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)

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)

This essay is concerned with solipsism, understood as the extreme sceptical view that I have no knowledge except of my subjective state. A less rough formulation of the view is mooted, inspired by a Quinean combination of naturalism and empiricism. An objection to the resultant position is then considered, based on Putnam’s argument that we are not brains in vats. This objection is first outlined, then pitted against a series of counter-objections. Eventually it is endorsed, but only at the price (...) of exposing the formulation of solipsism in question as not, after all, a satisfactory formulation. This leads to further speculation about the status of solipsism itself. Two of the possibilities that are considered are, firstly, that it is incoherent and, secondly, that it is inexpressible. (shrink)

'PERHAPS WHAT is inexpressible (what I find mysterious and am not able to express)', wrote Wittgenstein, 'is the background against which whatever I could express has its meaning'. Wittgenstein's remark is a useful reminder to all who attempt to write about the nature and the value of art, for there our powers of expression often seem inadequate to the phenomena we aim to describe. In such cases it is natural to direct attention to the 'background' of aesthetic experience itself. (...) In consequence, many philosophical elucidations of art works will make good sense only to whose who are already engaged with them on their own terms—engaged with their distinctive character and forms. That this is so is perhaps most evident when the philosopher's target is the art of music. Roger Scruton's latest contribution to philosophical aesthetics, The Aesthetics of MusIc, is guided by a deep appreciation of the background of musical experience and he often allows music to speak for itself, through musical example and illustration. This study is exceptionally, if not uniquely, informed by a wide and thorough acquaintance with its subject matter, and it is commendably replete with references to, andmusic examples illustrating specific compositions. (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)

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)

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)

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)

This essay is divided into two parts, deeply intermingled. Part I examines not only the origin of conscious experience but also how it is possible to ask of our own consciousness how it came to be. Part II examines the origin of experience itself, which soon reveals itself as the ontological question of Being. The chief premise of Part I is that symbolic communion and the categorizations of language have enabled human organisms to distinguish between themselves as actually existing entities (...) and their own immediate experience of themselves and their world. This enables them to reflect upon abstract concepts, including “self,” “experience,” and “world.” Symbolic communication and conceptualization grow out of identification, the act of first observing conscious experiencing and intimating what it is like, mimesis, a gestural protolanguage learned through imitation, and reflection, seeing oneself through the eyes of others. The step into actual intentional speech is made through self-assertion, narrative, and intersubjectivity. These three become the spiral of human cultural development that includes not only the adaptive satisfaction of our biological needs, but also the creativity of thought. With the mental-conceptual separation of subject and object – of self and world – the human ability to witness the universe (and each other) is the ground of our genuinely human quality. Consciousness gives human life its distinctively human reality. It is, therefore, one and the same ability that enables us to shape planet Earth by means of conceptual representations (rather than by means of our hands alone) while also awakening us to the significance of being. -/- Looking beyond human self-consciousness to investigate the origin and nature of awareness itself in Part 2, reductive objective materialism is found to be of little use. Direct experience also falls short in that, in order to be transformed into objective knowledge about itself, it must always be interpreted through and limited by the symbolic contexts of culture and the idiosyncratic conceptualizations of the individual. Awareness-in-itself must thus be considered ultimately unexplainable, but this may more indicate its inexpressible transcendence of all symbolic qualifiers than its nonexistence. It is suggested that awareness is not “self-aware” (as in deity) but is instead unknowing yet identical with the only true universal: the impetus of creative unfolding. Our human knowledge, as an expression of this unfolding, is seen to emerge from our conscious experiencing and, in turn, to have the power – and enormous responsibility – of directing that experience. Our underlying symbolic worldviews are found to be autopoietic: They limit or open our conscious experience, which, in turn, confirms those worldview expectations. As we explore a future of unforeseeable technological breakthroughs on an ailing planet who patiently copes with our “success,” truly vital decisions about the nature, meaning, extent, and future of conscious experience will have to be made. (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)

The value of extending the human lifespan remains a key philosophical debate in bioethics. In building a case against the extension of the species-typical human life, Nicolas Agar considers the prospect of transforming human beings near the end of their lives into Galapagos tortoises, which would then live on decades longer. A central question at stake in this transformation is the persistence of human consciousness as a condition of the value of the transformation. Agar entertains the idea that consciousness could (...) persist in some measure, but he thinks little is to be gained from the transformation because the experiences available to tortoises pale in comparison to those available to human beings. Moreover, he thinks persisting human consciousness and values would degrade over time, being remade by tortoise needs and environment. The value available in the transformation would not, then, make the additional years of life desirable. Agar’s account does not, however, dispose of the tortoise transformation as a defensible preference. Some people might still want this kind of transformation for symbolic reasons, but it would probably be better that no continuing human consciousness persist, since that consciousness would be inexpressible as such. Even so, it is not irrational to prefer various kinds of lifespan extension even if they involve significant modifications to human consciousness and values. (shrink)

In his article untitled Messages in Art Jerrold Levinson discusses the idea of a message behind a work of art. He argues that despite certain disclaimers put forward by artists it is „hard to deny that artworks (...) very often do have messages, and far from inexpressible ones”. From given examples it would seem that Levinson assumes that musical work just as other artworks sometimes generate messages and that in order for a work of music to be successful in (...) expression this message should be comprehensible and certainly not incoherent. The author of this paper draws on Levinson's “Messages in Art” as well as his “Music as Narrative and Music as Drama” to explore further the issues mentioned above. In particular the author argues that seeing musical works through the message it may generate is somewhat reductive and that musical work as well as other artworks are prone to abiding by an aesthetic code and therefore even when they allow for interpretation in terms of messages or morals these messages are incoherent or vague at best. (shrink)

In this article I am interpreting Friedrich Nietzsche's piece of writing "How the "True World" finally became a fable - The History of an Error" in the context of 20th-century analytical philosophy of language. In particular, I am going to argue that the main theme in this text - the issue of abolishing "the true world" - can be interpreted as Hilary Putnam's model-theoretic arguments against external realism and Saul Kripke's Wittgensteinian arguments against truth-conditional meaning theories. Interpreting this Nietzsche's text (...) with the help of these arguments gives rise to two options determining Nietzsche's own position. The perspective of Putnam's argument seems to push Nietzsche to the quietist camp - the view that significant metaphysical debate between external realism and its opposite is impossible or inexpressible. On the other hand, the Kripkensteinian perspective gives us reasons to interpret Nietzsche as an adherer of the pragmatic account of semantics, which explains meaning through the use of language. (shrink)

The objectively best language is intended to refer to some metaphysically privileged language that ‘carves reality at its joints’ perfectly. That is, it is the kind of language that various ‘metaphysical deflationists’ have argued is impossible. One common line of argument amongst deflationists is that we have no means to compare languages that all express true facts about the world in such a way to decide which is ‘better’. For example, the language is physics is not objectively better than the (...) language of economics, as each language has the semantic purpose of expressing some domain of truths about the world inexpressible in the other language, and therefore neither could be ‘objectively best’. In this paper, I argue that metaphysical deflationists have failed to recognise a distinction between fine- and coarse-grained semantic purposes of languages, and that a recognition of that distinction provides us grounds to compare languages to see which is objectively best. I argue that once we recognise the distinction between fine- and coarse-grained semantic purposes, then we can see that it is relative to the coarse-grained purpose that we must compare putative objectively best ontological languages. (shrink)

In Jeffrey King’s theory of structured propositions, propositional structure mirrors the syntactic structure of natural language sentences that express it. I provide cases where this claim individuates propositions too finely across languages. Crucially, King’s paradigmatic proposition-fact ^that Dara swims^ cannot be believed by a monolingual Greek speaker, due to Greek syntax requiring an obligatory article in front of proper names. King’s two possible replies are: (i) to try to streamline the syntax of Greek and English; or (ii) to insist that (...) English speakers can believe propositions inexpressible in Greek. I argue that the former option entails giving up a neo-Russelian framework, and the latter makes King’s account arbitrary or trivial. I conclude that the mirroring claim is untenable. (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)

This essay provides an overview of the ways in which contemporary philosophers have tried to make sense of ineffability as encountered in aesthetic contexts. Section 1 sets up the problem of aesthetic ineffability by putting it into historical perspective. Section 2 specifies the kinds of questions that may be raised with regard to aesthetic ineffability, as well as the kinds of answer each one of those questions would require. Section 3 investigates arguments that seek to locate aesthetic ineffability within the (...) object of aesthetic experiences, i.e. within aesthetic content. Section 4 discusses arguments that seek to locate aesthetic ineffability within the subject of aesthetic experience. (shrink)

Human beings seem to capture time and the temporal properties of events and things in thought by having beliefs usually expressed with statements using tense, or notions such as ‘now’, ‘past’ or ‘future’. Tensed beliefs like these seem indispensable for correct reasoning and timely action. For instance, my belief that my root canal is over seems inexpressible with a statement that does not use tense or a temporal indexical. However, the dominant view on the nature of time is that (...) it forms, with space, a four-dimensional continuum where time does not encompass private perspectives or an absolute, fixed present. This ‘tenseless’ theory of time encounters a challenge in integrating tensed belief, because it cannot easily explain what constitutes a tensed belief in a tenseless world and how such a belief works inside our cognitive network to bring about the actions it does. Providing such an account is the main goal of this dissertation. -/- I argue here that the correct way to proceed would be to utilize philosophical theories dealing with indexicality, as the puzzling features of tensed belief are shared with beliefs expressed by first-person or spatial indexicals. In chapters II and III I expand the dominant theories about indexicality (Lewis, Perry, Kaplan) and apply them to tensed belief. I show that each is in certain respects incomplete or inadequate. -/- My preferred account critiques the preceding theories as mis-attributing the indexicality involved to a fully conceptual element in the way people think about time. I argue that we should instead connect tensed belief to not fully conceptual elements thought. For support I turn to work in perceptual psychology that connects beliefs about space to perceptions of spatial features. In chapter IV I develop an analogous argument about temporal thought and discuss how mental representations involved in perceptions are constitutively related to the formation and preservation of tensed beliefs. Combining this story with a tenseless theory of time should give us a complete, metaphysically uncontroversial, account of the way a tensed belief functions in reasoning and produces timely action. (shrink)

The Identity of Indiscernibles is the principle that objects cannot differ only numerically. It is widely held that one interpretation of this principle is trivially true: the claim that objects that bear all of the same properties are identical. This triviality ostensibly arises from haecceities (properties like \textit{is identical to a}). I argue that this is not the case; we do not trivialize the Identity of Indiscernibles with haecceities, because it is impossible to express the haecceities of indiscernible objects. I (...) then argue that this inexpressibility generalizes to all of their trivializing properties. Whether the Identity of Indiscernibles is trivially true ultimately turns on whether we can quantify over properties that we cannot express. (shrink)

Beyond “A Lecture on Ethics,” Wittgenstein says little on the topic of ethics, despite professing a great respect for ethics. I argue that while Wittgenstein ceases to speak of ethics, his account fits equally within his Tractarian and post-Tractarian writing. On both accounts of language, ethics remains nonsense, but it is not insignificant nonsense. However, because Wittgenstein holds ethics to concern absolute values that are in principle inexpressible, his anti-theoretical conception of ethics fails to offer guidance in how one (...) ought to live. That is, ethics ultimately cannot be show unless it can, in some sense, be said. (shrink)

The generalized conclusion of the Tarski and Gödel proofs: All formal systems of greater expressive power than arithmetic necessarily have undecidable sentences. Is not the immutable truth that Tarski made it out to be it is only based on his starting assumptions. -/- When we reexamine these starting assumptions from the perspective of the philosophy of logic we find that there are alternative ways that formal systems can be defined that make undecidability inexpressible in all of these formal systems.

Get used to it: paradox and contradiction are inherent in human experience. Australian philosopher of logic Graham Priest takes us on a historical tour of paradox and limitation in human conception, expression, cognition, and calculation. Along the way we meet the many, mostly western, philosophers who've struggled with expressing the inexpressible and conceiving the inconceivable. Priest arrives at a general schema for representing these limit encounters from the standpoint of contemporary logic.

It is commonly supposed that a certain kind of belief is necessary for religious experience. Yet it is not clear that this must be so. In this article, I defend the possibility that a subject could have a genuine emotional religious experience without thereby necessarily believing that the purported object of her experience corresponds to reality and/or is the cause of her experience. Imaginative engagement, I argue, may evoke emotional religious experiences that may be said to be both genuine and (...) appropriate, despite not necessarily including beliefs of the aforementioned kind.I go on to maintain that such religious engagement is compatible not only with non-belief but also with disbelief. (shrink)