Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...) Q is one whose existentialization, ∃ x Q, is logically true; otherwise, Q is existential-import-free or simply import-free.How abundant or widespread is existential import? How abundant or widespread are existential-import predicates in themselves or in comparison to import-free predicates? We show that existential-import predicates are quite abundant, and no less so than import-free predicates. Existential.. (shrink)

►JOHN CORCORAN AND IDRIS SAMAWI HAMID, Two-method errors: having it both ways. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: corcoran@buffalo.edu Philosophy, Colorado State University, Fort Collins, CO 80523-1781 USA E-mail: [email protected] 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 or not Ben draws’ or ‘Abe knows whether Ben draws or not’. But a stylistic TME occurs in ‘Abe knows whether or not Ben draws or not’. One can say “Abe knows how Ben looks” using ‘Abe knows what Ben looks like’. But syntactical TMEs are in ‘Abe knows what Ben looks’ and in ‘Abe knows how Ben looks like’. One can deny that Abe knows Ben by prefixing ‘It isn’t that’ or by interpolating ‘doesn’t’. But a pragmatic TME occurs in trying to deny that Abe knows Ben by using ‘It isn’t that Abe doesn’t know Ben’. There are several standard ways of defining truth using sequences. Quine’s discussions in the 1970 first printing of Philosophy of logic [3] and in previous lectures were vitiated by mixing two [1, p. 98]. The logical TME in [3], which eluded Quine’s colleagues, was corrected in the 1978 sixth printing [2]. But Quine never explicitly acknowledged, described, or even mentioned the error. This lecture presents and analyses two-method errors in the logic literature. [1] JOHN CORCORAN, Review of Quine’s 1970 Philosophy of Logic. In Philosophy of Science, vol. 39 (1972), pp. 97–99. [2] JOHN CORCORAN, Review of sixth printing of Quine’s 1970 Philosophy of Logic. In Mathematical Reviews MR0469684 (1979): 57 #9465. [3] WILLARD VAN ORMAN QUINE, Philosophy of logic, Harvard, 1970/1986. (shrink)

JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 253. 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 propositions that have no counterexamples in common, i. e., that no counterexample for one is a counterexample for the other. Some people would be surprised (...) to find out that in normal first-order logic existential import is quite common: some universals “Everything that is S is P” —actually quite a few—imply their corresponding existentials “Something that is S is P”. Anyway, perhaps contrary to its title, this paper is not a cataloging of surprises in logic but rather about the mistakes that did or might have or might still lead people to think that there are no surprises in logic. The paper cataloging of surprises in logic is on our “to-do” list. -/- ► JOHN CORCORAN AND WILIAM FRANK, Surprises in logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: corcoran@buffalo.edu There are many surprises in logic. Peirce gave us a few. Russell gave Frege one. Löwenheim gave Zermelo one. Gödel gave some to Hilbert. Tarski gave us several. When we get a surprise, we are often delighted, puzzled, or skeptical. Sometimes we feel or say “Nice!”, “Wow, I didn’t know that!”, “Is that so?”, or the like. Every surprise belongs to someone. There are no disembodied surprises. Saying there are surprises in logic means that logicians experience surprises doing logic—not that among logical propositions some are intrinsically or objectively “surprising”. The expression “That isn’t surprising” often denigrates logical results. Logicians often aim for surprises. In fact, [1] argues that logic’s potential for surprises helps motivate its study and, indeed, helps justify logic’s existence as a discipline. Besides big surprises that change logicians’ perspectives, the logician’s daily life brings little surprises, e.g. that Gödel’s induction axiom alone implies Robinson’s axiom. Sometimes wild guesses succeed. Sometimes promising ideas fail. Perhaps one of the least surprising things about logic is that it is full of surprises. Against the above is Wittgenstein’s surprising conclusion : “Hence there can never be surprises in logic”. This paper unearths basic mistakes in [2] that might help to explain how Wittgenstein arrived at his false conclusion and why he never caught it. The mistakes include: unawareness that surprise is personal, confusing logicians having certainty with propositions having logical necessity, confusing definitions with criteria, and thinking that facts demonstrate truths. People demonstrate truths using their deductive know-how and their knowledge of facts: facts per se are epistemically inert. [1] JOHN CORCORAN, Hidden consequence and hidden independence. This Bulletin, vol.16, p. 443. [2] LUDWIG WITTGENSTEIN, Tractatus Logico-Philosophicus, Kegan Paul, London, 1921. -/-. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

Pv~P: Cambridge Journal of Undergraduate Philosophy, Issue 1, 1982.

The widely cited Nuffield Council on Bioethics ‘Intervention Ladder’ structurally embodies the assumption that personal autonomy is maximized by non-intervention. Consequently, the Intervention Ladder encourages an extreme ‘negative liberty’ view of autonomy. Yet there are several alternative accounts of autonomy that are both arguably superior as accounts of autonomy and better suited to the issues facing public health ethics. We propose to replace the one-sided ladder, which has any intervention coming at a cost to autonomy, with a two-sided ‘Balanced Intervention (...) Ladder,’ where intervention can either enhance or diminish autonomy. We show that not only the alternative, richer accounts of autonomy but even Mill’s classic version of negative liberty puts some interventions on the positive side of the ladder. (shrink)

Philosophers have had an interest in language from the earliest times but the twentieth century, with its so-called 'linguistic turn' in philosophy, has seen a huge expansion of work focused specifically on language and its foundations. No branch of philosophy has been unaffected by this shift of emphasis. It is timely at the end of the century to review and assess the vast range of issues that have been developed and debated in this central area. The distinguished international contributors present (...) a clear, accessible guide to the fundamental questions raised by the philosophers about language. Contributions include Graeme Forbes on necessity, Susan Haack on deviant logics, Paul Horwich on truth, Charles Travis on Wittgenstein, L.J. Cohen on linguistic philosophy, Ruth Kempson on semantics and syntax and Christopher Hookway on ontology, to name but a few. A wide range of topics are covered from the metaphysics and ontology of language, language and mind, truth and meaning, to theories or reference, speech act theory, philosophy of logic and formal semantics. There are also articles on key figures from the twentieth century and earlier. Based on the foundation provided by the award-winning Encyclopedia of Language and Linguistics this single volume provides a collection of articles that will be an invaluable reference tool for all those interested in the area of philosophy of language, and also to those in cognitive science and psychology. All the articles have been thoroughly revised and updated. This volume gives a unique survey of topics that are at the very core of contemporary philosophy. (shrink)

I adopt a cladistic view of species, and explore the possibility that there exists an equally valuable cladistic view of organismic traits. This suggestion seems to run counter to the stress on functional views of biological traits in recent work in philosophy and psychology. I show how the tension between these two views can be defused with a multilevel view of biological explanation. Despite the attractions of this compromise, I conclude that we must reject it, and adopt an essentially cladistic (...) conception of biological traits. (shrink)

Digeser contends that our rich and varied practices of friendship multiply and moderate connections to politics. Along the way, she sets forth a series of ideals that appreciates friendship's many forms and its dynamic relationship to individuality, citizenship, political and legal institutions, and international relations.

Assuming it rational to treat other persons' probabilities as epistemically significant, how shall their judgements be weighted (Barnes [1998])? Several plausible methods exist, but theorems in classical psychometrics greatly reduce the importance of the problem. If scientists' judgements tend to be positively correlated, the difference between two randomly weighted composites shrinks as the number of judges rises. Since, for reasons such as representative coverage, minimizing bias, and avoiding elitism, we would rarely employ small numbers of judges (e.g. less than 10), (...) the difference between two weighting systems becomes negligible. Suggestions are made for quantifying verisimilitude, identifying 'types' of scientists or theories (taxometrics), inferring latent factors, and estimating reliability of pooled judgements. (shrink)

Rufus of Ephesus (fl.c.a.d.100) wrote a large body of works on a variety of medical topics. Generally speaking, the Arabic tradition is particularly important for the reconstruction of much of his œuvre. In the present article, I am going to present four new fragments of Rufus’On Melancholyand a fragment from an otherwise unknown monographOn Preferring Fresh Poppies. These new fragments provide fascinating new insights into Rufus’ approach to recording case histories.