conventional wisdom in print? Of course, the writings of respected authors are preferred.

Q2. Where can one find philosophers’ statements deploring or ridiculing platonism?

Q3. Where can one find mathematicians’ statements deploring or ridiculing logicism?

Q4. Where can one find mathematicians’ statements deploring or ridiculing people who reject platonism?

Q5. Where can one find philosophers’ statements deploring or ridiculing people who reject logicism?

Peirce’s law, (((P-->Q)-->P)-->P), is a law of the Pure Conditional Sentential Logic.

Q1: Who proved that it is not intuitionistically provable? Q1.1: What is the proof?

Q2: Who proved that it is not classically provable using only the standard -->Intelim rules? Q2.1: What is the proof?

Q3: What “meanings” have been suggested for it? How could it have been discovered? Why should anyone conjecture it?

Q4: What good is it? What results in logic use it?

Q5: Hassan Masoud observed that its unprovability using only the standard -->Intelim rules suggests that the standard -->Intelim rules should not be regarded as “determining the meaning" of the connective --> Has this or related observations been discussed in print?

Is "discharging assumptions" a deliberate, separate act or do we simply close a subdeduction?

How did such an error-ridden book as HORSTEN 2011 get published? How did favorable reviews get published in such top journals as BSL, STUDIA LOGICA, and NDPB?

## Projects

Project (1)

Pen questions in the below. EG, the nature and diversity of import-carrying predicates.
John Corcoran and Hassan Masoud. 2014. Existential import today: New metatheorems; historical, philosophical, and pedagogical misconceptions. History and Philosophy of Logic. 36: 39–61.
http://www.tandfonline.com/doi/full/10.1080/01445340.2014.952947