Frege and Heidegger appear to appear to have diametrically opposed attitudes towards logic. Frege thinks logic must govern any investigation whatsoever, whereas Heidegger (in "What is Metaphysics?") apparently wants to dismantle logic. But when they try to explicate the nature of judgment, a striking similarity emerges. For while their accounts of judgment are radically different, each finds his account to be, by his own lights, _inexpressible<D>. This paper shows how Heidegger and Frege arrive at their respective accounts of judgment, explains (...) why they regard the status of their accounts as problematic, and explores and evaluates their responses to their parallel predicaments. (shrink)

Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no (...) theory which interprets Q closed under the standard structural rules can define nor express validity, on pain of triviality. The results put pressure on the widespread view that there is an asymmetry between truth and validity, viz. that while the former cannot be defined within the language, the latter can. I argue that Vann McGee's and Hartry Field's arguments for the asymmetry view are problematic. (shrink)

My propositions are elucidatory in this way: he who understands them eventually recognizes them as senseless [unsinnig], when he has climbed out through them, on them, over them… He must surmount these propositions; then he sees the world rightly. (Tractatus 6.54) These statements must be taken seriously and therefore must be interpreted as literally possible. They have nevertheless been experienced by some philosophers as posing a major interpretational problem. For if Wittgenstein’s words are taken literally, we seem to have a (...) major problem in our hands. If what Wittgenstein had said before proposition 6.54 is literally nonsense, we apparently cannot understand his book at its face value. And, as was pointed out, this face value is that of a treatise in logical semantics. Hence.. (shrink)

Let us assume that you are entrusted by UNESCO with an important task. You are asked to devise a universal logical language, a Begriffsschrift in Frege's sense, which is to serve the purposes of science, business and everyday life. What requirements should such a “conceptual notation” satisfy? There are undoubtedly many relevant desiderata, but here I am focusing on one unmistakable one. In order to be a viable lingua universalis, your language must in any case be capable of representing (...) any possible configuration of dependence and independence between different variables. For if such a configuration is possible in principle, there is no guarantee that it might not one day show up among the natural, human or social phenomena we have to study.But how are dependencies and independencies between variables expressed in our familiar logical notation? Every logician worth his or her truth-table knows the answer. Dependencies between two variables are expressed by dependencies between the quantifiers to which they are bound. For instance, inthe variable y depends on x, while inz depends on x but not on y, while u depends on both x and y.But how is the dependence of a quantifier on another one expressed in familiar logical languages? Obviously by occurring in its scope, indicated by the pair of parentheses following it. But the nesting of scopes is a transitive and antisymmetrical relation which allows branching only in one direction. Hence other kinds of structures of dependence and independence between variables are not representable in the received logical notation. Such previously inexpressible structures form the subject matter of what has been referred to as independence-friendly logic. (shrink)

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

Let us assume that you are entrusted by UNESCO with an important task. You are asked to devise a universal logical language, a Begriffsschrift in Frege's sense, which is to serve the purposes of science, business and everyday life. What requirements should such a “conceptual notation” satisfy? There are undoubtedly many relevant desiderata, but here I am focusing on one unmistakable one. In order to be a viable lingua universalis, your language must in any case be capable of representing (...) any possible configuration of dependence and independence between different variables. For if such a configuration is possible in principle, there is no guarantee that it might not one day show up among the natural, human or social phenomena we have to study.But how are dependencies and independencies between variables expressed in our familiar logical notation? Every logician worth his or her truth-table knows the answer. Dependencies between two variables are expressed by dependencies between the quantifiers to which they are bound. For instance, inthe variable y depends on x, while inz depends on x but not on y, while u depends on both x and y.But how is the dependence of a quantifier on another one expressed in familiar logical languages? Obviously by occurring in its scope, indicated by the pair of parentheses following it. But the nesting of scopes is a transitive and antisymmetrical relation which allows branching only in one direction. Hence other kinds of structures of dependence and independence between variables are not representable in the received logical notation. Such previously inexpressible structures form the subject matter of what has been referred to as independence-friendly logic. (shrink)

Unification in description logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive description logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has been shown to be NP-complete and, thus, of considerably lower complexity than unification in other description logics of similarly restricted expressive power. However, EL allows (...) the use of the top concept, which represents the whole interpretation domain, whereas the large medical ontology SNOMED CT makes no use of this feature. Surprisingly, removing the top concept from EL makes the unification problem considerably harder. More precisely, we will show that unification in EL without the top concept is PSPACE-complete. In addition to the decision problem, we also consider the problem of actually computing EL−⊤-unifiers. (shrink)

In his recent paper in History and Philosophy of Logic, John Kearns argues for a solution of the Liar paradox using an illocutionary logic (Kearns 2007 ). Paraconsistent approaches, especially dialetheism, which accepts the Liar as being both true and false, are rejected by Kearns as making no ?clear sense? (p. 51). In this critical note, I want to highlight some shortcomings of Kearns' approach that concern a general difficulty for supposed solutions to (semantic) antinomies like the Liar. It is (...) not controversial that there are languages which avoid the Liar. For example, the language which consists of the single sentence ?Benedict XVI was born in Germany? lacks the resources to talk about semantics at all and thus avoids the Liar. Similarly, more interesting languages such as the propositional calculus avoid the Liar by lacking the power to express semantic concepts or to quantify over propositions. Kearns also agrees with the dialetheist claim that natural languages are semantically closed (i.e. are able to talk about their sentences and the semantic concepts and distinctions they employ). Without semantic closure, the Liar would be no real problem for us (speakers of natural languages). But given the claim, the expressive power of natural languages may lead to the semantic antinomies. The dialetheist argues for his position by proposing a general hypothesis (cf. Bremer 2005 , pp. 27?28): ?(Dilemma) A linguistic framework that solves some antinomies and is able to express its linguistic resources is confronted with strengthened versions of the antinomies?. Thus, the dialetheist claims that either some semantic concepts used in a supposed solution to a semantic antinomy are inexpressible in the framework used (and so, in view of the claim, violate the aim of being a model of natural language), or else old antinomies are exchanged for new ones. One horn of the dilemma is having inexpressible semantic properties. The other is having strengthened versions of the antinomies, once all semantic properties used are expressible. This dilemma applies, I claim, to Kearns' approach as well. (shrink)

This paper introduces a new Ehrenfeucht-Fraïssé type game that is played on two classes of models rather than just two models. This game extends and generalizes the known Ajtai-Fagin game to the case when there are several alternating moves played in different models. The game allows Duplicator to delay her choices of the models till the very end of the game, making it easier for her to win. This adds on the toolkit of winning strategies for Duplicator in Ehrenfeucht-Fraïssé type (...) games and opens up new methods for tackling some open problems in descriptive complexity theory. As an application of the class game, it is shown that, if m is a power of a prime, then first order logic augmented with function quantifiers F1n of arity 1 and height n < m can not express that the size of the model is divisible by m. This, together with some new expressibility results for Henkin quantifiers H1n gives some new separation results on the class of finite models among various F1n on one hand and between F1n and H1n on the other. Since function quantifiers involve a bounded type of second order existential quantifiers, the class game solves an open problem raised by Fagin, which asks for some inexpressibility result using a winning strategy by Duplicator in a game that involves more than one coloring round. (shrink)

One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most of the (...) propositions which can be constructed from possible and impossible worlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (shrink)

Inexpressibility results in Finite Model Theory are often proved by showing that Duplicator, one of the two players of an Ehrenfeucht game, has a winning strategy on certain structures.In this article a new method is introduced that allows, under certain conditions, the extension of a winning strategy of Duplicator on some small parts of two finite structures to a global winning strategy.As applications of this technique it is shown that • — Graph Connectivity is not expressible in existential monadic (...) second-order logic , even in the presence of a built-in linear order,• — Graph Connectivity is not expressible in MonNP even in the presence of arbitrary built-in relations of degree n0, and• — the presence of a built-in linear order gives MonNP more expressive power than the presence of a built-in successor relation. (shrink)

Perhaps the most important work of philosophy written in the twentieth century, the Tractatus Logico-Philosophicus first appeared in 1921 and was the only philosophical work that Ludwig Wittgenstein (1889-1951) published during his lifetime. Written in short, carefully numbered paragraphs of extreme compression and brilliance, it immediately convinced many of its readers and captivated the imagination of all. Its chief influence, at first, was on the Logical Positivists of the 1920s and 30s, but many other philosophers were stimulated by its (...) philosophy of language, finding attractive, if ultimately unsatisfactory, its view that propositions were pictures of reality. Perhaps most of all, Wittgenstein himself, after his return to philosophy in the late 1920s, was fascinated by its vision of an inexpressible, crystalline world of logical relationships. The posthumous publication of other writings has, therefore, only served to reawaken interest in the Tractatus and to illuminate its more neglected aspects. David Pears and Brian McGuinness revised their translation in the light of Wittgenstein's own suggestions and comments in his correspondence with C.K. Ogden about the first translation. In addition, this edition contains the introduction by Bertrand Russell which appeared in the original English translation. (shrink)

Perhaps the most important work of philosophy written in the twentieth century, the Tractatus Logico-Philosophicus first appeared in 1921 and was the only philosophical work that Ludwig Wittgenstein (1889-1951) published during his lifetime. Written in short, carefully numbered paragraphs of extreme compression and brilliance, it immediately convinced many of its readers and captivated the imagination of all. Its chief influence, at first, was on the Logical Positivists of the 1920s and 30s, but many other philosophers were stimulated by its (...) philosophy of language, finding attractive, if ultimately unsatisfactory, its view that propositions were pictures of reality. Perhaps most of all, Wittgenstein himself, after his return to philosophy in the late 1920s, was fascinated by its vision of an inexpressible, crystalline world of logical relationships. The posthumous publication of other writings has, therefore, only served to reawaken interest in the Tractatus and to illuminate its more neglected aspects. David Pears and Brian McGuinness revised their translation in the light of Wittgenstein's own suggestions and comments in his correspondence with C.K. Ogden about the first translation. In addition, this edition contains the introduction by Bertrand Russell which appeared in the original English translation. (shrink)

It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are (...) adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis' counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics. (shrink)

I argue that Frege's so-called "concept 'horse' problem" is not one problem but many. When these different sub-problems are distinguished, some emerge as more tractable than others. I argue that, contrary to a widespread scholarly assumption originating with Peter Geach, there is scant evidence that Frege engaged with the general problem of the inexpressibility of logical category distinctions in writings available to Wittgenstein. In consequence, Geach is mistaken in his claim that in the Tractatus Wittgenstein simply accepts from (...) Frege certain lessons about the inexpressibility of logical category distinctions and the say-show distinction. In truth, Wittgenstein drew his own morals about these matters, quite possibly as the result of reflecting on how the general problem of the inexpressibility of logical category distinctions arises in Frege's writings , but also, quite possibly, by discerning certain glimmerings of these doctrines in the writings of Russell. (shrink)

Typical applications of Hintikka’s game-theoretical semantics give rise to semantic attributes—truth, falsity—expressible in the $\Sigma^{1}_{1}$-fragment of second-order logic. Actually a much more general notion of semantic attribute is motivated by strategic considerations. When identifying such a generalization, the notion of classical negation plays a crucial role. We study two languages, $L_{1}$ and $L_{2}$, in both of which two negation signs are available: $\rightharpoondown $ and $\sim$. The latter is the usual GTS negation which transposes the players’ roles, while the former (...) will be interpreted via the notion of mode. Logic $L_{1}$ extends independence-friendly logic; $\rightharpoondown $ behaves as classical negation in $L_{1}$. Logic $L_{2}$ extends $L_{1}$, and it is shown to capture the $\Sigma^{2}_{1}$-fragment of third-order logic. Consequently the classical negation remains inexpressible in $L_{2}$. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:706 BOOK REVIEWS struments of redemption for others. Mary is the primary exemplar of receiving her Son's redeeming love in freedom and of wholeheartedly mediating his graces to all he has redeemed. The final essay, "Mary and Modernity," is most timely for American Christians and ecumenists. It is a very worthwhile attempt to compare and contrast the secular triad of virtues, liberty, equality, and fraternity with the Christian triad (...) of theological virtues, faith, hope, and love, especially as they are exemplified in Mary. Although this approach perceives Mary more as a " sign of contradiction " to our secularistic culture, she will help us to avoid the extremes of confusing true freedom with licence, genuine equality with egalitarianism, and authentic fraternity with collectivism by helping inspire in us the really liberating values of her Son's Gospel. Everyone can benefit immensely from the intelligent reading of this book. Mt. St. Mary's Seminary Emmitsburg, Maryland FREDERICK M. JELLY, O.P. Dieu et l'etre d'apres Thomas d'Aquin et Hegel. By EMILIO BRITO. Paris: Presses Universitaires de France, 1991. Pp. 422. 245 francs. Sprung from premature fears of post-modernity or from an ignorant nostalgia for a monoform Catholicism which never existed, universal dismissals of " modernity " still appear occasionally in Catholic j ournals. They recall,the neo-scholastic te:xitbooks prior to Vatican II in whose pages the " moderni " (among whom were numbered not only "Kantiani" but "Hegeliani ") were dismissed by authors who, having read a few pages, were incapable of grasping the basic directions of philosophy from Herder to Heidegger. Emilio Brito, S.J., however, follows in the line of the French and German Jesuits: through this century they have sustained a varied dialogue, in philosophy and theology, between Thomas Aquinas and the important figures of modern philosophy. His two works on Hegel's Christology, and a third large study of God and creation in Schelling are now followed by this comparative work. The theology of Aquinas and the philosophy of Hegel are like two galaxies. Do they move past each other at a distance, or do they move through each other guarding a proper identity with similar forces and shared motifs? Brito has chosen one theme within these two vast realms of thought: his topic (and the book's title can mislead) is God; 'being' BOOK REVIEWS 707 is present as a stimulus to our reflection about God. After an introduction on recent interpretations of Hegel, particularly by Catholics, pages which should be read by all interested in contemporary theology, there are three sections: " the knowledge and naming of God," " the divine substance and the cycle of its attributes," and " the operations of absolute spirit." The chapters in each of the three areas present Aquinas's and then Hegel's thought, and sometimes a section of further comparison. At the end of the work Brito offers a conclusion ("God's Goodness") and a postlude ("God's Beauty"). Finally there is a "Resume." According to Brito, Aquinas's thought is clear (his Aristotelian logic is readily understandable), and his emphasis lies with the divine transcendence. Despite the process-format of the Summa theologiae and the traces of history in the headship of Christ, the diversity of sacraments, and the theologies of faith and natural law, his modest description of movement in God and in God's world of beings stands in contrast to the unleashed and unresolved development penetrating Hegel's Geist. The concluding " Resume " of nine pages is particularly valuable as it brings together the author's synthetic insights into Aquinas and Hegel (one might hope that at least it would appear in translation). The following excerpt displays its balance and clarity. The God of the Summa tends to stay back from mediation, letting itself exist in a certain exteriority, while the Hegelian absolute " raises out" the determinations it posits only by also absorbing them negatively. In the same vein, the Hegelian parousia of the negative abolishes absolutely the distance maintained by the inexpressible in language. In an opposite direction, the originating positivity of the God of Thomas grounds the irreducible presence of a reality represented in discourse. If he is a stranger to this approach and more... (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

Oxford Studies in Metaphysics is the forum for the best new work in this flourishing field. Much of the most interesting work in philosophy today is metaphysical in character: this new series is a much-needed focus for it. OSM offers a broad view of the subject, featuring not only the traditionally central topics such as existence, identity, modality, time, and causation, but also the rich clusters of metaphysical questions in neighbouring fields, such as philosophy of mind and philosophy of science. (...) Besides independent essays, volumes will often contain a critical essay on a recent book, or a symposium that allows participants to respond to one another's criticisms and questions. Anyone who wants to know what's happening in metaphysics can start here. Volume Two begins with a major paper on consciousness by Ned Block. Block examines 'Max Black's Objection to Mind-Body Identity', an argument for a dualism of physical and phenomenal properties, closely related to Jackson's 'knowledge argument'. His extensive exploration of this family of arguments for property dualism includes considerable discussion of John Perry and Stephen White; their responses to Block's paper complete the section on the metaphysics of consciousness.Three papers consider the thesis that the future is, in some sense, 'open'. Eli Hirsch elaborates a view according to which contingent statements about the future can be indeterminate in truth-value, while preserving 'straight logic', including a principle of bivalence. Peter Forrest defends a sort of 'growing block' theory of the passage of time, emphasizing the way such a metaphysics, combined with a truth-maker principle, can provide an analysis of natural necessity. Trenton Merricks presents a trenchant and original criticism of the 'growing block' theory of time.The volume continues with a group of papers on problems of ontology. Thomas Hofweber's paper, defending nominalism from the objection that there are 'inexpressible' properties and propositions, won the first annual Oxford Studies in Metaphysics Younger Scholar Prize. The papers by Phillip Bricker and Michael Loux examine a couple of deep divides within ontology. John Hawthorne's paper raises some extremely puzzling questions about the nature of persons, given the ontology needed for Timothy Williamson's theory of vagueness. Hawthorne uses these problems to motivate an alternative style of epistemicism. The final three papers take up several issues in the metaphysics of traditional theism. Michael Bergmann and Jeffrey Brower raise objections to combining a Platonic conception of universals with the doctrine of divine aseity; while Brian Leftow defends a non-Platonic theory of universals - a kind of divine-concept nominalism. Hud Hudson suggests that contemplation of the possibility of higher dimensions opens up new avenues in theodicy. (shrink)

In a series of papers, 137–158; 1994, Midwest Studies in Philosophy, 23, 61–74, 1999) Fine develops his hylomorphic theory of embodiments. In this article, we supply a formal semantics for this theory that is adequate to the principles laid down for it in. In Section 1, we lay out the theory of embodiments as Fine presents it. In Section 2, we argue on Cantorian grounds that the theory needs to be stabilized, and sketch some ways forward, discussing various choice points (...) in modeling the view. In Section 3, we develop a formal semantics for the theory of embodiments by constructing embodiments in stages and restricting the domain of the second-order quantifiers. In Section 4 we give a few illustrative examples to show how the models deliver Finean hylomorphic consequences. In Section 5, we prove that Fine’s principles are sound with respect to this semantics. In Section 6 we present some inexpressibility results concerning Fine’s various notions of parthood and show that in our formal semantics these notions are all expressible using a single mereological primitive. In Section 7, we prove several mereological results stemming from the model theory, showing that the mereology is surprisingly robust. In Section 8, we draw some philosophical lessons from the formal semantics, and in particular respond to Koslicki’s main objection to Fine’s theory. In the appendix we present proofs of the inexpressibility results of Section 6. (shrink)

I critically examine some deflationary theories of properties, according to which properties are ‘shadows of predicates’ and quantification over them serves a mere quasi-logical function. I start by considering Hofweber’s internalist theory, and pose a problem for his account of inexpressible properties. I then introduce a theory of properties that closely resembles Horwich’s minimalist theory of truth. This theory overcomes the problem of inexpressible properties, but its formulation presupposes the existence of various kinds of abstract objects. I discuss some (...) ways to reduce these existence assumptions, but ultimately suggest that deflationists can hardly avoid quantification over abstract objects of one sort or another. I conclude that property deflationism is perhaps not as deflationary as some philosophers want it to be, but that it’s still apt to call the position ‘deflationary’. (shrink)

This paper introduces and explores a conservative extension of inquisitive logic. In particular, weak negation is added to the standard propositional language of inquisitive semantics, and it is shown that, although we lose some general semantic properties of the original framework, such an enrichment enables us to model some previously inexpressible speech acts such as weak denial and ‘might’-assertions. As a result, a new modal logic emerges. For this logic, a Fitch-style system of natural deduction is formulated. The main result (...) of this paper is a theorem establishing the completeness of the system with respect to inquisitive semantics with weak negation. At the conclusion of the paper, the possibility of extending the framework to the level of first order logic is briefly discussed. (shrink)

Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a language, higher-order (...) contingentists cannot express what is communicated using various instances of talk of ‘possible things’, such as ‘there are uncountably many possible stars’. (shrink)

The Tractatus Logico-Philosophicus first appeared in 1921 and was the only philosophical work that Ludwig Wittgenstein (1889-1951) published during his lifetime. Written in short, carefully numbered paragraphs of extreme compression and brilliance, it immediately convinced many of its readers and captured the imagination of all. Its chief influence, at first, was on the Logical Positivists of the 1920s and 1930s, but many other philosophers were stimulated by its philosophy of language, finding attractive, even if ultimately unsatisfactory, its view that (...) propositions were pictures of reality. Perhaps most of all, its own author, after his return to philosophy in the late 1920s, was fascinated by its vision of an inexpressible, crystalline world of logical relationships. C.K. Ogden's translation of the Tractatus Logico-Philosophicus has a unique provenance. As revealed in Letters of C.K. Ogden (1973) and in correspondence in The Times Literary Supplement , Wittgenstein, Ramsey and Moore all worked with Ogden on the translation, which had Wittgenstein's complete approval. The very name Tractatus Logico-Philosophicus was of Ogden's devising; and there is very strong feeling among philosophers that, among the differing translations of this work, Ogden's is the definitive text - and Wittgenstein's version of the English equivalent of his Logisch-Philosophische Abhandlung. (shrink)

While committed to the view that Buddhist Reductionism offers the best account of the Abhidharma distinction of the two truths, Siderits (2009) argues that Buddhist Reductionism has the surprising consequence of making itself inexpressible. This inexpressibility follows from the semantic insulation between conventional and ultimate discourses that Siderits argues is required in order to preserve classical logic for both types of discourse, avoiding contradiction and bivalence failure. I argue that inexpressibility is a problematic consequence that threatens to constitute (...) a reductio of Buddhist Reductionism. (shrink)

The paper presents the theological and philosophical category of Deus absconditus and shows it in the perspective of Nicholas of Cusa’s ideas contained in his dialogue De Deo Abscondito. The hidden God is the totally transcendent God that is beyond creation both ontologically and logically. Deus absconditus is God that cannot be the object of rational cognition and positive knowledge, hence the only way to acquire any knowledge of him is the method of negative theology. Therefore, the hidden God is (...) the subject of mystical epistemology. Cusanus’s Deus absconditus is also called Truth and as such he is not only incomprehensible, but also incommunicable. God’s transcendence, rational unintelligibility and inexpressibility are the aspects which the considerations presented in this paper build on. (shrink)

The language of quantification theory does not seem to adequately reflect the logic of mass terms in ordinary english. Mass terms are treated as though they are true of objects which can be counted. In this paper, It is argued that by placing certain restrictions upon formulas which contain the identity sign it is possible to arrive at a formalization of mass term sentences which avoids this difficulty. The proposed restrictions are defended against charges that certain mass term sentences seem (...) to be rendered inexpressible. (shrink)

The Tractatus Logico-Philosophicus first appeared in 1921 and was the only philosophical work that Ludwig Wittgenstein published during his lifetime. Written in short, carefully numbered paragraphs of extreme compression and brilliance, it immediately convinced many of its readers and captured the imagination of all. Its chief influence, at first, was on the Logical Positivists of the 1920s and 1930s, but many other philosophers were stimulated by its philosophy of language, finding attractive, even if ultimately unsatisfactory, its view that propositions (...) were pictures of reality. Perhaps most of all, its own author, after his return to philosophy in the late 1920s, was fascinated by its vision of an inexpressible, crystalline world of logical relationships. C.K. Ogden's translation of the Tractatus Logico-Philosophicus has a unique provenance. As revealed in Letters of C.K. Ogden and in correspondence in The Times Literary Supplement , Wittgenstein, Ramsey and Moore all worked with Ogden on the translation, which had Wittgenstein's complete approval. The very name Tractatus Logico-Philosophicus was of Ogden's devising; and there is very strong feeling among philosophers that, among the differing translations of this work, Ogden's is the definitive text - and Wittgenstein's version of the English equivalent of his Logisch-Philosophische Abhandlung. (shrink)

A selection of essays dedicated to Hans Herzberger with affection and gratitude for both his profound work and his lasting example. Contributors: I. Levi (on whether and how a rational agent should be seen as a maximizer of some cognitive value), C. Normore (on medieval accounts of logical validity), J. P. Tappenden (on the local influences on Frege's doctrines), A. Urquhart (on the inexpressible), A. C. Varzi (on dimensionality and the sense of possibility), and S. Yablo (on content and (...) carvings, and from there to mathematical realism). (shrink)

Wittgenstein's middle period work has been brought into the current debate on rule following and representation by Kripke and the Hintikkas. In my dissertation, I argue that approaches which aim at a consistent reconstruction of Wittgenstein's argument, while valuable in their own right, fail to do justice to his focus on the conflicting intuitions that lie behind philosophical theory building. For this hidden and ambiguous side to his thought is the turning point in his philosophical development. ;One can summarise my (...) findings as follows: In 1929, Wittgenstein recognised that the analysis of colour propositions forced him to give up the Tractarian doctrine that analysis must end in logically independent elementary propositions. From this point, his work branched out in two main directions. On the one hand, he worked on 'philosophical grammar': analyses of the rules we follow in talking about such matters as colour, visual experience, intention, time, memory and the philosophical subject. Here, the picture theory provided the basis for an account of how the mind represents the world. On the other hand, he also thought of language as a 'secondary' system, to be contrasted with direct apprehension of the 'primary' phenomena. This view, which is set out most fully in several chapters of an unpublished typescript , led to a seemingly inexpressible solipsism on which 'all is in flux.' The attempt to reconcile the two conceptions of the pictorial analogy--language as a system of representational conventions and experience as a direct presentation of the phenomena--ultimately led him to see the dangers in that analogy and thus to his later notion of a 'philosophical picture.'. (shrink)

This is a sweeping and provocative work of aesthetic theory: a trenchant critique of the philosophy of art as it developed from the eighteenth century to the early twentieth century, combined with a carefully reasoned plea for a new and more flexible approach to art.Jean-Marie Schaeffer, one of France's leading aestheticians, explores the writings of Kant, Schlegel, Novalis, Hegel, Schopenhauer, Nietzsche, and Heidegger to show that these diverse thinkers shared a common approach to art, which he calls the "speculative theory." (...) According to this theory, art offers a special kind of intuitive, quasi-mystical knowledge, radically different from the rational knowledge acquired by science. This view encouraged theorists to consider artistic geniuses the high-priests of humanity, creators of works that reveal the invisible essence of the world. Philosophers came to regard inexpressibility as the aim of art, refused to consider second-tier creations genuine art, and helped to create conditions in which the genius was expected to shock, puzzle, and mystify the public. Schaeffer shows that this speculative theory helped give birth to romanticism, modernism, and the avant-garde, and paved the way for an unfortunate divorce between art and enjoyment, between "high art" and popular art, and between artists and their public.Rejecting the speculative approach, Schaeffer concludes by defending a more tolerant theory of art that gives pleasure its due, includes popular art, tolerates less successful works, and accounts for personal tastes."[A] remarkable work.... [Schaeffer's] writing is governed by... the ideals of clarity and consequence, the ideas of logic, truth, and evidence.... Schaeffer is so precise and unrelenting a philosophical critic that one wonders how some of the philosophies he anatomizes here can possibly survive the operation."--From the foreword by Arthur C. Danto. (shrink)

The Jaina _saptabhaṅgī_ (seven angles of analysis or types of sentences) has drawn the attention of non-classical logicians due to its unique use of negation, contradiction, and _avaktavya_ (‘unutterable’). In its most basic structure, the _saptabhaṅgī_ appears as: (i) in a certain sense, _P_; (ii) in a certain sense, not _P_; (iii) in a certain sense, _P_ and not _P_; (iv) in a certain sense, inexpressibility of _P_; (v) in a certain sense, _P_ and inexpressibility of _P_; (vi) (...) in a certain sense, not _P_ and inexpressibility of _P_; (vii) in a certain sense, _P_, not _P_, and inexpressibility of _P_. This appearance has led many (e.g., Ganeri and Priest) to claim that the _saptabhaṅgī_ supports non-classical systems of logic, but such a reading is contested by Balcerowicz. Focusing on Vādidevasūri’s (12th c. CE) and Yaśovijaya’s (17th c. CE) accounts of the _saptabhaṅgī_, this paper puts forward a formalization of the _saptabhaṅgī_ that brings together the non-classical views and Balcerowicz’s view through relating the _saptabhaṅgī_ to the Buddhist unanswerable questions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Bergsonism and the History of Analytic Philosophy by Andreas VrahimisLeonard LawlorAndreas Vrahimis. Bergsonism and the History of Analytic Philosophy. History of Analytic Philosophy. Cham: Palgrave Macmillan, 2022. Pp. xix + 395. Hardback, $139.99.Bergsonism and the History of Analytic Philosophy is a great achievement in the history of ideas in general. The wealth of historical details that Andreas Vrahimis musters indicates that he has a profound understanding of twentieth-century (...) philosophy. More importantly, this book overflows with philosophical insights. The wealth of insights indicates that Bergsonism and the History of Analytic Philosophy is also a great achievement in philosophy as such. Andreas Vrahimis has written a remarkable book.Bergsonism and the History of Analytic Philosophy presents the origins of the division between analytic philosophy and continental philosophy. This story is familiar, with analytic philosophy siding with science and continental with poetry; with analytic philosophy being a kind of rationalism and continental a kind of irrationalism; with analytic philosophy using a writing style of dry, logical argumentation and continental using a writing style of images and emotions; and finally, with analytic philosophy writing only of what can be expressed and continental writing of the ineffable. Yet, Bergsonism and the History of Analytic Philosophy tells a story that is unfamiliar and even novel. The genealogy Vrahimis lays out is not of the rift between analytic philosophy and phenomenology (although this rift appears in the book's final chapters) but between analytic philosophy and Bergson. As Vrahimis clearly shows, the popularity of Bergson's thought at the beginning of the twentieth century caused the split, and even the hostility, between analytic and continental [End Page 332] philosophy. Therefore, Vrahimis does not title his book Bergson and the History of Analytic Philosophy, but Bergsonism and the History of Analytic Philosophy (2). Bergsonism is the popular view of Bergson's thought. It turned Bergson's thought into a "fad" (263). But Bergsonism contained many misunderstandings of Bergson. In the early twentieth century, Bergson was, in short, "a misunderstood celebrity." Unfortunately for Bergson's legacy, Bergson himself allowed Bergsonism to flourish as a cultural movement. Until The Creative Mind (published in 1934 in France as La pensée et le mouvant, after "the demise of Bergsonism"), Bergson never attempted to correct the misinterpretations of his thought that Bergsonism presented. Chapter by chapter, Vrahimis shows how the analytic philosophy criticisms leveled against Bergson are based in Bergsonism's distortions of Bergson's thought. The founding members of analytic philosophy aimed their attacks at a strawman Bergson.Bergsonism and the History of Analytic Philosophy's first three chapters set the stage for the analytic philosophers' attacks on Bergson. In fact, chapter 3 contains one of the clearest summaries of Bergson's thought I have ever read. Then, the book is arranged chronologically, starting with William James's 1905 "The Experience of Activity" in chapter 4 and ending with Ryle's 1958 "Phenomenology versus The Concept of Mind" in chapter 12. William James is not one of Bergson's critics. Chapter 4 shows how James praised Bergson's thought because of its similarity with pragmatism. This praise popularized Bergson's thought and thus led to Bergsonism. Chapters 4 through 12 (there is also a chapter 13 that serves as the book's conclusion) concern specific philosophers' criticisms of Bergson and then, in the final chapters, specific philosophers' criticisms of Lebensphilosophie and continental philosophy. There are chapters on Russell, Karin Costelloe-Stephen, L. Susan Stebbing, Neurath and the Vienna Circle (against Lebensphilosophie), Schlick (against Bergson as the originator of Lebensphilosophie), Carnap and Ayer (against Heidegger and Sartre), and Ryle (against Husserl). Most of the chapters concern the criticisms that resulted from Bergson's valorization of intuition as a source of knowledge. Bergson's definitions of intuition contribute to the belief that he is antiscience and an anti-intellectualist. Because intuition is introspection, it even suggests that Bergson's own philosophy is a kind of individualism. Because intuition is inexpressible, it also raises the problem that Bergson's own intuition of time as duration cannot be verified; rather, it can be challenged only by someone else's own intuition. Chapter 11 then shows how Heideggerian Angst challenges... (shrink)

Nominalists need some account of correctness for sentences committed to the existence of abstract objects. This paper proposes a new statement of such conditions specifically for properties. The account builds on an earlier proposal of mine, but avoids the counter-examples against the latter pointed out by Thomas Schindler, particularly, the sentence ‘There are inexpressible properties’. I argue that the new proposal is independently motivated and more faithful to the spirit of the kind of error-theoretic nominalism that the original proposal was (...) part of. Along the way, I also propose novel treatments of Arthur Pap’s and W.V.O. Quine’s notoriously hard-to-paraphrase sentences about abstracta. (shrink)

At the mid-point of the twentieth century, many philosophers in the English-speaking world regarded political and moral philosophy as all but moribund. Thinkers influenced by logical positivism believe that ethical statements are merely disguised expressions of individual emotion lacking propositional force, or that the conditions for the validation of ethical statements could not be specified, or that their content, however humanly meaningful, is inexpressible. Philosophical Dimensions of Public Policy presents thirty-four articles written by research scholars numerous fields-philosophy, political theory, (...) medicine, law, biology, economics, ecology and sociology-treating a broad range of topics in practical philosophy. The Institute for Philosophy and Public Affairs has been home for these ideas, pioneering a distinctive method of conducting inquiry into the moral dimensions of public life, and contributing to public discussion and deliberation. Members of the Institute reject the idea that public philosophy means reaching into the philosopher's tool-kit and "applying" prefabricated theories to particular problems. They set in motion a dialogue between the distinctive moral features of practical problems and the more general moral theories or considerations that seem most likely to elucidate these problems. The volume is divided into five areas: "Politics, Civic Life, and Moral Education"; "Diversity, Identity, and Equal Opportunity"; "Human Rights, Development Ethics, and International Justice"; "Biotechnology, Genetic Research, and Health Policy"; and "Natural Environment, Human Communities." Philosophical Dimensions of Public Policy presents empirical data and philosophical arguments with the intention of informing public policy and public deliberation. Scholars as well as graduate and undergraduate students are certain to find it useful to their research work. Verna V. Gehring is editor at the Institute for Philosophy and Public Policy at the School of Public Affairs, University of Maryland. She serves as editor of Philosophy & Public Policy Quarterly, reviewer of ethics manuscripts for Oxford University Press, and moderator for the Aspen Institute. William A. Galston is director at the Institute for Philosophy and Public Policy at the School of Public Affairs, University of Maryland. He is a political theorist who both studies and participates in American politics and domestic policy. Galston is the author of nearly one hundred articles on moral and political theory, American politics, and public policy, and the author of five books, including Liberal Purposes. (shrink)

The distinction between saying and showing in Tractatus Logico-Philosophicus is not self-refuting, unbelievable or nonsensical. It makes good sense given Wittgenstein's equation of saying with communicable information and showing with necessarily true thought. The key to understanding his thinking is his claim in the Preface that unassailable and definitive truths are expressed in the book, and the subsidiary assumption that asserting empty truths is nonsensical. His conception of pictures, propositions, logic, mathematics, mathematical physics, mysticism, the inexpressible and solipsism as showing (...) is of a piece with his conception of necessary/a priori truths as tautologies broadly understood. (shrink)

Contacts of the two logicians are listed, and all Gödel's written mentions of Tarski's work are quoted. Why did Gödel almost never mention Tarski's definition of truth in his notes and papers? This puzzle of Gödel's silence, proposed by Feferman, is not merely biographical or psychological but has interesting connections to Gödel's philosophical views.No satisfactory answer is given by the three “standard” explanations: no need to repeat the work already done; Tarski's achievement was obvious to Gödel; Gödel's exceptional caution. In (...) fact, , Tarski had done the work, but Gödel almost never mentioned the achievement; , the obviousness is no explanation for the omission of Tarski's work in contexts in which an application of the definition of satisfaction was useful, and even necessary; , the point was not just caution: if Gödel had felt the need to mention the program of scientific semantics he could easily have done that in his manuscripts, or in conversations.Three ideas, detectable in Gödel's approach, can help us understand Gödel's silence: the idea of truth as the intuitive provability in the most general sense; defining it set-theoretically would contribute nothing. the idea of truth as an inexhaustible idea in the sense of Kant; “truth in general” is a category that must be applicable to all kinds of sentential expressions; also, while for Gödel language was secondary, Tarski's definition is focused on language. the idea of logic as the universal language, in Hintikka's sense, as opposed to the perception of logic as a reinterpretable calculus; hence the thesis that semantics is inexpressible. Gödel always remains a Platonist who asks a natural question: what does really happen in the realm of abstract objects? (shrink)

SummaryIf there is truth, there is formal truth and finally truth in the set universe \V. Confiding in formal truth and reflecting this confidence we are led beyond all set and class theories to the Absolute Indefinite und formal inexpressibility of the whole concept of formal truth – a logical path to Mahlyha Buddhism.

The first section of this chapter presents a close reading of Wittgenstein’s “Remarks on Logical Form”, focusing on the conception of the relationship between language and experience, and the nature of the analysis of immediate experience that are set out there. Section two sets out an interpretation of what Wittgenstein meant when he said that he had rejected “phenomenological language” or “primary language” as his goal. Distinguishing between a weak and a strong sense of these terms shows how he (...) could have given up the goal of formulating a language that would amount to a complete analysis of immediate experience, yet retain the goal of finding ways of clarifying what we say about experience. Section three discusses Wittgenstein’s use of the analogy of the pictures on a roll of film in a movie projector and the pictures on a cinema screen for the relationship between world and experience. The final section analyzes how and why the analogy leads Wittgenstein to a paradoxical conception of immediate experience as a separate realm, “timeless” and “neighborless”, a conception of the “world as idea” that is supposedly inexpressible. (shrink)

The first section of this paper introduces talk about absolutely everything -- the world as a totality -- as an integral element in the project of natural theology, as it has been presented by Fergus Kerr and Denys Turner respectively. The following section presents talk about the world as a totality of facts as a theme in philosophical logic and outlines a problem it has given rise to there. After confronting the solution originally suggested by Bertrand Russell and defended by (...) David Armstrong, the paper points to key elements of the solution presented by Wittgenstein in Tractatus Logico-Philosophicus. I show how Wittgenstein’s answer to the question of unrestricted quantification draws on his notion of showing and the inexpressible. Against this background, the concluding section draws attention to an important difference in ambition between Kerr’s and Turner’s description of the prospects for natural theology. (shrink)

If you believe in the existence of an infinitely good, all-knowing, and all-powerful deity (‘God’), how do you explain the reality of evil – including the inexpressible suffering and death of innocents? Wouldn't God be forced to vanquish such suffering due to God's very nature? Alvin Plantinga has argued, convincingly, that if the possibility of ultimate goodness somehow necessarily required that evil be allowed to exist, God, being omnibenevolent, would have to allow it. But as John Hick has noted, the (...) mere logical possibility of such a situation might not be enough to console the doubting theist. We need a positive reason to believe that evil as we know it is compatible with God's existence. So, Hick offers a ‘soul-making’ theodicy – or vindication – of God, suggesting that the human soul cannot fully progress to spiritual maturity (a kind of ultimate good on his account) without grappling with evil. In this short piece I argue that, if we accept Hick's premises about souls and soul-making, we can indeed make sense of evil to some extent. But, I suggest, his account cannot justify the type or amount of evil we see in the world, so his theodicy does not succeed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Religious Identity and Openness in a Pluralistic WorldRita M. GrossIn our final sessions after twenty years of working together, we have been asked to reflect in some way on identity and openness in a pluralistic world. Specifically, the question is, "How do I understand my own identity as a religious Buddhist or Christian in light of the fact that I am open to the validity of the beliefs held (...) by the other tradition?"Frankly, this puzzle seems like a no-brainer to me and always has. Religions are language systems, and no language is universal and absolute. End of problem. In one fell swoop, as we concede the relativity of all our language games, we also recognize that more than one language could be "valid," whatever that might mean. There is no reason to assume that all people speak my language and it would be illogical to claim that people who don't speak my language are deficient. The worth and utility of my language is in no way diminished because it is not the only language in the world. Language is a tool through which we communicate, and any language could be a useful tool, so long as we don't endow it with universal relevance, more freight than it can bear.There may or may not be a formless absolute that grounds all finite existence. All religions assert that there is, whether as a being or as an experience. But beyond that assertion nothing can be determined because all such assertions must be expressed in language or some other limited expression—an expression in form. There is no other option. Much as we might long to transcend expression in form and leap into mind-to-mind transmission, in a public medium that is not possible. Many of us may have intuited such experiences of mind-to-mind transmission, but when we open our mouths to speak, we can only do so in the realm of form. And so we are stuck with our myriad expressions of a formless, transcendent absolute and cannot even determine for sure if we are talking about the same thing when we try to express the inexpressible.Therefore, we are compelled to concede the limits of language. This is the solution to the problem of the coexistence of a strong individual religious identity with openness to the relevance of other religious languages. Other religions, as well as my [End Page 15] own, are nothing more than highly relative language systems. There is no logical or spiritual way for them to be anything more. It seems to me that copping to the limitations of language, to the inability of language ever to capture truth completely, is completely essential in the pluralistic world we now inhabit. It is hard to imagine how people could believe that the deity speaks Arabic, not Hebrew, or Hebrew, not Arabic, and biblical Hebrew (rather than any other version of Hebrew) at that! It is hard to imagine how people could believe that they have the actual words of Jesus in the red print in their new testaments, even though those words were originally written in a language he never spoke and were translated into an archaic English that we no longer speak and barely understand. Nothing but egotistical pride can drive such self-aggrandizement, such identification of my viewpoint, my verbal attempts to express my experience, with the eternal and ultimate Way Things Are.In light of the historical and cross-cultural information that is now more than abundantly available, the only rational and humane conclusion to be drawn is that all religious institutions and creedal systems are human constructions dependent at least in part, if not wholly dependent, on the particular circumstances of those who construct and utter them. Therefore, they are of limited rather than universal relevance. Their cultural specificity is too obvious for any other conclusion to be feasible. Arabic, Hebrew, Greek, and English are not universal languages, and only extreme hubris could claim the Formless Absolute speaks my language, not yours. Thus, even if our religions owe their genesis to some transcendent, nonhistorical source, they can be codified and captured only in a relative... (shrink)

Some of the most interesting recent work in philosophy of language and metaphysics is focused on questions about propositions, the abstract, truth-bearing contents of sentences and beliefs. The aim of this guide is to give instructors and students a road map for some significant work on propositions since the mid-1990s. This work falls roughly into two areas: challenges to the existence of propositions and theories about the nature and structure of propositions. The former includes both a widely discussed puzzle about (...) propositional designators as well as direct and indirect arguments against the existence of propositions. The latter is dominated by what is currently the central debate about the metaphysics of propositions, i.e. whether they are structured, composite entities or unstructured ontological simples. This issue has eclipsed older debates about whether propositions can be identified with sets of possible worlds or other kinds of sentence intensions. Author Recommends 1. Soames, Scott. 'Direct Reference, Propositional Attitudes, and Semantic Content.' Philosophical Topics 15 (1987): 47–87. Reprinted in Propositions and Attitudes . Eds. N. Salmon and S. Soames. Oxford: Oxford University Press, 1988. 197–239. Essential groundwork for more recent work on propositions. Soames gives a careful and exacting presentation of the case against identifying propositions with sets of possible worlds or other truth-supporting circumstances. Also contains a detailed statement of the Russellian conception of propositions on which propositions are ordered sets of objects, properties and relations. 2. King, Jeffrey. 'Designating Propositions.' The Philosophical Review 111 (2002): 341–71. Sometimes substituting a definite description for a corresponding 'that'-clause can lead to bizarre changes in truth-conditions: compare 'Bill fears that Hillary will be president' with 'Bill fears the proposition that Hillary will be president'. This puzzle about propositional designators threatens the relational analysis of propositional attitude reports, the view that 'believes' expresses a relation to the proposition designated by its 'that'-clause, and thereby poses an indirect threat to the existence of propositions. King's solution posits an ambiguity in verbs like 'fear' that embed both 'that'-clauses and definite descriptions. 3. Jubien, Michael. 'Propositions and the Objects of Thought.' Philosophical Studies 104 (2001): 47–62. A direct attack on the existence of propositions. Jubien deploys an analogue of the problem that Paul Benacerraf raised for set-theoretical reductions of numbers against metaphysical reductions of propositions. Just as numbers can be reduced to sets in many different ways, any reduction of propositions brings with it equally good variants, thus making any such reduction arbitrary and unmotivated. The only alternative is to treat propositions as abstract metaphysical primitives. As Jubien argues, however, abstract primitive entities are incapable of doing what propositions must do, i.e. represent objects and states of affairs on their own, without the input of thinking subjects. The upshot is the propositions cannot be reduced and they cannot be primitive, and so they must not exist. 4. Hanks, Peter. 'How Wittgenstein Defeated Russell's Multiple Relation Theory of Judgment.' Synthese 154 (2007): 121–46. Scepticism about propositions has recently led some philosophers, Jubien included, to resuscitate Russell's multiple relation theory of judgment, the idea that judgment is a many-place relation to objects, properties and relations. This paper explains why Russell himself abandoned that theory, and why the theory is still refuted by an objection due to Wittgenstein. 5. Hofweber, Thomas. 'Inexpressible Properties and Propositions.' Oxford Studies in Metaphysics . 2 vols. Ed. D. Zimmerman. Oxford: Oxford University Press, 2006. 155–206. An indirect attack on the existence of propositions. Hofweber argues that sentences like 'Bill believes something that Hillary asserted' do not commit us to the existence of propositions. His view is that propositional quantification is an instance of what he calls 'internal' or 'inferential role' quantification, a kind of quantification that carries no ontological implications. 6. Schiffer, Stephen. The Things We Mean . Oxford: Oxford University Press, 2003. esp. chs 1–2. Schiffer defends his theory of pleonastic propositions, on which propositions are unstructured, have no parts, and are very finely grained. 7. Bealer, George. 'Propositions.' Mind 107 (1998): 1–32. Bealer defends his algebraic theory of propositions, which, like Schiffer's pleonastic account, treats propositions as unstructured metaphysical simples. 8. King, Jeffrey. The Nature of and Structure of Content . Oxford: Oxford University Press, 2007. The best developed current theory of the structure in structured propositions. King identifies propositions with certain kinds of facts in which objects, properties and relations are bound together by amalgams of syntactic and semantic relations. 9. Hanks, Peter. 'Recent Work on Propositions.' Philosophy Compass 4 (2009): 1–18. A survey of work on propositions since the mid-1990s that complements this teaching and learning guide. Contains responses to Jubien's and Hofweber's arguments against propositions and critical discussions of Schiffer's pleonastic propositions and King's theory of propositional structure. Online Resources 1. http://plato.stanford.edu/entries/propositions/ Propositions (Matthew McGrath) 2. http://plato.stanford.edu/entries/propositions-structured/ Structured Propositions (Jeffrey King) 3. http://plato.stanford.edu/entries/propositions-singular/ Singular Propositions (Greg Fitch) Sample Partial Syllabus The following partial syllabus can be used as a unit on recent work on propositions in graduate level courses in philosophy of language or metaphysics. Week 1: A Substitution Puzzle About Propositional Designators King, Jeffrey. 'Designating Propositions'. Moltmann, Friederike. 'Propositional Attitudes Without Propositions.' Synthese 135 (2003): 77–118. Week 2: The Benacerraf Problem and Propositional Representation Benacerraf, Paul. 'What Numbers Could Not Be.' Philosophical Review 74 (1965): 47–73. Jubien, Michael. 'Propositions and the Objects of Thought.' Week 3: Propositional Quantification Hofweber, Thomas. 'Inexpressible Properties and Propositions'. Hofweber, Thomas. 'A Puzzle about Ontology.' Noûs 39 (2005): 256–83. Week 4: Schiffer on Pleonastic Propositions Schiffer, Stephen. 'Language-Created Language-Independent Entities.' Philosophical Topics 24 (1996): 149–67. Schiffer, Stephen. The Things We Mean , chs 1–2. Week 5: King on Structured Propositions King, Jeffrey. 'Structured Propositions and Complex Predicates.' Noûs , 29 (1995): 516–35. King, Jeffrey. The Nature and Structure of Content , chs 1–3. Focus Questions 1. Why does identifying propositions with sentence intensions, e.g. sets of possible worlds, 'require the attitudes to have a particular sort of closure under logical consequence, which they clearly don't have' (Mark Richard)? 2. How does the difference between (a) and (b) pose a threat to the existence of propositions? (a) Bill fears that Hillary will be president. (b) Bill fears the proposition that Hillary will be president. 3. What is the Benacerraf problem for metaphysical reductions of propositions? 4. Why must a proposition represent 'on its own cuff' (Michael Jubien)? Why is this a problem for the view that propositions are primitive abstract entities? 5. What does it mean to say that propositions are structured ? Give two different accounts of what propositional structure might be. (shrink)

This paper, through a realist reading of Husserlian phenomenology, aims to explain how the consciousness-sense has access to reality and, in general, to objectivity. There is a ‘strife’ between the essence of a thing and the specific concreteness in which it always becomes manifest, such that the identical object is indicated by changeable predicates, but at the same time always distinguishes itself from them. Language can express the evidence of the thing - which makes the determinable aspects of the thing (...) exist and which is inexpressible through definitions - only “for conjectures”, showing the difference between its own expression and the thing. And it can do this by analogy, the only device that exhibits the antinomic relationship between the object and its determinations, and, in the meantime, makes possible not so much their composition, but rather their transformation. Analogy, in fact, operating through a logic of contradiction, grasps, within each object, the tension between the element of permanence and the element of emergency; shows how the object is a unity-without-a-mixture of absolutely distinct forms; and so it comes to think about the relationship between the in-definable forms of the possible representations of the thing and the impossible expression of its singularity. (shrink)

The deepest crises cannot destroy the universal model of literariness. It maintains its appeal for participants in literary communication as a -contradictory- model. This thought recurs in many epochs. Literariness involves suspending the formal or logical norms of contradiction ("lex contraditionis"). In everyday speech, it is not permissible for -A- to simultaneously be -not-A-; in literary structures this is the norm. This is both in the ideas, and in the tensions between the artificiality and naturalness of speech, the structure (...) and the chaos of the plot, experimentation and revitalization of tradition, objective observation and a biased vision of the world, its visibility and invisibility, expressibility and inexpressibility, and a realistic and an imaginative focus. Executions of this model are gradative.". (shrink)

We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier $\sf Q$ in ${\rm FO}({\vec Q}_k)$ , the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two ${\rm FO}({\vec Q}_1)$ -equivalent models with certain additional structure, yields a pair of ${\rm FO}({\vec Q}_k)$ -equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties, such as connectivity (...) and planarity. (shrink)

Pretheoretically, truth is a correspondence between a sentence and facts. Other so-called theories of truth have typically been resorted to because such a correspondence is thought of as being inexpressible or as being incapable of yielding a definition of truth which expresses what we actually mean. It can be shown that truth is indefinable in the paradigm case of ordinary first-order languages only because they cannot express informational independence. As soon as this is corrected, as in independence-friendly first-order logic, truth (...) predicates are readily definable, Tarski notwithstanding. Hence, there is no reason to think that truth cannot also be defined for our actual working language—Tarski’s “colloquial language.”. (shrink)

I do not for a moment question the fact that many people have experiences of a special type which may be termed “religious”, The extent to which religious experience may be regarded as a reasonably common phenomenon in present-day Britain is shown clearly by David Hay in his Exploring Inner Space, Harmondsworth 1982. that such experiences often involve reference to something which appears to display a radical unlikeness to all else and that they are therefore in some sense inexpressible. Doubtless (...) the ideas I have put forward about the possible source of such unlikeness and ineffability might suggest models of God which would not find much theological approval, at least within any mainstream theistic tradition, since some sort of pantheism seems inevitably to be implied. But however this might be, the concept of radical unlikeness as it has been analyzed here can, I think, help us towards understanding certain problematic areas in religion quite apart from the issue of intelligibility, which has been the focus of this discussion. To begin with, radical unlikeness suggests a way in which the historical continuity of concepts of the transcendent might be upheld against the discontinuity suggested by the diversity of interpretations through which they have moved. Ancient and modern outlooks on, say, God differ enormously, as indeed do the range of co-temporal accounts at many particular moments. But, by and large, theologians firmly maintain that it is a single and unchanging phenomenon which is being dealt with. Unless we can point to some common element which is both specific enough to create a binding sense of common tradition, yet never completely expressed by any attempt at understanding it within that tradition (thus persistently demanding new attempts to apprehend it), then given the widely differing views of God within, for example, the Christian community, it is difficult to see how we could assume that in fact they all stemmed from the same source and were talking about the same thing. The idea of radical unlikeness could provide an element with just these required characteristics: it could be seen as what all the accounts attempt to net, with varying degrees of adequacy, within their offered interpretations. It could be seen as what remains constant, constantly elusive yet constantly generative of fresh attempts to apprehend it, throughout a history of intra-religious diversity. This sort of explanation could, presumably, be applied to the intra-religious diversity of the non-Christian traditions too.Secondly, radical unlikeness might suggest a possible way of understanding inter-religious diversity in a way which allows that whilst such diversity exists, whilst the differences between religions are real, they are grounded in a similar root-experience. It may, at first sight, seem difficult to continue thinking of the various religious traditions as truly separate phenomena if they are taken as being grounded on experiences whose ineffability stems from the unlikeness of experiencing things as a whole. Here we must stress again that if they are to be considered intelligible, radically unlike experiences cannot be considered completely so - or putting this another way, we cannot more than approach experience of totality. Sense can be given to religious claims of ineffability by suggesting experience of near totality, where we reach the last point on the scale of inclusiveness which complies with the logical criteria demanded of something for it to be possible for us to be aware of it. We might thus attempt an explanation of inter-religious diversity based on the view that Hinduism, Buddhism, Christianity, Islam etc. acquire their differences from the different elements included in their experience of near totality. Taking totality to be represented by the scale of one to ten, Hinduism might be seen as grounded on experience of 1-2-3-4-5-6-7-9-10, Buddhism on experience of 1-3-4-5-6-7-8-9-10 and so on. The resulting dissimilarities are thus centred not on different types of experience, but on different areas of inclusiveness. This is, of course, to suppose that the various religious traditions are all based on the same degree (as opposed to the same elements) of inclusiveness, but it is by no means clear that such a supposition is justified. Continuing with our decimal analogy, might it not be suggested that whilst Christianity stemmed from experience of 2-3-4-5-6-7-8-9-10, Jainism was founded on a less extensive encounter with the divine (say 4-5-6-7-8-9-10)? It is, however, uncertain how we can compare and evaluate different religious traditions in such a way as to be able to comment on such claims. A definite danger of comparative religion is that by concentrating on establishing and exploring inter-religious likenesses, it may obscure the radical unlikeness of religious phenomena. It should be borne firmly in mind that such likenesses as may be established within comparative studies may not win religious phenomena a place within our understanding comparable to objects of more everyday concern. Statements found in the Old Testament, the Qur'an and the Vedas, for example, may, on occasion, be alike, but at the end of the day such things are often alike only, or chiefly, in so far as they display the same radical unlikeness in relation to the non-religious elements in our outlook.The analysis of radical unlikeness and ineffability which has been advanced might also suggest a way in which certain passages in religious writings could be understood, passages which at first sight can be seriously perplexing. If, for example, to return to the quotation given in the introductory section of this paper, we continue to think of accounts of the nature of Shiva as being attempts to describe some discrete, objective entity, then it is inevitable that either we will share the Puranic writer's puzzlement or that much of what we read about Shiva will appear as the muddled and extravagant thinking thrown up by an uncritical and over-fertile mythological imagination, consisting of little more than a hotch-potch of contradictory elements. But if we see such accounts as attempting to say something about everything, as symbols of near totality stemming from experiences which verge on the holistic, then what we read - with all its ambiguities - may become somewhat more meaningful. Thus W.D. O'Flaherty comments that Shiva “embodies all of life in all its detail at every minute” (Asceticism and Eroticism in the Mythology of Shiva, London 1973, p. 315). Similarly Alain Dani41ou sees Shiva, ultimately, in terms of his being "the supreme state of reality" beyond whom there is only "non-existence" (Hindu Polytheism, London 1964, p. 190).This analysis of ineffability and intelligibility seeks to introduce for debate a possible way of understanding the radical unlikeness which accounts of religious experience apparently attempt to speak about. It does not, however, claim to present an exhaustive treatment of the issues raised, on the contrary, I am conscious of many shortcomings and omissions. For instance, it remains to be seen under precisely what conditions something counts as being an elucidating likeness (presumably all experiences are, for example, temporal, yet temporality alone would not seem to offer a particularly elucidating comparison). Moreover, the degree to which appeal to likeness is allowed operation in actual accounts of religious experience needs to be explored. In addition, the notion of categorizing experiences according to the extent to which they approach a point of total inclusion requires careful clarification. To begin with, according to what criteria could we establish that one experience was more inclusive than another? However, such issues can only be mentioned here, any adequate consideration of them would require a separate paper.In conclusion, I would suggest that to use radical unlikeness and/or ineffability simply as devices by which to halt any process of investigation, proclaiming that the thing in question is not like anything and so is beyond all words, risks making unintelligible and placing beyond all further inquiry an important and extensive area of human experience. As William Alston put it, to label something ineffable in an unqualified way is to shirk the job of making explicit the ways in which it can be talked about. William P. Alston, “ineffability”, Philosophical Review 65 (1956), 522. It is surely more accurate to take ineffability as a “qualifier”I.T. Ramsey, Models and Mystery (Oxford 1964), p. 60. which “multiplies models without end”Ibid. than as an absolute which prevents the construction of any elucidating models. (shrink)