Consider two standard quantified modal languages A and P whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of A are actualist while those of P are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive-i.e., so that for each sentence (...) of one language there is a sentence of the other language such that given any model, the former sentence is true at the actual world of the model iff the latter is? Forbes (1989) shows that this can be done by adding to both languages a pair of sentential operators called Vlach-operators, and imposing a syntactic restriction on their occurrences in formulas. As Forbes himself recognizes, this restriction is somewhat artificial. The first result I establish in this paper is that one gets sameness of expressivity by introducing infinitely many distinct pairs of indexed Vlach-operators. I then study the effect of adding to our enriched modal languages a rigid actuality operator. Finally, I discuss another means of enriching both languages which makes them expressively equivalent, one that exploits devices introduced in Peacocke (1978). Forbes himself mentions that option but does not prove that the resulting languages are equally expressive. I do, and I also compare the Peacockian and the Vlachian methods. In due course, I introduce an alternative notion of expressivity and I compare the Peacockian and the Vlachian languages in terms of that other notion. (shrink)

Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions are often (...) justified only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (shrink)

According to Hans Kamp and Frank Vlach, the two-dimensional tense operators “now” and “then” are ineliminable in quantified tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It shows that “now” and “then” are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The (...) operators might not be redundant in some other systems of tense logic, but this merely indicates a lack of quantificational resources and does not show any deep-seated inability of tense logic to express claims about time. The paper closes with a brief discussion of the modal analogue of this issue, which concerns the role of the actuality operator in quantified modal logic. (shrink)

The strongest objection to (15) is that speaker's meaning is defined in terms of commitment, a notion which is itself something of a challenge and for which no definition has been given. This would be a strong reason to prefer a definition in terms of some more tractable concept, all things being equal; but it does not lessen the probability that commitment or some similar notion is indispensable to the definition of speaker's meaning.The philosophical writings discussed in this paper all (...) proceed something like this: Particular cases are discussed and a description is given of the mechanisms by which communication takes place. An attempt is made to say something that applies to all instances of speaker's meaning. Words like ‘analysis’, ‘account’ ‘explanation’, ‘explication’, and ‘theory’ are used here, the suggestion being that the objective is to provide for all cases at once what has already been provided for particular cases-an explanation of how meaning works. What is produced, however, looks like adefinition of speaker's meaning, a statement of necessary and sufficient conditions. This definition is then evaluated largely in terms of what counterexamples it does or does not allow.It seems that there is some tendency to conflate two quite distinct objectives: (i) a theory of speaker's meaning-a general description of how it is that speakers are able to communicate; and (ii) a statement of necessary and sufficient conditions for speaker's meaning. Objective (i) might plausibly be regarded as the goal of the study of communication. Objective (ii) is the definition of a certain intuitive, pretheoretical concept of meaning, which might or might not prove to be an important concept with respect to objective (i). The Gricean mechanism and the notion of conventional meaning, on the other hand, are indispensable to (i)-few instances of speaker's meaning could be adequately described without recourse to at least one of these notions. Thus nothing in this paper should be construed as trying to downgrade the importance of the Gricean mechanism for the theory of communication. If objective (ii) and the Gricean mechanism are not as closely associated as has been claimed, this is, if anything, a reason to doubt the importance of (ii) for the theory of communication. (shrink)

[...] No momento atual, parece-nos possível afirmar que discussões atinentes à epistemologia em Geografia, explicitando a questão da teoria, do método e do objeto no seu interior, têm-se difundido em proporções consideráveis, embora muitas vezes inseridas no bojo do cientificismo, isto é, sob os cânones positivistas da "verdadeira ciência" — aquela que é imune às ideologias. Na medida em que o método científico atua corno o "divisor de águas" entre ciência e ideologia (ou ciência e política), e em que há (...) um certo consenso, até por parte dos geógrafos, a respeito do seu näo-privilegiamento dentro da vasta produção geográfica tradicional, cumpre indagar, inicialmente, se a chamada Geografia crítica não corre o risco de, primeiro, apenas inverter o discurso; segundo, de continuar abordando os mesmos assuntos; terceiro, de fazer a apologia de um único caminho para este saber (e sua prática), o que se nos afigura como um perigoso "passo para trás" nesse percurso decisivo da Geografia em direção ao desvendamento do social (sentido lato), como um importante momento do amplo e complexo processo de constituição de uma outra sociedade. [...] Palavras-chave: Positivismo; Geografia; Método; Científico; Teoria. (shrink)

Machery proposes that the construct of detracts from research progress. However, ignoring development also detracts from research progress. Developmental research has advanced our understanding of how concepts are acquired and thus is essential to a complete theory. We propose a framework that both accounts for development and holds great promise as a new direction for thinking about concepts.

Cross‐situational word learning (XSWL) tasks present multiple words and candidate referents within a learning trial such that word–referent pairings can be inferred only across trials. Adults encode fine phonological detail when two words and candidate referents are presented in each learning trial (2 × 2 scenario; Escudero, Mulak, & Vlach, ). To test the relationship between XSWL task difficulty and phonological encoding, we examined XSWL of words differing by one vowel or consonant across degrees of within‐learning trial ambiguity (1 (...) × 1 to 4 × 4). Word identification was assessed alongside three distractors. Adults finely encoded words via XSWL: Learning occurred in all conditions, though accuracy decreased across the 1 × 1 to 3 × 3 conditions. Accuracy was highest for the 1 × 1 condition, suggesting fast‐mapping is a stronger learning strategy here. Accuracy was higher for consonant than vowel set targets, and having more distractors from the same set mitigated identification of vowel set targets only, suggesting possible stronger encoding of consonants than vowels. (shrink)

Previous research on cross-situational word learning has demonstrated that learners are able to reduce ambiguity in mapping words to referents by tracking co-occurrence probabilities across learning events. In the current experiments, we examined whether learners are able to retain mappings over time. The results revealed that learners are able to retain mappings for up to 1 week later. However, there were interactions between the amount of retention and the different learning conditions. Interestingly, the strongest retention was associated with a learning (...) condition that engendered retrieval dynamics that initially challenged the learner but eventually led to more successful retrieval toward the end of learning. The ease/difficulty of retrieval is a critical process underlying cross-situational word learning and is a powerful example of how learning dynamics affect long-term learning outcomes. (shrink)

Já tivemos a oportunidade de colocar, após uma reflexão sobre a Geografia, o que inclui necessariamente o ensino, pois, o seu prestígio resulta de sua institucionalização escolar, que caberia a nós, professores de Geografia, a elaboração de um contra-discurso. Se falamos em contra-discurso, é porque sentimos a necessidade de mudança na maneira como se ensina tradicionalmente a Geografia. Lacoste é claríssimo: de modo geral, a Geografia escolar (e os respectivos livros didáticos) se limita (m) a “ensinar sem compreender”. Ou seja, (...) os alunos são obrigados a estudar esta disciplina mesmo sem compreendê-la. Evidentemente, isso não faz sentido, considerando-se que ela deveria – e pode, efetivamente – contribuir decisivamente para uma compreensão crítica de realidade, por parte do educando. Porém, a necessidade de um contra-discurso geográfico advém do seguinte: o discurso geográfico, seja o veiculado pelos meios de comunicação, o dos professores, é essencialmente ideológico. Nossas atenções se voltam especificamente para o discurso escolar, ideológico no sentido de que lhe coube, historicamente, “passar” a ideia de pátria. [...] Palavras-chave: Geografia; Ensino; Discurso; Livros didáticos. (shrink)

Estamos reunidos, futuros professores de 1º e 2º graus, em um espaço institucional: a escola, que pretendemos discutir, e em cujo interior interessa-nos particularmente a questão do ensino da Geografia. Quem institucionalizou a escola? Por quê? As mesmas perguntas (e outras) devem se voltar à nossa questão central. Ao mesmo tempo, a escola é aquela instituição social em que parte da população (nem todos têm acesso a ela), em um dado período, assinala, de uma maneira específica, a sua participação na (...) sociedade mais ampla. Ora, participamos da vida social no sentido lato através do trabalho. Nesse sentido, ainda que soe como paradoxo, a escola é também um espaço de trabalho. Certamente, não é o espaço da fábrica, mas exige disciplina (intelectual); nem o do folguedo, embora às vezes se transforme no “jogo de ensinar”. […] Será que estamos negando o conhecimento, que, sob a forma de conteúdos “didaticamente” selecionados e distribuídos, parece ter sustentado a escola durante muito tempo? […] Palavras-chave: Ideologia; Geografia; Escola; Instituição social; Espaço da fábrica; Ensino. (shrink)

Let be a model of a theory T. Depending on wether is decidable or recursive, and on whether T is strongly minimal or -minimal, we find conditions on which guarantee that every infinite independent subset of is not recursively enumerable. For each of the same four cases we also find conditions on which guarantee that every infinite independent subset of has Turing degree 0'. More generally, let be a recursive -structure, R a relation symbol not in , ψ a recursive (...) infiniatary Π2 sentence in the language {R}, and let 0<α<ωCK1. We discuss conditions under which we can construct a recursive -structure such that ,Rψ for every Δ0α relation R on. (shrink)

Children ask many questions, but do not always receive answers to the questions they ask. We were interested in whether the act of generating questions, in the absence of an answer, is related to children’s later thinking. Two experiments examined whether children retain the questions they ask in working memory, and whether the type of questions asked relate to their categorization. Four to ten-year-old children (N= 42 in Experiment 1,N= 41 in Experiment 2) were shown 12 novel objects, asked three (...) questions about each, and did not receive answers to their questions. Children recalled their questions in the first experiment and categorized variants of the novel objects in the second experiment. We found that children have robust working memory for their questions, indicating that these questions may relate to their subsequent thinking. Additionally, children generalize category boundaries more narrowly or broadly depending on the type of question they ask, indicating that children’s questions may reflect an underlying bias in how they think about the world. These findings suggest that future research should examine questions in the absence of answers to understand how inquiry affects children’s cognitive development. (shrink)

Cross-situational statistical learning of words involves tracking co-occurrences of auditory words and objects across time to infer word-referent mappings. Previous research has demonstrated that learners can infer referents across sets of very phonologically distinct words, but it remains unknown whether learners can encode fine phonological differences during cross-situational statistical learning. This study examined learners’ cross-situational statistical learning of minimal pairs that differed on one consonant segment, minimal pairs that differed on one vowel segment, and non-minimal pairs that differed on two (...) or three segments. Learners performed above chance for all pairs, but performed worse on vowel minimal pairs than on consonant minimal pairs or non-minimal pairs. These findings demonstrate that learners can encode fine phonetic detail while tracking word-referent co-occurrence probabilities, but they suggest that phonological encoding may be weaker for vowels than for consonants. (shrink)

We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.(1) The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going beyond (...) it, by a more general theory of single events, using hidden variables, for example. (shrink)

This essay argues that there are theoretical benefits to keeping distinct—more pervasively than the literature has done so far—the psychological states of imagining that p versus believing that in-the-story p, when it comes to cognition of fiction and other forms of narrative. Positing both in the minds of a story’s audience helps explain the full range of reactions characteristic of story consumption. This distinction also has interesting conceptual and explanatory dimensions that haven’t been carefully observed, and the two mental state (...) types make distinct contributions to generating emotional responses to stories. Finally, the differences between the mental states illuminate how a given story can be both shared with others and at the same time experienced as personal. (shrink)

Given current data, only a few binary Boolean operators are expressed in lexically simple fashion in the world's languages: and, or, nor. These do not occur in every combination, for example, nor is not observed by itself. To explain these cross‐linguistic patterns, we propose an encoding of Boolean operators as update procedures to accept or reject information in a context. We define a measure of conceptual simplicity for such updates, on which attested operators are conceptually simpler than (...) the remaining Booleans. Moreover, we show that language evolution selects for the attested lexical inventories by minimizing the complexity of using a lexical inventory compositionally to convey precise information. (shrink)

Adams’ thesis is generally agreed to be linguistically compelling for simple conditionals with factual antecedent and consequent. We propose a derivation of Adams’ thesis from the Lewis- Kratzer analysis of if-clauses as domain restrictors, applied to probability operators. We argue that Lewis’s triviality result may be seen as a result of inexpressibility of the kind familiar in generalized quantifier theory. Some implications of the Lewis- Kratzer analysis are presented concerning the assignment of probabilities to compounds of conditionals.

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...) states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

Cappelen and Hawthorne’s Relativism and Monadic Truth (2009) offers an extended defense of a thesis they call simplicity, which, in brief, holds that propositions are true or false simpliciter. Propositions are cast in their traditional roles as the contents of assertions, and as the semantic values of declarative sentences in contexts. Simplicity stands in sharp contrast to forms of relativism including, for instance, a form that hold that our claims are true or false only relative to a judge. This applies (...) especially to claims of taste, which come out true or false only relative to the judge who finds things tasty (e.g. Glanzberg 2007, Lasersohn 2005). But simplicity also rejects the more widespread temporalist view that propositions are true or false only relative to a time, and it rejects the even more widely held view that propositions are true or false only relative to a world. One reason that has been advanced for temporalism, e.g. by Kaplan (1989), is that our languages seem to contain non-trivial temporal operators. Hence, the argument goes, the semantic values of sentences need to be temporally neutral, i.e. vary for truth or falsehood with time. The same goes for possible worlds and modal operators. Hence, Kaplan and many others think of the semantic values of sentences as sets of world-time pairs. It has been tempting to apply this sort of argument much more widely, to see the semantic values of sentences as varying not just with world and time, but perhaps with location and other parameters as well. Kaplan.. (shrink)

In Entities and Indices, M. J. Cresswell argued that a first-order modal language can reach the expressive power of natural-language modal discourse only if we give to the formal language a semantics with indices containing infinite possible worlds and we add to it an infinite collection of operators $${{\varvec{actually}}}_n$$ actually n and $$ Ref _n$$ R e f n which store and retrieve worlds. In the fourth chapter of the book, Cresswell gave a proof that the resulting intensional language, (...) which he called $${\mathscr {L}}^*$$ L ∗, is as expressive as an extensional variant of it, called $${\mathscr {L}}$$ L, which has full quantification over worlds. In both linguistics and philosophy, Cresswell’s book has been viewed as offering a compelling argument for preferring extensional systems in the study of natural language. In this paper, after providing a model-theoretic definition of the relation being as expressive as that can be applied to Cresswell’s languages $${\mathscr {L}}$$ L and $${\mathscr {L}}^*$$ L ∗, we show that the intensional language $${\mathscr {L}}^*$$ L ∗ is not as expressive as the extensional language $${\mathscr {L}}$$ L. This result, we claim, undermines Cresswell’s argument to the effect that English modal discourse has the power of explicit quantification over worlds. Additionally, we show that $${\mathscr {L}}^*$$ L ∗ does become as expressive as $${\mathscr {L}}$$ L when we add Cresswell’s operator of universal modality $$\square $$ □ to $${\mathscr {L}}^*$$ L ∗, which provides an extra amount of expressive power. Recently, I. Yanovich has advocated a view that is similar to ours in important respects. At the end of the paper we offer a short discussion of his formalism. (shrink)

Montague, Prior, von Wright and others drew attention to resemblances between modal operators and quantifiers. In this paper we show that classical quantifiers can, in fact, be regarded as S5-like operators in a purely propositional modal logic. This logic is axiomatized and some interesting fragments of it are investigated.

In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics.

We investigate the join semilattice of modal operators on a Boolean algebra B. Furthermore, we consider pairs ⟨f,g⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle f,g \rangle $$\end{document} of modal operators whose supremum is the unary discriminator on B, and study the associated bi-modal algebras.

Presents a series of generalizations of distributivity operators across a type hierarchy, in order to account for collective-distributive ambiguities for non-subject arguments.

There are a considerable number of logics that do not seem to share the same inferential principles. Intuitionistic logics do not include the law of the exclude.

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over some point (...) on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

Logical frameworks that are sensitive to features of sentences’ subject-matter—like Berto’s topic-sensitive intentional modals (TSIMs)—demand a maximally faithful model of the topics of sentences. This is an especially difficult task in the case in which topics are assigned to intensional formulae. In two previous papers, a framework was developed whose model of intensional subject-matter could accommodate a wider range of intuitions about particular intensional conditionals. Although resolving a number of counterintuitive features, the work made an implicit assumption that the subject-matter (...) of an intensional conditional is a function of the subject-matters of its subformulae. This assumption—which I will call a principle of topic sufficiency—runs counter to some natural intuitions concerning topic. In this paper, we will investigate topic sufficiency and offer a semantic account that is state-sensitive, providing an implementation through the introduction of topic-sensitive logics related to William Parry’s prototypical $\mathsf {PAI}$. (shrink)

This is my contribution to a symposium on Berit Brogaard's book "Transient Truths" in which I criticize her treatment of various linguistic phenomena related to tense.

Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...) random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. (shrink)

Since the turn of the century, the number of small-scale farmers in the U.S. and farmlands they owned have declined very sharply (structural change). Although the decrease in number is generally true for both white and Black farm operators, it has been more significant for Blackfarm operators than whites. The declining trend in the number of Blackfarm operators in the country is derived from individual state experiences that resulted from a combination of various political and economic factors. (...) Using the census of agriculture data from 1900 to 1987, this paper gives a brief historical overview of Black farm operators in Maryland. The census data for the study period shows that at their peak number in 1910, there were 6,382 Blackfarmers in the state of Maryland. However, by 1987, only 371 of that number remained, representing a loss of 94 percent since 1910. According to the 1987 census data almost all Black operated farms in Maryland were not only small-scale but also in the lower sales class, less than $20,000 a year. Their household net family income is below that of non-metropolitan median household income. This concentration of Blacks in the lower economic class of farm operators in the state, for the most part, is closely related to their resource endowments, patterns of tenure, type of farm enterprises, and government farm programs and policies. On the average, Blackfarmers in Maryland have less land, capital and management skills than their white counterparts. Government policies and programs had, and continue to have, a devastating effect on Maryland Black farmers because they were tied to productive resources rather than farm income needs. Under conditions of low income, years of neglect by federal and state programs and policies, and limited resources Blackfarmers were unable to adopt capital intensive production practices and expand their farm operations. This resulted in most of them leaving agriculture, in the past and today, at a faster rate than whites. To avert or at least lessen the unfortunate situation of Black farm operators, projections and possible solutions are offered. This includes how the 1890 Land-Grant institutions because of their tradition, expertise and experience of research, teaching and outreach can take the leadership role in shaping the future direction of these farmers and their operations. (shrink)

The addition of "actually" operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing "actually" operators has concentrated entirely upon extensions of KT5 and has employed a particular modeltheoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing "actually" operators, the weakest of which are conservative (...) extensions of K, using a novel generalisation of the standard semantics. (shrink)

Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: the linearly ordered systems Ł3,..., Open image in new window,..., \; the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining (...) truth-functional modal logics. The systems we define lack “Łukasiewicz type paradoxes”. Following Brady, we endow them with Belnap–Dunn type bivalent semantics. (shrink)