Rudolf Carnap proposed three reduction rules to improve scientific language. Those rules indicate when it is correct to add a property in situations in which other properties are already had. Assuming the theory of mental models, it has been shown that the rules are not hard to use from the cognitive point of view. The key to argue that is to accept that the human mind works as dual-process theories claim. According to these theories, people can use two different (...) systems. One of them implies effort but the other one does not. Thus, the idea is that Carnap’s reduction rules can be applied resorting just to the system not implying cognitive effort. This paper goes one step further and poses that even from a Popperian perspective the reduction rules keep not being difficult. One might think that falsifiability requires cognitive effort because it needs to address situations in which the sentences are false. However, this paper tries to explain that, following the theory of mental models, that is not hard if the sentences are conditionals, and the sentences in the reduction rules have conditional structures. (shrink)

The theory of mental models considers sentential connectives to refer to semantic possibilities. The theory also proposes that the possibilities can be amended by virtue of modulation processes, that is, processes in which semantics or pragmatics can have an influence. The definition of modulation the theory of mental models gives has been deemed as a scientific definition within Carnap’s framework. This is because it is easy to find reduction sentences corresponding to it. What seems to be harder is to (...) think about bilateral reduction sentences for that definition. This paper addresses this issue. It shows that at least a bilateral reduction sentence is possible for modulation. (shrink)

The entropy-reduction hypothesis claims that the cognitive processing difficulty on a word in sentence context is determined by the word's effect on the uncertainty about the sentence. Here, this hypothesis is tested more thoroughly than has been done before, using a recurrent neural network for estimating entropy and self-paced reading for obtaining measures of cognitive processing load. Results show a positive relation between reading time on a word and the reduction in entropy due to processing that (...) word, supporting the entropy-reduction hypothesis. Although this effect is independent from the effect of word surprisal, we find no evidence that these two measures correspond to cognitively distinct processes. (shrink)

It is common practice in the United Kingdom, the United States, and other common law countries to reduce criminal sentences in response to guilty pleas. This chapter contends that this practice violates the commonly accepted prohibiton on punishment of the innocent. I first consider various interpretations of what this prohibition requires of a system of punishment. Then I contend that insofar as sentence reductions provide significant prudential incentives to innocent people to plead guilty, these reductions run afoul of the (...) most plausible construal of the prohibition on punishment of the innocent. I consider and respond to some possible objections, and then I consider the implications of my account. (shrink)

Steven Tudor defends the mitigation of criminal sentences in cases in which offenders are genuinely remorseful for their crimes. More than this, he takes the principle that such remorse-based sentence reductions are appropriate to be a ‘well-settled legal principle’—so well settled, in fact, that ‘it is among those deep-seated commitments which can serve to test general theories as much as they are tested by them’. However, his account of why remorse should reduce punishment is strongly philosophical in character. He (...) sets to one side the many practical difficulties in implementing such reductions in the real world of criminal justice institutions so that he can focus on the question of whether a plausible account of sentencing can show that remorse should mitigate punishment. I contend that Tudor’s defense of such reductions is unpersuasive in certain respects. Yet even if it can be made more persuasive, I argue that the conditions that would have to be satisfied for remorse-based sentence reductions to be justifiably implemented are so many and various that they would likely exceed our abilities to responsibly grant them in real world legal contexts. I therefore claim that Tudor has failed to provide a defense of the ‘remorse principle’ that serves to explain or justify existing legal practices. (shrink)

Back cover: This book develops a philosophical account that reveals the major characteristics that make an explanation in the life sciences reductive and distinguish them from non-reductive explanations. Understanding what reductive explanations are enables one to assess the conditions under which reductive explanations are adequate and thus enhances debates about explanatory reductionism. The account of reductive explanation presented in this book has three major characteristics. First, it emerges from a critical reconstruction of the explanatory practice of the life sciences itself. (...) Second, the account is monistic since it specifies one set of criteria that apply to explanations in the life sciences in general. Finally, the account is ontic in that it traces the reductivity of an explanation back to certain relations that exist between objects in the world (such as part-whole relations and level relations), rather than to the logical relations between sentences. Beginning with a disclosure of the meta-philosophical assumptions that underlie the author’s analysis of reductive explanation, the book leads into the debate about reduction(ism) in the philosophy of biology and continues with a discussion on the two perspectives on explanatory reduction that have been proposed in the philosophy of biology so far. The author scrutinizes how the issue of reduction becomes entangled with explanation and analyzes two concepts, the concept of a biological part and the concept of a level of organization. The results of these five chapters constitute the ground on which the author bases her final chapter, developing her ontic account of reductive explanation. (shrink)

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as ‘informational entropy’), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper (...) establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same ‘modal content’; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks. (shrink)

According to conceptual reductive accounts, if properties of one domain can be conceptually reduced to properties of another domain, then the former properties are ontologically reduced to the latter properties. I will argue that conceptual reductive accounts face problems: either they do not recognise that many higher-level properties are correlated with multiple physical properties, or they do not clarify how we can discover new truthmakers of sentences about a higher-level property. Still, there is another way to motivate ontological reduction, (...) the truthmaker reductive explanations (TRE). TRE can be given by using resources from John Heil’s truthmaker theory and the a priori entailment view or the a posteriori entailment view. I will argue that we can give these truthmaker reductive explanations if there are various less-than-perfectly similar physical properties that can be the truthmakers of sentences about higher-level properties and the physical similarity between them can explain why an irreducible higher-level property is not needed. (shrink)

There is now considerable evidence that human sentence processing is expectation based: As people read a sentence, they use their statistical experience with their language to generate predictions about upcoming syntactic structure. This study examines how sentence processing is affected by readers' uncertainty about those expectations. In a self-paced reading study, we use lexical subcategorization distributions to factorially manipulate both the strength of expectations and the uncertainty about them. We compare two types of uncertainty: uncertainty about the (...) verb's complement, reflecting the next prediction step; and uncertainty about the full sentence, reflecting an unbounded number of prediction steps. We find that uncertainty about the full structure, but not about the next step, was a significant predictor of processing difficulty: Greater reduction in uncertainty was correlated with increased reading times. We additionally replicated previously observed effects of expectation violation, orthogonal to the effect of uncertainty. This suggests that both surprisal and uncertainty affect human RTs. We discuss the consequences for theories of sentence comprehension. (shrink)

Theories in the usual sense, as characterized by a language and a set of theorems in that language ("statement view"), are related to theories in the structuralist sense, in turn characterized by a set of potential models and a subset thereof as models ("non-statement view", J. Sneed, W. Stegmüller). It is shown that reductions of theories in the structuralist sense (that is, functions on structures) give rise to so-called "representations" of theories in the statement sense and vice versa, where representations (...) are understood as functions that map sentences of one theory into another theory. It is argued that commensurability between theories should be based on functions on open formulas and open terms so that reducibility does not necessarily imply commensurability. This is in accordance with a central claim by Stegmüller on the compatibility of reducibility and incommensurability that has recently been challenged by D. Pearce. (shrink)

Let A be an admissible set. A sentence of the form ∀R̄φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence if φ ∈ A (φ is $\bigvee\Phi$ , where Φ is an A-r.e. set of sentences from A; φ ∈ Lω1ω). A sentence of the form ∃R̄φ is an ∃2(A) (∃s 2(A),∃2(Lω1ω)) sentence if φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence. A class of structures is, for example, a ∀1(A) class if it is the class of models (...) of a ∀1(A) sentence. Thus ∀1(A) is a class of classes of structures, and so forth. Let Mi be the structure $\langle i, 0$. Let Γ be a class of classes of structures. We say that a sequence $J_1,\ldots,J_i,\ldots, i < \omega$, of classes of structures is a Γ sequence if $J_i \in \Gamma, i < \omega$, and there is I ∈ Γ such that M ∈ Ji if and only if [M, Mi] ∈ I, where [,] is the disjoint sum. A class Γ of classes of structures has the easy uniformization property if for every Γ sequence $J_1,\ldots,J_i, \ldots, i < \omega$, there is a Γ sequence $J'_1,\ldots,J'_i,\ldots, i < \omega$, such that $J'_i \subseteq J_i, i < \omega, \bigcup J'_i = \bigcup J_i$, and the J'i are pairwise disjoint. The easy uniformization property is an effective version of Kuratowski's generalized reduction property that is closely related to Moschovakis's (topological) easy uniformization property. We show over countable structures that ∀1(A) and ∃2(A) have the easy uniformization property if A is a countable admissible set with an infinite member, that ∀s 1(Lα) and ∃s 2(Lα) have the easy uniformization property if α is countable, admissible, and not weakly stable, and that ∀1(Lω1ω) and ∃2(Lω1ω) have the easy uniformization property. The results proved are more general. The result for ∀s 1(Lα) answers a question of Vaught (1980). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reduction's FutureTheology, Technology, and the Order of KnowledgeKevin L. HughesLet me begin with something of a confession. When as a young undergraduate I first encountered medieval texts, and so, for the first time, began to know something of the medieval "way of seeing," I was intoxicated. And I was intoxicated, in part, by the comprehensiveness and unity of this worldview, where God, humans, the cosmos, science, theology, philosophy, (...) nature, supernature – all of these elements fit. So often in my thinking I have repaired to those famous last lines of Dante's Comedy, to the "Love which moves the sun and other stars," as the epitome of the comprehension, coherence, and harmony of the medieval worldview.Perhaps this is one of the reasons I have been attracted to the work of St. Bonaventure. We may all be familiar with the statements that now have become almost truisms, that to know Bonaventure at all, one needs to know the whole system, and that the whole system is found in every kind of work that he had done. "Procession, exemplarity, return, this is the whole of our metaphysics."1 This principle of Order in Bonaventure, as described and analyzed by Wayne Hellmann, is a kind of keystone to all of Bonaventure's work.2 [End Page 227]If you understand the "order," you understand Bonaventure. Such admirable consistency and harmony! Such remarkable unity of perspective! And, at least by many accounts, the Reduction of the Arts to Theology3 is a perfect concise instance of Bonaventure's synthetic vision.It is precisely this unity, as found in the Reduction of the Arts to Theology, that Dieter Hattrup finds problematic. For Hattrup, the notion of unity itself is not problematic; rather, it is the unity of knowledge as conveyed in the Reduction that approaches a deeply problematic modern understanding of knowledge. Hattrup believes he has discovered in this brief treatise the seeds of what we might call a technological or manipulative knowledge. Whatever the limits of Dieter Hattrup's historical and textual brief against the authenticity of the Reduction, his theological queries should put us all on guard if we are to imagine a future for any "reduction of the arts to theology," Bonaventurean or otherwise.A Theological QuestionBonaventura zwischen Mystik und Mystifikation4 begins with a basic theological premise: Christian theology is interested in the relationship between faith and reason, and this interest follows from the even more basic Christian claim that God is distinct from the world. If one has an intra-cosmic notion of the divine, wherein gods are the greatest or most powerful beings among all other beings, then the question between faith and reason does not arise. Gods who are beings can be known in the way we know all other beings, i.e., through reason. Faith, on the other hand, describes the kind of knowledge we can have of the One who is not part but [End Page 228] Maker of the created order. From the time of Philo on, Jewish and Christian believers5 have drawn this careful distinction and explored how faith and reason might be related without being reduced one into the other. Hattrup suggests that this perpetual question is raised with particular intensity with the revival of Aristotelian philosophy in the High Middle Ages, and Bonaventure stands as a major figure in scholastic inquiry. But, he tells us, this question remains crucial to our own time under the sign of "secularization."6It is important to note this opening overture, as it tells us that Hattrup is exploring what he takes to be first and foremost a theological puzzle: Does the Reduction of the Arts to Theology faithfully represent Bonaventure's understanding of the relationship between faith and reason as ways of knowing? Is it consistent with what we find (and what Hattrup has studied elsewhere)7 in his Sentence Commentary, Disputed Questions on the Knowledge of Christ, and the Collations on the Hexaëmeron? Most importantly, and more theologically, does the Reduction distinguish properly between faith and reason, as would befit this Doctor of the Church? Or is it the beginning of the collapse of this classic distinction... (shrink)

Individuals with agrammatic Broca's aphasia experience difficulty when processing reversible non-canonical sentences. Different accounts have been proposed to explain this phenomenon. The Trace Deletion account attributes this deficit to an impairment in syntactic representations, whereas others propose that the underlying structural representations are unimpaired, but sentence comprehension is affected by processing deficits, such as slow lexical activation, reduction in memory resources, slowed processing and/or intermittent deficiency, among others. We test the claims of two processing accounts, slowed processing and (...) intermittent deficiency, and two versions of the Trace Deletion Hypothesis, in a computational framework for sentence processing implemented in ACT-R. The assumption of slowed processing is operationalized as slow procedural memory, so that each processing action is performed slower than normal, and intermittent deficiency as extra noise in the procedural memory, so that the parsing steps are more noisy than normal. We operationalize the TDH as an absence of trace information in the parse tree. To test the predictions of the models implementing these theories, we use the data from a German sentence—picture matching study reported in Hanne, Sekerina, Vasishth, Burchert, and De Bleser. The data consist of offline and online measures. From among the models considered, the model assuming that both slowed processing and intermittent deficiency are present emerges as the best model of sentence processing difficulty in aphasia. The modeling of individual differences suggests that, if we assume that patients have both slowed processing and intermittent deficiency, they have them in differing degrees. (shrink)

While I do not accept any current analysis of theoretical terms I also reject certain criticisms of them. Specifically, I reject the criticism that the paradoxes of material implication and the counterfactual problem eliminate the explicit definition view; and I also reject the criticism that explicitly defined theoretical terms do not refer to anything which "really exists" or do not have "excess meaning." I do argue, however, that the explicit definition view confuses and conflates the concepts of criterion and meaning (...) analysis. I also defend reduction sentences against the counterfactual difficulty, but show, too, how this view is already logically committed to the network or postulational view of meaning. Finally, I show how the concept of reduction sentences confuses in several ways the concepts of criterion and meaning analysis--although not in quite the same way as explicit definitions do. (shrink)

In this paper, we describe "metaphysical reductions", in which the well-defined terms and predicates of arbitrary mathematical theories are uniquely interpreted within an axiomatic, metaphysical theory of abstract objects. Once certain (constitutive) facts about a mathematical theory T have been added to the metaphysical theory of objects, theorems of the metaphysical theory yield both an analysis of the reference of the terms and predicates of T and an analysis of the truth of the sentences of T. The well-defined terms and (...) predicates of T are analyzed as denoting abstract objects and abstract relations, respectively, in the background metaphysics, and the sentences of T have a reading on which they are true. After the technical details are sketched, the paper concludes with some observations about the approach. One important observation concerns the fact that the proper axioms of the background theory abstract objects can be reformulated in a way that makes them sound more like logical axioms. Some philosophers have argued that we should accept (something like) them as being logical. (shrink)

We present a general schema of easy normalization proofs for finite systems S like first-order arithmetic or subsystems of analysis, which have good infinitary counterparts S ∞ . We consider a new system S ∞ + with essentially the same rules as S ∞ but different derivable objects: a derivation d∈S ∞ + of a sequent Γ contains a derivation Φ∈S of Γ . Three simple conditions on Φ including a normal form theorem for S ∞ + easily imply a (...) weak normalization theorem for S . We give three examples of application of this schema. First, we take S≡PA but restrict the attention to derivations of Σ 1 0 -sentences. In this case it is possible to take S ∞ + to be essentially standard formulation of PA ∞ . Next, we illustrate extension to subsystems of analysis and consider the system BI 1 ∗ of W. Buchholz having the strength of ID 1 , again for derivations of Σ 1 0 -sentences. Finally, we return to the first-order arithmetic to illustrate changes needed to treat derivations of arbitrary formulas. (shrink)

What are the effects of word-by-word predictability on sentence processing times during the natural reading of a text? Although information complexity metrics such as surprisal and entropy reduction have been useful in addressing this question, these metrics tend to be estimated using computational language models, which require some degree of commitment to a particular theory of language processing. Taking a different approach, this study implemented a large-scale cumulative cloze task to collect word-by-word predictability data for 40 passages and (...) compute surprisal and entropy reduction values in a theory-neutral manner. A separate group of participants read the same texts while their eye movements were recorded. Results showed that increases in surprisal and entropy reduction were both associated with increases in reading times. Furthermore, these effects did not depend on the global difficulty of the text. The findings suggest that surprisal and entropy reduction independently contribute to variation in reading times, as these metrics seem to capture different aspects of lexical predictability. (shrink)

Those found liable for negligently injuring others are required to compensate them, but current practices permit most tort feasors to spread the costs of their liability burdens through the purchase of insurance. Those found guilty of criminal offences, however, are not allowed to shift the burdens of their sentences onto others. Yet the reasons for not allowing criminal offenders to shift such burdens – harm reduction, retribution, and moral education – also appear to retain some force in relation to (...) negligent tort feasors. Arguments for and against limiting the abilities of negligent tort feasors to spread such costs, thus imposing a penalty on them, are discussed. The conclusion reached is that further consideration of such a penalty is warranted. (shrink)

We confirm a conjecture, about neat embeddings of cylindric algebras, made in 1969 by J. D. Monk, and a later conjecture by Maddux about relation algebras obtained from cylindric algebras. These results in algebraic logic have the following consequence for predicate logic: for every finite cardinal α ≥ 3 there is a logically valid sentence X, in a first-order language L with equality and exactly one nonlogical binary relation symbol E, such that X contains only 3 variables (each of (...) which may occur arbitrarily many times), X has a proof containing exactly α + 1 variables, but X has no proof containing only α variables. This solves a problem posed by Tarski and Givant in 1987. (shrink)

We present a computational evaluation of three hypotheses about sources of deficit in sentence comprehension in aphasia: slowed processing, intermittent deficiency, and resource reduction. The ACT-R based Lewis and Vasishth model is used to implement these three proposals. Slowed processing is implemented as slowed execution time of parse steps; intermittent deficiency as increased random noise in activation of elements in memory; and resource reduction as reduced spreading activation. As data, we considered subject vs. object relative sentences, presented (...) in a self-paced listening modality to 56 individuals with aphasia and 46 matched controls. The participants heard the sentences and carried out a picture verification task to decide on an interpretation of the sentence. These response accuracies are used to identify the best parameters that correspond to the three hypotheses mentioned above. We show that controls have more tightly clustered parameter values than IWA; specifically, compared to controls, among IWA there are more individuals with slow parsing times, high noise, and low spreading activation. We find that individual IWA show differential amounts of deficit along the three dimensions of slowed processing, intermittent deficiency, and resource reduction, overall, there is evidence for all three sources of deficit playing a role, and IWA have a more variable range of parameter values than controls. An important implication is that it may be meaningless to talk about sources of deficit with respect to an abstract verage IWA; the focus should be on the individual's differential degrees of deficit along different dimensions, and on understanding the causes of variability in deficit between participants. (shrink)

After surveying the many practical difficulties sentencing judges must confront in determining whether the offenders who appear before them are genuinely remorseful, recent dialogical accounts of remorse-based sentence reductions are examined. These accounts depend on a morally communicative approach to legal punishment’s justification and seem to confine such communication to offenders. They contend that, in order to respect remorseful offenders, sentencing judges must reduce their sentences. Why they should do so, by how much they should do so, and whether (...) they should do so when the individuals being sentenced are recidivists, are among the questions discussed. Also examined is whether remorse should be a prominent mitigating factor in sentencing or only one among many aggravating or mitigating factors. In conclusion, it is suggested that existing sentencing practices might make more sense if we suppose judges to be looking for things other than genuine remorse in the individuals who appear before them. (shrink)

A word-by-word human sentence processing complexity metric is presented. This metric formalizes the intuition that comprehenders have more trouble on words contributing larger amounts of information about the syntactic structure of the sentence as a whole. The formalization is in terms of the conditional entropy of grammatical continuations, given the words that have been heard so far. To calculate the predictions of this metric, Wilson and Carroll's (1954) original entropy reduction idea is extended to infinite languages. This (...) is demonstrated with a mildly context-sensitive language that includes relative clauses formed on a variety of grammatical relations across the Accessibility Hierarchy of Keenan and Comrie (1977). Predictions are derived that correlate significantly with repetition accuracy results obtained in a sentence-memory experiment (Keenan & Hawkins, 1987). (shrink)

Chapter V attempts to provide the elements of a solution to the problem of how terms in theoretical sciences acquire their reference. Its proposal is that a theory of reference-acquisition for theoretical terms should acknowledge the fact that what fixes the reference of a theoretical term is typically the embedding theory as a whole, not an austere causal description like 'the item causally responsible for event E.' It is argued that there are epistemic reasons for the existence of this phenomenon, (...) and an attempt is made to show how, by appealing to these reasons, it is nonetheless possible to understand the reference-determining role of theories in such a way that occurrences of a term embedded in incompatible theoretical frameworks can often be interpreted as co-referential. ;Chapter IV is an interlude. It argues for the relevance of the theory of reference to the topic of intertheoretic reduction. It does this by attempting to demonstrate that intertheoretic reduction in the natural sciences requires intertheoretic identities involving theoretical terms, and that making sense of such identities demands a theory of reference-acquisition for theoretical terms. The chapter also argues that the problem of how mathematical terms secure their reference precludes an obvious extension of this model to examples of reduction in mathematics. It further criticizes attempts to make sense of mathematical reductions in terms of concepts of ontological reduction, and it suggests that much recent work on ontological reduction, especially the attempt to exclude all-out 'Pythagorean' reductions, is flawed through its failure to take referential semantics seriously. ;Chapter II contains exposition and criticism of both the descriptivist account of reference and Kripke's version of the 'causal' account of reference. The latter account is represented as a recursive account, with a base clause specifying how terms initially acquire their reference and a recursion clause specifying how the ability to use a term with a certain reference is transmitted to other users . It is argued that the Kripkean formulation of referential intentions at the reference-transmission stage is flawed, in part because the formulation makes his account unable to capture the dynamics of the way in which a person's use of a term may undergo reference-shifts without these shifts in reference being intended. ;The third chapter suggests an alternative account. It motivates and sketches a mixed causal-descriptivist theory speaker's reference, formulated in terms of first-order referential intentions, and then uses this theory to sketch aspects of a mixed causal-descriptivist account of term reference, formulated in terms of second-order intentions to intend the 'right' object . It is argued that such an account provides a plausible solution to a number of problems confronting Kripke's account, including that of unintended reference-shifts. ;This dissertation consists of five chapters whose unifying theme is the theory of term-reference. The first chapter offers an overview and critical comparison of two opposing approaches to the topic of reference: the semantic holism of Quine-Davidson, and the semantic atomism of those who treat reference as a relation that grounds the assignment of truth-conditions to sentences. The chapter argues that the apparent theoretical importance of referential intentions, emphasised in Saul Kripke's work on reference and argued for in detail in chapter III of the dissertation, provides strong support for semantic atomism, since such intentions are used to explain reference-assignments and, indirectly, truth-conditions. (shrink)

In this note we give an interpretation of cylindric algebras as algebras of sentences of first order logic. We show that the isomorphism types of such algebras of sentences coincide with the class of neat reducts of cylindric algebras. Also we show how this interpretation sheds light on some recent results. This is done by likening Henkin's Neat Embedding Theorem to his celebrated completeness proof.

It is assumed that a Kripke–Joyal semantics \({\mathcal{A} = \left\langle \mathbb{C},{\rm Cov}, {\it F},\Vdash \right\rangle}\) has been defined for a first-order language \({\mathcal{L}}\) . To transform \({\mathbb{C}}\) into a Heyting algebra \({\overline{\mathbb{C}}}\) on which the forcing relation is preserved, a standard construction is used to obtain a complete Heyting algebra made up of cribles of \({\mathbb{C}}\) . A pretopology \({\overline{{\rm Cov}}}\) is defined on \({\overline{\mathbb{C}}}\) using the pretopology on \({\mathbb{C}}\) . A sheaf \({\overline{{\it F}}}\) is made up of sections of (...) F that obey functoriality. A forcing relation \({\overline{\Vdash}}\) is defined and it is shown that \({\overline{\mathcal{A}} = \left\langle \overline{\mathbb{C}},\overline{\rm{Cov}},\overline{{\it F}}, \overline{\Vdash} \right\rangle }\) is a Kripke–Joyal semantics that faithfully preserves the notion of forcing of \({\mathcal{A}}\) . That is to say, an object a of \({\mathbb{C}Ob}\) forces a sentence with respect to \({\mathcal{A}}\) if and only if the maximal a-crible forces it with respect to \({\overline{\mathcal{A}}}\) . This reduces a Kripke–Joyal semantics defined over an arbitrary site to a Kripke–Joyal semantics defined over a site which is based on a complete Heyting algebra. (shrink)

This paper presents a theory of the syntactic aspects of human sentence production. An important characteristic of unprepared speech is that overt pronunciation of a sentence can be initiated before the speaker has completely worked out the meaning content he or she is going to express in that sentence. Apparently, the speaker is able to build up a syntactically coherent utterance out of a series of syntactic fragments each rendering a new part of the meaning content. This (...) incremental, left‐to‐right mode of sentence production is the central capability of the proposed Incremental Procedural Grammar (IPG). Certain other properties of spontaneous speech, as derivable from speech errors, hesitations, self‐repairs, and language pathology, are accounted for as well.The psychological plausibility thus gained by the grammar appears compatible with a satisfactory level of linguistic plausibility in that sentences receive structural descriptions which are in line with current theories of grammar. More importantly, an explanation for the existence of configurational conditions on transformations and other linguistics rules is proposed.The basic design feature of IPG which gives rise to these psychologically and linguistically desirable properties, is the “Procedures + Stack” concept. Sentences are built not by a central constructing agency which overlooks the whole process but by a team of syntactic procedures (modules) which work—in parallel—on small parts of the sentence, have only a limited overview, and whose sole communication channel is a stack.IPG covers object complement constructions, interrogatives, and word order in main and subordinate clauses. It handles unbounded dependencies, crossserial dependencies and coordination phenomena such as gapping and conjunction reduction. It is also capable of generating self‐repairs and elliptical answers to questions. IPG has been implemented as an incremental Dutch sentence generator written in LISP. (shrink)

In his late philosophy, Quine generalized the structuralist view in the philosophy of mathematics that mathematical theories are indifferent to the ontology we choose for them. According to his ‘global structuralism’, the choice of objects does not matter to any scientific theory. In the literature, this doctrine is mainly understood as an epistemological thesis claiming that the empirical evidence for a theory does not depend on the choice of its objects. The present paper proposes a new interpretation suggested by Quine’s (...) recently published Kant Lectures from 1980 according to which his global structuralism is a semantic thesis that belongs to his theory of ontological reduction. It claims that a theory can always be reformulated in such a way that its truth does not presuppose the existence of the original objects, but only of some objects that can be considered as their proxies. Quine derives this claim from the principle of the semantic primacy of sentences, which is supposed to license the ontological reductions he uses to establish his global structuralism. It is argued that these reductions do not actually work because they do not account for some hidden ontological commitments that are not detected by his criterion of ontological commitment. (shrink)

‘Epistemic structural realism’ (ESR) insists that all that we know of the world is its structure, and that the ‘nature’ of the underlying elements remains hidden. With structure represented via Ramsey sentences, the question arises as to how ‘hidden natures’ might also be represented. If the Ramsey sentence describes a class of realisers for the relevant theory, one way of answering this question is through the notion of multiple realisability. We explore this answer in the context of the work (...) of Carnap, Hintikka and Lewis. Both Carnap and Hintikka offer clear structuralist perspectives which, crucially, accommodate the openness inherent in theory change. Unfortunately there is little purchase for a viable form of realism in either case. Lewis’s approach, on the other hand, offers more scope for realism but, as we shall see, concerns arise as to whether a relevant form of structuralism can be maintained. In particular his thesis of Ramseyan humility undermines certain conceptions of scientific laws that the structural realist might naturally cleave to. Our overall conclusion is that the representational device of Ramsey sentence plus multiple realisability can accommodate either the structuralist or realist aspects of ESR but has difficulties capturing both. (shrink)

One of Etchemendy's arguments against the Tarskian and model‐theoretic notion of logical truth is based on a reduction principle according to which a universally quantified sentence is true if, and only if, all of its instances are logically true. The reduction of logical truth to mere truth reveals that the concept of validity at play in Tarski and in model‐theory relies upon extra‐logical assumptions. A similar reduction had already been put forward by Prawitz, although not with (...) focus on extra‐logical assumptions. Prawitz's reduction concerns rather the possibility of understanding the Tarskian and model‐theoretic approach as implying any epistemic modality. We take into account a possible strategy that an advocate of Tarski and model‐theory may use against Etchemendy's objection, and argue that this strategy fails with respect to Prawitz's criticism. This permits us to shed light upon a difference between Prawitz's and Etchemendy's standpoints: while Etchemendy's reduction shows that the Tarskian and model‐theoretic notion of logical truth cannot be understood as an adequate formal counterpart of truth‐preservation solely by virtue of logical form, Prawitz's reduction insists on the fact that truth‐preservation solely by virtue of logical form is insufficient for epistemic modality to obtain. (shrink)

Some revisionary ontologies are highly parsimonious: they posit far fewer entities than what we quantify over in ordinary discourse. The most radical examples are minimal ontologies, on which physical simples are the only things that exist. Highly parsimonious ontologies, and especially minimal ones, face the challenge of either accounting for the truth of our ordinary quantificational discourse, or paraphrasing such discourse away. Common strategies for addressing this challenge include classical reduction, paraphrase nihilism, and a distinction between ontological and existence (...) commitments. I argue, however, that these strategies are either implausible or fail to provide truth conditions consistent with minimal or parsimonious ontologies. I then discuss, defend, and suggest ways to strengthen an alternative framework for reduction, on which the sentences of reducing theories ground those of reducible theories. Relative to the other options for defending minimal ontology, a strengthened grounding-reductive approach can provide more defensible truth conditions for minimal ontology, better preserve scientific realist intuitions, set a more attainable standard for reduction, and allow our existence commitments to be more responsive to empirical evidence and scientific expertise. As a result, I argue that minimal ontology becomes more defensible—though not certain—on a grounding-reductive framework. But even if minimal ontology were wrong, the grounding-reductive framework makes other parsimonious but non-minimal ontologies more plausible. (shrink)

For persons serving life-without-parole (LWOP) sentences in California, a commutation usually offers them the sole glimpse of hope for release from prison. While governors were reluctant to consider any sentence reductions from 1975 to 2016, commutations—including those for LWOP—have become a more frequent occurrence since. Yet, little is still known about how governors have justified reducing a sentence that initially offered no prospect of release from prison. Given the apparent change in practice, themes emerging from the content of (...) 177 gubernatorial commutation summaries granted to persons serving LWOP sentences between 2017 and 2021 are analyzed in this paper. Through open coding, rehabilitative indicators (programming and institutional conduct) emerged as necessary preconditions for a commutation, while retributive factors (a reassessment of the nature of the crime and the prerogative to adjust excessive prison sentences or to correct sentencing errors) complemented sentence reductions. The findings expose the ethical issues that arise from an LWOP sentence and the subsequent commutation. More specifically, they shed light on the commitment offenses underlying commuted LWOP sentences and raise questions regarding the penal objectives that are supposed to be accomplished with permanent imprisonment. (shrink)

In this note we give an interpretation of cylindric algebras as algebras of sentences of first order logic. We show that the isomorphism types of such algebras of sentences coincide with the class of neat reducts of cylindric algebras. Also we show how this interpretation sheds light on some recent results. This is done by likening Henkin's Neat Embedding Theorem to his celebrated completeness proof.

The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated in this paper (...) have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims atproviding an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic hasfewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic PPC3, with two kinds of falsity and two negations. It introduces the notion of -space for a sentence A as the basis of logical model theory, and the notion of P A /, functioning as a `private' subuniverse for A/A. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. PPC3 and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of PPC3 as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: 1a for the conjoined presuppositions of a, ã for the complement of a within 1a, and â for the complement of 1a within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned. (shrink)

The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical (Boolean) foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated in this (...) paper have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims at providing an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic has fewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic ${\rm PPC}_{3}$ , with two kinds of falsity and two negations. It introduces the notion of Σ-space for a sentence A (or / A /, the set of situations in which A is true) as the basis of logical model theory, and the notion of / ${\bf P}^{A}$ / (the Σ-space of the presuppositions of A), functioning as a 'private' subuniverse for / A /. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. ${\rm PPC}_{3}$ and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of ${\rm PPC}_{3}$ as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: $1_{a}$ for the conjoined presuppositions of a, ã for the complement of a within $1_{a}$ , and â for the complement of $1_{a}$ within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned. (shrink)

Recent work has shown that linguistic and visual contexts jointly modulate linguistic expectancy and, thus, the processing effort for a expected critical word. According to these findings, uncertainty about the upcoming referent in a visually-situated sentence can be reduced by exploiting the selectional restrictions of a preceding word, which then reduces processing effort on the critical word. Interestingly, however, no such modulation was observed in these studies on the expectation-generating word itself. The goal of the current study is to (...) investigate whether the reduction of uncertainty simply does not modulate processing effort-or whether the particular subject-verb-object sentence structure used in these studies accounts for the observed pattern. To test these questions, the current design reverses the functional roles of nouns and verbs by using sentence constructions in which the noun reduces uncertainty about upcoming verbs, and the verb provides the disambiguating and reference-resolving piece of information. Experiment 1 and Experiment 2 both replicate the effect found in previous work, albeit on the verb in the current study. Results on the noun, where uncertainty is reduced and expectations are generated in the current design, were mixed and were most likely influenced by design decisions specific to each experiment. These results show that processing of the reference-resolving word—whether it be a noun or a verb—reliably benefits from the prior linguistic and visual information that lead to the generation of concrete expectations. (shrink)

The original version of this article unfortunately contained a mistake. The fourth sentence of third paragraph under section Do Harm Reduction Programs Condone Harm? Should be “One of us ” instead of “One of us ”. The original article has been corrected.