A natural approach to representing and reasoning about temporal propositions (i.e., statements with time-dependent truth-values) is to associate them with time elements. In the literature, there are three choices regarding the primitive for the ontology of time: (1) instantaneous points, (2) durative intervals and (3) both points and intervals. Problems may arise when one conflates different views of temporal structure and questions whether some certain types of temporal propositions can be validly and meaningfully associated with different time elements. In this (...) paper, we shall summarize an ontological glossary with respect to time elements, and diversify a wider range of meta-predicates for ascribing temporal propositions to time elements. Based on these, we shall also devise a versatile categorization of temporal propositions, which can subsume those representative categories proposed in the literature, including that of Vendler, of McDermott, of Allen, of Shoham, of Galton and of Terenziani and Torasso. It is demonstrated that the new categorization of propositions, together with the proposed range of meta-predicates, provides the expressive power for modeling some typical temporal terms/phenomena, such as starting-instant, stopping-instant, dividing-instant, instigation, termination and intermingling etc. (shrink)

In this paper the general notion of Bourbaki structures, interpreted in terms of Suppes predicates, will be used to axiomatize a system of meta-rankings in the sense introduced by A. K. Sen. It will be argued that this axiomatization must take place in a Kantian-ruled world in order to provide a link between meta-rankings and individual actions.Dedicated to Prof. Francisco A. Doria on his 50th birthday.

Nous étudions dans cet article les différentes formes de prédication seconde détachée en position initiale dans un corpus comparable composé de textes d’économie en anglais et en français. Ce corpus a été annoté sous le logiciel Analec. L’enjeu est de montrer en quoi un même phénomène syntaxique est exploité, sur le plan discursif, de façon divergente dans chacune des deux langues. Une étude qualitative et quantitative des prédications secondes du corpus montre que la prédication seconde prend le plus souvent la (...) forme d’une participiale en –ing en anglais, où elle se spécialise dans un rôle méta-énonciatif de balise textuelle pour le lecteur, ce qui n’est pas le cas en français. (shrink)

Meta-ontology (in van Inwagen's sense) concerns the methodology of ontology, and a controversial meta-ontological issue is to what extent ontology can rely on linguistic analysis while establishing the furniture of the world. This paper discusses an argument advanced by some ontologists (I call them unifiers) against supporters of or coincident entities (I call them multipliers) and its meta-ontological import. Multipliers resort to Leibniz's Law to establish that spatiotemporally coincident entities a and b are distinct, by pointing at (...) a predicate F () made true by a and false by b . Unifiers try to put multipliers in front of a dilemma: in attempting to introduce metaphysical differences on the basis of semantic distinctions, multipliers either (a) rest on a fallacy of verbalism, entailed by a trade-off between a de dicto and a de re reading of modal claims, or (b) beg the question against unifiers by having to assume the distinction between a and b beforehand. I shall rise a tu quoque, showing that unifiers couldn't even distinguish material objects (or events) from the spatiotemporal regions they occupy unless they also resorted to linguistic distinctions. Their methodological aim to emancipate themselves from linguistic analysis in ontological businesses is therefore problematic. (shrink)

The paper addresses issues of predicates of taste, both gustatory and aesthetic in dialogue with Michael Glanzberg. The first part briefly discusses his view of anaphora in the determination of the semantics of such predicates, and attempts a friendly generalization of his strategy. The second part discusses his contextualism about statements of taste, of the form A is Φ, and then proposes a pluralist alternative. The literature normally confronts contextualism and relativism here, but the pluralist proposal introduces further (...) options. First, it distinguishes first-level and second-level, more theoretical, approaches. At the first level it introduces the naïve view option, the naive non-dogmatist experiencer who simply claims that A is Φ and that’s it. On meta-level such an experiencer is simply agnostic about further matters. Then, there is the first-level dogmatist stance, characteristic for people who do sincerely debate the issues, who naively believe they are objectively right. The third option is the tolerant, liberal one: “A is Φ; for me, I mean. How do you find it?” On the meta-level, dogmatic disagreement goes well with value-absolutism, entailing that one of the parties is simply wrong, and with relativism. If one is not dogmatist about taste predicates, one should accept that dogmatist is simply wrong; no faultlessness is present. The liberal stance goes well with contextualism. If one is liberal there is no deep disagreement. So, the idea of faultless disagreement is a myth. But the proposal notes that language is open to all possibilities, there is no single option that is obligatory for all speakers. (shrink)

The possibility of formal representation of Aristotle’s discussion about singular predication in Categories 10, 13b27-35 is investigated through three symbolic idioms: the first-order language with identity, with and without definitive description, and through the languages of free logics. I show that such representations are not fully adequate. According to the first option, we are committing Aristotle with some (meta)logical implications he is not willing to accept. According to the second option, we are burdening Aristotle with Russell’s theory of names. (...) Finally, the third option leaves us with the assumption that ‘exist(s)’ could be represented with a predicate. This assumption, however, Aristotle emphatically rejects. (shrink)

Many accept David Lewis's (1983) claim that, among the candidate meanings for our predicates, some are more natural than others -- they do better or worse at ``carving nature at its joints''. Call this claim predicate naturalism. Disagreement remains over whether the notion of naturalness extends ``beyond the predicate'' (à la Sider, 2011). Are the candidate meanings of logical vocabulary also more or less natural? Call this claim logical naturalism. -/- One motivation for predicate naturalism comes from its supposed (...) ability to help rebut various radical indeterminacy arguments associated with Hilary Putnam (1977, 1980, 1981). It does so in combination with a popular meta-semantic theory called reference magnetism. I argue that the same threats of Putnam-style radical indeterminacy rearise for proponents of predicate naturalism -- threats which logical naturalism helps rebuts. So, if we accept predicate naturalism because it helps fend off threats of indeterminacy, we should also accept logical naturalism. (shrink)

In this paper, I use an example from the history of philosophy to show how independently defining each side of a pair of contrary predicates is apt to lead to contradiction. In the Euthyphro, piety is defined as that which is loved by some of the gods while impiety is defined as that which is hated by some of the gods. Socrates points out that since the gods harbor contrary sentiments, some things are both pious and impious. But “pious” (...) and “impious” are contrary predicates; they cannot simultaneously characterize the same thing. Euthyphro changes his definition, but the problem of recognizing emotional ambivalence is only side-stepped. I go on to show how contemporary philosophers run into a similar problem. According to Prinz, something is good if and only if we harbor positive sentiments towards it and bad if and only if we harbor negative sentiments towards it. Thus, if we are ambivalent towards something (if we harbor both positive and negative sentiments towards it), then it is both good and bad. Like “pious” and “impious”, “good” and “bad” are contraries. Next, according to the fitting-attitude theory first elaborated by Brentano and favored by contemporary meta-ethicists like Blackburn, Brandt, Ewing, Garcia, Gibbard, McDowell, and Wiggins, something is good if and only if it is a fitting (appropriate) object of approbation, and something is bad if and only if it is a fitting (appropriate) object of disapprobation. I argue that moral ambivalence is sometimes appropriate, i.e., that the correct response to some things is to both love and hate them. Hence, according to the fitting-attitudes theory, some things are both good and bad. I conclude by discussing a variety of ways in which the problem of ambivalence may be solved, suggesting that attitudes of approbation and disapprobation be further individuated by the reasons for them. (shrink)

Recently, it has been proposed to understand a logic as containing not only a validity canon for inferences but also a validity canon for metainferences of any finite level. Then, it has been shown that it is possible to construct infinite hierarchies of ‘increasingly classical’ logics—that is, logics that are classical at the level of inferences and of increasingly higher metainferences—all of which admit a transparent truth predicate. In this paper, we extend this line of investigation by taking a somehow (...) different route. We explore logics that are different from classical logic at the level of inferences, but recover some important aspects of classical logic at every metainferential level. We dub such systems meta-classical non-classical logics. We argue that the systems presented deserve to be regarded as logics in their own right and, moreover, are potentially useful for the non-classical logician. (shrink)

Huw Price’s neo-pragmatist programme of global expressivism (see Huw Price "Naturalism Without Mirrors" (2011) and "Expressivism, Pragmatism and Representationalism" (2013)) faces a challenge — it is susceptible to the charge that the proposed combination of expressivism with a deflationary account of semantics leads to inconsistency. Expressivists about a particular discourse deny that it is representational. Global expressivists face the threat of inconsistency due to their attempts to generalise this denial to include the discourse of semantics. In this paper, I explicate (...) two meta-semantic presuppositions of this charge. I argue that such an explication enables us to construct a consistent account of global expressivism. The key point is that global expressivists should adopt two truth predicates and treat meta-semantics as non-substantial. I argue that this framework provides us with a better grasp of Price’s response to the problem of inconsistency and enables global expressivists to accommodate the correspondence intuition. (shrink)

In this thesis, Semantics, Meta-Semantics, and Ontology, I provide a critique of the method of truth in metaphysics. Davidson has suggested that we can determine the metaphysical nature and structure of reality through semantic investigations. By contrast, I argue that it is not semantics, but meta-semantics, which reveals the metaphysically necessary and sufficient truth conditions of our claims. As a consequence I reject the Quinean criterion of ontological commitment. In Part I, chapter 1, I argue that the metaphysically (...) primary truth bearers are not propositions, but rather concrete representations, either beliefs or sentences. I show, in chapter 2, that we can give sense to a truth predicate applying to sentences, given a truth operator and quantification into sentence position. I argue that this strategy does not commit us to the existence of propositions serving as truth bearers. In Part II I argue that although we must assign semantic values to sentences and/or predicates, the meaningfulness of these expressions is not thereby explained. In chapter 3 I articulate Davidson’s problem of predication and his solution, but argue that he was wrong to attribute this solution to Tarski. In chapter 4 I examine the semantics of modal languages; I conclude that although they require semantic values for predicates and/or sentences we should be instrumentalists about these theories. In Part III I consider the relationship between truth and existence. In chapter 5, I defend Pluralism about truth: in some domains of discourse, I claim, semantic reference plays a merely instrumental role in explaining truth. In chapter 6, I show that Hume’s Principle, which is committed by the Quinean criterion to the existence of numbers, can be true even though numbers do not exist. In doing so, I appeal to meta-semantic and diachronic considerations. In the conclusion I compare my views on ontology and commitment to Jody Azzouni’s; and in the appendix I suggest how one might pursue diachronic linguistics. (shrink)

This paper presents an enhanced ontology formalization, combining previous work in Conceptual Structure Theory and Order-Sorted Logic. Most existing ontology formalisms place greater importance on concept types, but in this paper we focus on relation types, which are in essence predicates on concept types. We formalize the notion of ‘predicate of predicates’ as meta-relation type and introduce the new hierarchy of meta-relation types as part of the ontology definition. The new notion of closure of a relation (...) or meta-relation type is presented as a means to complete that relation or meta-relation type by transferring extra arguments and properties from other related types. The end result is an expanded ontology, called the closure of the original ontology, on which automated inference could be more easily performed. Our proposal could be viewed as a novel and improved ontology formalization within Conceptual Structure Theory and a contribution to knowledge representation and formal reasoning (e.g., to build a query-answering system for legal knowledge). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:META-ONTOLOGY AND META-FICTION by Denis E. B. Pollard Peter van inwagen's attempt to explain the nature of fiction makes use of Quine's program in meta-ontology.1 This program comprises four basic theses: (i) that being is the same as existence, (ii) that being is univocal, (iii) that this univocal sense is best captured, for the purposes of formalization, by die existential quantifier, and (iv) that deciding what (...) to believe about what there is comes to a decision about what theories we should accept. As the aim of formalization is explicitness, then theories should be rendered into canonicalese and their commitments identified through those sentences which are prefaced with the existential quantifier. For Inwagen, as for his mentor Quine, acceptance of theory expressed in this canonical form entails acceptance of the ontology expressed in those quantified sentences. Bringing these considerations to bear on fiction, Inwagen asks, "What are theories about fiction?" and replies that they are "theories that treat stories as having an internal structure" (p. 72). The upshot of this is that such theories contain sentences which, when formally rendered, revead commitments to fictional objects. It is further claimed that such sentences can be vehicles of objective truth. Thus Inwagen finds he cannot wholeheartedly dismiss Sarah Gamp as a nonentity. In this respect, his view contrasts with two contemporary accounts, the "reductivist" one which denies Sarah Gamp's existence and her possession of any properties whatever, and the more recent "Meinongian" view which would agree that Sarah Gamp does not exist, but would nonetheless strenuously maintain that she is a nurse, fat, old, and decidedly the worse for drink. Inwagen's Sarah is neither ofthese: pace both these positions, she exists all right, but with properties such as being a theoretical entity of criticism, being a satiric villainess, not being a woman, and not being fond of gin. Inwagen's attempt to steer what seems to be a middle course has yielded, if anything, a more counterintuitive result than either ofthe other views. What is die explanation for this? 244 Denis E. B. Pollard245 To begin with, it is important to note a distinction, which Inwagen himself accepts, between two kinds of sentences. Let us take the following elementary examples: (1) "Sarah Gamp is a nurse," and (2) "Sarah Gamp is a character in a nineteenth-century novel." With specimens like (1), Inwagen sides with the reductivist: such sentences asefalse, and are not about anything. But it is with examples like (2) that ontology becomes a real issue, since sentences of this kind belong to literary theory. Neither authors nor critics who make use of sentences of the first kind are committed to the existence of fictional entities. So far, so good. But what is it that compels such commitment in the second case? Inwagen is sceptical about reductivist analyses which seek to paraphrase such sentences in order to remove any "misleading" implications. Such paraphrases he would regard as at best "messy," and more seriously, unlikely to preserve intuitive meaning without appearing to say that there are fictional characters. Unfortunately, he brushes this aside as a "narrow technical issue" at the very point where rather more argument is needed. However, on the issue of preservation of intuitive meaning, it might well be argued that his contention is somewhat question-begging, suggesting a rather literal reading of (2) above as a straightforward predication superficially akin to (3) "McEnroe is a seeded player in this year's Wimbledon tournament." So by a strange alchemy, the expression "Sarah Gamp" in (2) is accorded a referential status denied to it in (1). It is at this point that the notion of"theoretical entity" is introduced to supply the need for a referent dictated by the Quinean program. Inwagen's Sarah Gamp, in this theoretical disguise, can now literally satisfy predicates like "... is a character in a nineteenth-century novel," but not predicates like "... is a nurse." The parallel being exploited here is that with scientific theory. An ideal gas can satisfy Boyle's Law, but cannot literally be ignited, put into containers, or have an offensive smell. But there is more than a suspicion of equivocation over the term... (shrink)

In order to defend the Cornell variety of naturalistic moral realism from Horgan and Timmons’ Moral Twin Earth objection, several philosophers have proposed what I call Normatively Enriched Moral Meta-Semantics. According to NEMMS, the natural properties that serve as the contents of moral predicates are fixed by non- moral normative facts. In this paper, I elucidate two versions of NEMMS: one proposed by David Brink, and the other proposed by Mark van Roojen. I show what these meta-semantics (...) have in common, and how each one promises the Cornell realist a response to the Moral Twin Earth objection. I then argue that Cornell realists ought to be wary of adopting NEMMS. A naturalist realist who adopts this meta-semantics confronts a trilemma. The proponent of NEMMS owes a meta-ethical account of the relevant content-fixing normative facts. Such facts are either reducible to recognizably natural facts or they are not. If they are not reducible, then NEMMS entails the denial of ethical naturalism. If such facts are taken to be reducible to facts about agents’ actual or hypothetical attitudes, then the account renders moral facts stance-dependent. Consequently, moral realism is false. Alternatively, one might propose that the content-fixing normative facts are reducible to attitude-independent natural facts. However, such a proposal is refuted by its own Twin Earth objection. (shrink)

This book explores two questions that are integral to the question of the existence of God. The first question concerns the meaning of "existence" and the second concerns the meaning of "God". Regarding the first question, this book motivates, presents and defends the meta-ontology found in Gottlob Frege's writings and defended by Michael Dummett, Crispin Wright and Bob Hale. Frege's approach to questions of existence has mainly found use in connection with abstract objects such as numbers. This is one (...) of the first studies to systematically present Fregean meta-ontology and apply it to theology. Frege's meta-ontology is informed by his context principle. According to this, logico-syntactic notions such as "singular term" and "predicate" are pivotal to questions of what exists. These notions serve to throw light on the second question. Through thorough engagement with Old as well and New Testament texts, the book shows how Frege's logico-syntactic notions are of crucial importance when seeking to understand the meaning and use of "God". To complete the defence of Fregean meta-ontology, the book concludes by pointing to important differences between the otherwise closely associated concepts of an object found in Wittgenstein's Tractatus Logico-Philosophicus and Frege's writings. (shrink)

In Fallibilism Democracy and the Market, Calvin Hayes proposes an original solution to the major meta-theoretical issue in moral philosophy, the is-ought problem, then utilizes it to define and/or solve practical problems in both applied ethics and public policy. The solution and its applications are based on a unified theory of rationality applicable to epistemology, ethics and public policy, predicated on a revised Popperian fallibilism. It is intended as a defense of Karl Popper's political philosophy but only after a (...) substantial revision of its theoretical and meta-theoretical basis. (shrink)

The ancient puzzle of the Liar was shown by Tarski to be a genuine paradox or antinomy. I show, analogously, that certain puzzles of contemporary game theory are genuinely paradoxical, i.e., certain very plausible principles of rationality, which are in fact presupposed by game theorists, are inconsistent as naively formulated. ;I use Godel theory to construct three versions of this new paradox, in which the role of 'true' in the Liar paradox is played, respectively, by 'provable', 'self-evident', and 'justifiable'. I (...) also construct in modal operator logic a paradox involving reflexive empirical reasoning. Unlike the paradox of the Liar, the paradox of reflexive reasoning does not depend on self-reference. ;I consider various solutions to the Liar paradox and evaluate how well these solutions cope with the paradox of reflexive reasoning. I then formalize the solution to the paradoxes which I favor: the indexical-hierarchical approach, first sketched out by Charles Parsons and Tyler Burge. In this solution, occurrences of the predicate 'true' in sentence-tokens are contextually relativized to levels of a hierarchy. Drawing also on some brief remarks of Bertrand Russell and Charles Parsons, I develop an account of the kind of schematic generality needed for this theory to be statable. ;Finally, I demonstrate that the principles shown to be paradoxical are in fact presupposed by contemporary game theorists in their reliance on the notion of common knowledge or, more precisely, mutual belief. I create novel analyses of and corresponding solutions to several recalcitrant puzzles within game theory, including the "chain-store paradox". (shrink)

Recently, and rather startlingly, given the history of the debate about a name's semantic content, some claim that names are in fact predicates -- predicativism. Some of predicativists claim that a name's semantic content involves the concept of being called -- calling accounts that have been traditionally meta-linguistic. However, these accounts fail to be informative. Inspired by Burge's claim that proper names are literally true of the individuals that have them, Fara develops a non-meta-linguistic concept of being (...) called analysed in terms of property attributions. I offer seven separate reasons for rejecting the account, one of which is that Fara's development of the view, at least, has implausible consequences for a theory of name acquisition. I sketch an alternative account of name acquisition that is meta-linguistic in nature, but because it is not offered as a theory of name's content, the standard worries fail to apply. In fact, I argue that an account of name acquisition must be meta-linguistic, and therefore a more nuanced conception of meta-linguistic speech acts is required. The account invokes Austin's performative-constative distinction. It analyses name acquisition as due to performative meta-linguistic speech acts. (shrink)

This chapter contains sections titled: What is First Philosophy? The Science of Being qua Being Categories and Change What Being is Primary? Overview of Metaphysics Z Subject Essence The Problem of Matter The Status of Form Potentiality and Actuality Form–Matter Predication Form and Functional Matter Primary Substances Theology Bibliography.

Sentences containing predicates of personal taste (for example, ‘tasty’, ‘funny’) and aesthetic predicates (for example, ‘beautiful’) give rise to an acquaintance inference: They convey the information that speakers have first-hand experience with the object of predication, and that they can only be uttered appropriately if that is the case. This is surprisingly hard to explain. I will concentrate on aesthetic predicates, and firstly criticize previous attempts to explain the acquaintance phenomena. Second, I will suggest an explanation that (...) rests on a speech act theoretical version of hybrid expressivism, according to which, in uttering ‘X is beautiful’ speakers perform two illocutionary acts simultaneously: an expressive and an assertive one. I will spell out this suggestion in detail and defend it against objections. Considering puzzles related to the acquaintance inference will lead to a new argument for a promising version of hybrid expressivism in meta-aesthetics. (shrink)

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and (...) in particular the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail. (shrink)

In this paper I will argue that there is a bi-directional relationship between philosophy and meaning such that doing philosophy can change the meaning of terms. A rhetorically powerful work of philosophy that garners widespread interest has the potential to change how people use a predicate. This gives rise to three concerns. First, one’s conclusion can become right in virtue of one doing a particularly good job arguing for it. Second, it may be implausible to take philosophy to be a (...) primarily descriptive enterprise. Part of the job of the philosopher is to proselytize about the correct usage of a word. Lastly, and most worrisome of all, the age-old method of the dialectic, a centerpiece of the philosophical project for thousands of years, threatens to plunge a range of domains of philosophical discourse into incoherence. (shrink)

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professional basketball players. The main feature (...) of Shapiro's account is that the extensions of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann.The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects. (shrink)

In vol. 2 of Grundlagen der Mathematik Hilbert and Bernays carry out their undecid- ability proof of predicate logic basing it on their undecidability proof of the arithmeti- cal systemZ00. In this paper, the latter proof is reconstructed and summarized within a formal derivation schema. Formalizing the proof makes the presumed use of a meta language explicit by employing formal predicates as propositional functions, with ex- pressions as their arguments. In the final section of the paper, the proof (...) is analyzed critically by applying Wittgenstein’s view on meta language, which does not lead to a questioning of the assumptions on which the proof is based but of its presumed use of meta language. Finally, it will be argued that determining if it is the undecidability proof or Wittgenstein’s analysis of meta language that is right depends on whether a decision procedure for a predicate that undecidability proofs have seemingly proven undecidable can nonetheless be defined. Thus serious attempts to define a procedure for such a predicate should not be ruled out without studying them. (shrink)

We will present a three-valued consequence relation for metainferences, called CM, defined through ST and TS, two well known substructural consequence relations for inferences. While ST recovers every classically valid inference, it invalidates some classically valid metainferences. While CM works as ST at the inferential level, it also recovers every classically valid metainference. Moreover, CM can be safely expanded with a transparent truth predicate. Nevertheless, CM cannot recapture every classically valid meta-metainference. We will afterwards develop a hierarchy of consequence (...) relations CMn for metainferences of level n. Each CMn recovers every metainference of level n or less, and can be nontrivially expanded with a transparent truth predicate, but cannot recapture every classically valid metainferences of higher levels. Finally, we will present a logic CMω, based on the hierarchy of logics CMn, that is fully classical, in the sense that every classically valid metainference of any level is valid in it. Moreover, CMω can be nontrivially expanded with a transparent truth predicate. (shrink)

A category is at least a way of dividing up the world, whether it is formulated in the object-language, like final cause, or in the meta-language, like individual concept. It is always an anticipation of experience as well, since it provides a pair of pigeonholes that future experience is to be put into. There is no handy way of deciding what degree of generality a predicate must possess in order to be called a "category"; presumably event and cause are (...) categories, but apple and hominoid are not. In any case, it seems that if we make any distinctions at all in the world, they will begin to order themselves in terms of relative generality as soon as we reflect upon them, and those distinctions that appear to cut most deeply across the variety of things will give rise to specifically philosophical questions about their consistency, coherence, clarity, and justification. This is, then, the point at which we divide into schools and programs. (shrink)

This much-needed book provides a thorough account of temporal logic, one of the most important areas of logic in computer science today. The book begins with a solid introduction to semantical and axiomatic approaches to temporal logic. It goes on to cover predicate temporal logic, meta-languages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results. With its inclusion of cutting-edge results and unifying methodologies, this book is an indispensable (...) reference for both the pure logician and the theoretical computer scientist. (shrink)

I will consider the question what the meaning of the unity of thought and thing is. This unity is introduced by Hegel as the main precondition of the science of logic, when it is understood as the definiens of the logical. I will try to clarify this issue primarily by interpreting chosen fragments in the chapter “Force and the Understanding, Phenomenon and the supra-sensible World” in the Phenomenology of Spirit. Here, Hegel exposes the result of the dialectics of the passage (...) “Perception or Thing and Illusion” as the “unity of the being-for-itself and the beingfor- other”, and along with this result, he notes: “At first it seems they only pertain to the form of moments; but this being-for-itself and being for-other is also content itself,…” . I understand this unity as that between thought and thing. It appears when categories, as Hegel expressed it in logic and Encyclopedia, are seen in themselves. I determine the relationship between the speculative observance and unity of thought and thing as follows:categories are seen in themselves when they neither relate to instances of an extralogical area of use, nor are they considered as the content of meta-level predicates. When, for example, I observe the eidos “difference” in itself, than I think about this as a thing of “difference“, that is, as a differentiation. The unity of thought and thing is a derivation of itself and not the result of an interpretation or outside manipulation. I will try to profile my interpretation by criticizing other approaches. (shrink)

The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result. (...) Utilizing recent developments in structural proof theory, we develop a G3-style sequent calculus for Quarc and briefly demonstrate its structural properties. We put these properties to use immediately to construct direct proofs of the meta-theoretical properties of the system. We then incorporate an abstract (and, as we shall see, logical) predicate into the system in a way that preserves all the structural properties. This allows us to identify a system of Quarc which is deductively equivalent to PC, and also yields a constructive method of demonstrating the Craig interpolation theorem (which speaks in favor of the aforementioned predicate being logical). We further generalize this extension to develop a bivalent system of Quarc with defining clauses that still maintains all the desirable properties of a good proof system. (shrink)

We discuss the principles for a primitive, object-linguistic notion of consequence proposed by ) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a (...) notion of logical consequence: we study the corresponding theory of validity by showing that it is conservative over a wide range of base theories: this result is achieved via a well-behaved form of local reduction. The theory of logical consequence is based on a restriction of the introduction rule for the consequence predicate. To unrestrictedly maintain this principle, we develop a conception of object-linguistic consequence, which we call grounded consequence, that displays a restriction of the structural rule of reflexivity. This construction is obtained by generalizing Saul Kripke’s inductive theory of truth. Grounded validity will be shown to satisfy several desirable principles for a naïve, self-applicable notion of consequence. (shrink)

This monograph details a new solution to an old problem of metaphysics. It presents an improved version of Ostrich Nominalism to solve the Problem of Universals. This innovative approach allows one to resolve the different formulations of the Problem, which represents an important meta-metaphysical achievement. In order to accomplish this ambitious task, the author appeals to the notion and logic of ontological grounding. Instead of defending Quine’s original principle of ontological commitment, he proposes the principle of grounded ontological commitment. (...) This represents an entirely new application of grounding. Some metaphysicians regard Ostrich Nominalism as a rejection of the problem rather than a proper solution to it. To counter this, the author presents solutions for each of the formulations. These include: the problem of predication, the problem of abstract reference, and the One Over Many as well as the Many Over One and the Similar but Different variants. This book will appeal to anyone interested in contemporary metaphysics. It will also serve as an ideal resource to scholars working on the history of philosophy. Many will recognize in the solution insights resembling those of traditional philosophers, especially of the Middle Ages. (shrink)

There are five basic ways to resolve disagreements: keep arguing until capitulation, compromise, locate an ambiguity or contextual factors, accept Pyrrhonian skepticism, and adopt relativism. Relativism is perhaps the most radical and least popular solution to a disagreement, and its defenders generally think the best motivator for relativism is to be found in disputes over predicates of personal taste. I argue that taste predicates do not adequately motivate relativism over the other possible solutions, and argue that relativism looks (...) like the most promising approach when disputants cannot even agree on the meta-evidence for a contested proposition. (shrink)

Substructural solutions to the semantic paradoxes have been broadly discussed in recent years. In particular, according to the non-transitive solution, we have to give up the metarule of Cut, whose role is to guarantee that the consequence relation is transitive. This concession—giving up a meta rule—allows us to maintain the entire consequence relation of classical logic. The non-transitive solution has been generalized in recent works into a hierarchy of logics where classicality is maintained at more and more metainferential levels. (...) All the logics in this hierarchy can accommodate a truth predicate, including the logic at the top of the hierarchy—known as CMω—which presumably maintains classicality at all levels. CMω has so far been accounted for exclusively in model-theoretic terms. Therefore, there remains an open question: how do we account for this logic in proof-theoretic terms? Can there be found a proof system that admits each and every classical principle—at all inferential levels—but nevertheless blocks the derivation of the liar? In the present paper, I solve this problem by providing such a proof system and establishing soundness and completeness results. Yet, I also argue that the outcome is philosophically unsatisfactory. In fact, I’m afraid that in light of my results this metainferential solution to the paradoxes can hardly be called a “solution,” let alone a good one. (shrink)

The problem of existence is reputed to be one of the oldest and most intractable of philosophy: What do we mean when we say that something exists or, even more challengingly, that something does not exist? Intuitively, it seems that we all have a firm grip upon what we are saying. But how should we explain the difference–if there is any–between statements about existence and other, garden-variety predicative statements? What is the difference between saying that something exists and saying, for (...) instance, that something is red, heavy, soft, etc.? These questions provide the focus of the present study. In the first part, this study addresses those authors that have been most effective and influential at widening the gap between statements about existence and garden-variety predicative statements. These are David Hume, Immanuel Kant, Franz Brentano, and Gottlob Frege. According to this family of approaches, existence becomes something very different from a property of objects. In the second part, this study turns to more recent attempts that have moved in the opposite direction by trying to reduce existence to a–more or less–plain property of objects. The philosophers that are going to be discussed here are Alexius Meinong, Richard Routley, Terence Parsons, William Rapaport, Edward Zalta, and Graham Priest. Between the first and the second part, an extensive chapter is dedicated to the approaches to existence developed under the heading of free logics. Finally, the third part of this study develops a deflationist account of existence: We should abandon the assumption shared by all accounts discussed in this study, namely that the notion of existence adds something to the content of a statement. To the contrary, we should think of existence as a redundant notion. The advantage of this strategy is that it does not make it contradictory to say that something does not exist – a frequent upshot of the approaches discussed in the first part. At the same time, this strategy avoids the epicycles common to the approaches discussed in the second part, which are strictly linked to the reduction of existence to a property of objects. (shrink)

There have been recent arguments against the idea that substructural solutions are uniform. The claim is that even if the substructuralist solves the common semantic paradoxes uniformly by targeting Cut or Contraction, with additional machinery, we can construct higher-level paradoxes (e.g., a higher-level Liar, a higher-level Curry, and a meta-validity Curry). These higher-level paradoxes do not use metainferential Cut or Contraction, but rather, higher-level Cuts and higher-level Contractions. These kinds of paradoxes suggest that targeting Cut or Contraction is not (...) enough for solving semantic paradoxes; the substructuralist must target Cut of every level or Contraction of every level to solve the paradoxes. Hence, the substructuralists do not provide as uniform of a solution as they hoped they did. In response, we argue that the substructuralists need not admit these additional machineries. In fact, they are redundant in light of the validity predicate (i.e., there is no gain in terms of expressive power). The validity predicate is powerful enough to creep these paradoxes in the object level. The substructuralist does not need to ascend to metainferences to construct higher-level paradoxes. Moreover, there is a reading available to the substructuralist such that all the higher-level structural rules would collapse to instances of the object-level structural rules (e.g., meta $_n$ Cut and meta $_n$ Contraction would become instances of Cut and Contraction). We then address Barrio et al.’s worry that the validity predicate has its shortcomings; the substructuralist cannot internalize some of its metarules. We claim that the validity of metarules can be internalized without the need to strengthen the validity predicate. However, a problem raised by Barrio et al. is still present—the problem of internalizing unwanted instances of Cut in Cut-free approaches. We argue that this internalization problem is not unique to the validity predicate; the same problem is present with other problematic predicates, such as the truth predicate and the provability predicate. (shrink)

Mereological theories are theories based on a binary predicate ‘being a part of’. It is believed that such a predicate must at least define a partial ordering. A mereological theory can be obtained by adding on top of the basic axioms of partial orderings some of the other axioms posited based on pertinent philosophical insights. Though mereological theories have aroused quite a few philosophers’ interest recently, not much has been said about their meta-logical properties. In this paper, I will (...) look into whether those theories are decidable or not. Besides, since theories of Boolean algebras are in some sense upper bounds of mereological theories which can be found in the literature, I shall also make some observations about the possibility of getting mereological theories beyond Boolean algebras. (shrink)

Much contemporary metaphysics, moved by an apparent necessity to take reality to consist of given beings and properties, presents us with what appear to be deep problems requiring radical changes in the common sense conception of persons and the world. Contemporary meta-ethics ignores questions about logical form and formulates questions in ways that make the possibility of correct value judgments mysterious. In this book, Wheeler argues that given a Davidsonian understanding of truth, predication, and interpretation, and given a relativised (...) version of Aristotelian essentialism compatible with Davidson’s basic thinking, many metaphysical problems are not very deep. Likewise, many philosophers' claims that common sense needs to be modified are unfounded. He argues further that a proper consideration of questions of logical form clarifies and illuminates meta-ethical questions. Although the analyses and arguments he gives are often at odds with those at which Davidson arrived, they apply the central Davidsonian insights about semantics, understanding, and interpretation. (shrink)

Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour (...) as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided. (shrink)

The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “set-like entities”—is that it is ultimately incoherent. The most forceful form of this charge is due to Barry Schein, who argues that singularists must accept a certain comprehension principle which entails the existence of things having the contradictory property of being both atomic and non-atomic. The purpose of this paper is to defuse Schein’s argument, by noting three necessary and independently motivated restrictions on (...) the metalinguistic predicates ‘atom’ and ‘non-atom’: both are sort, property, and context-relative. With these restrictions in place, Schein’s problematic assumption becomes evident: his presumed singularist analysis of ‘non-atom’ conflates the metalanguage with the meta-metalanguage, i.e. the language used to talk about the metalanguage. (shrink)

Church’s type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type theory. It is particularly well suited to the formalization of mathematics and other disciplines and to specifying and verifying hardware and software. It also plays an important role in the study of the formal semantics of natural language. When utilizing (...) it as a meta-logic to semantically embed expressive non-classical logics further topical applications are enabled in artificial intelligence and philosophy. A great wealth of technical knowledge can be expressed very naturally in it. With possible enhancements, Church’s type theory constitutes an excellent formal language for representing the knowledge in automated information systems, sophisticated automated reasoning systems, systems for verifying the correctness of mathematical proofs, and a range of projects involving logic and artificial intelligence. Some examples and further references are given in Sections 1.2.2 and 5 below. Type theories are also called higher-order logics, since they allow quantification not only over individual variables, but also over function, predicate, and even higher order variables. Type theories characteristically assign types to entities, distinguishing, for example, between numbers, sets of numbers, functions from numbers to sets of numbers, and sets of such functions. As illustrated in Section 1.2.2 below, these distinctions allow one to discuss the conceptually rich world of sets and functions without encountering the paradoxes of naive set theory. Church’s type theory is a formulation of type theory that was introduced by Alonzo Church in Church 1940. In certain respects, it is simpler and more general than the type theory introduced by Bertrand Russell in Russell 1908 and Whitehead & Russell 1927a. Since properties and relations can be regarded as functions from entities to truth values, the concept of a function is taken as primitive in Church’s type theory, and the λ-notation which Church introduced in Church 1932 and Church 1941 is incorporated into the formal language. Moreover, quantifiers and description operators are introduced in a way so that additional binding mechanisms can be avoided, λ-notation is reused instead. λ-notation is thus the only binding mechanism employed in Church’s type theory. (shrink)

It is widely assumed in philosophy that there is a tight connection between semantics and metaphysics. Semantic theories about the meanings of natural language terms and phrases are taken to provide evidence for and against various metaphysical theses about the nature of non-linguistic parts of the world. Call this view the widespread thesis. I argue that the widespread thesis is mistaken: semantic theories do not generally have robust metaphysical consequences. I contend that the best arguments for the widespread thesis turn (...) on an interpretation of semantic theories according to which they are metaphysically illuminating: the metaphysical structure of the world is directly mirrored in the structure of the theory. Terms and existential quantification in the theory signal the existence of entities in the world, predicates signal the existence of properties, and the structures of set theoretic objects invoked by the theory directly correspond to structural features of the world. Such an interpretation is not the only one available, however, and it is a substantive philosophical (and linguistic) issue which interpretation is correct. Accordingly, I develop and defend an alternative interpretation of semantic theories according to which the structural features of these theories and of their theorems reflect biological and computational constraints on the architecture of the language faculty and historical contingencies in its evolutionary development. Supposedly metaphysically committing features of the theory—including the appearance of quantification and (ostensibly) referring terms—may thus be arepresentational artifacts of these constraints, rather than representational features that reflect metaphysical reality. To determine the metaphysical consequences of a semantic theory then, we must determine which of its features represent language-independent characteristics of the world and which are arepresentational consequences of the structure of the language faculty. To do this, however, we must have some prior idea what the language-independent world is like—that is, we must engage in prior metaphysical theorizing that is not beholden to the semantic theory itself. (shrink)

My first paper on the Is/Ought issue. The young Arthur Prior endorsed the Autonomy of Ethics, in the form of Hume’s No-Ought-From-Is (NOFI) but the later Prior developed a seemingly devastating counter-argument. I defend Prior's earlier logical thesis (albeit in a modified form) against his later self. However it is important to distinguish between three versions of the Autonomy of Ethics: Ontological, Semantic and Ontological. Ontological Autonomy is the thesis that moral judgments, to be true, must answer to a realm (...) of sui generis non-natural PROPERTIES. Semantic autonomy insists on a realm of sui generis non-natural PREDICATES which do not mean the same as any natural counterparts. Logical Autonomy maintains that moral conclusions cannot be derived from non-moral premises.-moral premises with the aid of logic alone. Logical Autonomy does not entail Semantic Autonomy and Semantic Autonomy does not entail Ontological Autonomy. But, given some plausible assumptions Ontological Autonomy entails Semantic Autonomy and given the conservativeness of logic – the idea that in a valid argument you don’t get out what you haven’t put in – Semantic Autonomy entails Logical Autonomy. So if Logical Autonomy is false – as Prior appears to prove – then Semantic and Ontological Autonomy would appear to be false too! I develop a version of Logical Autonomy (or NOFI) and vindicate it against Prior’s counterexamples, which are also counterexamples to the conservativeness of logic as traditionally conceived. The key concept here is an idea derived in part from Quine - that of INFERENCE-RELATIVE VACUITY. I prove that you cannot derive conclusions in which the moral terms appear non-vacuously from premises from which they are absent. But this is because you cannot derive conclusions in which ANY (non-logical) terms appear non-vacuously from premises from which they are absent Thus NOFI or Logical Autonomy comes out as an instance of the conservativeness of logic. This means that the reverse entailment that I have suggested turns out to be a mistake. The falsehood of Logical Autonomy would not entail either the falsehood Semantic Autonomy or the falsehood of Ontological Autonomy, since Semantic Autonomy only entails Logical Autonomy with the aid of the conservativeness of logic of which Logical Autonomy is simply an instance. Thus NOFI or Logical Autonomy is vindicated, but it turns out to be a less world-shattering thesis than some have supposed. It provides no support for either non-cognitivism or non-naturalism. (shrink)

For semantic inferentialists, the basic semantic concept is validity. An inferentialist theory of meaning should offer an account of the meaning of "valid." If one tries to add a validity predicate to one's object language, however, one runs into problems like the v-Curry paradox. In previous work, I presented a validity predicate for a non-transitive logic that can adequately capture its own meta-inferences. Unfortunately, in that system, one cannot show of any inference that it is invalid. Here I extend (...) the system so that it can capture invalidities. (shrink)

We furnish a core-logical development of the Gödel numbering framework that allows metamathematicians to attain limitative results about arithmetical truth without incorporating a genuine truth predicate into the language in a way that would lead to semantic closure. We show how Tarski’s celebrated theorem on the arithmetical undefinability of arithmetical truth can be established using only core logic in both the object language and the metalanguage. We do so at a high level of abstraction, by augmenting the usual first-order language (...) of arithmetic with a primitive predicate Tr and then showing how it cannot be a truth predicate for the augmented language. McGee established an important result about consistent theories that are in the language of arithmetic augmented by such a “truth predicate” Tr and that use Gödel numbering to refer to expressions of the augmented language. Given the nature of his sought result, he was forced to use classical reasoning at the meta level. He did so, however, on the additional and tacit presupposition that the arithmetical theories in question (in the object language) would be closed under classical logic. That left open the dialectical possibility that a constructivist (or intuitionist) could claim not to be discomfited by the results, even if they were to “give a pass” on the unavoidably classical reasoning at the meta level. In this study we “constructivize” McGee’s result, by presuming only core logic for the object language. This shows that the perplexity induced by McGee’s result will confront the constructivist (or intuitionist) as well. (shrink)

Natural deduction (for short: nd-) calculi have not been used systematically as a basis for automated theorem proving in classical logic. To remove objective obstacles to their use we describe (1) a method that allows to give semantic proofs of normal form theorems for nd-calculi and (2) a framework that allows to search directly for normal nd-proofs. Thus, one can try to answer the question: How do we bridge the gap between claims and assumptions in heuristically motivated ways? This informal (...) question motivates the formulation of intercalation calculi. Ic-calculi are the technical underpinnings for (1) and (2), and our paper focuses on their detailed presentation and meta-mathematical investigation in the case of classical predicate logic. As a central theme emerges the connection between restricted forms of nd-proofs and (strategies for) proof search: normal forms are not obtained by removing local "detours", but rather by constructing proofs that directly reflect proof-strategic considerations. That theme warrants further investigation. (shrink)

Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative (...) semantics for classical proof theory. The key features of the account are: there is a single notion of truth—definite truth—and a single notion of validity; sentences can be true, false, or undetermined; all classical theorems and all classical inference rule are valid; the sorites argument is unsound; ‘definitely’ is treated as a meta-language predicate; higher-order vagueness is handled via semantic ascent. (shrink)

Cook regards Sorenson’s so-called ‘the no-no paradox’ as only a kind of ‘meta-paradox’ or ‘quasi-paradox’ because the symmetry principle that Sorenson imposes on the paradox is meta-theoretic. He rebuilds this paradox at the object-language level by replacing the symmetry principle with some ‘background principles governing the truth predicate’. He thus argues that the no-no paradox is a ‘new type of paradox’ in that its paradoxicality depends on these principles. This paper shows that any theory is inconsistent with the (...) T-schema instances for the no-no sentences, plus the T-schema instance for a Curry sentence associated with the symmetry of the no-no sentences. It turns out that the no-no paradox still depends on the problematic instances of the T-schema in a way that the liar paradox does. What distinguishes the no-no paradox is the T-schema instance for the above Curry sentence, which encodes Sorensen’s symmetry principle at the object-language level. (shrink)

Journal of International Political Theory, Ahead of Print. Practice turn marks an important advancement in International Relations theorizing. In challenging abstract meta-theoretical debates, practice theorizing in International Relations aims to get close to the lifeworld of the actual practitioners of politics. Scholars from different positions such as constructivism, critical theory, and post-structuralism have critically interrogated the analytical framework of practices in international politics. Building upon these works, we are concerned with a question of how to examine the context of (...) international practices that unfolds in multiple ways in practitioners’ performances. Our central thesis is that a distinct pragmatic methodology offers an opportunity to keep with the practice turn and avoid the problematic foundational moves of mainstream practice theorizing. This involves foregrounding three interrelated processes in examining practices: the role of exceptions in the normal stream of performances, normative uptake of the analysts, and the semantic field that actors navigate in political performances. We argue that this methodology is predicated on its usefulness to interpret practices through reflective social-science inquiry. (shrink)

In his celebrated 'Good and Evil' (l956) Professor Geach argues as against the non-naturalists that ‘good’ is attributive and that the predicative 'good', as used by Moore, is senseless.. 'Good' when properly used is attributive. 'There is no such thing as being just good or bad, [that is, no predicative 'good'] there is only being a good or bad so and so'. On the other hand, Geach insists, as against non-cognitivists, that good-judgments are entirely 'descriptive'. By a consideration of what (...) it is to be an A, we can determine what it is to be a good A, even where the ‘A’ in question is ‘human being’. These battles are fought on behalf of naturalism, indeed, of an up-to-date Aristotelianism. Geach plans to 'pass' from the 'purely descriptive' man to good/bad man, and from human act to good/bad human act. I argue: (l) That the predicative 'good' does have a genuine sense and that it is a mistake to suppose that ‘good’ is a purely attributive adjective. This does not entail that the predicative good (as used by Moore) denotes a non-natural property, but his mistake, if any is metaphysical or ontological not conceptual. (2) That the attributive 'good' cannot be used to generate a naturalistic ethic. It is difficult to extract a set of biologically based requirements out of human nature that are a) reasonably specific; b) rationally binding or at least highly persuasive; and c) morally credible. -/- On the way I protest against Geach’s tendency to try to win arguments by affecting not to understand things. -/- My views to some extent anticipate those of Kraut in *Against Absolute Goodness*. (shrink)

In jurisprudential literature, the adjective ‘defeasible’ appears as a predicate of many terms: concepts, laws, rules, reasoning, justification, proof, and so on. In this paper, we analyze the effects of some versions of the thesis of the defeasibility of legal norms on the reconstruction of the notion of legal validity. We analyze some possible justifications of this thesis considered as a claim concerning validity, and enquire into two possible sets of problems related to the defeasibility of the criteria of identification (...) of a legal system. We also provide a formalization of some options regarding defeasible criteria of identification, which can be used as a tool for meta-jurisprudential analysis. Finally, the thesis according to which defeasibility is better conceived of as a feature of legal application is examined and questioned. (shrink)