In this paper I investigate Putnam’s model-theoretic argument from a transcendent standpoint, in spite of Putnam’s well-known objections to such a standpoint. This transcendence, however, requires ascent to something more like a Tarskian meta-level than what Putnam regards as a “God’s eye view”. Still, it is methodologically quite powerful, leading to a significant increase in our investigative tools. The result is a shift from Putnam’s skeptical conclusion to a new understanding of realism, truth, correspondence, knowledge, and theories, (...) or certain aspects thereof, based on, among other things, a better understanding of what models are designed (and not designed) to do. (shrink)

In "Realism and Reason" Hilary Putnam has offered an apparently strong argument that the position of metaphysical realism provides an incoherent model of the relation of a correct scientific theory to the world. However, although Putnam's attack upon the notion of the "intended" interpretation of a scientific theory is sound, it is shown here that realism may be formulated in such a way that the realist need make no appeal to any "intended" interpretation of such a theory. Consequently, (...) it can be shown that realism is immune to Putnam's criticism and that attempts at reformulating this criticism are not likely to meet with success. (shrink)

Abstract: Hilary Putnam has reformulated his model-theoretic argument as an argument against indirect realism in the philosophy of perception. This new argument is reviewed and defended. Putnam’s new focus on philosophical theories of perception (instead of metaphysical realism) makes better sense of his previous responses to the objection from the causal theory of reference. It is argued that the model-theoretic argument can also be construed as an argument that holders of a (...) causal theory of reference should adopt direct realism in the philosophy of perception. (shrink)

The first section of the paper gives a very condensed history of the evolution of the author’s views on realism and anti-realism. It emphasizes that his previously accepted form of anti-realism was abandoned not because of the alleged fallacies in the model-theoretic argument against metaphysical realism, but due to his rejection of some of the assumptions on which it rests - assumptions which have been almost universal in philosophy after Descartes. The second section discusses and defends the (...) part of the model-theoretic argument that many critics have almost universally found fallacious, namely the „just more theory” move. In the appendix to the paper the author elaborates what does his return to common sense realism mean. He points out that his position involves a negative element, the rejection of the idea that truth cannot outrun verifiability, and two positive elements: returning (as close as possible) to „naive realism” with respect to perception, and a disquotational account of truth similar to one endorsed by Wittgenstein. (shrink)

This chapter contains sections titled: Abstract The Model ‐ Theoretic Argument Difficulties and Differences Putnam's Progress Implications Objections and Replies References.

Putnam's model theoretic argument against metaphysical realism can be reconstructed as valid, with premises acceptable to the realist. There is no illegitimate assumption that the causal theory of reference is false.

In a recent article, James Van Cleve joins a growing throng who have argued that Hilary Putnam's model-theoretic argument (and his "just more theory" response) begs the question against those who hold externalist theories of reference. Van Cleve has misinterpreted Putnam's argument. Putnam does not demand that the statements which make up the causal theory of reference must, themselves, do the reference-fixing. That would be question-begging. Rather, Putnam's argument is a "reductio", which can only be (...) blocked with a theory of reference that is both substantive and plausible. Putnam argues that there is no interpretation of "causality" that meets both conditions. (shrink)

Two of Hilary Putnam's model-theoretic arguments against metaphysical realism are examined in detail. One of them is developed as an extension of a model-theoretic argument against mathematical realism based on considerations concerning the so-called Skolem-Paradox in set theory. This argument against mathematical realism is also treated explicitly. The article concentrates on the fine structure of the arguments because most commentators have concentrated on the major premisses of Putnam's argument and especially on his treatment (...) of metaphysical realism. It is shown that the validity of Putnam's arguments is doubtful and that realists are by no means forced to accept the theses Putnam ascribes to them. It is concluded that Putnam fails to give convincing arguments for rejecting mathematical or metaphysical realism. Furthermore, Putnam's internal realism is discussed critically. (shrink)

The model-theoretic argument, which Putnam employs to argue againstmetaphysical realism, has faced serious objections of many realist opponents.Igor Douven in his recent paper offers a new interpretation of the model-theoreticargument, which avoids the previous objections. The purpose of this paper is toshow that Douven's reconstruction of Putnam's argument is not successful, andhence that the realist objections still stand.

Putnam's Model-Theoretic argument purports to show that, contrary to what the metaphysical realist is committed to, an epistemically ideal theory which satisfies all operational and theoretical constraints can be guaranteed to be true. He draws the additional antirealist conclusion that there can be no single privileged relation of reference. I argue that the very possibility of a so-called ideal theory satisfying all operational constraints presupposes a determinate relation of reference, and hence Putnam must assume precisely what he (...) denies. (shrink)

In “Models and Reality”, H. Putnam formulated his model-theoretic argument against “metaphysical realism”. The article proposes a meta-reconstruction of Putnam’s model-theoretic argument in the light of two mutually compatible interpretations of it–elaborated by Manuel Garcia-Carpintero and Igor van Douven. A critical reflection on these interpretations and their adequacy for Putnam’s argument allows us to expose new theses coherent with Putnam’s reasoning and indicate new paths to improve this argument for our reconstruction task. (...) In particular, we show that Putnam’s position may be coherent with van Douven’s versions of Global Descriptivism under some conditions, but Putnam cannot reject realism as quickly as Carpintero suggests. We show that Suszko’s canonic axiomatic system and Sneed’s concept of theory may provide valuable support for Putnam’s argument. Finally, we critically evaluate Carpintero’s theses about the genesis of unintended interpretations of our languages, adopting the machinery of the Upward Skolem–Loewenheim Theorem and Knight’s Theorem. (shrink)

This chapter concentrates on the version of Putnam's argument set forth in his Reason, Truth and History. It explains how, in general terms, that argument is best conceived as working. Cursory inspection of Putnam's overall dialectic reveals it to incorporate three sub‐arguments, collectively designed to show that the metaphysical realist confronts an insuperable problem over explaining how our words may possess determinate reference. The chapter considers Putnam's version of the Permutation Argument, aimed at showing that reference cannot (...) be determined by fixing the truth‐conditions of whole sentences. It then reviews Putnam's 'just more theory' argument, designed to show that the metaphysical realist cannot rescue the situation by appeal to causal or other natural connections between our words and the world. The chapter considers how the considerations adduced by Hilary Putnam might be seen as an argument telling selectively against metaphysical realism. (shrink)

Putnam famously attempted to use model theory to draw metaphysical conclusions. His Skolemisation argument sought to show metaphysical realists that their favourite theories have countable models. His permutation argument sought to show that they have permuted models. His constructivisation argument sought to show that any empirical evidence is compatible with the Axiom of Constructibility. Here, I examine the metamathematics of all three model-theoretic arguments, and I argue against Bays (2001, 2007) that Putnam is largely (...) immune to metamathematical challenges. (shrink)

Bas van Fraassen has recently argued for a "dissolution" of Hilary Putnam's well-known model-theoretic argument. In this paper I argue that, as it stands, van Fraassen's reply to Putnam is unsuccessful. Nonetheless, it suggests the form a successful response might take.

Putnam’s model-theoretic arguments for the indeterminacy of reference have been taken to pose a special problem for mathematical languages. In this paper, I argue that if one accepts that there are theory-external constraints on the reference of at least some expressions of ordinary language, then Putnam’s model-theoretic arguments for mathematical languages don’t go through. In particular, I argue for a kind of descriptivism about mathematical expressions according to which their reference is “anchored” in the reference of (...) expressions of ordinary language. These anchors add enough to the content of mathematical expressions to forestall the radical kind of indeterminacy that model-theoretic arguments are purported to show, while still leaving room for a plausible, moderate kind of indeterminacy. (shrink)

Igor Douven has offered an original reconstruction and defence of Putnam's model-theoretic argument against metaphysical realism. Douven's construal has notable exegetical virtues, since it makes sense of some assumptions in Putnam's argument which his opponents have considered question-begging or puzzling. In this article I provide an indirect defence of metaphysical realism, by showing why this new version of the anti-realist argument should also be rejected. The main problems in the Douven-Putnam argument come from ascribing (...) to the realist a distorted view of correspondence truth. The view entails that when no feature selects just one of all the possible interpretations of language the existence of an interpretation suffices to make true a theory. The sensible realist is not committed to this extreme conception of correspondence truth. /// Igor Douven ha presentado y defendido una reconstructión del argumento teórico-modelista de Putnam contra el realismo metafísico. Esta versión tiene ciertas virtudes exegéticas, pues hace inteligible algunos presu- puestos putnamianos que sus críticos han considerado injustificados o sorprendentes. En este artículo proporciono una defensa indirecta del realismo metafisico, mostrando por qué debe también rechazarse el argumento antirrealista bajo esta nueva forma. Los problemas principales del argumento Douven-Putnam proceden de atribuir al realista una concepción distorsionada de la idea de verdad como correspondencia. Conforme a esa concepción, la ausencia de factores que seleccionen una única interpretación del lenguaje de entre las muchas posibles conlleva que la existencia de alguna interpretación ya es suficiente para hacer verdadera a una teoría que sea consistente. El realista sensato no está obligado a aceptar esa tesis. (shrink)

Since 1976 Hilary Putnam has on many occasions proposed an argument, founded on some model-theoretic results, to the effect that any philosophical programme whose purpose is to naturalize semantics would fail to account for an important feature of every natural language, the determinacy of reference. Here, after having presented the argument, I will suggest that it does not work, because it simply assumes what it should prove, that is that we cannot extend the metatheory: Putnam appears (...) to think that all we may determinately say about the relations between words and entities in the world is what the model theory tells us, but he has never offered justifications for that. At the end of the article, I will discuss the apparently reliable intuition that seems to me to be at the root of the argument, that is that, given a formal theory, there is an infinite number of ways of connecting it to, or of projecting it onto, the world. I will suggest that we should resist this intuition, because it rests on a very doubtful notion of world, which assumes that for any class of objects there is a corresponding property. (shrink)

The major argument against Ramsey-style epistemic structural realism is the model-theoretic refinement of Newman’s objection against Russell, presented in Ketland : 409–424, 2004), where a technical result is interpreted as showing that the Ramsey-sentence approach collapses into instrumentalism. This paper addresses some questions raised by the application of model theory to the scientific realism debate. Firstly, I will suggest three different formal semantics for the positions in the debate. Then, some technicalities of Ketland’s result will be (...) scrutinized in light of comments by Zahar and Demopoulos. Finally, I will formalize Ketland’s argument by means of an intensional operator and focus on one problematic premise. The conclusion is that, with some adjustments, the Ramsey-sentence approach can represent an intermediate position between realism and instrumentalism, but the term “structuralism” does not suit it well. (shrink)

Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate. In this paper, I focus on revenge arguments that employ the model-theoretic semantics of a target theory and I argue, contra the current revenge-theoretic wisdom, that they can constitute genuine expressive limitations. I consider the anti-revenge strategy elaborated by Field and argue that it does not offer a way out of the revenge problem. More (...) generally, I argue that the difference between ‘standard’ and ‘revenge’ paradoxes is ill-conceived and should be abandoned. This will contribute to show that the theories that provide a uniform account of truth and other semantic notions are the ones best equipped to avoid the paradoxes altogether—‘standard’ and ‘revenge’ alike. (shrink)

In the early days of natural language semantics, Donald Davidson issued a challenge to those, like Richard Montague, who would do semantics in a model-theoretic framework that gives a central role to a model-relative notion of truth. Davidson argued that no theory of this kind can claim to be an account of real truth conditions unless it first makes clear how the relativized notion relates to our ordinary non-relativized notion of truth. In the 1990s, Davidson’s challenge was (...) developed by Etchemendy into an argument against the model-theoretic account of logical consequence, one that also threatens the attempt to capture natural language entailment relations in modeltheoretic terms—one of the central desiderata of semantics. Nevertheless, the modeltheoretic framework has flourished within natural language semantics. But it has flourished without any consensus among semanticists as to how to answer Davidson’s challenge. The aim of this essay is to develop an answer. I argue that model-theoretic semantics is best understood as model-based science: a semantics for a natural language is a scientific model of truth conditions. This makes good sense of the way model-theoretic tools are used in natural language semantics. And it allows us to answer Davidson’s challenge by showing how a theory that employs a relativized notion of truth manages to tell us about ordinary truth conditions. Moreover, I argue that it helps us see how semantics can provide genuine explanations for natural language entailment and other truth-conditional phenomena. (shrink)

Weakly Aggregative Modal Logic ) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. \ has interesting applications on epistemic logic, deontic logic, and the logic of belief. In this paper, we study some basic model theoretical aspects of \. Specifically, we first give a van Benthem–Rosen characterization theorem of \ based on an intuitive notion of bisimulation. Then, in contrast to many well known normal or non-normal modal logics, we show (...) that each basic \ system \ lacks Craig interpolation. Finally, by model theoretical techniques, we show that an extension of \ does have Craig interpolation, as an example of amending the interpolation problem of \. (shrink)

The paper describes a computational model that we have implemented in an experimental dialogue system. Communication in a natural language between two participants A and B is considered, where A has a communicative goal that his/her partner B will make a decision to perform an action D. A argues the usefulness, pleasantness, etc. of D, in order to guide B's reasoning in a desirable direction. A computational model of argumentation is developed, which includes reasoning. Our model is (...) based on the studies in the common-sense conception of how the human mind works in such situations. Theoretical considerations are followed by an analysis of Estonian spoken human–human dialogues. First, calls of clients to travel agencies are studied where a travel agent could use various arguments in order to persuade a client to book a trip. The analysis demonstrates that clients are primarily looking for information; argumentation occurs in a small number of dialogues. Secondly, calls of s... (shrink)

This article discusses two coextensive concepts of logical consequence that are implicit in the two fundamental logical practices of establishing validity and invalidity for premise-conclusion arguments. The premises and conclusion of an argument have information content (they ?say? something), and they have subject matter (they are ?about? something). The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through an information-processing procedure exhibiting a step-by-step deduction of the conclusion from the premise-set. Invalidity is established (...) by exhibiting a countermodel satisfying the premises but not the conclusion. The process of establishing validity focuses on information content; the process of establishing invalidity focuses on subject matter. Corcoran's information-theoretic concept of logical consequence corresponds to the former. Tarski's model-theoretic concept of logical consequence formulated in his famous 1936 no-countermodels definition corresponds to the latter. Both are found to be indispensable for understanding the rationale of the deductive method and each complements the other. This study discusses the ontic question of the nature of logical consequence and the epistemic question of the human capabilities presupposed by practical applications of these two concepts as they make validity and invalidity accessible to human knowledge. (shrink)

I distinguish two versions of kin selection theory—a purely genetic version and a version that also appeals to cultural forms of cooperation —and present an argument in favor of using the former when it comes to accounting for the evolution of cooperation in non-human organisms. Specifically, I first show that both GKST and WKST are equally mathematically coherent—they can both be derived from the Price equation—but not necessarily equally empirically plausible, as they are based on different assumptions about the (...) inheritance system underlying the cooperative phenotype. Given this, I then, second, present a model selection theoretic argument in favor of GKST over WKST. This argument is based on the fact that, in non-human cases, the former theory is likely to be as empirically successful as WKST, while containing fewer degrees of freedom. I end by defending both the intrinsic importance of this argument and its relevance to the discussion surrounding the “gene’s eye view of evolution.”. (shrink)

One of Etchemendy's arguments against the Tarskian and model‐theoretic notion of logical truth is based on a reduction principle according to which a universally quantified sentence is true if, and only if, all of its instances are logically true. The reduction of logical truth to mere truth reveals that the concept of validity at play in Tarski and in model‐theory relies upon extra‐logical assumptions. A similar reduction had already been put forward by Prawitz, although not with focus (...) on extra‐logical assumptions. Prawitz's reduction concerns rather the possibility of understanding the Tarskian and model‐theoretic approach as implying any epistemic modality. We take into account a possible strategy that an advocate of Tarski and model‐theory may use against Etchemendy's objection, and argue that this strategy fails with respect to Prawitz's criticism. This permits us to shed light upon a difference between Prawitz's and Etchemendy's standpoints: while Etchemendy's reduction shows that the Tarskian and model‐theoretic notion of logical truth cannot be understood as an adequate formal counterpart of truth‐preservation solely by virtue of logical form, Prawitz's reduction insists on the fact that truth‐preservation solely by virtue of logical form is insufficient for epistemic modality to obtain. (shrink)

The paper addresses the manner in which the theory of Coalescent Argumentation [CA] has been received by the Argumentation Theory community. I begin (section 2) by providing a theoretical overview of the Coalescent model of argumentation as developed by Michael A. Gilbert (1997). I next engage the several objections that have been raised against CA (section 3). I contend that objectors to the Coalescent model are not properly sensitive to the theoretical consequences of the genuinely situated nature of (...) argument. I conclude (section 4) by suggesting that the resolution to the dispute between Gilbert and his objectors hinges on the outcome of several foundational theoretical questions identified over the course of the paper. (shrink)

Tait's proof of strong normalization for the simply typed λ-calculus is interpreted in a general model theoretical framework by means of the specification of a certain theory T and a certain model /oU of T. The argumentation is partly reduced to formal predicate logic by the application of certain derivability properties of T. The resulting version of Tait's proof is, within the same framework, systematically generalized to the Calculus of Constructions and other advanced type systems. The generalization proceeds (...) along the formal level in the sense that T is modified first and that the new theory partly dictates the subsequent transformation of /oU, which is carried out in stages. The uniform and standardized character of the argumentation contributes to its perspicuity. (shrink)

When discussing dialogue, argumentation researchers rarely draw the distinction between the story world and interactional world. While mediators often help to shape the interactions among agonists in the emerging flow of spoken discourse, writers of postulated dialogues narrate them, constructing a story world that depicts the agonists, depicts their utterances and their circumstances. In this paper, I ask where the agonists of the dialogue model of argument interact, and I show that they often interact in the story world (...) of postulated dialogues. Postulated dialogues are story problem conversations. Common in textbooks, exams, and standardized tests, story problems create hypothetical situations to illustrate formal relationships among variables, and are designed to be read in a theoretical attitude that treats the characters, objects, and circumstances that they depict as given. When argumentation researchers examine postulated dialogues, they tend to adopt a theoretical attitude, limiting their analysis to the conversation between the agonists depicted in the story world. Reading this way makes it easier to overlook the interactional world where the writing and reading of the texts takes place, obscuring the fact that they are narrated dialogues, often written by researchers. Reading this way also makes it easier to confirm the traditional participation framework of the dialogue model of argument. (shrink)

I show that words with indefinite implicit complements occasion a dilemma for their model theory. There has been only two previous attempts to address this problem, one by Fodor and Fodor (1980) and one by Dowty (1981). Each requires that any word tolerating an implicit complement be treated as ambiguous between two different lexical entries and that a meaning postulate or lexical rule be given to constrain suitably the meanings of the various entries for the word. I show that (...) the positing of such an ambiguity runs counter to the facts and propose an alternative solution which does not appeal to ambiguity, meaning postulates or lexical rules. Indeed, I show that the dilemma posed by indefinite implicit complements is posed by all implicit complements and that a general solution to the problem of implicit complements follows from an independently motivated, single treatment of five other problems, that of subcategorization, that of phrasal projections of words, that of defining a model theoretic structure for phrase structure grammars, that of complement polyvalence and that of complement polyadicity. (shrink)

Although it is not yet officially recognized as a clinical entity which is diagnosable, Internet Gaming Disorder (IGD) has been included in section III for further study in the DSM-5 by the American Psychiatric Association (APA, 2013). This is important because there is increasing evidence that people of all ages, in particular teens and young adults, are facing very real and sometimes very severe consequences in daily life resulting from an addictive use of online games. This article summarizes general aspects (...) of IGD including diagnostic criteria and arguments for the classification as an addictive disorder including evidence from neurobiological studies. Based on previous theoretical considerations and empirical findings, this paper examines the use of one recently proposed model, the Interaction of Person-Affect-Cognition-Execution (I-PACE) model, for inspiring future research and for developing new treatment protocols for IGD. The I-PACE model is a theoretical framework that explains symptoms of Internet addiction by looking at interactions between predisposing factors, moderators, and mediators in combination with reduced executive functioning and diminished decision making. Finally, the paper discusses how current treatment protocols focusing on Cognitive-Behavioral Therapy for Internet addiction (CBT-IA) fit with the processes hypothesized in the I-PACE model. (shrink)

This paper focuses on the inferential configuration of arguments, generally referred to as argument scheme. After outlining our approach, denominated Argumentum Model of Topics (AMT, see Rigotti and Greco Morasso 2006, 2009; Rigotti 2006, 2008, 2009), we compare it to other modern and contemporary approaches, to eventually illustrate some advantages offered by it. In spite of the evident connection with the tradition of topics, emerging also from AMT’s denomination, its involvement in the contemporary dialogue on argument schemes (...) should not be overlooked. The model builds in particular on the theoretical and methodological perspective of pragma-dialectics in its extended version, reconciling dialectic and rhetoric; nevertheless, it also takes into account numerous other contributions to the study of argument schemes. Aiming at a representation of argument schemes able to monitor the inferential cohesion and completeness of arguments, AMT focuses on two components of argument scheme that could be distinguished, readapting pragma-dialectical terms, as procedural and material respectively. The procedural component is based on the semantic-ontological structure, which generates the inferential connection from which the logical form of the argument is derived. The material component integrates into the argument scheme the implicit and explicit premises bound to the contextual common ground (Rigotti 2006). In this paper, the comparison of the AMT to other approaches focuses on the inferential configuration of arguments and not on the typologies of argument schemes and on the principles they are based on, which the authors intend to tackle in a further paper. (shrink)

Theories and models are not equivalent. I argue that an orientation towards models as a primary carrier of nursing knowledge overcomes many ongoing challenges in philosophy of nursing science, including the theory–practice divide and the paradoxical pursuit of predictive theories in a discipline that is defined by process and a commitment to the non‐reducibility of the health/care experience. Scientific models describe and explain the dynamics of specific phenomenon. This is distinct from theory, which is traditionally defined as propositions that explain (...) and/or predict the world. The philosophical case has been made against theoretical universalism, showing that a theory can be true in its domain, but that no domain is universal. Subsequently, philosophers focused on scientific models argued that they do the work of defining the boundary conditions—the domain(s)—of a theory. Further analysis has shown the ways models can be constructed and function independent of theory, meaning models can comprise distinct, autonomous “carriers of scientific knowledge.” Models are viewed as representations of the active dynamics, or mechanisms, of a phenomenon. Mechanisms are entities and activities organized such that they are productive of regular changes. Importantly, mechanisms are by definition not static: change may alter the mechanism and thereby alter or create entirely new phenomena. Orienting away from theory, and towards models, focuses scholarly activity on dynamics and change. This makes models arguably critical to nursing science, enabling the production of actionable knowledge about the dynamics of process and change in health/care. I briefly explore the implications for nursing—and health/care—knowledge and practice. (shrink)

In this paper I discuss how, given the complexity of biological systems, reliance on theoretical models in the development and testing of biological theories leads to an uncomfortable form of anti-realism. I locate the source of this discomfort in the uniqueness and hence diversity of biological phenomena, in contrast with the simplicity and uniformity of the subject matter of physics. I have argued elsewhere that the use of theoretical models creates an unresolvable tension between the explanatory strength and predictive power (...) of hypotheses, and I review this argument again here. My discussion parallels that of Nancy Cartwright, who claims that the use of ceteris paribus laws in physics creates an antagonism between truth and explanation that requires theoretical models to figure centrally in scientific explanation, thereby precluding realism. I argue instead that in biology it is the use of theoretical models that creates this conflict, and conclude that adequate biological explanation cannot rely on the modeling approach alone. Finally, I claim that if we accept the semantic view of theories, which makes theoretical models an integral part of our conception of theories, we must accept anti-realism as well. (shrink)

This paper presents an extended version of the Quantified Argument Calculus (Quarc). Quarc is a logic comparable to the first-order predicate calculus. It employs several nonstandard syntactic and semantic devices, which bring it closer to natural language in several respects. Most notably, quantifiers in this logic are attached to one-place predicates; the resulting quantified constructions are then allowed to occupy the argument places of predicates. The version presented here is capable of straightforwardly translating natural-language sentences involving defining clauses. (...) A three-valued, model-theoretic semantics for Quarc is presented. Interpretations in this semantics are not equipped with domains of quantification: they are just interpretation functions. This reflects the analysis of natural-language quantification on which Quarc is based. A proof system is presented, and a completeness result is obtained. The logic presented here is capable of straightforward translation of the classical first-order predicate calculus, the translation preserving truth values as well as entailment. The first-order predicate calculus and its devices of quantification can be seen as resulting from Quarc on certain semantic and syntactic restrictions, akin to simplifying assumptions. An analogous, straightforward translation of Quarc into the first-order predicate calculus is impossible. (shrink)

$${{{\mathcal {F}}}}$$ -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ $$\ldots $$ affirms the falsity of $$\ldots $$ ’ among them. The possible existence of non-referential sentences was also considered. To model the (...) sets of all the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of $$\mathcal{F}$$ -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory. (shrink)