In this paper, we want to present the genesis of Stanisław Leśniewski’s mereology. Although ‘mereology’ comes from theword ‘part’, mereology arose as a theory of collective classes. That is why we present the differences between the concepts of being a distributive class and being a collective class. Next, we present Leśniewski’s original mereology from 1927, but with a modern approach. Leśniewski was inspired to create his concept of classes and their elements by Russell’s antinomy. To face it, Leśniewski had to (...) define the concept of being an element of based on the concept of being part of. Leśniewski showed that in his theory, there is no equivalent to Russell’s antinomy. We will show that his solution has nothing to do with the original approach because, in both cases, we are talking about objects of a different kind. Russell’s original antinomy concerned distributive classes, and Leśsniewski’s considerations concerned collective classes. (shrink)

The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the arguments (...) advanced by dialetheists, many logicians and philosophers still hold the opinion that contradictions cannot be true. -/- Rather than advocating the truth of certain contradictions, this thesis offers a different challenge to the classical logician. By showing that it can be philosophically coherent to propose that true contradictions are metaphysically possible, the thesis suggests that the classical logician must do more than she currently has to justify her confidence in the impossibility of true contradictions. Simply fighting off the dialetheist’s putative examples of true contradictions at the actual world isn’t enough to justify the classical logician’s conclusion that true contradictions are impossible. -/- To aid the thesis dialectically, we introduce a new position, absolutism, which hypothesises that it’s metaphysically possible for at least one contradiction to be true, contrasting with the dialetheic hypothesis that some contradictions are true in the actual world. We demonstrate that absolutism can be given a philosophically coherent interpretation, an appropriate logic, and that certain criticisms are completely toothless against absolutism. The challenge put to the classical logician is then: On what logical or philosophical grounds can we rule out the metaphysical possibility of true contradictions? (shrink)

In this paper we present a solution to Saul Kripke’s Puzzle About Belief Meaning and use, Dordrecht, 1979) based on Kaplan’s metaphysical picture of words. Although it is widely accepted that providing such a solution was one of the main incentives for the development of Kaplan’s theory, it was never presented by Kaplan in a systematic manner and was regarded by many as unsatisfactory. We agree with these critiques, and develop an extension of Kaplan’s theory by introducing the notion of (...) “conservative” word uses, as well as arguing for the restriction of Kripke’s Disquotational Principle only to such uses. This restriction allows us to solve Kripke’s Puzzle by arguing that the assent of the puzzle’s protagonist does not allow disquotation and ascription of corresponding inconsistent belief, as it contains the non-conservative use of a proper name. At the end of the paper, we defend two of Kaplan’s theses that we find essential for our argument to work: that individuation of word tokens involves taking into account the intention of the speaker, and that different uniquely referring proper names of the same shape should be regarded as different homonymous words. (shrink)

Mi objetivo es discutir las principales dificultades que Frank P. Ramsey encontró en Principia Mathematica y la solución que, vía el Tractatus Logico-Philosophicus, propuso al respecto. Sostengo que las principales dificultades que Ramsey encontró en Principia Mathematica están, todas, relacionadas con que Russell y Whitehead desatendieron la forma lógica de las proposiciones matemáticas, las cuales, según Ramsey, deben ser tautológicas.

The question of ontological foundation has undergone a noteworthy revival in recent years: metaphysicians today quarrel about how exactly to understand the asymmetrical and hyperintensional relationship of grounding. One of the reasons for this revival is that the old quantificationalist meta-ontology inherited from Quine has been effectively criticised by leading philosophers favourable to a meta-ontology, the aim of which is to come to know “which facts/items ground (constitute the base of) which other facts/items”, thus to examine the relation of ontological (...) dependence between beings (e.g. chemical properties depend on physical properties, the economic situation on the behaviour of individuals etc.), i.e. to explore the hierarchical structure of reality. I shall not discuss here the relationship of grounding in itself, but make some historical-formal remarks on the properties of the ultimate ontological foundational item itself and its aporetic nature. To do so I explore various more or less exotic philosophical ecosystems in the following order: Heidegger (Seyn), Plato (ἕν), Wáng Bi (道, dào). On the way I shall propose a new interpretation both of certain hypotheses in the Parmenides and of the nature of the opposition between Wáng Bì and Guō Xiàng in regard to the logical grammar of the expression “nothing (無, wú)” (transl. J. Dudley). (shrink)

Among philosophers, Fregeanism and sententialism are widely considered two of the leading theories of the semantics of attitude reports. Among linguists, these approaches have received little recent sustained discussion. This paper aims to bridge this divide. I present a new formal implementation of Fregeanism and sententialism, with the goal of showing that these theories can be developed in sufficient detail and concreteness to be serious competitors to the theories which are more popular among semanticists. I develop a modern treatment of (...) quantifying in for Fregeanism and sententialism, in the style of Heim and Kratzer, and then show how these theories can—somewhat surprisingly—account for “third readings” on the model of the “Standard Solution” from possible-worlds semantics. The resulting Fregean/sententialist proposal has a distinctive attraction: it treats data related to counterfactual attitudes —which have proven challenging to accommodate in the setting of possible worlds semantics—straightforwardly as third readings. (shrink)

Anscombe raises a difficulty for the very idea of quotation. Davidson seeks to dissolve this difficulty. But the difficulty is real. And its lesson is that, in quotation, language takes itself as its topic in a non-objectifying manner. The idea of a non-objectifying manner of being a topic is crucial, not merely for understanding quotation, but for understanding the distinctive form of sensory consciousness in which language is perceived.

Abstract: An indirect report typically takes the form of a speaker using the locution “said that” to report an earlier utterance. In what follows, I introduce the principal philosophical and pragmatic points of interest in the study of indirect reports, including the extent to which context sensitivity affects the content of an indirect report, the constraints on the substitution of co-referential terms in reports, the extent of felicitous paraphrase and translation, the way in which indirect reports are opaque, and the (...) use of indirect reports as pragmatic vehicles for other speech acts such as humor, insult, or irony. Throughout I develop several positions: (i) that a semantic analysis of indirect reports is insufficient, (ii) that the distinction between direct and indirect reports is not clear and that indirect reports are the predominate way of reporting while direct reports may be a para-linguistic variation on them, (iii) that most questions about the semantics and pragmatics of indirect reports will rely on a full understanding of the nature of what is reported and how it gets reported, (iv) that an analysis of reporting requires the pragmatic tools of metarepresentation and a social, inter-personal understanding of relevance and shared knowledge. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I (...) argue that we have this ability. My argument looks to our best current theories of inference and considers examples of apparent infinite reasoning. My position is controversial, but if I'm right, our theories of truth, mathematics, and beyond could be transformed. And even if I'm wrong, a more careful consideration of infinite reasoning can only deepen our understanding of thinking and reasoning. -/- (Note for readers: the paper's brief discussion of uniform reflection and omega inconsistency is misleading. The imagined interlocutor's argument makes an assumption about the PA-provability of provability generalizations that, while true for the Godel sentence's instances, is unjustified, in general. This means my position is stronger against this objection than the paper suggests, since omega inconsistent theories are not automatically inconsistent with their uniform reflection principles, you also need to assume the arithmetically true Pi-2 sentences.). (shrink)

The principle of compositionality requires that the meaning of a complex expression remains the same after substitution of synonymous expressions. Alleged counterexamples to compositionality seem to force a theoretical choice: either apparent synonyms are not synonyms or synonyms do not syntactically occur where they appear to occur. Some theorists have instead looked to Frege’s doctrine of “reference shift” according to which the meaning of an expression is sensitive to its linguistic context. This doctrine is alleged to retain the relevant claims (...) about synonymy and substitution while respecting the compositionality principle. Thus, Salmon (Philos Rev 115(4):415, 2006) and Glanzberg and King (Philosophers’ Imprint 20(2):1–29, 2020) offer occurrence-based accounts of variable binding, and Pagin and Westerståhl (Linguist Philos 33(5):381–415, 2010c) argue that an occurrence-based semantics delivers a compositional account of quotation. Our thesis is this: the occurrence-based strategies resolve the apparent failures of substitutivity in the same general way as the standard expression-based semantics do. So it is a myth that a Frege-inspired occurrence-based semantics affords a genuine alternative strategy. (shrink)

Putnam’s most famous contribution to mathematical logic was his role in investigating Hilbert’s Tenth Problem; Putnam is the ‘P’ in the MRDP Theorem. This volume, though, focusses mostly on Putnam’s work on the philosophy of logic and mathematics. It is a somewhat bumpy ride. Of the twelve papers, two scarcely mention Putnam. Three others focus primarily on Putnam’s ‘Mathematics without foundations’ (1967), but with no interplay between them. The remaining seven papers apparently tackle unrelated themes. Some of this disjointedness would (...) doubtless have been addressed, if Putnam had been able to compose his replies to these papers; sadly, he died before this was possible. In this review, I do my best to tease out some connections between the paper; and there are some really interesting connections to be made. (shrink)

The unification argument, usually regarded as the main argument for predicativism about proper names, has recently been attacked by Robin Jeshion. According to Jeshion, the unification argument is based on the assumption of the literality of predicative uses of proper names in statements such as “There is one Alfred in Princeton.” In such a use, a proper name ‘N’ is used predicatively to denote those, and only those, objects called N. As Jeshion argues, however, there are many other examples in (...) which a proper name ‘N’ is used predicatively to denote objects which are not called N. Based on such cases, Jeshion challenges the predicativist to provide a justification for assuming that the original predicative use of proper names, to which the predicativist appeals in the unification argument, is literal. My aim in this paper is to defend predicativism by arguing that the predicativist’s assumption is well motivated. To this end, I first present the unification argument for predicativism and Jeshion’s challenge to it. Then, I argue that the answer provided by Delia Graff Fara to Jeshion’s challenge is unsatisfactory. Finally, I meet Jeshion’s challenge by extending the phenomena highlighted in Jeshion’s examples to the referential uses of proper names. (shrink)

During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a ‘naturalistic’ approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy—the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning—philosophers today largely (...) follow Willard Van Orman Quine (1908-2000) in his seminal rejection of this distinction. -/- This book offers a comprehensive study of Quine’s naturalism. Building on Quine’s published corpus as well as thousands of unpublished letters, notes, lectures, papers, proposals, and annotations from the Quine archives, this book aims to reconstruct both the nature (chapters 2-4) and the development (chapter 5-7) of his naturalism. As such, this book aims to contribute to the rapidly developing historiography of analytic philosophy, and to provide a better, historically informed, understanding of what is philosophically at stake in the contemporary naturalistic turn. (shrink)

In §93 of The Principles of Mathematics, Bertrand Russell observes that “the variable is a very complicated logical entity, by no means easy to analyze correctly”. This assessment is borne out by the fact that even now we have no fully satisfactory understanding of the role of variables in a compositional semantics for first-order logic. In standard Tarskian semantics, variables are treated as meaning-bearing entities; moreover, they serve as the basic building blocks of all meanings, which are constructed out of (...) variable assignments. But this has disquieting consequences, including Fine’s antinomy of the variable and an undue dependence of meanings on language. Here I develop an alternative, Fregean version of predicate logic that uses the traditional quantifier–variable apparatus for the expression of generality, possesses a fully compositional, non-representational semantics, and is not subject to the antinomy of the variable. The advantages of Fregean over Tarskian predicate logic are due to the former’s treating variables not as meaningful lexical items, but as mere marks of punctuation, similar to parentheses. I submit that this is indeed how the variables of predicate logic should be construed. (shrink)

W. V. Quine’s first philosophical monograph, Word and Object, is widely recognized as one of the most influential books of twentieth century philosophy. Notes, letters, and draft manuscripts at the Quine Archives, however, reveal that Quine was already working on a philosophical book in the early 1940s; a project entitled Sign and Object. In this paper, I examine these and other unpublished documents and show that Sign and Object sheds new light on the evolution of Quine’s ideas. Where “Two Dogmas (...) of Empiricism” is usually considered to be a turning point in Quine’s development, this paper redefines the place of ‘Two Dogmas’ in his oeuvre. Not only does Quine’s book project reveal that his views were already fairly naturalistic in the early 1940s ; Sign and Object also unearths the steps Quine had to take in maturing his perspective; steps that will be traced in the second half of this paper. (shrink)

This paper proposes a reading of the history of equivalence in mathematics. The paper has two main parts. The first part focuses on a relatively short historical period when the notion of equivalence is about to be decontextualized, but yet, has no commonly agreed-upon name. The method for this part is rather straightforward: following the clues left by the others for the ‘first’ modern use of equivalence. The second part focuses on a relatively long historical period when equivalence is experienced (...) in context. The method for this part is to strip the ideas from their set-theoretic formulations and methodically examine the variations in the ways equivalence appears in some prominent historical texts. The paper reveals several critical differences in the conceptions of equivalence at different points in history that are at variance with the standard account of the mathematical notion of equivalence encompassing the concepts of equivalence relation and equivalence class. (shrink)

This chapter argues that while quotation marks are polysemous, the thread that runs through all uses of quotation marks that involve reference to expressions is pure quotation, in which an expression formed by enclosing another expression in quotation marks refers to that enclosed expression. We defend a version of the so-called disquotational theory of pure quotation and show how this device is used in direct discourse and attitude attributions, in exposition in scholarly contexts, and in so-called mixed quotation in indirect (...) discourse and attitude attributions. We argue that uses of quotation marks that extend beyond pure quotation have two features in common. First, the expressions appearing in quotation marks are intended to be understood, and that they are intended to be understood is essential to the function that such quotations play in communication, though this does not always involve the expressions contributing their extensional properties to fixing truth conditions for the sentences in which they appear. Second, they appeal to a relation to the expression appearing in quotation marks that plays a role in determining the truth conditions of the sentences in which they appear. (shrink)

Arguments against the Russellian theory of definite descriptions based on cases that involve failures of uniqueness are a recurrent theme in the relevant literature. In this paper, I discuss a number of such arguments, from Strawson (1950), Ramachandran (1993) and Szabo (2005). I argue that the Russellian has resources to account for these data by deploying a variety of mechanisms of quantifier domain restrictions. Finally, I present a case that is more problematic for the Russellian. While the previous cases all (...) involve referential uses of descriptions (or some variations of such uses), the most effective objection to the uniqueness condition draws on genuine attributive uses. (shrink)

Montague and Kaplan began a revolution in semantics, which promised to explain how a univocal expression could make distinct truth-conditional contributions in its various occurrences. The idea was to treat context as a parameter at which a sentence is semantically evaluated. But the revolution has stalled. One salient problem comes from recurring demonstratives: "He is tall and he is not tall". For the sentence to be true at a context, each occurrence of the demonstrative must make a different truth-conditional contribution. (...) But this difference cannot be accounted for by standard parameter sensitivity. Semanticists, consoled by the thought that this ambiguity would ultimately be needed anyhow to explain anaphora, have been too content to posit massive ambiguities in demonstrative pronouns. This article aims to revived the parameter revolution by showing how to treat demonstrative pronouns as univocal while providing an account of anaphora that doesn't end up re-introducing the ambiguity. (shrink)

This paper systematically outlines Wittgenstein's ab-notation. The purpose of this notation is to provide a proof procedure in which ordinary logical formulas are converted into ideal symbols that identify the logical properties of the initial formulas. The general ideas underlying this procedure are in opposition to a traditional conception of axiomatic proof and are related to Peirce's iconic logic. Based on Wittgenstein's scanty remarks concerning his ab-notation, which almost all apply to propositional logic, this paper explains how to extend his (...) method to a subset of first-order formulas, namely, formulas that do not contain dyadic sentential connectives within the scope of any quantifier. (shrink)

Concept originalism, recently introduced and defended by Sainsbury and Tye, Tye, and Sainsbury, holds that “atomic concepts are to be individuated by their historical origins, as opposed to their semantic or epistemic properties”. The view is immune to Gareth Evans’s “Madagascar” objection to the Causal Theory of Reference since it allows a concept to change its reference over time without losing its identity. The possibility of reference-shift, however, raises the problem of misleading belief reports. S&T try to tackle the problem (...) by strengthening the sufficient condition for a truthful belief report. We will argue that, first, their solution fails, second, and more importantly, their diagnosis of the root of the problem is misguided, third, two initially appealing ways out of the problem fail, and fourth, the prospect of finding a solution to the problem within CO is dim. The view opens the Pandora’s box of reference-shift, in a wide range of cases, without providing the necessary semantic means to take care of them. (shrink)

Much contemporary ontological inquiry takes place within the so-called ‘Quinean tradition’ but, given that some aspects of Quine’s project have been widely abandoned even by those who consider themselves Quineans, it is unclear what this amounts to. Fortunately recent work in metaontology has produced two relevant results here: a clearer characterisation of the metaontology uniting the aforementioned Quineans, most notably undertaken by Peter van Inwagen, and a raft of criticisms of that metaontology. In this paper I critique van Inwagen’s Quinean (...) metaontology, finding that certain challenges, supplemented by pressure to reflect more closely Quine’s work, should drive Quineans to adopt a stronger metaontology incorporating more of Quine’s radical views. I conclude that while van Inwagen’s Quineanism is problematic there are prospects for a viable, more wholeheartedly Quinean, metaontology. (shrink)

In a series of recent works, Kit Fine, 605–631, 2003, 2007) has sketched a novel solution to Frege’s puzzle. Radically departing from previous solutions, Fine argues that Frege’s puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination schema. Given this enrichment, (...) we argue, that that the semantics is compositional. We then examine the deep consequences of this result for Fine’s proposed solution to Frege’s puzzle. We argue that Fine has mis-diagnosed his own solution–his attempted solution does not deny compositionality. The correct characterization of Fine’s solution fits him more comfortably among familiar solutions to the puzzle. (shrink)

The implicit content associated with incomplete definite descriptions is contributed in the form of definite descriptions of situations. A definite description of this kind is contributed by a small structure in the syntax, which is interpreted, in general terms, as ‘the situation that bears R to s’.

Sometimes form-meaning mappings in language are not arbitrary, but iconic: they depict what they represent. Incorporating iconic elements of language into a compositional semantics faces a number of challenges in formal frameworks as evidenced by the lengthy literature in linguistics and philosophy on quotation/direct speech, which iconically portrays the words of another in the form that they were used. This paper compares the well-studied type of iconicity found with verbs of quotation with another form of iconicity common in sign languages: (...) classifier predicates. I argue that these two types of verbal iconicity can, and should, incorporate their iconic elements in the same way using event modification via the notion of a context dependent demonstration. This unified formal account of quotation and classifier predicates predicts that a language might use the same strategy for conveying both, and I argue that this is the case with role shift in American Sign Language. Role shift is used to report others’ language and thoughts as well as their actions, and recently has been argued to provide evidence in favor of Kaplanian “monstrous” indexical expressions. By reimagining role shift as involving either quotation for language demonstrations or “body classifier” predicates for action demonstrations, the proposed account eliminates one major argument for these monsters coming from sign languages. Throughout this paper, sign languages provide a fruitful perspective for studying quotation and other forms of iconicity in natural language due to their lack of a commonly used writing system which is otherwise often mistaken as primary data instead of speech, the rich existing literature on iconicity within sign language linguistics, and the ability of role shift to overtly mark the scope of a language report. In this view, written language is merely a special case of a more general phenomenon of sign and speech demonstration, which accounts more accurately for natural language data by permitting more strict or loose verbatim interpretations of demonstrations through the context dependent pragmatics. (shrink)

In this paper, I examine Quine's views on the epistemology of logic. According to Quine's influential holistic account, logic is central in the “web of belief” that comprises our overall theory of the world. Because of this, revisions to logic would have devastating systematic consequences, and this explains why we are loath to make such revisions. In section1, I clarify this idea and thereby show that Quine actually takes the web of belief to have asymmetrical internal structure. This raises two (...) puzzles. First, as I show in section 2, Quine's mature thoroughly naturalized view has it that logic is simply obvious, and this is explains why we do not typically consider revising it. While Quine presents this naturalized view as a way to make good on his earlier metaphor of centrality in a web of belief, I argue that the resources of Quine's naturalized epistemology cannot adequately explain why we are reluctant to revise logic. And, Quine seems to recognize this point himself. In light of this, I explain in section 3 how Quine can allow that our overall scientific theory has systematic structure in a way that is consistent with his naturalistic strictures. Second, the asymmetrical internal structure of the web of belief seems to be inconsistent with its being a holistic web at all. I defuse this problem in section 4 by showing how Quine distinguishes between structural and confirmational considerations. I close by using this distinction to show how Quine's view can evade Michael Friedman’s criticisms, and allow for important methodological distinctions between areas of the web of belief. (shrink)

This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. The paper also shows how the always-self-predicative universals of category theory provide the "opposite bookend" to the never-self-predicative universals of iterative set theory and thus that the paradoxes arose from having (...) one theory (e.g., Frege's Paradise) where universals could be either self-predicative or non-self-predicative (instead of being always one or always the other). (shrink)

This paper is about the mode of being of names. The paper begins by explaining why the joke is on commentators who see Lewis Carroll's White Knight as applying the use/mention distinction. Then it argues that the real problem with the distinction is that the idea that names are used to mention what they name depends on mistakenly conceiving of language as existing autonomously; and that philosophers have this conception because they fail to appreciate what they are doing when they (...) philosophise about language. This failure also explains why philosophers mistakenly think of any manifestation of a name as a (physical) token. (shrink)

Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...) framework will permit us to address a puzzle raised by Elizabeth Barnes and Robert Williams. (shrink)

Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...) along with a new concept to abstractly model the functions of a brain. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

semantic minimalism and moderte contextualism.

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...) operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

Recent scholarship indicates that Quine’s “Truth by Convention” does not present the radical critiques of analytic truth found fifteen years later in “Two Dogmas of Empiricism.” This prompts a historical question: what caused Quine’s radicalization? I argue that two crucial components of Quine’s development can be traced to the academic year 1940–1941, when he, Russell, Carnap, Tarski, Hempel, and Goodman were all at Harvard together. First, during those meetings, Quine recognizes that Carnap has abandoned the extensional, syntactic approach to philosophical (...) analysis, an approach espoused in Carnap’s 1934 Logical Syntax of Language, and which Quine endorsed his entire career. Second, Tarski presents Quine with a philosophically well-motivated reason to think that an apparently analytic discipline, arithmetic, could be synthetic; this reflects one of the central assertions found in “Two Dogmas” but not in “Truth by Convention.” I use this account of Quine’s development to resolve a dispute between Creath and Mancosu concerning the timeline for Quine’s evolving critiques of analyticity. (shrink)

Resumo: No presente artigo, discutiremos os aspectos filosóficos de teorias de conjuntos paraconsistentes. A fim de ilustrar nossas considerações de modo mais concreto, abordaremos uma nova teoria de conjuntos baseada em um sistema bem conhecido de Quine e em um cálculo paraconsistente.Palavras-chave: existência, contradição, lógica e paraconsistência.: In the present paper we deal with the philosophical aspects of paraconsistent set theories. In order to illustrate our points more concretely, we will discuss new paraconsistent set theory based both on Quine's well-known (...) system and on a paraconsistent calculus.Keywords: existence, contradiction, logic and paraconsistency. (shrink)

En su obra de 1884, Die Grundlagen der Arithmetik [Gl.], Frege establece el principio del contexto como uno de sus principios fundamentales y propone valerse de él para dar con el concepto adecuado de número. Así, ofrece una definición de tipo contextual de número cardinal, pero ante una objeción que le resulta insalvable se decide por una definición explicita. La cuestión acerca de cuál ha sido entonces el sentido de establecer con tanto énfasis el principio del contexto admite más de (...) una respuesta. Mi texto polemiza con la interpretación canónica que se ha dado al papel de este principio en Gl., acusándola de permanecer encandilada por lo que se lee de manera inmediata en desmedro de una evaluación más integral y crítica. En particular, defenderé que: i) a diferencia de lo afirmado en Dummett 1991, la definición contextual de número cardinal no es abandonada por Frege al dar su definición explícita de número, ii) el principio del contexto tiene en Gl. un papel erístico fundamental de eliminar posiciones rivales acerca de la naturaleza de los números, iii) dicha definición contextual de número tiene un papel heurístico en el contexto de descubrimiento, en el sentido de que ofrece una intuición clave que permite llegar a la formulación final, iv) a su vez, la definición contextual es una condición necesaria de la definición explícita en el contexto de justificación, siendo que esta última se ha construido a partir de la primera. Por todo ello, sostengo que la función del principio del contexto no es la que prioriza Dummett, i. e., la fallida función de resolver el problema ontológico de la naturaleza de los números, sino que es fundamentalmente metodológica. En efecto, es en su función erística y heurística en donde debe ubicarse su relevancia para la investigación llevada a cabo en Gl. In his masterpiece of 1884, Die Grundlagen der Arithmetik [Gl.] Frege presents the context principle as a fundamental one in his investigation à propos an accurate concept of number. Thus, resting on it he offers a contextual definition of cardinal number; but after analyzing some objections he realizes that this definition does not work and decides himself for an explicit one. The question about what is the purport of the context principle when something that appeared to be the consequence is put aside admits more than a single answer. In this paper I argue against the canonic interpretation for, even while keeping next to the Fregean text, it fails to offer an integral explanation of how the context principle works all along Gl. In particular, I will defend that: i) contrary with Dummett 1991, the contextual definition of cardinal number is not abandoned by Frege when giving his explicit definition of number, ii) the context principle has in Gl. a fundamental eristic role of crossing out rival positions about the nature of numbers, iii) such contextual definition of number has an heuristic role in the discovery context, in the sense it offers a key intuition towards the final formulation, iv) furthermore, the contextual definition is a necessary condition in the justification context for the latest has been built up through the first one. For all this, I maintain that the function of the context principle is not the one Dummett prioritizes, i. e., the failed function of solving the ontological problem of the nature of numbers; the function of the context principle is rather and fundamentally methodological. It is on its eristic and heuristic function that its relevance to the Gl. investigation must be looked for. (shrink)

Sometimes two expressions in a discourse can be about the same thing in a way that makes that very fact evident to the participants. Consider, for example, 'he' and 'John' in 'John went to the store and he bought some milk'. Let us call this 'de jure' coreference. Other times, coreference is 'de facto' as with 'Mark Twain' and 'Samuel Clemens' in a sincere use of 'Mark Twain is not Samuel Clemens'. Here, agents can understand the speech without knowing that (...) the names refer to the same person. After surveying many available linguistic and pragmatic tools (intentions to corefer, presuppositions, meanings, indexing, discourse referents, binding etc.) I conclude that we must posit a new semantic primitive to account for de jure coreference. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

O presente manual tem como intenção constituir um guia para uma disciplina introdutória de filosofia da linguagem. Foi elaborado a partir da leccionação da disciplina de Filosofia da Linguagem I na Faculdade de Letras da Universidade do Porto desde 2001. A disciplina de Filosofia da Linguagem I ocupa um semestre lectivo e proporciona aos estudantes o primeiro contacto sistemático com a área da filosofia da linguagem. Pretende-se que este manual ofereça aos estudantes os instrumentos necessários não apenas para acompanhar uma (...) iniciação ao campo da filosofia da linguagem mas também para o estudo e a investigação autónomos posteriores. Para isso é percorrido um trajecto que conduz das intuições pré-teóricas acerca de linguagem, de que todos dispomos, até um conhecimento disciplinar específico, histórico e temático, da filosofia da linguagem. Em termos práticos, são considerados como precedentes da disciplina de Filosofia da Linguagem I – mesmo se, pelo existem actualmente precedências em sentido estrito – as disciplinas de Lógica I e II e de Filosofia do Conhecimento I e II. Os programas dessas disciplinas nos últimos anos estiveram presentes por trás da elaboração do manual. (shrink)

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...) universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell successfully antedates (...) Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain. (shrink)

My main aim is to clarify what we mean by ‘look’ sentences such as (1) below – ones that we use to talk about visual experience: -/- (1) The ball looked red to Sue -/- This is to help better understand a part of natural language that has so far resisted treatment, and also to help better understand the nature of visual experience. -/- By appealing to general linguistic principles I argue for the following account. First, we use (1) to (...) talk about an event. Second, we use the verb ‘look’ to specify the kind of event about which we are talking – it is a looking event. Third, we use the subject ‘the ball’ to specify a stimulus of the event – something that looks some way in the event. Fourth, we use the adjunct ‘to Sue’ to specify an experiencer of the event – someone to whom things look some way in the event. Finally, we use the complement ‘red’ to specify a way of the event – a way in which the event occurs (I take ways of occurring to be properties of events). Which way do we use ‘red’ in (1) to specify? I argue: the maximally specific way w such that the following is generically true: looking events whose stimulus is red occur in way w (it is important that this is understood generically: this is what does much of the work in explaining our use of (1) and other ‘look’ sentences). Putting this together, what we mean by (1) is: there was a looking event whose stimulus was the ball, whose experiencer was Sue, and which occurred in the maximally specific way that looking events occur when their stimulus is red. -/- This account of how we use ‘red’ in (1) is one of the most interesting aspects of my thesis. It extends to an account of how we use ‘proud’ in ‘John walks proud’, ‘as if he is American’ in ‘John talks as if he is American’, ‘like a duck’ in ‘John sounds like a duck’, and so on. In each case we use the expression in question to specify a way: the maximally specific way proud people walk, the maximally specific way American people talk, and so on. So the study of ‘look’ sentences has much to tell us about the functioning of many other English language constructions, and suggests that ways have a significant role to play in the semantics of natural language – a fact that has not yet been sufficiently recognised by linguists or philosophers of language. -/- My thesis also has implications for the philosophy of perception. One of the central questions about perception is: What is the nature of visual experience? What is it, for example, for a ball to look red to Sue? My thesis offers an answer: What it is for the ball to look red to Sue is for whatever it is that we mean by ‘The ball looks red to Sue’ to be the case, and what we mean by ‘The ball looks red to Sue’ is that there is a looking event whose stimulus is the ball, whose experiencer is Sue, and which is occurring in a certain way. It thus delivers an adverbial account of visual experience, one that has the resources to better deal with problems that are traditionally thought to be decisive against adverbial accounts. (shrink)

To understand the thesis of actualism, consider the following example. Imagine a race of beings — call them ‘Aliens’ — that is very different from any life-form that exists anywhere in the universe; different enough, in fact, that no actually existing thing could have been an Alien, any more than a given gorilla could have been a fruitfly. Now, even though there are no Aliens, it seems intuitively the case that there could have been such things. After all, life might (...) have evolved very differently than the way it did in fact. So in virtue of what is it true that there could have been Aliens when in fact there are none, and when, moreover, nothing that exists in fact could have been an Alien? So-called "possibilists" offer the following answer: ‘It is possible that there are Aliens’ is true because there are in fact individuals that could have been Aliens. At first blush, this might appear directly to contradict the premise that no existing thing could possibly have been an Alien. The possibilist's thesis, however, is that existence, or actuality, encompasses only a subset of the things that, in the broadest sense, are. So for the possibilist, ‘It is possible that there are Aliens’ is true simply in virtue of the fact that there are possible-but-nonactual Aliens, i.e., things that could have existed (but do not) and which would have been Aliens if they had. Actualists reject this answer; they deny that there are any nonactual individuals. Thus, actualism is the philosophical position that everything there is — everything that can in any sense be said to be — exists, or is actual. (shrink)

The conclusion of this chapter is that higher-order vagueness is universal: no sentence whatsoever is definitely true, definitely definitely true, definitely definitely definitely true, and so on ad infinitum. The argument, of which there are several versions, turns on the existence of Sorites sequences of possible worlds connecting the actual world to possible worlds where a given sentence is used in such a way that its meaning is very different. The chapter attempts to be neutral between competing accounts of the (...) nature of vagueness and definiteness. (shrink)

We consider certain predicative classes with respect to their bearing on set theory, namely on its semantics, and on its ontological power. On the one hand, our predicative classes will turn out to be perfectly suited for establishing a nice hierarchy of metalanguages starting from the usual set theoretical language. On the other hand, these classes will be seen to be fairly inappropriate for the formulation of strong principles of infinity. The motivation for considering this very type of classes is (...) a reasonable philosophy of set theory. Familiarity is assumed only with basic concepts of both set theory and its philosophy. (shrink)