Enligt ett realistiskt synsätt kan ett påstående vara sant trots att det inte ens i princip är möjligt att veta att det är sant. En sanningsteoretisk antirealist kan inte godta denna möjlighet utan accepterar en eller annan version av Dummetts vetbarhetsprincip: (K) Om ett påstående är sant, så måste det i princip vara möjligt att veta att det är sant. Det kan dock förefalla rimligt, även för en antirealist, att gå̊ med på̊ att det kan finnas sanningar som ingen faktiskt (...) vet (har vetat, eller kommer att veta) är sanna. Man kan därför tänka sig att en antirealist skulle acceptera principen (K) utan att därför gå med på den till synes starkare principen: (SK) Om ett påstående är sant, så måste det faktiskt finnas någon som vet att det är sant. Ett mycket omdiskuterat argument – som ytterst går tillbaka till Alonzo Church, men som först publicerades i en uppsats av Frederic Fitch i Journal of Symbolic Logic 1963 – tycks emellertid visa att principen (K) implicerar principen (SK). Anta nämligen att (K) är sann, medan (SK) inte är det. Men om (SK) är falsk, så finns det ett påstående som är sant men som ingen faktiskt vet är sant. Anta nu att p är ett sådant påstående. Låt Kp betyda att någon vet att p är sant. Det galler alltså̊ att p är sant samtidigt som Kp inte är det. Betrakta nu påståendet (p ∧ −Kp). Enligt antagandet är detta påstående sant. Enligt (K) måste det då vara möjligt att någon vet att (p ∧ −Kp). D.v.s., det måste vara möjligt att påståendet K(p ∧ −Kp) är sant. Men i så fall är det också̊ möjligt att påståendet Kp ∧ K−Kp är sant, vilket i sin tur implicerar att det är möjligt att Kp ∧ −Kp är sant, vilket ju är absurt. Således kan inte (K) vara sann samtidigt som (SK) är falsk. Vi tycks således kunna sluta oss till att (K) implicerar (SK). I uppsatsen diskuterar jag några olika sätt att undgå̊ Church-Fitch paradoxala slutsats. Ett tillvägagångssätt är att ersätta kunskapsoperatorn med en hierarki av kunskapspredikat. Ett annat är baserat på distinktionen mellan faktisk och potentiell kunskap och ett förkastande av den vanliga modallogiska formaliseringen av principen (K). Den senare typen av lösning betraktas både från ett realistiskt och ett icke-realistiskt perspektiv. Utifrån denna analys kommer jag fram till slutsatsen att vi, vare sig vi är realister eller antirealister rörande sanning, kan sluta oroa oss för vetbarhetsparadoxen och ändå uppskatta Church-Fitchs argument. (shrink)

Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). -/- By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive (...) way of fleshing out this idea is synonymous with a ZF-like theory. -/- This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974). (shrink)

Alonzo Church famously provided three principal competing criteria for “strict synonymy,” i.e., sameness of semantic content. These are his Alternatives (0), (1), and (2)—numbered in order of increasing course-grainedness of content. On Alternative (2), expressions are deemed strictly synonymous iff they are logically equivalent. This criterion seems hopeless as an account of the objects of propositional attitude. On Alternative (1), expressions are deemed synonymous iff they are λ-convertible. Alternative (1) also evidently conflicts with discourse about the attitudes. On (...) Alternative (0), expressions are deemed strictly synonymous iff they are “synonymously isomorphic” in Church’s sense. On Alternative (0), semantic content is so fine-grained that not even “Romeo loves Juliet” and “Juliet is loved by Romeo” qualify as strictly synonymous. A fourth alternative, here called “Alternative (3),” deems expressions strictly synonymous iff they are co-intensional, i.e., they have the same semantic extension with respect to the same possible worlds. This criterion’s notion of content is even more course grained than that of Alternative (2). Several objections to Alternative (3) are considered. (shrink)

In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion (...) focuses on: (1) the fine-grained/coarse-grained distinction, (2) proper names and definite descriptions, (3) the paradox of analysis and Mates’ puzzle, and (4) the logical, semantical, and intentional paradoxes. (shrink)

There is an inconsistency among claims made (or apparently made) in separate articles by Alonzo Church concerning Frege's distinction between sense and denotation taken together with plausible assertions by Frege concerning his notion of ungerade Sinn-i.e., the sense that an expression allegedly takes on in positions in which it has ungerade Bedeutung, denoting its own customary sense. As with any inconsistency, the difficulty can be avoided by relinquishing one of the joint assumptions from which contradiction may be derived. (...) Yet what seems the most plausible resolution, in light of Church's own arguments, involves abandoning the theory of sense and denotation, in the form in which it has been staunchly advocated by both Frege and Church. That theory has come under sustained criticism from several quarters. Whereas the present difficulty supplements the case against the theory, it is unlike more familiar criticisms, since it is not framed from the perspective of an alternative theory (or picture) but is based instead on an internal conflict, and therefore has special force. (shrink)

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for (...) equating any two senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory. (shrink)

The problem of evil is broadly considered to be one of the greatest intellectual threats to traditional brands of theism. And William Rowe’s 1979 formulation of the problem in “The Problem of Evil and Some Varieties of Atheism” is the most cited formulation in the contemporary philosophical literature. In this paper, we explore how the tools and resources of experimental philosophy might be brought to bear on Rowe’s seminal formulation, arguing that our empirical findings raise significant questions regarding the ultimate (...) success of Rowe’s argument. Such a result would be quite notable within philosophy of religion, since this is considered one of the most formidable arguments against theism. However, further testing is needed before any firm conclusions can be drawn. -/- In section 1, we elucidate Rowe’s formulation of the problem of evil and the intuitions that seem to underwrite it. In section 2, we explore how the tools and resources of experimental philosophy might be brought to bear on Rowe’s formulation, outlining our hypotheses and our methods for testing them before showcasing our results. In section 3, we discuss the philosophical import of our results–arguing that our results, when taken together, pose an initial challenge to Rowe’s seminal argument. (shrink)

This paper will be broken down into four sections. In §1, I try to assuage a worry that intellectual humility is not really an intellectual virtue. In §2, we will consider the two dominant accounts of intellectual humility in the philosophical literature—the low concern for status account the limitations-owing account—and I will argue that both accounts face serious worries. Then in §3, I will unpack my own view, the doxastic account of intellectual humility, as a viable alternative and potentially a (...) better starting place for thinking about this virtue. And I’ll conclude in §4 by trying to defend the doxastic account against some possible objections. (shrink)

We critique two popular philosophical definitions of intellectual humility: the “low concern for status” and the “limitations-owning.” accounts. Based upon our analysis, we offer an alternative working definition of intellectual humility: the virtue of accurately tracking what one could non-culpably take to be the positive epistemic status of one’s own beliefs. We regard this view of intellectual humility both as a virtuous mean between intellectual arrogance and diffidence and as having advantages over other recent conceptions of intellectual humility. After defending (...) this view, we sketch remaining questions and issues that may bear upon the psychological treatment of intellectual humility such as whether evidence will help determine how this construct relates to general social humility on the one hand, and intellectual traits such as open-mindedness, curiosity, and honesty on the other. (shrink)

Recent work in cognitive science of religion (CSR) is beginning to converge on a very interesting thesis—that, given the ordinary features of human minds operating in typical human environments, we are naturally disposed to believe in the existence of gods, among other religious ideas (e.g., seeAtran [2002], Barrett [2004; 2012], Bering [2011], Boyer [2001], Guthrie [1993], McCauley [2011], Pyysiäinen [2004; 2009]). In this paper, we explore whether such a discovery ultimately helps or hurts the atheist position—whether, for example, it lends (...) credence to atheism by explaining away religious belief or whether it actually strengthens some already powerful arguments against atheism in the relevant philosophical literature.We argue that the recent discoveries of CSR hurt, not help, the atheist position—that CSR, if anything, should not give atheists epistemic assurance. (shrink)

In this chapter, we will explore the luck at issue in Gettier-styled counterexamples and the subsequent problem it poses to any viable reductive analysis of knowledge. In the 1st section, we will consider the specific species of luck that is at issue in Gettier counterexamples, then, in the next section, I will briefly sketch a diagnosis of the Gettier Problem and try to explain why the relevant species of luck has proven to be extremely difficult to avoid. And finally, I (...) will consider a prominent objection to the proposed diagnosis of the Problem. (shrink)

A case could be made that the practice of philosophy demands a certain humility, or at least intellectual humility, requiring such traits as inquisitiveness, openness to new ideas, and a shared interest in pursuing truth. In the positive psychology movement, the study of both humility and intellectual humility has been grounded in the methods and approach of personality psychology, specifically the examination of these virtues as traits. Consistent with this approach, the chapter begins with a discussion of the examination of (...) intellectual humility as a “character trait,” comparing intellectual humility to various well-known traits in the personality psychology literature (e.g the “Big 5” and the “Big 2”) as well as other key traits such as the need for cognition and the need for closure. The chapter then turns to the proverbial issue of whether virtues in general, and intellectual humility in particular, are a matter of “nature”- that is, an innate trait determined by heritability, or “nurture” – a trait mostly shaped by situation and environment. While the chapter does not resolve the issue, it provides occasion for an examination of the role of situations in the expression of intellectual humility, and for the interaction of “situation” and “trait.” The chapter concludes with a discussion of how the interaction of trait with situation provides the most robust understanding of the psychology of any character virtue, including humility and intellectual humility. (shrink)

Addressing the ‘virtue conflation’ problem requires the preservation of intuitive distinctions between virtue types, that is, between intellectual and moral virtues. According to one influential attempt to avoid this problem proposed by Julia Driver, moral virtues produce benefits to others—in particular, they promote the well-being of others—while the intellectual virtues, as such, produce epistemic good for the agent. We show that Driver's demarcation of intellectual virtue, by adverting to the self-/other distinction, leads to a reductio, and ultimately, that the prospects (...) for resolving the virtue conflation problem look dim within an epistemic consequentialist approach to the epistemic right and the epistemic good. (shrink)

The Gettier dilemma facing reductive analyses of knowledge has not been properly appreciated by virtue epistemologist or even virtue epistemology’s most vocal critics. In §1, we start by considering how recent critics of virtue epistemology understand the Gettier Problem facing virtue-theoretic accounts of knowledge. I highlight how the dilemma facing virtue- theoretic analyses of knowledge is more general than these critics seem to suggest. In §2, I elucidate the worry that the threat facing virtue epistemology is really a dilemma between (...) Gettier counterexamples and radical skepticism. In §3, we will consider how some recent virtue epistemologists have tried to viably defuse the Gettier Problem. We will see (i) just how the critiques elucidated in §1 have (mis)shaped the dialectic between virtue epistemology and what is required in solving Gettier counterexamples and (ii) how this has led to virtue epistemologists underestimating the widespread insidiousness of Gettier counterexamples. (shrink)

While experimental philosophy has fruitfully applied the tools and resources of psychology and cognitive science to debates within epistemology, metaphysics, and ethics, relatively little work has been done within philosophy of religion. And this isn’t due to a lack of need! Philosophers of religion frequently rely on empirical claims that can be either verified or disproven, but without exploring whether they are. And philosophers of religion frequently appeal to intuitions which may vary wildly according to education level, theological background, etc., (...) without concern for whether or not the psychological mechanisms that underwrite those intuitions are broadly shared or reliable. In this chapter, I explore some of the fruit and possibilities for the emerging field of experimental philosophy of religion. First, in Section 1, I will elucidate some of the historical grounding for experimental philosophy of religion. Then in Section 2, I briefly consider how the tools and resources of experimental philosophy might be fruitfully applied to a seminal topic within philosophy of religion, namely, the problem of evil. In Section 3, we’ll sketch some broader applications of experimental philosophy of religion. (shrink)

In this exploratory paper, I consider how intellectual humility and epistemic injustice might contribute to the failure of testimonial exchanges. In §1, I will briefly highlight four broad ways a testimonial exchange might fail. In §2, I will very briefly review the nature of epistemic injustice. In §3, I will explore how both epistemic injustice and intellectual humility can lead to failures in testimonial exchange, and I’ll conclude by suggesting how intellectual humility and epistemic injustice might be related.

In this chapter: I distinguish the existential problem of divine hiddenness from the evidential problem of divine hiddenness. The former being primarily concerned with the apparent hiddenness of a personal God in the lives of believers amidst terrible suffering. The latter being primarily concerned with the apparent hiddenness of God being evidence against God’s existence. In the first section, I highlight the basic contours of the evidential problem of divine hiddenness, and suggested that the argument rests on two important assumptions: (...) the perfectly loving assumption and the no-fault assumption. In the second section, a few possible responses to the evidential problem of divine hiddenness were considered, which center on rejecting either the perfectly loving assumption or the no-fault assumption. (shrink)

Does intellectual humility preclude the possibility of religious dogmatism and firm religious commitments? Does intellectual humility require religious beliefs to be held with diffidence? What is intellectual humility anyway? There are two things I aim to do in this short article. First, I want to briefly sketch an account of intellectual humility. Second, drawing from such an account, I want to explore whether intellectual humility could be compatible with virtuous religious dogmatism.

There are two issues I want to very briefly raise in response to Robin McKenna’s paper, “Epistemic Contextualism, Epistemic Relativism, and Disagreement.” First, I want to question whether or not the disagreement problem faced by indexical contextualism is truly a problem. Secondly, I want to consider whether or not McKenna’s solution is really in keeping with indexical contextualism.

Although the historical reputation of Gottfried Wilhelm Leibniz (1646–1716) largely rests on his philosophical and mathematical work, it is widely known that he made important contributions to many of the emerging but still inchoate branches of natural science of his day. Among the many scientific papers Leibniz published during his lifetime are ones on the nascent science we now know as hydrology. While Leibniz’s other scientific work has become of increasing interest to scholars in recent years, his thinking about hydrology (...) has been neglected, despite being relatively broad in extent, including as it does papers on the ‘raising of vapours’ and the formation of ice, as well as the separation of salt and fresh water. That list can now be extended still further following the discovery of a previously unpublished letter of Leibniz’s on the causes of the devastating Lombardy flood of October and November 1705. This letter, which will be the focus of our paper, reveals the depth of Leibniz’s understanding of key hydrological processes. In it, he considers various mechanisms for the flood, such as heavy rains on high ground, underwater earthquakes, and a mountain collapse. Over the course of the paper we examine each of these mechanisms in depth, and show that Leibniz was in the vanguard of hydrological thinking. We also show that the letter contains one of the first scholarly attempts to apply aspects of the still-forming notion of the hydrological cycle to account for a flood event. (shrink)

Critique of Alonzo Church's Translation Test. Church's test is based on a common misconception of the grammar of (so-called) quotations. His conclusion (that metalogical truths are actually contingent empirical truths) is a reductio of that conception. Chruch's argument begs the question by assuming that translation must preserve reference despite altering logical form of statements whose truth is explained by their form.

Propositional attitude sentences, such as (1) Pierre believes that snow is white, have proved to be formidably difficult to account for in a semantic theory. It is generally agreed that the that-clause ‘that snow is white’ purports to refer to the proposition that snow is white, but no agreement has been reached on what this proposition is. Sententialism is a semantic theory which tries to undermine the very enterprise of understanding what proposition is referred to in (1): according to sententialists, (...) in (1) reference is made to the sentence “Snow is white”. Sententialism is generally considered doomed. The two main reasons why are the famous translation argument, firstly suggested by Alonzo Church, and a problem raised by Stephen Schiffer. The purpose of this paper is to provide a unified solution to both criticisms. What I take to be the key ingredient sententialists may exploit is an observation that concerns the nature of languages and quotations: since quotation marks display the quoted material, if you are a speaker of the language the quoted material belongs to, you usually cannot but understand what is quoted. Moreover, I show that sententialists may appeal to that very observation also in order to answer another problem, pointed out by Kent Bach. I conclude that there are good reasons for resisting the temptation of introducing propositions in order to account for propositional attitude sentences. (shrink)

As emphasized by Alonzo Church and David Kaplan (Church 1974, Kaplan 1975), the philosophies of language of Frege and Russell incorporate quite different methods of semantic analysis with different basic concepts and different ontologies. Accordingly we distinguish between a Fregean and a Russellian tradition in intensional semantics. The purpose of this paper is to pursue the Russellian alternative and to provide a language of intensional logic with a model-theoretic semantics. We also discuss the so-called Russell-Myhill paradox that (...) threatens simple Russellian type theory if propositions satisfies very strict principles of individuation. One way of avoiding the paradox is to adopt a ramified rather than a simple theory of types. (shrink)

Standard compositionality is the doctrine that the semantic content of a compound expression is a function of the semantic contents of the contentful component expressions. In 1954 Hilary Putnam proposed that standard compositionality be replaced by a stricter version according to which even sentences that are synonymously isomorphic (in the sense of Alonzo Church) are not strictly synonymous unless they have the same logical form. On Putnam’s proposal, the semantic content of a compound expression is a function of: (...) (i) the contentful component expressions; and (ii) the expression’s logical form. Kit Fine recently expanded and modified Putnam’s idea into a sweeping theory in philosophy of language and philosophy of mind. The present paper is a detailed critique of Fine’s “semantic relationism.” Fine’s notion of coordination is explained in terms of the familiar pragmatic phenomenon of recognition. A serious error in Fine’s formal disproof of standard Millianism is exposed. It is demonstrated furthermore that Church’s original criticism of Putnam’s proposal can be extended to Fine’s semantic relationism. Finally, it is also demonstrated that the positive position Fine proffers to supplant standard Millianism is in fact exactly equivalent to standard Millianism, so that Fine’s overall position not only does not displace standard Millianism but is in fact inconsistent. (shrink)

W. V. Quine’s criterion of ontological commitment is commonly presented as the slogan: “to be is to be the value of a variable”. More specifically, to be is to be in the domain of values of a bound variable attached to a existential quantifier in the body of a theory. If a sentence of our best available theory quantifies over bachelors, so we conclude that, according to it, there are bachelors. Simplicity and the use of logical apparatus for determining this (...) criterion are responsible for many philosophers to adhere to this standpoint within analytical metaphysics. I will argue that despite this strong influence of the Quinean criterion of ontological commitment in many debates, we find at least three interlinked problems in its original formulation: (1) The criterion depends of a clear definition of theory for the determination of the quantifications counting as entailers of ontological commitments. However, Quine does not present such clear concept of what would be a theory and of how to formalize it. Quine develops this notion under just the metaphor of the knowledge fabric, in which we have a group of sentences, which does not suffice for the required account of ontological commitment. (2) There are distinct possibilities of quantifying over given sentences, which leaves room for different ontological commitments associated with the same statement. In that sense, someone could argue that the Quinean solution would be to endorse just the first order predicate logic. Nonetheless, the Quinean should explain why we ought to be restricted to this logic. (3) The previous problems lead to a possible explosion of the Quinean criterion of ontological commitment, making it trivial, because it permits the quantification over any supposed entities and, hence, that anything can exist. Thus, I will discuss Quine’s criterion of ontological commitment in the light of the abovementioned problems, showing that, unless the Quinean presents a more specific definition of theory beyond just a group of sentences, he leads to an explosion of commitments with different entities. I will conclude that, if you understand ‘theory’ as Alonzo Church’s concept of ‘formalized language’, this knot can be undone. However, Church’s concept is much more akin to Carnap’s linguistic framework than to a notion of knowledge fabric “without borders” as the one proposed by Quine. (shrink)

This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell (...) and others are given. It is in the end shown that developing Frege’s theory in these ways reveals serious problems hitherto largely unnoticed, including those possibly rendering a Fregean intensional logic inconsistent even if his naïve class theory is excluded. (shrink)

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- 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 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 formalism created by specialists for technical purposes. To illustrate some of the main relationships between second-order logic and first-order logic, this paper introduces basic logic, a kind of zero-order logic, which is more rudimentary than first-order and which is transcended by first-order in the same way that first-order is transcended by second-order. The heuristic effectiveness and the historical importance of second-order logic are reviewed in the context of the contemporary debate over the legitimacy of second-order logic. Rejection of second-order logic is viewed as radical: an incipient paradigm shift involving radical repudiation of a part of our scientific tradition, a tradition that is defended by classical logicians. But it is also viewed as reactionary: as being analogous to the reactionary repudiation of symbolic logic by supporters of “Aristotelian” traditional logic. But even if “genuine” logic comes to be regarded as excluding second-order reasoning, which seems less likely today than fifty years ago, its effectiveness as a heuristic instrument will remain and its importance for understanding the history of logic and mathematics will not be diminished. Second-order logic may someday be gone, but it will never be forgotten. Technical formalisms have been avoided entirely in an effort to reach a wide audience, but every effort has been made to limit the inevitable sacrifice of rigor. People who do not know second-order logic cannot understand the modern debate over its legitimacy and they are cut-off from the heuristic advantages of second-order logic. And, what may be worse, they are cut-off from an understanding of the history of logic and thus are constrained to have distorted views of the nature of the subject. As Aristotle first said, we do not understand a discipline until we have seen its development. It is a truism that a person's conceptions of what a discipline is and of what it can become are predicated on their conception of what it has been. (shrink)

Expressions are synonymous if they have the same semantic content. Complex expressions are synonymously isomorphic in Alonzo Church’s sense if one is obtainable from the other by a sequence of alphabetic changes of bound variables or replacements of component expressions by syntactically simple synonyms. Synonymous isomorphism provides a very strict criterion for synonymy of sentences. Several eminent philosophers of language hold that synonymous isomorphism is not strict enough. These philosophers hold that ‘Greeks prefer Greeks’ and ‘Greeks prefer Hellenes’ (...) express different propositions even if they are synonymously isomorphic. They hold that the very recurrence (multiple occurrence) of ‘Greeks’ contributes to the proposition expressed something that indicates the very recurrence in question. Kit Fine argues that this thesis, which he labels semantic relationism calls for a radically new conception of semantics. I have argued that the relevant phenomenon is wholly pragmatic, entirely non-semantic. Here I supplement the case with a new argument. No cognition without recognition—or almost none. With this observation, standard Millianism has sufficient resources to confront Frege’s puzzle and related problems without injecting pragmatic phenomena where they do not belong. (shrink)

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other (...) functions as value. Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at (...) more than one website. Paste the whole URL. http://archive.org/stream/RobertiAudi_The.Cambridge.Dictionary.of.Philosophy/Robert.Audi_The.Cambrid ge.Dictionary.of.Philosophy -/- The 2015 third edition will be available soon. Before you think of buying it read some reviews on Amazon and read reviews of its competition: For example, my review of the 2008 Oxford Companion to Philosophy, History and Philosophy of Logic,29:3,291-292. URL: http://dx.doi.org/10.1080/01445340701300429 -/- Some of the entries have already been found to be flawed. For example, Tarski’s expression ‘materially adequate’ was misinterpreted in at least one article and it was misused in another where ‘materially correct’ should have been used. The discussion provides an opportunity to bring more flaws to light. -/- Acknowledgements: Each of these entries was presented at meetings of The Buffalo Logic Dictionary Project sponsored by The Buffalo Logic Colloquium. The members of the colloquium read drafts before the meetings and were generous with corrections, objections, and suggestions. Usually one 90-minute meeting was devoted to one entry although in some cases, for example, “axiomatic method”, took more than one meeting. Moreover, about half of the entries are rewrites of similarly named entries in the 1995 first edition. Besides the help received from people in Buffalo, help from elsewhere was received by email. We gratefully acknowledge the following: José Miguel Sagüillo, John Zeis, Stewart Shapiro, Davis Plache, Joseph Ernst, Richard Hull, Concha Martinez, Laura Arcila, James Gasser, Barry Smith, Randall Dipert, Stanley Ziewacz, Gerald Rising, Leonard Jacuzzo, George Boger, William Demopolous, David Hitchcock, John Dawson, Daniel Halpern, William Lawvere, John Kearns, Ky Herreid, Nicolas Goodman, William Parry, Charles Lambros, Harvey Friedman, George Weaver, Hughes Leblanc, James Munz, Herbert Bohnert, Robert Tragesser, David Levin, Sriram Nambiar, and others. -/- . (shrink)

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and (...) a natural extension of BLT is definitionally equivalent with ZF. (shrink)

El objetivo de este artículo es presentar dos tópicos de Lógica matemática y sus fundamentos: El primer tópico es una actualización de la demostración de Alonzo Church del Teorema de completitud de Gödel para la Lógica de primer orden, la cual aparece en su texto "Introduction to Mathematical Logic" (1956) y usa el procedimientos efectivos de Forma normal prenexa y Forma normal de Skolem; y el segundo tópico es una demostración de que la propiedad de partición (tipo Ramsey) (...) del espacio topológico de Baire llamada "Propiedad de partición polarizada" es falsa en el Modelo Básico de Cohen. (shrink)

Imagine an equilateral triangle “pointing upward”—its horizontal base under its apex angle. A semiotic triangle has the following three “vertexes”: (apex) an expression, (lower-left) one of the expression’s conceptual meanings or senses, and (lower-right) the referent or denotation determined by the sense [1, pp. 88ff]. One example: the eight-letter string ‘coleslaw’ (apex), the concept “coleslaw” (lower-left), and the salad coleslaw (lower-right) [1, p. 84f]. Using Church’s terminology [2, pp. 6, 41]—modifying Frege’s—the word ‘coleslaw’ expresses the concept “coleslaw”, the word (...) ‘coleslaw’ denotes or names the salad coleslaw, and the concept “coleslaw” determines the salad coleslaw—recalling Frege’s principle that sense determines denotation. Church [2, p. 6] wrote: -/- We shall say that a name denotes or names its denotation and expresses its sense. […] Of the sense we say that it determines its denotation, or is a concept of the denotation. -/- Aristotle seems cognizant of distinctions going beyond those in semiotic triangles. The expression Aristotle’s semiotic pyramids seem warranted by Aristotle’s Categories, 1a1: -/- When [two] things have a name (onoma) in common and the concept (logos) of being (ousia) which corresponds to the name in each case is different, they are called same-named (homonuma). Thus, for example, both a man and a picture [of an animal] are called animals. These have only a name in common. In each case the name’s concept of being [an animal] is different; for if one says what being an animal is for each of them, one will give two distinct concepts. -/- Semiotic triangles and pyramids in Aristotle’s logic are compared to those in Church’s [2]. [1] JOHN CORCORAN, Sentence, proposition, judgment, statement, and fact, Many Sides of Logic, College Publications, 2009. [2] ALONZO CHURCH, Introduction to Mathematical Logic, Princeton, 1956. -/- The semiotic pyramid in Categories, 1a1 has a square base under the vertex ‘animal’. On the corners of the square are: the concept “animal”, the concept “animal picture”, the animals, and the animal pictures. The animals are homonymous with the animal pictures. People find Aristotle’s example far-fetched or inept even if the experience of pointing to a picture while saying “That is Tarski” is familiar. Imagine looking at a painting while thinking “That is an animal”. Without putting too fine a point on this, notice that in Aristotle’s sense it is individual things that are homonymous, not words. It would be natural to say also in his sense that two things are homonyms if one is homonymous with the other. In contrast, we use the words homonym and homonymous to relate words that are spelled the same and pronounced the same but have different meaning. Consider the noun ‘center’ and the verb ‘center’. Consider the noun ‘smell’ and the verb ‘smell’. The spelling of two homonyms is an ambiguity, or an ambiguous spelling. We need appropriate adjectives to distinguish the Categorical senses of ‘homonym’ and ‘homonymous’ from the current English sense just mentioned. I propose ‘ontological’ for the sense relating things and ‘linguistic’ for that relating words. Given that all words are things but not all things are words, we ask are words that are linguistically homonymous also ontologically homonymous? END OF POST ABSTRACT. (shrink)

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 of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...) universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

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 parallel with logicism is incomplete. Logicism with respect to a given branch of knowledge is the view that the branch is ultimately reducible to logic. Every branch of (...) knowledge depends on logic. Psychologism is found in several fields including history, political science, economics, ethics, epistemology, linguistics, aesthetics, mathematics, and logic. Logicism is found mainly in branches of mathematics: number theory, analysis, and, more rarely, geometry. Although the ambiguous term ‘psychologism’ has senses with entirely descriptive connotations, it is widely used in senses that are derogatory. No writers with any appreciation of this point will label their own views as psychologistic. It is usually used pejoratively by people who disapprove of psychologism. The term ‘scientism’ is similar in that it too has both pejorative and descriptive senses but its descriptive senses are rarely used any more. It is almost a law of linguistics that the negative connotations tend to drive out the neutral and the positive. Dictionaries sometimes mark both words with a usage label such as “Usually disparaging”. In this article, the word is used descriptively mainly because there are many psychologistic views that are perfectly respectable and even endorsed by people who would be offended to have their views labeled psychologism. A person who subscribes to logicism is called a logicist, but there is no standard word for a person who subscribes to psychologism. ‘Psychologist’, which is not suitable, occurs in this sense. ‘Psychologician’, with stress on the second syllable as in ‘psychologist’, has been proposed. In the last century, some of the most prominent forms of psychologism pertained to logic; the rest of this article treats only such forms. Psychologism in logic is very “natural”. After all, logic studies reasoning, which is done by the mind, whose nature and functioning is studied in psychology—using the word ‘psychology’ in its broadest etymological sense. (shrink)

This paper sketches a framework for the separation of church and state and, with the framework in view, indicates why a government’s maintaining such separation poses challenges for balancing two major democratic ideals: preserving equality before the law and protecting liberty, including religious liberty. The challenge is particularly complex where healthcare is either provided or regulated by government. The contemporary problem in question here is the contraception coverage requirement in the Obama Administration’s healthcare mandate. Many institutions have mounted legal (...) challenges to the mandate on grounds of religious freedom. The paper proposes a number of interconnected principles toward a resolution of the problem: for the institutional realm, specific principles for church-state separation and a principle concerning the protection of citizens’sense of identity; and for the ethics of citizenship in the conduct individuals, principles that provide an adequate place for natural (thus secular) reason in lawmaking and political decisions. (shrink)

This article aims to provide a framework for the attitude of the Orthodox Church towards other religions, an attitude that must be expressed today in the public space. Contemporary global society is a society of the plurality of religious identities. Nowadays, the Orthodox Church has to rethink the pastoral missionary program taking into account this new reality.

This article aims to provide a framework for the attitude of the Orthodox Church towards other religions, an attitude that must be expressed today in the public space. Contemporary global society is a society of the plurality of religious identities. Nowadays, the Orthodox Church has to rethink the pastoral missionary program taking into account this new reality.

Somewhat traumatized by the Galileo Affair the Church until recently showed low profile in the conflicts with science, evolutionary theory included. The talk presents a categorization of possible relationships between science and religion by distinguishing between "Galilean conflicts", which are about mutually exclusive statements about matters of fact, and Freudian conflicts where an empirical science tries to explain away religion as a phenomenon in its own right. In the light of this distinction I deal with the reactions of the (...) Church since 1859, particularly with the ambiguous position of the present Pope. (shrink)

The church-funded CARFO or KARFO (Afrikaans Christian Filmmaking Organisation) was established in 1947, and aimed to ‘[socialise] the newly urbanized Afrikaner into a Christian urban society’ (Tomaselli 1985:25; Paleker 2009:45). This initiative was supported and sustained by the Dutch Reformed Church (DRC), which had itself been part of the sociopolitical and ideological fabric of Afrikaans religious life for a while and would guide Afrikaners through tensions between religious conservatism and liberalism and into apartheid. Given Afrikaans cinema’s ties with (...) Christian religious and political conservatism, we explore the role – even the centrality – of the Afrikaans church in cultural activity before 1994, and then after 1994. Here, Afrikaans church is an inclusive term that brings together various denominations of Afrikaans-speaking churches, but which mainly suggests the domination of the DRC. After establishing the role of the Afrikaans church in the way described above, we move towards the primary focus of our study: exploring the representation of clergy in the contemporary Afrikaans film Faan se Trein in order to describe certain theological implications of this representation. With reference to Faan se Trein, our article notes and comments on the shifts that have occurred in clergy representation in Afrikaans cinema over the past decades. Osmer’s four tasks of practical theology, namely, descriptive, interpretive, normative and strategic are used for theological reflection. With due contextual reference to Afrikaans film dramas such as Broer Matie [Brother Matie], Saak van Geloof [A Matter of Faith], Roepman [Stargazer], Stilte [Silence], Suiderkruis [Southern Cross] and Faan se Trein, we arrive at some preliminary conclusions about the representation of clergy in mainly contemporary Afrikaans cinema. (shrink)

In this article, chronological information will be given about the takkas established in the church buildings in Istanbul. After the conquest of Istanbul in 1453 Mehmet II started to establish works of foundation in the city in order to reorganise the city and the statesmen were encouraged the creation of such charitable works. In order to provide the current needs in the city, some of the churches were converted into mosques, masjids, madrasah, lodges- takkas and public soup kitchens. Among (...) these structures, there were double-function buildings serving both as a mosque and as a takka. Many of these mosques and masjids were used as a religious ceremony place/tevhidhane, suffering place/çilehane and training place. There are mosque and takkas were build on the grounds of many ruin churches, which could not be restored due to various reasons. In Istanbul, there were eighteen churches which were used as tevhidhane where the chanting of the tariqah was made on certain days of the week, and takkas were built in their places. (shrink)