Models and Logical Consequence

This paper deals with the adequacy of the model-theoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have a crucial role in determining logical consequence. Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a model-theoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro's blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formal-structural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed.     

Pragmatism and revisionism: James's conception of truth

Abstract

The paper argues that James's conception of truth is non‐revisionist, that is, it sanctions common use of the notion of truth, but criticizes foundation‐alist philosophical accounts of that notion. This interpretation conflicts with traditional interpretations of James such as Russell's and Moore's, and contemporary interpretations such as Dummett's, all of which are revisionist. To the extent that objections raised against James's pragmatism depend on such revisionist reading, this paper constitutes a defence of James. The paper argues, further, that non‐revisionism distinguishes James from logical positivism and contemporary verificationism, and that James seeks to defend rather than renounce metaphysics. On this issue the paper disagrees with Rorty, who ascribes to James an extreme anti‐metaphysical stance.     

Friendship and epistemic norms

Simon Keller and Sarah Stroud have both argued that the demands of being a good friend can conflict with the demands of standard epistemic norms. Intuitively, good friends will tend to seek favorable interpretations of their friends’ behaviors, interpretations that they would not apply to strangers; as such they seem prone to form unjustified beliefs. I argue that there is no such clash of norms. In particular, I argue that friendship does not require us to form beliefs about our friends in the biased fashion suggested by Stroud and Keller. I further argue that while some slight bias in belief-formation might be permitted by friendship, any such bias would fall within the bounds of epistemic propriety.     

Quantum Logic in Intuitionistic Perspective

In their seminal paper Birkhoff and von Neumann revealed the following dilemma:[ ] whereas for logicians the orthocomplementation properties of negation were the ones least able to withstand a critical analysis, the study of mechanics points to the distributive identities as the weakest link in the algebra of logic.In this paper we eliminate this dilemma, providing a way for maintaining both. Via the introduction of the "missing" disjunctions in the lattice of properties of a physical system while inheriting the meet as a conjunction we obtain a complete Heyting algebra of propositions on physical properties. In particular there is a bijective correspondence between property lattices and propositional lattices equipped with a so called operational resolution, an operation that exposes the properties on the level of the propositions. If the property lattice goes equipped with an orthocomplementation, then this bijective correspondence can be refined to one with propositional lattices equipped with an operational complementation, as such establishing the claim made above. Formally one rediscovers via physical and logical considerations as such respectively a specification and a refinement of the purely mathematical result by Bruns and Lakser (1970) on injective hulls of meet-semilattices. From our representation we can derive a truly intuitionistic functional implication on property lattices, as such confronting claims made in previous writings on the matter. We also make a detailed analysis of disjunctivity vs. distributivity and finitary vs. infinitary conjunctivity, we briefly review the Bruns-Lakser construction and indicate some questions which are left open.     

Ist die linguistische Theorie des logischen Apriori obsolet?

The linguistic theory of the logical A Priori: is it obsolete In holistic interpretations, the logical truths are considered as continuous with empirical science: they are revisable, a posteriori, though very near to the centre of our web of belief. In this paper, we consider the merits and demerits of this approach, and we propose that it is necessary to revaluate holistic philosophies of logic. Some arguments are put forward which point in favour of the logical empiricists’ theory of logical truth. We argue (following Hartry Field) that the concept of “correlation between logical facts and logical beliefs” (which is at the heart of the holistic theory) is inconsistent. Finally, we concentrate on the principle of contradiction and argue (following Manley Thompson) that this principle is fundamental for meaning, truth, and thinking. This thesis is derived from considerations on the nature of intentionality. This revised version was published online in August 2006 with corrections to the Cover Date.     

Remarks on Independence Proofs and Indirect Reference

In the last two decades, there has been increasing interest in a re-evaluation of Frege's stance towards consistency- and independence proofs. Papers by several authors deal with Frege's views on these topics. In this note, I want to discuss one particular problem, which seems to be a main reason for Frege's reluctant attitude towards his own proposed method of proving the independence of axioms, namely his view that thoughts, that is, intensional entities are the objects of metatheoretical investigations. This stands in contrast to more straightforward interpretations, which claim that Frege's hesitancy is mainly due to worries concerning the logical constants or what counts as a logical inference.     

Merging Frameworks for Interaction

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall, No Miracles, and Bisimulation Invariance. We then focus on new issues of completeness. One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL.     

A Presuppositional Account of Causal and Temporal Interpretations of <Emphasis Type="Italic">and</Emphasis>

Despite extensive studies, the issue concerning the pragmatic mechanisms leading to causal and temporal interpretations of and remains problematic and has not yet been addressed in its totality within one framework. This paper proposes a solution based on presuppositional mechanisms built into a comprehensive analysis that accounts for both the various interpretations of and-sentences as well as those of other types of sentences involving similar interpretations. This account is a specific part of a unified solution to the knotty problem of different manners of conveying causal and temporal relations both with connectives and also with juxtaposed sentences. It is formulated within the Relevance Nomological Model which provides a general framework for the analysis of causal constructions such as the connective because and why-questions.     

Concessive knowledge-attributions: fallibilism and gradualism

Any knowledge-fallibilist needs to solve the conceptual problem posed by concessive knowledge-attributions (such as ‘I know that p, but possibly not-p’). These seem to challenge the coherence of knowledge-fallibilism. This paper defuses that challenge via a gradualist refinement of what Fantl and McGrath (2009) call weak epistemic fallibilism.     

Employing emotions to drive plot generation in a computer-based storyteller

Emotions are an integral part of the creative process; however, it is hard to find computer models of creativity where emotions play a fundamental role. This paper describes a computer model for plot generation based on emotions and tensions between characters. In particular, the document illustrates how emotions are employed to progress a story in a coherent way and generate novel situations, and how the dramatic tension of the story in progress can be employed to evaluate its interestingness. The model is implemented in a computer program named MEXICA [Pérez y Pérez, R., & Sharples, M. (2001). MEXICA: a computer model of a cognitive account of creative writing. Journal of Experimental and Theoretical Artificial Intelligence, 13(2), 119–139]; this work concentrates on the role of emotions in plot generation. The main claim is that a story can be represented as a cluster or group of emotional links and tensions between characters that progresses over story-time; story-actions work as operators that modify such clusters. I present results showing how story generation is affected by various model parameters. This approach means the program is flexible, as it avoids using predefined story-structures or characters’ goals to drive story generation. Furthermore, evaluation of computer generated stories showed that MEXICA’s stories were most often selected as the best story. This suggests that the story-generation mechanisms within MEXICA are sufficiently rich to generate interesting and novel stories.     

Modality and Children’s Scope Understanding

This study intends to shed light on the inconclusive argument pertaining to children’s acquisition of logical form (LF) operation. Specifically, we examined children’s interpretations of sentences with the ambiguous modal verb yinggai ‘should,’ like ‘Xiaohua yinggai shangchuang shuijiao le’, whose meanings depend on the landing sites of yinggai at LF (root interpretation: Xiaohua is obligated to go to bed now. epistemic interpretation: It is the case that Xiaohua has gone to bed.). The results of truth value judgment task from 15 children (range: 4;8–6;2, mean: 5;4) and 37 adults indicate that both groups tend to interpret the ambiguous yinggai as epistemic readings and that children’s interpretation is adult-like. Thus, this study supports (Syrett and Lidz’s in Lang Acquis 16:67–81, 2009) view that 5-year-olds have adult-like LF development and their difficulties in interpreting covert movements may be reduced to extra-grammatical factors.     

What logical pluralism cannot be

Logical Pluralists maintain that there is more than one genuine/true logical consequence relation. This paper seeks to understand what the position could amount to and some of the challenges faced by its formulation and defence. I consider in detail Beall and Restall’s Logical Pluralism—which seeks to accommodate radically different logics by stressing the way that they each fit a general form, the Generalised Tarski Thesis (GTT)—arguing against the claim that different instances of GTT are admissible precisifications of logical consequence. I then consider what it is to endorse a logic within a pluralist framework and criticise the options Beall and Restall entertain. A case study involving many-valued logics is examined. I next turn to issues of the applications of different logics and questions of which logic a pluralist should use in particular contexts. A dilemma regarding the applicability of admissible logics is tackled and it is argued that application is a red herring in relation to both understanding and defending a plausible form of logical pluralism. In the final section, I consider other ways to be and not to be a logical pluralist by examining analogous positions in debates over religious pluralism: this, I maintain, illustrates further limitations and challenges for a very general logical pluralism. Certain less wide-ranging pluralist positions are more plausible in both cases, I suggest, but assessment of those positions needs to be undertaken on a case-by-case basis.     

Why logical pluralism?

This paper scrutinizes the debate over logical pluralism. I hope to make this debate more tractable by addressing the question of motivating data: what would count as strong evidence in favor of logical pluralism? Any research program should be able to answer this question, but when faced with this task, many logical pluralists fall back on brute intuitions. This sets logical pluralism on a weak foundation and makes it seem as if nothing pressing is at stake in the debate. The present paper aims to improve this situation by looking at a promising case study and drawing general lessons about the kind of evidence that would support logical pluralism. I argue that the best motivation for logical pluralism will ultimately be rooted in certain kinds of performative data.

     

Logics for Epistemic Programs

We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general, the semantics of an epistemic program is what we call aprogram model. This is a Kripke model of ‘actions’,representing the agents' uncertainty about the current action in a similar way that Kripke models of ‘states’ are commonly used in epistemic logic to represent the agents' uncertainty about the current state of the system. Program models induce changes affecting agents' information, which we represent as changes of the state model, called epistemic updates. Formally, an update consists of two operations: the first is called the update map, and it takes every state model to another state model, called the updated model; the second gives, for each input state model, a transition relation between the states of that model and the states of the updated model. Each variety of epistemic actions, such as public announcements or completely private announcements to groups, gives what we call an action signature, and then each family of action signatures gives a logical language. The construction of these languages is the main topic of this paper. We also mention the systems that capture the valid sentences of our logics. But we defer to a separate paper the completeness proof. The basic operation used in the semantics is called the update product. A version of this was introduced in Baltag et al. (1998), and the presentation here improves on the earlier one. The update product is used to obtain from any program model the corresponding epistemic update, thus allowing us to compute changes of information or belief. This point is of interest independently of our logical languages. We illustrate the update product and our logical languages with many examples throughout the paper.     

Subjective well-being,social interpretation,and relationship thriving

Social interactions are open to a range of interpretations. We examine the associations among subjective well-being, social interpretations, and social thriving. In Study 1 (N = 276) positive affect (PA) was associated with positive interpretations of neutral faces. In Studies 2 and 3 (Ns = 295, 298) PA and life satisfaction were associated with positive interpretations of ambiguous and positive, but not negative, social interaction vignettes. In Study 4 (N = 501) there were indirect relationships of PA and life satisfaction on social thriving through interpretations. Subjective well-being’s association with social interpretations provides a critical base of support for conclusions from previous methodologically limited mood and social interpretation studies. This work also provides initial evidence for a role of social interpretation tendencies in social thriving.     

A catalog of Boolean concepts

Boolean concepts are concepts whose membership is determined by a Boolean function, such as that expressed by a formula of propositional logic. Certain Boolean concepts have been much studied in the psychological literature, in particular with regard to their ease of learning. But research attention has been somewhat uneven, with a great deal of attention paid to certain concepts and little to others, in part because of the unavailability of a comprehensive catalog. This paper gives a complete classification of Boolean concepts up to congruence (isomorphism of logical form). Tables give complete details of all concepts determined by up to four Boolean variables. For each concept type, the tables give a canonic logical expression, an approximately minimal logical expression, the Boolean complexity (length of the minimal expression), the number of distinct Boolean concepts of that type, and a pictorial depiction of the concept as a set of vertices in Boolean D-space. Some psychological properties of Boolean concepts are also discussed.     

The property of rationality: a guide to what rationality requires?

Can we employ the property of rationality in establishing what rationality requires? According to a central and formal thesis of John Broome’s work on rational requirements, the answer is ‘no’—at least if we expect a precise answer. In particular, Broome argues that (i) the property of full rationality (i.e. whether or not you are fully rational) is independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. That is, (ii) by replacing a wide-scope requirement with a corresponding narrow-scope requirement (or vice versa), we do not alter the situations in which a person is fully rational. As a consequence, (iii) the property of full rationality is unable to guide us in determining whether a rational requirement has a wide or a narrow logical scope. We cannot resolve the wide/narrow scope debate by appealing to a theory of fully rational attitudes. This paper argues that (i), (ii) and (iii) are incorrect. Replacing a wide- with a corresponding narrow-scope requirement (or vice versa) can alter the set of circumstances in which a person is fully rational. The property of full rationality is therefore not independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. As a consequence, the property of full rationality can guide us in determining what rationality requires—even in cases where we expect a precise answer.     

Logically Incorrect Arguments

What do we learn when we find out that an argument is logically incorrect? If logically incorrect means the same as not logically correct, which in turn means not having a valid logical form, it seems that we do not learn anything too useful—an argument which is logically incorrect can still be conclusive. Thus, it seems that it makes sense to fix a stronger interpretation of the term under which a logically incorrect argument is guaranteed to be wrong (and is such for purely logical reasons). In this paper, we show that pinpointing this stronger sense is much trickier than one would expect; but eventually we reach an explication of the notion of (strong) logical incorrectness which we find non-trivial and viable.     

Instrumentalist Interpretations of Hindu Environmental Ethics

Many environmental ethicists believe that any adequate environmental ethic should attribute ‘direct moral standing’ (often glossed in terms of intrinsic value) to plants, animals, and the rest of nature. But certain interpretations of Hindu environmental ethics apparently attribute only instrumental value to nature. This places them in direct conflict with the purported adequacy condition on an environmental ethic. So, is such a Hindu ethical view really inadequate? In his recent book Hinduism and Environmental Ethics, Christopher Framarin claims that it is because Hindu instrumentalism about nature is either viciously circular or unacceptably arbitrary. I argue, however, that Framarin’s claim founders in virtue of his misconstruing the logical structure of instrumental value.