Despite its enormous popularity, Russell’s theory of definite descriptions has received various criticisms. Two of the most important objections against this theory are those arising from the Argument from Incompleteness and the Argument from Donnellan’s Distinction. According to the former although a speaker may say something true by assertively uttering a sentence containing an incomplete description , on the Russellian analysis such a sentence expresses a false proposition; so, Russell’s theory cannot adequately deal with such sentences. According (...) to the latter objection a descriptive sentence is actually ambiguous—it expresses a general proposition when the description contained in it is used attributively, and a singular proposition when the description in question is used referentially; Russell’s theory is inadequate as it fails to capture this ambiguity and offers an analysis according to which a descriptive sentence expresses only a general proposition. These objections are examined in the present dissertation. It is shown here that these objections arise from: (i) ignoring the distinction between the meaning of a sentence and the assertions made by using it, (ii) the failure to distinguish between the semantic meaning of a sentence and the pragmatic meaning with which it is used on a particular occasion. To make the distinction mentioned in (i), a significant part of Scott Soames’ theory concerning meaning and assertions has been adopted in this dissertation; and, to make the distinction mentioned in (ii), a test, namely the cancellability test, and two Distinguishing Criteria, namely DC-1 and DC-2, have been developed here. It has been argued here that if we properly make the relevant distinctions, then we will find that: (a) the phenomenon cited by the Argument from Incompleteness can be well explained keeping the Russellian analysis of descriptive sentences intact, (b) the phenomenon arising from the Argument from Donnellan’s Distinction raises an issue of pragmatics and is irrelevant to Russell’s semantic analysis of descriptive sentences. So, none of the above criticisms poses a genuine threat to Russell’s theory of definite descriptions; his theory actually provides, to a large extent, a correct semantic analysis of descriptive sentences. (shrink)

In this paper I offer a defence of a Russellian analysis of the referential uses of incomplete (mis)descriptions, in a contextual setting. With regard to the debate between a unificationist and an ambiguity approach to the formal treatment of definite descriptions (introduction), I will support the former against the latter. In 1. I explain what I mean by "essentially" incomplete descriptions: incomplete descriptions are context dependent descriptions. In 2. I examine one (...) of the best versions of the unificationist “explicit” approach given by Buchanan and Ostertag. I then show that this proposal seems unable to treat the normal uses of misdescriptions. I then accept the challenge of treating misdescriptions as a key to solving the problem of context dependent descriptions. In 3. I briefly discuss Michael Devitt’s and Joseph Almog’s treatments of referential descriptions, showing that they find it difficult to explain misdescriptions. In 4. I suggest an alternative approach to DD as contextuals, under a normative epistemic stance. Definite descriptions express (i) what a speaker should have in mind in using certain words in a certain context and (ii) what a normal speaker is justified in saying in a context, given a common basic knowledge of the lexicon. In 5. I define a procedure running on contextual parameters (partiality, perspective and approximation) as a means of representing the role of pragmatics as a filter for semantic interpretation. In 6. I defend my procedural approach against possible objections concerning the problem of the boundaries between semantics and pragmatics, relying on the distinction between semantics and theory of meaning. (shrink)

This paper offers a unified, quantificational treatment of incomplete descriptions like ‘the table’. An incomplete quantified expression like ‘every bottle’ (as in “Every bottle is empty”) can feature in true utterances despite the fact that the world contains nonempty bottles. Positing a contextual restriction on the bottles being talked about is a straightforward solution. It is argued that the same strategy can be extended to incomplete definite descriptions across the board. ncorporating the contextual restrictions (...) into semantics involves meeting a complex array of desiderata, yet the apparently simpler pragmatic alternative faces severe problems and is therefore a nonstarter. (shrink)

The first aim of this paper is to elucidate Russell’s construction of spatial points, which is to be <br>considered as a paradigmatic case of the "logical constructions" that played a central role in his epistemology and theory of science. Comparing it with parallel endeavours carried out by Carnap and Stone it is argued that Russell’s construction is best understood as a structural representation. It is shown that Russell’s and Carnap’s representational constructions may be considered as incomplete and sketchy harbingers (...) of Stone’s representation theorems. The representational program inaugurated by Stone’s theorems was one of the success stories of 20th century’s mathematics. This suggests that representational constructions à la Stone could also be important for epistemology and philosophy of science. More specifically it is argued that the issues proposed by Russellian definite descriptions, logical constructions, and structural representations still have a place on the agenda of contemporary epistemology and philosophy of science. Finally, the representational interpretation of Russell’s logical constructivism is used to shed some new light on the recently vigorously discussed topic of his structural realism. (shrink)

Some contemporary semantic views defend an asymmetry thesis concerning defi-nite descriptions and indexicals. Semantically, indexicals are devices of singular refer-ence; they contribute objects to the contents of the speech acts made with utterances including them. Definite descriptions, on the other hand, are generalized quantifiers, behaving roughly the way Russell envisaged in “On Denoting”. The asymmetry thesis depends on the existence of a sufficiently clear-cut distinction between semantics and pragmatics, because indexicals and descriptions are often used in (...) ways that apparently contradict the asymmetry thesis; the semantics/pragmatics distinction is invoked to see behind the appearances. The paper critically examines arguments by Schiffer against the asymmetry thesis, based on referential uses of incomplete descriptions. (shrink)

We pose two arguments for the view that sentences containing definite descriptions semantically express multiple propositions: a general proposition as Russell suggested, and a singular proposition featuring the individual who uniquely satisfies the description at the world-time of utterance. One argument mirrors David Kaplan's arguments that indexicals express singular propositions through a context-sensitive character. The second argument mirrors Kent Bach's and Stephen Neale's arguments for pluralist views about terms putatively triggering conventional implicatures, appositive, and nonrestrictive relative clauses. After (...) presenting these arguments, we show that rival explanations (appeals to implicature, referential use, presupposition, etc.) do not offer equally compelling explanations of the data, and defend the methodology employed in the arguments against some criticisms. (shrink)

In some sentences, demonstratives can be substituted with definite descriptions without any change in meaning. In light of this, many have maintained that demonstratives are just a type of definite description. However, several theorists have drawn attention to a range of cases where definite descriptions are acceptable, but their demonstrative counterparts are not. Some have tried to account for this data by appealing to presupposition. I argue that such presuppositional approaches are problematic, and present a (...) pragmatic account of the target contrasts. On this approach, demonstratives take two arguments and generally require that the first, covert argument is non-redundant with respect to the second, overt argument. I derive this condition through an economy principle discussed by Schlenker (2005). (shrink)

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of (...) class='Hi'>definite descriptions recommended here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’. (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)

This paper challenges the first Gettier counterexample to the tripartite account of knowledge. Noting that 'the man who will get the job' is a description and invoking Donnellan's distinction between their 'referential' and 'attributive' uses, I argue that Smith does not actually believe that the man who will get the job has ten coins in his pocket. Smith's ignorance about who will get the job shows that the belief cannot be understood referentially, his ignorance of the coins in his pocket (...) shows that it cannot be understood attributively. An explanation for why Smith appeared to have justified true belief is given by distinguishing between 'belief' and 'belief in truth'. Smith believes the sentence 'the man who will get the job has ten coins in his pocket' to be true (he mistakenly believes that Jones will get the job, of whom he knows that he has ten coins in his pocket) (hence his 'belief'), the sentence is true (hence 'truth'), and he has sufficient reason to assent to it (hence his 'justification'). But he does not believe the proposition expressed. Hence he does not know it either. (shrink)

In this article, I use Edmund Gettier’s Ten Coins hypothetical scenario to illustrate some reasoning errors in the use of definite descriptions. The Gettier problem, central as it is to modern epistemology, is first and foremost an argument, which Gettier (Analysis 23(6):121–123, 1963) constructs to prove a contrary conclusion to a widely held view in epistemology. Whereas the epistemological claims in the case have been extensively analysed conceptually, the strategies and tools from other philosophical disciplines such as analytic (...) philosophy of language, logic and argumentation that Gettier deploys in the case have scarcely received any attention. This work abstracts from the epistemological content and examines Gettier’s handling of the definite description involved, and how that affects the cogency of his argument. (shrink)

Machery et al. presented data suggesting the existence of cross-cultural variation in judgments about the reference of proper names. In this paper, we examine a previously overlooked confound in the subsequent studies that attempt to replicate the results of Machery et al. using East Asian languages. Machery et al. and Sytsma et al. claim that they have successfully replicated the original finding with probes written in Chinese and Japanese, respectively. These studies, however, crucially rely on uses of articleless, ‘bare noun (...) phrases’ in Chinese and Japanese, which according to the linguistic literature are known to be multiply ambiguous. We argue that it becomes questionable whether the extant studies using East Asian languages revealed genuine cross-cultural variation when the probes are reevaluated based on a proper linguistic understanding of Chinese and Japanese bare noun phrases and English definite descriptions. We also present two experiments on native Japanese speakers that controlled the use of ambiguous bare noun phrases, the results of which suggest that the judgments of Japanese speakers concerning the reference of proper names may not diverge from those of English speakers. (shrink)

This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, (...) which was presented in (Kürbis 2019), INFι is first compared to a system of Tennant’s and an axiomatic treatment of a term forming ι operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INFι in which the G of ιx[F, G] is restricted to identity. INFι is then compared to an intuitionist version of a system of Lambert’s which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion. (shrink)

The paper revisits Sharvy's theory of plural definite descriptions. An alternative account of plural definite descriptions building on the ideas of plural quantification and non-distributive plural predication is developed. Finally, the alternative is extrapolated to account for generic uses of definite descriptions.

This paper challenges the first Gettier counterexample to the tripartite account of knowledge. Noting that 'the man who will get the job' is a description and invoking Donnellan's distinction between their 'referential' and 'attributive' uses, I argue that Smith does not actually believe that the man who will get the job has ten coins in his pocket. Smith's ignorance about who will get the job shows that the belief cannot be understood referentially, his ignorance of the coins in his pocket (...) shows that it cannot be understood attributively. An explanation for why Smith appeared to have justified true belief is given by distinguishing between 'belief' and 'belief in truth'. Smith believes the sentence 'the man who will get the job has ten coins in his pocket' to be true (he mistakenly believes that Jones will get the job, of whom he knows that he has ten coins in his pocket) (hence his 'belief'), the sentence is true (hence 'truth'), and he has sufficient reason to assent to it (hence his 'justification'). But he does not believe the proposition expressed. Hence he does not know it either. (shrink)

A reality may be defined incompletely as a perpetuating pattern of relations. This definition denies the name of reality to an utter and totalistic patternlessness, like a primal patternless stuff, because a patternless all-ness would be indistinguishable from a patternless nothingness. If reality began from a chaos or patternless stuff, it became a reality only when it became patterned. If there are orders of reality with perpetuating relations between them, as in Cartesian interactive substance dualism, the definition allows us to (...) say that these orders belong to a common reality by virtue of those relations. However, the definition is silent on the question of whether reality is ultimately pluralistic. Some suggestions are made about the possibility of stuffless patterns, including those of the physical world, but the definition is not dependent on the possibility of stufflessness. (shrink)

François Recanati; IV*—Contextual Dependence and Definite Descriptions, Proceedings of the Aristotelian Society, Volume 87, Issue 1, 1 June 1987, Pages 57–74, h.

This paper presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite (...) descriptions with a term forming operator. In the final section rules for I for negative free and classical logic are also mentioned. (shrink)

In this essay I argue that given Donnellan’s formulation of the attributive uses of definite descriptions, as well as Kripke’s [6] and Salmon’s [10] generalized accounts, most uses of definite descriptions that are taken to be attributive turn out not to be so. In building up to my main thesis, I first consider certain problematic cases of uses of definite descriptions that do not neatly fit into any category. I then argue that, in general, (...) a complete definite description we use is complex, in which there is an embedded singular term that is used referentially. From this I conclude that an attributive use of a definite description is an extremely rare linguistic phenomenon, much less frequent than what Donnellan, Kripke, and Salmon have presupposed; so much so that the standard examples given by Donnellan of the attributive use of definite descriptions do not qualify as attributive. (shrink)

A number of authors in favor of a unitary account of singular descriptions have alleged that the unitary account can be extrapolated to account for plural definite descriptions. In this paper I take a closer look at this suggestion. I argue that while the unitary account is clearly onto something right, it is in the end empirically inadequate. At the end of the paper I offer a new partitive account of plural definite descriptions that avoids (...) the problems with both the unitary account and standard Russellian analyses. (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)

This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown (...) to be sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising ‘the F ’ by a term forming operator. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive. (shrink)

This paper shows that Russell’s theory of descriptions gives the wrong se-mantics for definite descriptions occurring in questions and imperatives. Depending on how that theory is applied, it either assigns nonsense to per-fectly meaningful questions and assertions or it assigns meanings that di-verge from the actual semantics of such sentences, even after all pragmatic and contextual variables are allowed for. Given that Russell’s theory is wrong for questions and assertions, it must be wrong for assertoric state-ments; for (...) the semantics of ‘the phi’ obviously doesn’t vary depending on whether it occurs in a question or an assertion or a command. (shrink)

In this paper I respond to the objections put forth by Kresimir Agbaba 22: 1-6) against my earlier paper 20: 7-13) in which I argue that given Donnellan's formulation|as well as Kripke's and Salmon's gen- eralized accounts|an attributive use of a denite description is a very rare linguistic phenomenon.

This essay aims to coherently introduce a four-dimensional view adapting to the three-spatial-plus-one- temporal-dimensions (3+1) physical world. To orient the discussions, the essay presents several central claims. First, the only description a proper name abbreviates is that of being called, yet a proper name is capable of bringing up the entire object from its birth to its end. Second, there is a crucial difference in the behaviors of proper names and definite descriptions. Third, a co-knowing state may be (...) decisive in exchanging information about the physical world. Lastly, one way to consider the truth value of propositions containing fictional characters is to consider such propositions as about a summarized or entailed property of the physically stored coding texts. On the other hand, fictional worlds typically are well-established four-dimensional simulations. (shrink)

Almost entirely ignored in the linguistic theorising on names and descriptions is a hybrid form of expression which, like definite descriptions, begin with 'the' but which, like proper names, are capitalised and seem to lack descriptive content. These are expressions such as the following, 'the Holy Roman Empire', 'the Mississippi River', or 'the Space Needle'. Such capitalised descriptions are ubiquitous in natural language, but to which linguistic categories do they belong? Are they simply proper names? Or (...) are they definite descriptions with unique orthography? Or are they something else entirely? This paper assesses two obvious assimilation strategies: (i) assimilation to proper names and (ii) assimilation to definite descriptions. It is argued that both of these strategies face major difficulties. The primary goal is to lay the groundwork for a linguistic analysis of capitalised descriptions. Yet, the hope is that clearing the ground on capitalised descriptions may reveal useful insights for the on-going research into the semantics and syntax of their lower-case or 'the'-less relatives. (shrink)

This paper addresses a certain objection to the quantificational theory of definite descriptions. According to this objection, the quantificational account cannot provide correct interpretations of definite descriptions embedded in the non-doxastic attitude ascriptions and therefore ought to be rejected. In brief, the objection says that the quantificational theory is committed to the view that a sentence of the form “The F is G” is equivalent to the claim that there is a unique F and it is (...) G, while the ascription such as, e.g., “S wants the F to be G” is not equivalent to the statement that S wants there to be a F and for it to be G. I argue that this objection is invalid as it rests on a false assumption concerning the substitutivity of the relative clauses in the non-doxastic attitude ascriptions. (shrink)

We argue that definite noun phrases give rise to uniqueness inferences characterized by a pattern we call definiteness projection. Definiteness projection says that the uniqueness inference of a definite projects out unless there is an indefinite antecedent in a position that filters presuppositions. We argue that definiteness projection poses a serious puzzle for e-type theories of (in)definites; on such theories, indefinites should filter existence presuppositions but not uniqueness presuppositions. We argue that definiteness projection also poses challenges for dynamic (...) approaches, which have trouble generating uniqueness inferences and predicting some filtering behavior, though unlike the challenge for e-type theories, these challenges have mostly been noted in the literature, albeit in a piecemeal way. Our central aim, however, is not to argue for or against a particular view, but rather to formulate and motivate a generalization about definiteness which any adequate theory must account for. (shrink)

Estonian doesn't have a definite article. Instead, bare singular noun phrases can unambiguously bear either a definite interpretation or an indefinite interpretation. This paper argues that the pragmatic principles governing the felicitous use of three English articles ("a", "the" and "another"), described by A Grønn and KJ Sæbø (2012, 'A, the, another: A game of same and different' Journal of Logic, Language and Information 21, 75-95) can also account for the conditions under which a bare singular noun phrase (...) in Estonian bears a definite or instead an indefinite interpretation. The two languages use the same pragmatic principles to determine the definiteness interpretation of a noun phrase. The difference is just that in English (where definiteness meanings have been lexicalized) these pragmatic principles govern the felicity of article use, whereas in Estonian they govern the interpretation of a bare singular noun phrase. (shrink)

Although Strawson’s main aim in “On Referring” was to argue that definite descriptions can be used referentially – that is, “to mention or refer to some individual person or single object . . . , in the course of doing what we should normally describe as making a statement about that person [or] object” (1950, p. 320) – he denied that definite descriptions are always used referentially. The description in ‘Napoleon was the greatest French soldier’ is (...) not used referentially, says Strawson, since it is used not to mention an individual, but only “to say something about an individual already mentioned” (p. 320). This is an example of what we may call a predicative use of a definite description, though such uses might be better illustrated by considering the false sentence.. (shrink)

Scientists and philosophers frequently speak about levels of description, levels of explanation, and ontological levels. In this paper, I propose a unified framework for modelling levels. I give a general definition of a system of levels and show that it can accommodate descriptive, explanatory, and ontological notions of levels. I further illustrate the usefulness of this framework by applying it to some salient philosophical questions: (1) Is there a linear hierarchy of levels, with a fundamental level at the bottom? And (...) what does the answer to this question imply for physicalism, the thesis that everything supervenes on the physical? (2) Are there emergent properties? (3) Are higher-level descriptions reducible to lower-level ones? (4) Can the relationship between normative and non-normative domains be viewed as one involving levels? Although I use the terminology of “levels”, the proposed framework can also represent “scales”, “domains”, or “subject matters”, where these are not linearly but only partially ordered by relations of supervenience or inclusion. (shrink)

Standard rigid designator accounts of a name’s meaning have trouble accommodating what I will call a descriptive name’s “shifty” character -- its tendency to shift its referent over time in response to a discovery that the conventional referent of that name does not satisfy the description with which that name was introduced. I offer a variant of Kripke’s historical semantic theory of how names function, a variant that can accommodate the character of descriptive names while maintaining rigidity for proper names. (...) A descriptive name’s shiftiness calls for a semantic account of names that makes their semantic values bipartite, containing both traditional semantic contents and what I call "modes of introduction." Both parts of a name's semantic value are derived from the way a name gets introduced into discourse -- from what I refer to as its "context of introduction." Making a name's semantic value bipartite in this way allows for a definite description to be a part of proper name's meaning without thereby sacrificing that name’s status as a rigid designator. On my view, a definite description is part of descriptive name’s mode of introduction. That is, it is part of what determines the content assigned to that name. As it turns out, making a definite description part of a descriptive name’s mode of introduction allows for that definite description to play the role of a mere reference-fixer regarding that name’s content, as Kripke would have it. However, my account allows a definite description to fix a descriptive name’s content actively over time, thereby explaining its inherent shiftiness. (shrink)

In this study, I intend to show how and why, in the Port-Royal Logic, a singular term can reveal the nature of the logical judgment in the handbook. As I argue, the treatment given to one of thee singular terms, namely, the defined descriptions, in the terminology introduced by Russell, leads to an opening to langage that sounds unexpected and unjustified. Considering the privilege of thinking over langage and also that judgment is the mental act that defines logic, however, (...) we may understand how the authors regard langage, in relation to the epistemic constituents, namely, the mental acts within the terms. In doing so we are compelled to recognize the implications of this step towards pragmatism in fixing the meaning of defined descriptions to the nature of judgment in the handbook. This opening to langage reveals the conception of judgment as a twofold mental act: a formal and a practical (moral and theological) one. (shrink)

In “Descriptions as Predicates” (Fara 2001) I argued that definite and indefinite descriptions should be given a uniform semantic treatment as predicates rather than as quantifier phrases. The aim of the current paper is to clarify and elaborate one of the arguments for the descriptions-aspredicates view, one that concerns the interaction of descriptions with adverbs of quantification.

There is a long-standing gap in the literature as to whether Gödelian incompleteness constitutes a challenge for Neo-Logicism, and if so how serious it is. In this paper, I articulate and address the challenge in detail. The Neo-Logicist project is to demonstrate the analyticity of arithmetic by deriving all its truths from logical principles and suitable definitions. The specific concern raised by Gödel’s first incompleteness theorem is that no single sound system of logic syntactically implies all arithmetical truths. I set (...) out some responses that initially seem appealing and explain why they are not compelling. The upshot is that Neo-Logicism either offers an epistemic route only to some truths of arithmetic; or that it has to move from a syntactic to a semantic notion of logical consequence, which risks undermining its epistemic goals. I conclude by considering Crispin Wright’s recent attempt to address Gödelian incompleteness, which I argue is not satisfactory. (shrink)

We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable (...) nor disprovable only because they are self-contradictory we could define them as unsound instead of defining the formal system as incomplete. (shrink)

“Slingshot Arguments” are a family of arguments underlying the Fregean view that if sentences have reference at all, their references are their truth-values. Usually seen as a kind of collapsing argument, the slingshot consists in proving that, once you suppose that there are some items that are references of sentences (as facts or situations, for example), these items collapse into just two items: The True and The False. This dissertation treats of the slingshot dubbed “Gödel’s slingshot”. Gödel argued that there (...) is a deep connection between these arguments and definite descriptions. More precisely, according to Gödel, if one adopts Russell’s interpretation of definite descriptions (which clashes with Frege’s view that definite descriptions are singular terms), it is possible to evade the slingshot. We challenge Gödel’s view in two manners, first by presenting a slingshot even with a Russellian interpretation of definite descriptions and second by presenting a slingshot even when we change from singular terms to plural terms in the light of new developments of the so-called Plural Logic. The text is divided in three chapters, in the first, we present the discussion between Russell and Frege regarding definite descriptions, in the second, we present Gödel’s position and reconstructions of Gödel’s argument and in the third we prove our slingshot argument for Plural Logic. In light of these results we conclude that we can maintain the validity of slingshot arguments even within a Russellian interpretation of definite descriptions or in the context of Plural Logic. (shrink)

Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in `Deviational Syntactic Structures' under the label `EFA(X)3' (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point of view, OccL is (...) a formal logic that mainly deals with the occurrences of symbols as well as with their priorities within linguistic descriptions, i.e. natural language syntax, semantics and phonology. In this article---based on our OccL-based definitions of the concepts of `strong implication' and `occurrence value' as well as of the logical concept `identical occurrence constructor (IDOC)' that is the most fundamental logical concept in our formalism---we will model Occurrence Description Logic ($\mathcal{ODL}$). Accordingly, we will formally-logically analyse `occurrence(s) of symbol(s)' within descriptions of the world in $\mathcal{ODL}$. In addition, we will analyse and assess the logical concepts of `occurrence' and `occurrence priority' in $\mathcal{ODL}$. This research can make a strong logical background for our future research in the development of a Modal Occurrence Description Logic. (shrink)

In this paper I argue that philosophers of sport should avoid value-laden definitions of sport; that is, they should avoid building into the definition of sport that they are inherently worthwhile activities. Sports may very well often be worthwhile as a contingent matter, but this should not be taken to be a core feature included in the definition of sport. I start by outlining what I call the ‘legitimacy-conferring’ element of the category ‘sport’. I then argue that we ought not (...) to include such a dimension in our definition of sport, on the grounds that it confuses issues of description with issues of definition: the issue of what sport does with what sport is. Following this, I consider a Wittgensteinian family resemblance approach to defining sport; Kevin Schieman’s argument that sports are necessarily good games; and the oft-cited wide-following and institutional criteria, as arguments for including an evaluative dimension in the definition of sport. I conclude that none succeed, for similar reasons: they either fail to track our common sense intuitions about what does or does not count as a sport; and/or they make it impossible for us to ever describe something a ‘bad’ sport (or instance of sport). Just as a good definition of, say, art, shouldn’t make it impossible for us to describe something as ‘bad art’, I argue that our definition of sport shouldn’t build in a necessarily positive evaluation. I conclude by discussing some of the practical reasons why supporters of activities about which there is currently debate as to their status as sports might want to see those activities included under the sports umbrella, but suggest that this on its own isn’t a good reason for modifying a philosophical definition of sport to include them. (shrink)

Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical (...) truth verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic---classically accepted as the foundation of all our mathematical Languages---is verifiably complete in the above sense. We show how some paradoxical concepts of Quantum mechanics can, then, be expressed, and interpreted, naturally under a constructive definition of mathematical truth. (shrink)

The paper provides some introductory comments and a preliminary translation of Avicenna’s Burhān, IV, 2. I shall first set the stage by outlining the structure of the book (sec. 1). I will then briefly introduce (sec. 2) a number of notions that are dealt with in the first treatise of the Burhān (e.g. definition, description). Burhān, IV, 2 is split into two parts: the first focuses mainly on Aristotle’s An. Post., B, 4, whereas the second covers some of the topics (...) of B, 5 and B, 6. Accordingly, sec. 3 will be devoted to a cursory presentation of Aristotle’s arguments in An. Post., B, 4 along with a more detailed discussion of its Avicennan counterpart, focusing on the indemonstrability of definition; sec. 4, finally, will be a presentation of the second part of the chapter, concerning the relationship between definition and division. An English translation of the entire chapter is appended to the paper and is accompanied by some notes. (shrink)

This paper uses classical logic for a simultaneous description of the syntax and semantics of a fragment of English and it is argued that such an approach to natural language allows procedural aspects of linguistic theory to get a purely declarative formulation. In particular, it will be shown how certain construction rules in Discourse Representation Theory, such as the rule that indefinites create new discourse referents and definites pick up an existing referent, can be formulated declaratively if logic is used (...) as a metalanguage for English. In this case the declarative aspects of a rule are highlighted when we focus on the model theory of the description language while a procedural perspective is obtained when its proof theory is concentrated on. Themes of interest are Discourse Representation Theory, resolution of anaphora, resolution of presuppositions, and underspecification. (shrink)