Several writers have assumed that when in “Outline of a Theory of Truth” I wrote that “the orthodox approach” – that is, Tarski’s account of the truth definition – admits descending chains, I was relying on a simple compactness theorem argument, and that non-standard models must result. However, I was actually relying on a paper on ‘pseudo-well-orderings’ by Harrison. The descending hierarchy of languages I define is a standard model. Yablo’s Paradox later emerged as a key to interpreting the result.

A modification of Kripke’s theory of truth is proposed and it is shown how this modification solves some of the problems of expressive weakness in Kripke’s theory. This is accomplished by letting truth values be grounded in facts about other sentences’ ungroundedness.

What kinds of sentences with truth predicate may be inserted plausibly and consistently into the T-scheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on non-semantic states of affairs (only). In order to make this precise we introduce a theory of dependence according to which a sentence φ is said to depend on a set Φ of sentences iff the truth value of φ supervenes on the presence or absence of the sentences of (...) Φ in/from the extension of the truth predicate. Both φ and the members of Φ are allowed to contain the truth predicate. On that basis we are able define notions such as ungroundedness or self-referentiality within a classical semantics, and we can show that there is an adequate definition of truth for the class of sentences which depend on non-semantic states of affairs. (shrink)

The semantic paradoxes are often associated with self-reference or referential circularity. Yablo (Analysis 53(4):251–252, 1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop (...) a functionally complete infinitary propositional language endowed with a denotation assignment and extract the reference structural information in terms of graph-theoretic properties. We introduce the new concepts of dangerous and precarious reference graphs, which allows us to rigorously define the task: classify the dangerous and precarious directed graphs purely in terms of their graph-theoretic properties. Ungroundedness will be shown to fully characterize the precarious reference graphs and fully characterize the dangerous finite graphs. We prove that an undirected graph has a dangerous orientation if and only if it contains a cycle, providing some support for the traditional idea that cyclic structure is required for paradoxicality. This leaves the task of classifying danger for infinite acyclic reference graphs. We provide some compactness results, which give further necessary conditions on danger in infinite graphs, which in conjunction with a notion of self-containment allows us to prove that dangerous acyclic graphs must have infinitely many vertices with infinite out-degree. But a full characterization of danger remains an open question. In the appendices we relate our results to the results given in Cook (J Symb Log 69(3):767–774, 2004) and Yablo (2006) with respect to more restricted sentences systems, which we call $\mathcal{F}$ -systems. (shrink)

The notion of fundamentality, as it is used in metaphysics, aims to capture the idea that there is something basic or primitive in the world. This metaphysical notion is related to the vernacular use of “fundamental”, but philosophers have also put forward various technical definitions of the notion. Among the most influential of these is the definition of absolute fundamentality in terms of ontological independence or ungroundedness. Accordingly, the notion of fundamentality is often associated with these two other technical (...) notions. (shrink)

We model infinite regress structures — not arguments — by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.

Grounding is claimed to offer a promising characterization of the fundamental as thatwhich is ungrounded. Detractors of this view argue that there can be fundamental and yet mutuallygrounded entities. Such a possibility undermines the denition of the fundamental as theungrounded. I aim to show, however, that the possibility of fundamental mutually grounded entitiesdoes not force us to renounce the prospects of characterizing fundamentality in terms of ground-ing. To accomplish this aim, I defend a grounding-based view that accommodates fundamentalmutually grounded entities (...) straightforwardly. My denition of fundamentality is similar to, butimportantly different from, one that Karen Bennett discusses. I conclude by resisting two objec-tions raised by Jessica Wilson against the Bennettian framework that also target theproposed view. (shrink)

Ttler=‘Ttler is true’ says of itself that it is true. It is a truth-teller. I argue that we have equally telling arguments (i) to the effect that all truth-tellers must have the same truth-value (ii) and the effect that truth-tellers differ in truth-value. This is what I call the Truth-Tellers paradox. This paradox stems from the fact that the truth-value of a truth-teller like Ttler should be determined by the fact that it says of itself that it is true (which (...) entails (i)) but that it cannot be determined by that fact (as witnessed by (ii)). The Truth-Tellers paradox resem- bles the classical semantic paradoxes like the Liar. In both cases, a form of self-reference allows us to derive a contradiction from oth- erwise plausible semantic and logical principles. Furthermore the Truth-Tellers paradox can be formulated without using sentences which are in an intuitive sense ungrounded, it thus severs the link, almost universally taken for granted, between the semantic para- doxes and ungroundedness. Finally, some classical solutions to the Liar do not generalize to the Truth-Tellers paradox. (shrink)

Heidegger’s ontological account of affectivity provides an interesting angle to consider questions of politics. On the one hand, one might take some of what Heidegger wrote on affectivity in the late 1920s and early 1930s—usually couched in the idiom of Stimmungen and Befindlichkeit—as a foreshadowing of his involvement with Nazi politics, culminating in his time as Führer-Rektor of Freiburg University. On the other hand, Heidegger’s views on affectivity might be taken as a starting point for an ontological perspective on the (...) political as such. His perspective on Befindlichkeit as disclosive postures can prepare such a reading, while especially his views on the ontological character of anxiety and boredom lead into the founding dimension of the political as such.This is because these affective orientations reveal the ungroundedness and thus radical contingency of existence. The flip side of this ungroundedness is the inevitability for self-determination—in other words: the need for deciding the undecidable. Although Heidegger’s own politics—at least in the early 1930s—did not explicitly relate to the affectively disclosed ungroundedness of existence, but rather curtailed this openness and indeterminacy in an individualistic and decisionistic closure, we argue that Heidegger’s view yields to a radically political reading. Not least, this is evidenced in much of French political thought since the 1960s which heavily draws on Heidegger’s ontological difference. The political as such does not refer to politics as a sub-system of society, but to the questioning of the foundations of politics, which turn out to be necessarily “contingent foundations”. It is our aim to trace this line of thought back to its origins in Heidegger’s works, in order to assess the potentials and pitfalls of ‘Heidegger on politics’. (shrink)

The appeal to ordinary language is a central feature of Wittgenstein’s later philosophy: he reminds us that our words find meaning in the ordinary practices and forms of life in which they are used. This emphasis on the ordinary may seem to clash with Heidegger’s claim that average everyday understanding is marked by inauthenticity: is Wittgenstein’s emphasis on ordinary language fundamentally inauthentic? On the contrary, I argue, Wittgenstein’s emphasis on the ungroundedness of our ordinary practices parallels Heidegger’s discussion of (...) anxiety and uncanniness, suggesting that we can unearth something like a Heideggerian appeal to authenticity in Wittgenstein’s appeal to ordinary language. (shrink)

Universalist and nihilist answers to philosophical questions may be extreme, but they are clear enough. Aliquidist answers, by contrast, are typically caught between the Scylla of vagueness and indeterminacy and the Charybdis of ungroundedness and arbitrariness, and steering a proper middle course—saying exactly where in the middle one is going to settle—demands exceptional navigating powers. I myself tend to favor extreme answers precisely for this reason. Here, however, I consider one sense in which Something may claim superiority over its (...) polar competitors, Everything and Nothing, when it comes to answerting the ontological question, “What is there?”. (shrink)

This article is a critique of Étienne Balibar's philosophical orientation towards Europe, construed as both an ideal and an institutional reality, in light of recent European crises. I argue that Balibar's commitment to Europe follows from his longstanding political-philosophical preference for a compromise position between political utopianism and political realism, but that this compromise is ultimately incoherent, combining the ungroundedness of utopianism with the undue self-limitation of realism.

I explore a game-theoretic analysis of social interactions in which each agent’s well-being depends crucially on the well-being of another agent. As a result of this, payoffs are interdependent and cannot be fixed, and hence the overall assessment of strategies becomes ungrounded. A paradigmatic example of this general phenomenon occurs when both players are ‘reflective altruists’, in a sense to be explained. I argue that ungroundedness cannot be captured by standard games with incomplete information, but that it requires the (...) concept of an underspecified game; underspecified games have radically underdetermined matrices. Players locked in ungroundedness will be assumed to engage simultaneously in an implicit second-order game in which they try to coordinate their first-order matrices. If they fail to coordinate, their first-order interaction cannot be recast as a game in the first place. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 23 (2003) 170-174 [Access article in PDF] A Buddhist History of the West: Studies In Lack. By David R. Loy. Albany: State University of New York Press, 2002. 244 pp. The religious and philosophical situation of our time seems polarized between resurgent fundamentalisms and a cosmopolitan awareness bridging heretofore separated traditions. Even a few decades ago the notion of a dialogue between East and West was a (...) novelty in which demarcated traditions and cultures (say the Buddhist East and the Christian West) experimented with attempts to find a common language to speakacross the boundaries between their respective identities. In such a context,"Western Buddhists" were those pilgrims of the counterculture who "went East" in search of some civilizational and spiritual other; the West, abjected to the realm of soulless scientism or outdated religious authoritarianism, was left behind. The situation is different at the beginning of the twenty-first Christian century. The dialectical complexities, both inwardly in the soul or mind of seekers, and outwardly in the strange twists of contemporary history, emerge to forbid any simple assessments of what can be left behind or indeed what the use can be of what seekers have found in the "non-West." People of Western background begin to realize and consciously address the [End Page 170] karmic-historical presuppositions of their search, which continue to constitute a kind of historical unconscious to the formulation of any possible "Western Buddhisms." Meanwhile, while fundamentalists of many backgrounds posit "clashes of civilizations" that assume an absoluteness of traditional distinctions, cosmopolitans realize that, for all the particularity of their respective starting points, the global situation is inextricably a shared one. In such a context, what canWestern Buddhist intellectuals, cognizant of their own starting points but having learned some things along the Way that are perhaps of universal relevance, speak to our common condition?The "Buddhist History of the West" that David Loy provides is less a historical narrative of the events constitutive of the societies descending from Greco-Roman civilization through European epochs and American empire into the age of globalization than a form of psychoanalytic anamnesis of those societies' cultural constructions of reality. Loy's psychoanalytic interpretive frame is composed of Buddhist insight into the human mind's deep-seated grasping for solidity and certainty in the face of a reality fundamentally characterized by impermanence and ungroundedness (the "Lack" of the subtitle, our simultaneous awareness of death, impermanence, andontological emptiness and the ego's wish for eternal selfhood in an endless but impossibly fulfilling world). Loy's Buddhism is combined with the existential psychology of Ernest Becker and the revisionist Freudianism of Norman O. Brown called on as Western resources for the spiritual therapeutics "the West" seems to need as it enters the third Christian millennium both triumphant and in despair of any meaning to accompany its economic and pop-cultural hegemony.Seven anamnestic chapters take us through twenty-five hundred years of Western cultural constructions, from the Greek and Roman philosophical inquiries into Freedom, a kind of origin-tale of Humanism seen as a "religious" (religion for Loy being the way humans attempt to answer the problem of Lack as if to ground our groundlessness) vision of meaning as the development of human capacities for rational thought, through the intertwining of classical and Christian constructions in medieval and Renaissance periods, through the Protestant Reformation into the political and ideological space of modernity, culminating in a vision of the globalizing West as purveying a "Religion of the Market," an ironically meaningless (centered on the symbolic code for Value—Money—as a displacement of Value itself) system of meaning. This last, our contemporary situation, would perhaps be simply a problem of aesthetic tastelessness (American pop culture performing the dissolution of all surviving traditional sacred orders following the description of capitalism by Marx as causing "all that is sacred" to "melt into air") were it not for the massive social injustice and environmental devastation it structurally produces. Loy's therapeutic vision, following the Buddhist deconstruction of the demarcated "self" and Becker and Brown's cultural-historical or collective... (shrink)

Giorgio Agamben’s thought arises out of thinking through the concrete negativity or ungroundedness figured by “life” as understood under the sovereign exception. His work is sustained by the continuous exposure of philosophical concepts to what remains excluded, silenced, and to an extent unsayable for philosophy: Thus, disfiguring, decentering, and violating the temporality of Western history and philosophy as well as the concepts that order it. This means that Agamben thinks out of the ungrounded occurrences of language and history, and (...) that the transformative potency of his thought arises from sheer negativity and yet, in his engagement of thought’s concrete situation. (shrink)

Giorgio Agamben’s thought arises out of thinking through the concrete negativity or ungroundedness figured by “life” as understood under the sovereign exception. His work is sustained by the continuous exposure of philosophical concepts to what remains excluded, silenced, and to an extent unsayable for philosophy: Thus, disfiguring, decentering, and violating the temporality of Western history and philosophy as well as the concepts that order it. This means that Agamben thinks out of the ungrounded occurrences of language and history, and (...) that the transformative potency of his thought arises from sheer negativity and yet, in his engagement of thought’s concrete situation. (shrink)

The structure of Yablo’s paradox is analysed and generalised in order to show that beginningless step-by-step determination processes can be used to provoke antinomies, more concretely, to make our logical and our on-tological intuitions clash. The flow of time and the flow of causality are usually conceived of as intimately intertwined, so that temporal causation is the very paradigm of a step-by-step determination process. As a conse-quence, the paradoxical nature of beginningless step-by-step determina-tion processes concerns time and causality as usually (...) conceived. (shrink)

In his Paradoxes (1995: Cambridge University Press: 149) Mark Sainsbury presents the following pair of sentences: Line 1: The sentence written on Line 1 is nonsense. Line 2: The sentence written on Line 1 is nonsense. Sainsbury (1995: 149, 154) here makes three assertions: (1) The sentence in Line 1 is so viciously self-referential that it falls into the truth-value gap. The sentence is really nonsense. (2) The sentence in Line 2 is by contrast true. For it states precisely that (...) the sentence in Line 1 is nonsense. (3) The two sentences in Lines 1 and 2 are an example of the principle that two sentence tokens of the same sentence-type can have different truth-values, although they have the same reference and state the same property of the object of reference. In this paper, I argue that Sainsbury’s assumptions are false in all three cases. (shrink)

We model infinite regress structures -not arguments- by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.