Does truth attach to sentences, or to what sentences express? If to sentences, then certainly not to type sentences, such as ‘I am going to London tomorrow’, but only to token sentences, that is, sentences considered as uttered by a particular speaker at a particular time. It would, however, be inconvenient to restrict truth to utterances that are actually made; we may therefore adopt the device and terminology of Davidson, and speak of a ‘statement’ (...) constituted by a triple [s, i, t] of a type sentence s, an individual i and a time t, the existence of which does not depend on whether i in fact uttered s at t. I shall presume that the identification of a type sentence depends on identifying the language to which it belongs. A familiar, irritating obstacle prevents our explaining that, when i did not utter s at t, the ‘statement’ is to be said to be true just in case he would have said something true if he had done so; the obstacle consists in sentences like, ‘I am not now speaking.’ The difficulty is not serious. What more is needed in order to obtain, from a type sentence s, something apt to be characterised as true or false is an assignment of references to indexical and demonstrative expressions occurring in s; we may say that s ‘comes out’ true or false under such an assignment. We may therefore take a ‘statement’ [s, i, t] to be true or false according as s comes out true or false under the assignment of t to the word ‘now’, i to the words ‘I’, and ‘me’, the place where i is at t to the word ‘here’, and so on. There is no reason to be disconcerted by the fact that this will yield as true a ‘statement’ involving the sentence, ‘I have been dead for a hundred years.’ Demonstrative expressions like ‘that house’, ‘this country’, etc., are less easily dealt with. Many should be regarded as devoid of reference unless, at t, i actually makes a pointing gesture or the equivalent; but the question need not be pursued here. For convenience, however, we may continue to speak of the ascription of truth to sentences, as long as we bear in mind that it is to ‘statements’, in our special sense, to which it is really to be ascribed. (shrink)

The aim of this paper is to examine W. V.Quine's theory of infants' early acquisition oflanguage, with a narrow focus on Quine's theory ofobservation sentences. Intersubjectivity and sensoryexperiences, the two features that characterise thenotion, receive the most attention. It is argued,following a suggestion from Donald Davidson, thatQuine favours a proximal theory of languageacquisition, i.e., a theory which is focused onprivate experiences as ultimate sources ofstimulation, contrary to a distal theory, where thestimulus source is located in externally observableobjects and events. (...) I use the philosophical criticismof Donald Davidson, Dagfinn Føllesdal and CharlesTaylor to suggest an alternative account of languageacquisition, which emphasises the primacy ofparticipation and joint attention to external stimuli.I argue that such an alternative theory is moreconsistent with recent studies in child developmentand language acquisition. (shrink)

The aim of this work is to analyse the concept of semi-sentence from a linguistic, formal and computational point of view. A semi-sentence can be characterised as a sentence which, from a grammatical perspective, is neither absolutely correct nor incorrect . This study focuses on: - a characterisation of the semi-sentences in the setting of the grammar of a language. This study will help to analyse in depth the concept of grammaticality [3]; - the correlate of semi-sentences in (...) formal languages, i.e., semi-strings, which arise from applying productions that deviate from that which is strictly permitted by the rules of grammar [6]; - a Prolog program for handling semi-grammaticality in a computational manner [2]. (shrink)

Lautemann et al. (1995) gave a descriptive characterisation of the class of context-free languages, showing that a language is context-free iff it is definable as the set of words satisfying some sentence of a particular logic (fragment) over words. The present notes discuss how to specialise this result to the class of linear languages. Somewhat surprisingly, what would seem the most straightforward specialisation actually fails, due to the fact that linear grammars fail to admit a Greibach normal form. We identify (...) an alternative specialisation, based on an alternative characterisation of context-free languages, also noted by Lautemann et al. (1995). (shrink)

An infinitary characterisation of the first-order sentences true in all substructures of a structure M is used to obtain partial reduction of the decision problem for such sentences to that for Th(M). For the relational structure $\langle\mathbf{R}, \leq, +\rangle$ this gives a decision procedure for the ∃ x∀ y-part of the theory of all substructures, yet we show that the ∃ x 1x 2 ∀ y-part, and the entire theory, is Π 1 1 -complete. The theory of all (...) ordered subsemigroups of $\langle\mathbf{R}, \leq, +\rangle$ is also shown Π 1 1 -complete. Applications in the philosophy of science are mentioned. (shrink)

This article provides a corpus-based analysis of formal structure and rapport orientation of evaluative speech acts in written Mandarin starting from the Qing Dynasty leading up to the present. It focuses on illocutional concurrences where the change of rapport management with the interlocutor significantly correlates with evaluative speech acts. The IC are holistic patterns that emerge at various levels of an utterance. They contribute both locally and peripherally to the encoding of contextually and temporally situated speech acts or pragmemes. Mixed (...) methods of hierarchical clustering and multiple correspondence analysis indicate that the recent history of evaluative speech acts in written Chinese is characterised by a shift from prevalently rapport-maintaining orientation to utterances more overtly marked for politeness. Evaluative language in written Mandarin became less mitigated at the structural level and increasingly oriented towards rapport enhancement and rapport challenge. This shift significantly intersects with a progressive replacement of clause-final particles during the 20th century, especially after the so-called ‘May the 4th Movement’. (shrink)

There is a standard quantificational view of generic sentences according to which they have a tripartite logical form involving a phonologically null generic operator called 'Gen'. Recently, a number of theorists have questioned the standard view and revived a competing proposal according to which generics involve the predication of properties to kinds. This paper offers a novel argument against the kind-predication approach on the basis of the invalidity of Generic Excluded Middle, a principle according to which any sentence of (...) the form ⌜Either Fs are G or Fs are not G⌝ is true. I argue that the kind-predication approach erroneously predicts that GEM is valid, and that it can only avoid this conclusion by either collapsing into a form of the quantificational analysis or otherwise garnering unpalatable metaphysical commitments. I also show that, while the quantificational approach does not validate GEM as a matter of logical form, the principle may be validated on certain semantic analyses of the generic operator, and so, such theories should be rejected. (shrink)

Modal Meinongianism provides the semantics of sentences involving intentional verbs Priest. To that end, Modal Meinongianism employs a pointed non-normal quantified modal logic model. Like earlier Meinongian views Modal Meinongianism has a characterisation principle, that claims that any condition whatsoever is satisfied by some object in some world. Recently, Everett has proposed an argument against QCP that, if successful, gives rise to problems identical to those Russell raised for Naïve Meinongianism, namely that it allows for true contradictions, and allows (...) us to define anything into existence. Everett claims that the ordinary meanings of “actual” license an inference pattern, such that if an object satisfies Actual A at some world, then that object satisfies A in the actual world. Given that actual world is the designated point of evaluation for truth simpliciter, QCP would fall prey to Russell’s criticisms. As opposed to Everett, I argue that, even if we grant Everett the assumption that “actual” is a modal indexical that rigidly refers to the actual world, it does not conform to the inference pattern above. This is because when an object satisfies Actual A at some world, this alters the assertoric force of “actual”, because “actual” is interpreted in the scope of some modal or intentional operator. I also explain that Everett’s proposed example carries existential commitment because the problematic noun-phrase occurs outside the scope of a modal or intentional operator. (shrink)

Minimal semantics is sometimes characterised as a ‘neo-Gricean’ approach to meaning. This label seems reasonable since a key claim of minimal semantics is that the minimal contents possessed by sentences (akin to Grice’s technical notion of ‘what is said by a sentence’) need not be (and usually are not) what is communicated by a speaker who utters those sentences. However, given an affinity between the two approaches, we might expect that a well-known challenge for the Gricean – namely (...) that their account fails to fit with the psychological evidence concerning linguistic understanding – could also be levelled at the minimalist, and indeed this seems to be the basis of Recanati’s challenge to minimalism from his ‘availability principle’ (Recanati 2004). This paper aims to explore the relationship between semantics and psychology and show how both Gricean and minimalist approaches can avoid the challenge from psychological evidence. I conclude by suggesting that the way in which minimalism avoids this challenge also helps the account to defuse Clapp’s ‘naturalistic objection’ (Clapp 2007) that there are no grounds for selecting a correct minimal semantic theory. (shrink)

I characterise a relativist account of truth as one according to which the truth value of a sentence can vary without its meaning changing. Relativism is to be contrasted with absolutism, which states that the truth values of sentences cannot change, so long as their meanings remain constant. I argue that absolutism follows from the realist account of meaning and truth conditions. According to realism, the meaning of a sentence consists in objective truth conditions and sentences are true (...) if and only if certain objective conditions obtain. Relativism is a consequence of anti‐realism. Anti‐realists believe that the meanings of sentences consist in recognisable conditions and that sentences are true if and only if certain recognisable conditions obtain. I contrast the sorts of relativism which results from partial, empiricism‐based anti‐realisms, and global anti‐realism, which is linked to a coherence theory of knowledge. I offer a few remarks on how global anti‐realists can restrict the scope of their relativism. (shrink)

The aim of the paper is to formulate rules of inference for the predicate 'is true' applied to sentences. A distinction is recognised between (ordinary) truth and definite truth and consequently between two notions of validity, depending on whether truth or definite truth is the property preserved in valid arguments. Appropriate sets of rules of inference governing the two predicates are devised. In each case the consequence relation is in harmony with the respective predicate. Particularly appealing is a set (...) of ND rules for ordinary truth in which premises and assumptions play different roles, premises being taken to assert definite truth, assumptions to suppose truth. This set of rules can be said to capture everyday reasoning with truth. Also presented are formal characterisations, in the meta-language and in the object language, of paradoxical and 'truth teller'-like sentences. (shrink)

For the sentences of languages that contain operators that express the concepts of definiteness and indefiniteness, there is an unavoidable tension between a truth-theoretic semantics that delivers truth conditions for those sentences that capture their propositional contents and any model-theoretic semantics that has a story to tell about how indetifiniteness in a constituent affects the semantic value of sentences which imbed it. But semantic theories of both kinds play essential roles, so the tension needs to be resolved. (...) I argue that it is the truth theory which correctly characterises the notion of truth, per se. When we take into account the considerations required to bring model theory into harmony with truth theory, those considerations undermine the arguments standardly used to motivate supervaluational model theories designed to validate classical logic. But those considerations also show that celebration would be premature for advocates of the most frequently encountered rival approach - many-valued model theory. (shrink)

This book takes apart and problematises the whole process of identifying and explaining the patterning of words in sentences. It brings together two concepts - syntax and text - that are normally treated separately, and shows how they can best be understood in relation to each other. Part 1, Processing the text, concentrates on getting texts ready for syntactic analysis. Since the data needs to be mediated through the processing of the text, the nature of that processing and its (...) effects on subsequent analysis need to be made explicit. Part 2, Analysing the clause, introduces the relevant syntactic phenomena and the sorts of concepts normally used to explain them. It shows how many of the assumptions of traditional syntactic analysis derive from the languages which form the basis of the European tradition, and that different languages require the so-called basic categories of syntactic analysis to be rethought. Part 3, Theorising syntax, sketches the range of syntactic theories available for the consumer. It gives a sense of developments in the field over the last 50 years not just in terms of the usual schools, but by picking up on concepts such as the key complementarity between syntagmatic and paradigmatic to characterise the emphases and biases of different theories. (shrink)

In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I (...) illustrate the usefulness of bitheories by showing how they make available a technique for characterising different theories while abstracting away from logical vocabulary such as connectives or quanti- fiers, thereby making theoretical commitments independent of the choice of this or that particular non-classical logic. (shrink)

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...) to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (shrink)

Contextualism is a view about meaning, semantic content and truth-conditions, bearing significant consequences for the characterisation of explicit and implicit content, the decoding/inferring distinction and the semantics/pragmatics interface. According to the traditional perspective in semantics (called "literalism" or "semantic minimalism"), it is possible to attribute truth-conditions to a sentence independently of any context of utterance, i.e. in virtue of its meaning alone. We must then distinguish between the proposition literally expressed by a sentence ("what is said" by the sentence, its (...) literal truth-conditions) and the implicit meaning of the sentence ("what is implicated" by a speaker uttering the sentence). Over the past forty years, however, an increasing number of linguists and philosophers have begun to underline the phenomenon of semantic underdetermination: the encoded meaning of the sentence employed by a speaker underdetermines the proposition explicitly expressed by an utterance of that sentence. According to the extreme version of this perspective – labelled "radical contextualism" - no sentence of a natural language expresses a complete proposition, or has fixed truth-conditions, even when unambiguous and devoid of indexicals. A sentence expresses a proposition only when completed and enriched with pragmatic constituents that do not correspond to any syntactic element of the sentence and yet are part of its semantic interpretation. More broadly, "contextualism" may be used to refer to a family of views which includes moderate contextualism (also called "indexicalism"), radical contextualism and non-indexical contextualism – and which contrasts with semantic minimalism. (shrink)

The notion of subject matter is a key concern of contemporary philosophy of language and logic. A central task for a theory of subject matter is to characterise the notion of sentential subject matter, that is, to assign to each sentence of a given language a subject matter that may count as its subject matter. In this paper, we elaborate upon David Lewis’ account of subject matter. Lewis’ proposal is simple and elegant but lacks a satisfactory characterisation of sentential subject (...) matter. Drawing on linguistic literature on focus and on the question under discussion, we offer a neo-Lewisian account of subject matter, which retains all the virtues of Lewis’ but also includes an attractive characterisation of sentential subject matter. (shrink)

Stein once urged us not to confuse the means of representation with that which is being represented. Yet that is precisely what philosophers of science appear to have done at the meta-level when it comes to representing the practice of science. Proponents of the so-called ‘syntactic’ view identify theories as logically closed sets of sentences or propositions and models as idealised interpretations, or ‘theoruncula, as Braithwaite called them. Adherents of the ‘semantic’ approach, on the other hand, are typically characterised (...) as taking them to be families of models that are set-theoretic, according to Suppes and others, or abstract, as Giere has argued. da Costa and French (Science and Partial Truth. OUP, Oxford, 2003) suggested that we should refrain from ontological speculation as to the nature of scientific theories and models and focus on their appropriate representation for various purposes within the philosophy of science. Such an approach allows both linguistic and non-linguistic resources to play their appropriate role (see also French and Saatsi, Philosophy of Science, Proceedings of the 2004 PSA Meeting, 78:548–559, 2006) and can be supported by recent case studies illustrating the heterogeneity of scientific practice. My aim in this paper is to further develop this ‘quietist’ view, and to indicate how it offers a fruitful way forward for the philosophy of science. (shrink)

Taking into account that no subordering of a scattered partial ordering is dense, we are going to define one idea of rank of a partial ordering which will make possible an equivalent but more operative definition of a scattered partial ordering. Using this notion of rank and the Scott’s sentence associated with the ordering, we are going to characterise in the infinitary language Lw1.w each element of a subclass of the partial orderings, this of the strongly scattered countable partial orderings.

There are various ways of characterising Hume’s dictum that ‘you can’t get an ought from an is.’ Contributors to the literature directly addressing this question focus on logical characterisations of autonomy theses. Such theses maintain that certain logical relations do not obtain between ethical and non-ethical sentences, for instance that no non-ethical sentences logically entail an ethical sentence. I argue that this focus on logical autonomy is a mistake. The thesis so important to our metaethicists is not (...) a logical thesis but a metaphysical one. The relevant metaphysical autonomy thesis maintains that ethical facts are not fully grounded just in non-ethical facts. I defend this characterization. I also defend the converse thesis that all facts partly grounded in ethical facts are ethical facts. I then argue that this pair of theses can help with debates about the plausibility of nihilism and the classification of revisionary metaethical theses. (shrink)

In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic, an interesting variation upon the four-valued logic for first-degree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbert-style axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show that a calculus for (...) the Belnap-Dunn logic we have defined earlier can in fact be reused for the purpose of characterising ETL, provided a small alteration is made—initial assignments of signs to the sentences of a sequent to be proved must be different from those used for characterising FDE. While Pietz & Rivieccio define ETL on the language of classical propositional logic we also study its consequence relation on an extension of this language that is functionally complete for the underlying four truth values. On this extension the calculus gets a multiple-tree character—two proof trees may be needed to establish one proof. (shrink)

This work concerns itself with characterising the different types of contents that arise from uses of interrogative sentences, describing what meanings get associated with particular interrogative sentences, and explaining how these get put together compositionally on the basis of the meaning of their constituents, with particular attention to the meaning of interrogative phrases. ;Within most recent work in linguistic semantics, questions, the contents of query uses of interrogatives, have been analysed reductively as higher order propositional objects. The (...) current work argues against such an analysis. In its stead a view of questions is offered wherein these constitute the subclass of singular propositional entities, unresolved states-of-affairs , those that contain one or more argument roles of the propositional entity with whom no entity is associated. This view provides for an inherently richer notion of answerhood that is at the same time based on entities that are more plausibly available to cognitive agents engaged in querying. The need for a richer notion of answerhood is prompted by our demonstration that the class of answers to any given question--contents that can be conveyed by acceptable responses--has been considerably under-recognized in past work. An important gain made by the proposed approach is that it reveals and provides a simple account of systematic and cross-linguistically stable contrasts in the ability of a predicate to take an interrogative meaning as an argument. ;Our proposal for characterising the meaning of interrogative expressions argues that there exist three independent classes of uses which interrogative phrases can undergo, which we dub independent, dependent, and reprise uses. We argue extensively against an assumption common to most past work that interrogatives should be viewed as quantifiers on either syntactic or semantic grounds. We propose that dependent and reprise uses of interrogative expressions are each particular instances of use-types applicable to non-interrogative expressions. Dependent uses include bound variable anaphora as an instance. Reprise uses comprehend quotative uses of declarative sentences. We show how combining the general characteristics of each use type with the characterisation of independent interrogative uses we provide enables the defining conditions pertaining to these additional interrogative uses to be derived. This allows for a simple and comprehensive account of the available interrogative meanings. (shrink)

We revisit the foundations of positive model theory, introducing h-inductive sentences. These allow a considerably simplified presentation of positive model theory, as well as a characterisation of Hausdorff cats by an amalgamation property of their h-inductive theory.

Certain religious texts are deemed part of legal texts that are characterised by high sensitivity and sacredness. Amongst such religious texts are Islamic legal texts that are replete with Islamic legal terms that designate particular legal concepts peculiar to Islamic legal system and legal culture. However, from the syntactic perspective, Islamic legal texts prove lengthy and condensed, with an extensive use of coordinated, subordinate and relative clauses, which separate the main verb from the subject, and which, of course, carry a (...) heavy load of legal detail. The present paper seeks to examine the syntactic features of Islamic legal texts and the syntactic translation implications involved through studying three Islamic legal Arabic excerpts and their English translations. The paper argues that amongst the syntactic features of Islamic legal texts are nominalisation, participles, modals and complex structures. It also claims that the syntactic translation implications are indeed syntactic features of legal English, which are sentence combining versus sentence break, nominalisation, wh-deletion, passivisation, modals and multiple negations. Moreover, nominalisation, modality and complex structures are features of both Islamic legal texts and legal English, albeit with varying degrees. (shrink)

This paper establishes model-theoretic properties of \, a variation of monadic first-order logic that features the generalised quantifier \. We will also prove analogous versions of these results in the simpler setting of monadic first-order logic with and without equality and \, respectively). For each logic \ we will show the following. We provide syntactically defined fragments of \ characterising four different semantic properties of \-sentences: being monotone and continuous in a given set of monadic predicates; having truth (...) preserved under taking submodels or being truth invariant under taking quotients. In each case, we produce an effectively defined map that translates an arbitrary sentence \ to a sentence \ belonging to the corresponding syntactic fragment, with the property that \ is equivalent to \ precisely when it has the associated semantic property. As a corollary of our developments, we obtain that the four semantic properties above are decidable for \-sentences. (shrink)

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision operator ψ is similarly \Pi13 and (...) which is complete in Gödel’s universe of constructible sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points. (shrink)

In this paper we present a study of adjectival/adverbial modification using modern type theories, i.e. type theories within the tradition of Martin-Löf. We present an account of various issues concerning adjectival/adverbial modification and argue that MTTs can be used as an adequate language for interpreting NL semantics. MTTs are not only expressive enough to deal with a range of modification phenomena, but are furthermore well-suited to perform reasoning tasks that can be easily implemented given their proof-theoretic nature. In MTT-semantics, common (...) nouns are interpreted as types rather than predicates. Therefore, in order to capture the semantics of adjectives adequately, one needs to meet the challenge of modeling CNs modified by adjectives as types. To explicate that this can be done successfully, we first look at the mainstream classification of adjectives, i.e. intersective, subsective and non-subsective adjectives. There, we show that the rich type structure available in MTTs, along with a suitable subtyping framework, offers an adequate mechanism to model these cases. In particular, this modelling naturally takes care of the characterising inferences associated with each class of adjectives. Then, more advanced issues on adjectival modification are discussed: degree adjectives, comparatives and multidimensional adjectives. There, it is shown that the use of indexed types can be usefully applied in order to deal with these cases. In the same vein, the issue of adverbial modification is discussed. We study two general typings for sentence and VP adverbs respectively. It is shown that the rich type structure in MTTs further provides useful organisational mechanisms in giving formal semantics for adverbs. In particular, we discuss the use of \-types to capture the veridicality/non-veridicality distinction and further discuss cases of intensional adverbs using the type theoretic notion of context. We also look at manner, subject and speech act adverbials and propose solutions using MTTs. Finally, we show that the current proof technology can help mechanically check the associated inferences. A number of our proposals concerning adjectival and adverbial modification have been formalised in the proof assistant Coq and many of the associated inference patterns are checked to be correctly captured. (shrink)

The verification theory of meaning aims to characterise what it is for a sentence to be meaningful and also what kind of abstract object the meaning of a sentence is. A brief outline is given by Rudolph Carnap, one of the theory's most prominent defenders: If we knew what it would be for a given sentence to be found true then we would know what its meaning is. [...] thus the meaning of a sentence is in a certain sense identical (...) with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. [4: 420] In short, the verification theory of meaning claims that the meaning of a sentence is the method of its verification. (shrink)

Supervaluationism is one of the most discussed approaches to the semantics of future tense sentences in a branching time. In this paper, we consider the criticism advanced by Malpass against Supervaluationism. This criticism relies on the fact that supervaluationists must accept as supertrue disjunctions whose disjuncts are not only supertrue—which supervaluationists are ready to acknowledge—but also not satisfiable. In order to show this, Malpass proposes a formula, F F 1, which shows the existence of a satisfiable disjunction with unsatisfiable (...) disjuncts in supervaluationist models. In reply, we show that formula F F 1 cannot be expressed within a model (whether Ockhamist or supervaluationist) because it quantifies on models. It can be correctly characterised only within a meta-model that has the resources to quantify on various models. However, once that is done, F F 1 is, for the advocates of Supervaluationism, no more demanding than other disjunctions because it just generalises at the meta-theoretical level what supervaluationists already acknowledge at the theoretical level. (shrink)

In this note I revive a lingering (albeit dormant) account of rigid designation from the pages of Mind with the aim of laying it to rest. Why let a sleeping dog lie when you can put it down? André Gallois (1986) has proposed an account of rigid designators that allegedly squares with Saul Kripke’s (1980) characterisation of them as terms which designate the same object in all possible worlds, but on which, contra Kripke, identity sentences involving rigid designators may (...) be merely contingently true. This suits Gallois, as he finds the notion of contingent identity coherent. Thus, the thrust of Gallois’ thesis is that his account of rigidity is preferable to Kripke’s because his accommodates a coherent metaphysical viewpoint, whereas Kripke’s doesn’t. Gallois has thwarted one unconvincing challenge (see Carter 1987; Gallois 1988) and his account, as yet, remains untainted. But not for long, I hope.1 Let us assume, for the sake of argument, that the notion of contingent identity is coherent, that, in other words, it makes—or can make—sense to say that certain (possible) objects are identical in one world but distinct in another. What I shall argue here is that Gallois’ account of rigidity would prevent us from expressing the contingent nonidentity of objects; if so, this is a significant failing of the account, for, as it will emerge, clearly Gallois is committed to the contingency of non-identity. (shrink)

André Gallois’ (1993) modified account of restrictedly rigid designators (RRDs) does indeed block the objection I made to his original account (Gallois 1986; Ramachandran 1992). But, as I shall now show, there is a deeper problem with his approach which his modification does not shake off. The problem stems from the truth of the following compatibility claim: (CC) A term’s restrictedly rigidly designating (RR-designating) an object x is compatible with it designating an object y in a world W where x (...) exists but is distinct from y.1 It follows from (CC) that the necessary (contingent) truth of a sentence of the form “α is identical with β”, where “α” and “β” are RRDs of objects x and y respectively, does not require the necessary (contingent) identity of x and y. This is borne out by Gallois’ original example (see 1986, p. 58-63). Taking W to be the actual world, we have: (1) “Mary is identical with Mary” is necessarily true; yet “Mary” RR- designates Mary and Alice, which are only contingently identical. 1 I leave it to the reader to check that in Gallois’ own example (1986, p. 58), on the view he defends (pp. 62-63), and despite his modified characterisation of restricted rigidity, RDC# (1993, p. xx), “Mary” RR-designates Alice (as well as Mary) in W, but designates Mary and not A/ice in W1. Gallois has accepted this in correspondence. In light of (CC), while I agree with Gallois (1993, p. 153) that: (7) (a=b & ◊(a≠b)) → (∃x)(∃y)(x=y & ◊(x≠y)) is a theorem given RDC#, I dispute his defence of it (on p. 153). For, if (CC) is correct, the antecedent of (7) could be true even though a and b are identical in every world (where either exists)! (shrink)

By Solovay’s celebrated completeness result [31] on formal provability we know that the provability logic ${\textbf {GL}}$ describes exactly all provable structural properties for any sound and strong enough arithmetical theory with a decidable axiomatisation. Japaridze generalised this result in [22] by considering a polymodal version ${\mathsf {GLP}}$ of ${\textbf {GL}}$ with modalities $[n]$ for each natural number n referring to ever increasing notions of provability. Modern treatments of ${\mathsf {GLP}}$ tend to interpret the $[n]$ provability notion as “provable in (...) a base theory T together with all true $\Pi ^0_n$ formulas as oracles.” In this paper we generalise this interpretation into the transfinite. In order to do so, a main difficulty to overcome is to generalise the syntactical characterisations of the oracle formulas of complexity $\Pi ^0_n$ to the hyper-arithmetical hierarchy. The paper exploits the fact that provability is $\Sigma ^0_1$ complete and that similar results hold for stronger provability notions. As such, the oracle sentences to define provability at level $\alpha $ will recursively be taken to be consistency statements at lower levels: provability through provability whence the name of the paper. The paper proves soundness and completeness for the proposed interpretation for a wide class of theories, namely for any theory that can formalise the recursion described above and that has some further very natural properties. Some remarks are provided on how the recursion can be formalised into second order arithmetic and on lowering the proof-theoretical strength of these systems of second order arithmetic. (shrink)

Epistemic theories of truth, such as those presumed to be typical for anti-realism, can be characterised as saying that what is true can be known in principle: p → ◊Kp. However, with statements of the form “p & ¬Kp”, a contradiction arises if they are both true and known. Analysis of the nature of the paradox shows that such statements refute epistemic theories of truth only if the the anti-realist motivation for epistemic theories of truth is not taken into account. (...) The motivation in a link of understandability ans meaningful- ness suggests to change the above principle and to restrict the theory to logically simple sentences, in which case the paradox does not arise. This suggestion also allows to see the deep philosophical problems for anti-realism those counterexamples are pointing at. (shrink)

We observe a number of connections between recent developments in the study of constraint satisfaction problems, irredundant axiomatisation and the study of topological quasivarieties. Several restricted forms of a conjecture of Clark, Davey, Jackson and Pitkethly are solved: for example we show that if, for a finite relational structure M, the class of M-colourable structures has no finite axiomatisation in first order logic, then there is no set (even infinite) of first order sentences characterising the continuously M-colourable structures (...) amongst compact totally disconnected relational structures. We also refute a rather old conjecture of Gorbunov by presenting a finite structure with an infinite irredundant quasi-identity basis. (shrink)

Lyndon's Interpolation Theorem asserts that for any valid implication between two purely relational sentences of first-order logic, there is an interpolant in which each relation symbol appears positively (negatively) only if it appears positively (negatively) in both the antecedent and the succedent of the given implication. We prove a similar, more general interpolation result with the additional requirement that, for some fixed tuple U of unary predicates U, all formulae under consideration have all quantifiers explicitly relativised to one of (...) the U. Under this stipulation, existential (universal) quantification over U contributes a positive (negative) occurrence of U. It is shown how this single new interpolation theorem, obtained by a canonical and rather elementary model theoretic proof, unifies a number of related results: the classical characterisation theorems concerning extensions (substructures) with those concerning monotonicity, as well as a many-sorted interpolation theorem focusing on positive vs. negative occurrences of predicates and on existentially vs. universally quantified sorts. (shrink)

ABSTRACTOlder adults have greater difficulty than younger adults perceiving vocal emotions. To better characterise this effect, we explored its relation to age differences in sensory, cognitive and emotional functioning. Additionally, we examined the role of speaker age and listener sex. Participants aged 19–34 years and 60–85 years categorised neutral sentences spoken by ten younger and ten older speakers with a happy, neutral, sad, or angry voice. Acoustic analyses indicated that expressions from younger and older speakers denoted the intended emotion (...) with similar accuracy. As expected, younger participants outperformed older participants and this effect was statistically mediated by an age-related decline in both optimism and working-memory. Additionally, age differences in emotion perception were larger for younger as compared to older speakers and a better perception of younger as compared to older speakers was greater in younger as compared to older participants. Last, a female perception... (shrink)

Such a misconception of grammar characterises a very popular approach to indexicality which has been current since the 1970s, stemming from the work of Casteñeda, and Kaplan. Gareth Evans was inclined to allow, for instance, that one could say ‘“To the left (I am hot)” is true, as uttered by x at t iff there is someone moderately near to the left of x such that, if he were to utter the sentence “I am hot” at t, what he would (...) thereby say is true’ (Evans 1985: 358). But not only does this disturb the proper relation between direct and indirect speech, it continues a Fregean tradition which these very cases show to be quite mistaken about the logic of intensions. (shrink)

I have become more convinced, over the years, by the truth of Wittgenstein’s characterisation of philosophy as arising through misconceptions of grammar. Such a misconception of grammar characterises a very popular approach to indexicality which has been current since the 1970s, stemming from the work of Casteñeda, and Kaplan. Gareth Evans was inclined to allow, for instance, that one could say ‘“To the left (I am hot)” is true, as uttered by x at t iff there is someone moderately near (...) to the left of x such that, if he were to utter the sentence “I am hot” at t, what he would thereby say is true’ (Evans 1985: 358). But not only does this disturb the proper relation between direct and indirect speech, it continues a Fregean tradition which these very cases show to be quite mistaken about the logic of intensions. In this paper, however, I want primarily to point out how this misconception of grammar has distorted our view of people. For some of the above thinkers have tried to make out that human motivation is related to the possession of a certain category of indexical belief, by Lewis called ‘de se beliefs’. I shall look here at how the matter arises in Hugh Mellor’s work on Time. In connection with Time, indexicality arises in McTaggart’s ‘A-series’, and Mellor treats this indexicality in parallel with Evans’ language. First, therefore, I aim to show how Mellor’s discussion of Time grammatically misconceives the situation, and leads to a misrepresentation of the motivation of human action. But a larger conclusion about Fregean intensions is also then immediately available. (shrink)

As lawmakers produce norms, the underlying normative system is affected showing the intrinsic dynamism of law. Through undertaken actions of legal change, the normative system is continuously modified. In a usual legislative practice, the time for an enacted legal provision to be in force may differ from that of its inclusion to the legal system, or from that in which it produces legal effects. Even more, some provisions can produce effects retroactively in time. In this article we study a simulation (...) of such process through the formalisation of a temporalised logical framework upon which a novel belief revision model tackles the dynamic nature of law. Represented through intervals, the temporalisation of sentences allows differentiating the temporal parameters of norms. In addition, a proposed revision operator allows assessing change to the legal system by including a new temporalised literal while preserving the time-based consistency. This can be achieved either by pushing out conflictive pieces of pre-existing norms or through the modification of intervals in which such norms can be either in force, or produce effects. Finally, the construction of the temporalised revision operator is axiomatically characterised and its rational behavior proved through a corresponding representation theorem. (shrink)

We consider semi‐algebraic sets and properties of these sets that are expressible by sentences in first‐order logic over the reals. We are interested in first‐order properties that are invariant under topological transformations of the ambient space. Two semi‐algebraic sets are called topologically elementarily equivalent if they cannot be distinguished by such topological first‐order sentences. So far, only semi‐algebraic sets in one and two‐dimensional space have been considered in this context. Our contribution is a natural characterisation of topological elementary (...) equivalence of regular closed semi‐algebraic sets in three‐dimensional space, extending a known characterisation for the two‐dimensional case. Our characterisation is based on the local topological behaviour of semi‐algebraic sets and the key observation that topologically elementarily equivalent sets can be transformed into each other by means of geometric transformations, each of them mapping a set to a first‐order indistinguishable one. (shrink)

Besides their ordinary cardinal and proportional meanings, many and few have been argued to allow for a ‘reverse proportional’ reading. This reading has later been characterised in two opposite directions: Cohen’s reading where the proportion \ matters and Herburger’s where it does not. We develop a compositional analysis that derives the correct truth conditions for both characterisations of Westerståhl-style sentences while maintaining conservativity, assuming a standard syntax/semantics mapping and reducing their context-dependence to mechanisms independently needed for degree constructions in (...) general. In a nutshell, mirroring the decomposition of other degree expressions like tall, many is decomposed into the parametrized determiner many and the operator POS, where POS combines with a contextually salient comparison class C matching the alternatives triggered by some element X\ in the sentence. Non-reverse readings obtain when X\ is external to the original host NP and reverse readings when X\ is internal to the host NP. Cohen’s truth conditions for Westerståhl-style sentences are derived as a reverse proportional reading and Herburger’s interpretation as a sub-case of the non-reverse cardinal reading. (shrink)

The paper is devoted to the question of the principle of individuation in Bl. John Duns Scotus. This question is found in his commentary to Aristotle’s Metaphysics, namely the Quaestiones super libros Metaphysicorum Aristotelis VII, qu. 13. The first part of the paper discusses problems connected with the chronology and structure of the text, whereas the second one is presented as Scotus’s teaching on individuation. S. Dumont and T. Noone argue today on the traditional thesis about the origin of this (...) question and the remaining philosophical writings from the juvenile stage of Scotus’s philosophical work. They claim that some questions from the In Metaph., including also qu. 13 from the book, were written later or in the same time as the commentaries to Peter Lombard’s Sentences. The authors support their views by indicating the following: 1) the text the In Metaph. is better organised, 2) the vocabulary used with reference to the principle of individuation, especially the term haecceitas, is employed twice in the text In Metaph., 3) the quotations from the later works of Scotus and the works of authors who wrote somewhat later than that date of the In Metaph. hitherto presumed, 4) some stylistic terms indicate that the author of the text was a mature person. The traditional thesis is defended by I. Modrić on behalf of the Scotistic Commission. Having made a detailed analysis, Modrić rejected all the arguments from the introduction to the critical edition of the In Metaph. The author of this paper agrees with Modrić’s view. Therefore as long as we do not have a thesis to the contrary we shall hold the traditional opinion about the earlier origin of the In Metaph. in comparison to Peter Lombard’s commentaries on the Sentences. Scotus opens his lecture on individuation with a discussion of various standpoints on this issue. He divides them into positive and negative theories of individuation. This ordering ensures a clear exposition of various views without unnecessary repetitions and vagueness. Eventually, Doctor Subtilis rejects all hitherto views and provides his own solution. The principle of individuation is for him an individuating entity, the ultimate reality of the individual being. In combination with common nature it determines the most individual of possible characterisation of the individuum. This positive individuating entity is called an individual form (forma individualis) in the In Metaph., a degree of entity (gradus entis) and haecceitas. The latter became a technical term to define the Scotist principle of individuation. (shrink)

In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content that does not imply the existence of mathematical objects. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward assertions. In Part I, I argue that the role (...) played by mathematics in our scientific explanations is a purely expressive one, merely allowing us to say more about the physical world than we would otherwise be able to. Mathematical objects do not need to exist for mathematics to play this role. This proposal puts a normative constraint on our use of mathematical language: we ought to use mathematically presented theories to express belief only in the consequences they have for non-mathematical things. In Part II, I will argue that what the normative proposal recommends is in fact what people generally do in both pure and applied mathematical contexts. I motivate this claim by showing that it is predicted by our best general means of analysing natural language. I provide a semantic theory of applied arithmetical sentences that reveals they do not purport to refer to numbers, as well as a pragmatic theory for pure mathematical language use which reveals that pure mathematical utterances do not typically communicate content that implies the existence of mathematical objects. In conclusion, I show that the emerging hermeneutic fictionalist position is preferable to any alternative interpretation of mathematical discourse as aimed at describing a domain of independently existing abstract mathematical objects. (shrink)

For the purposes of this paper I shall assume that some definite singular terms for individual particulars are sometimes used purely referentially or, as I shall say, with the function of direct reference; and that they sometimes occur, so used, in the belief-specifying clauses of belief-attributing sentences. Direct reference can be characterised semantically, or in terms of truth-conditions, as follows: When a direct reference is made, by some term, to a particular individual, in an utterance in which that term (...) is coupled with a predicate, then there is uttered a proposition which is true if that individual satisfies that predicate, false if it does not. A full account of the pragmatics of direct reference would be a much more complicated matter; I shall refer briefly to just one aspect of the matter towards the end of the paper. (shrink)