Reconsidering the Logic of Emotion

It is customarily assumed that propositional attitudes present two independent components: a propositional component and a psychological component, in the form of an attitudes. These two components are caught by means of two different methods: propositions by some model theoretic theory, psychological attitudes by making appeal to their functional or psychological role. Some authors have seek a convergence by individuating propositions by some Functional role semantics. In this paper I show that when it comes to emotional attitudes with propositional content, either the independence of proposition and attitude collapses or functional role semantics brings to unstable individuation conditions for propositions. Some consequences of these two outcomes are considered.     

Measurement Theoretic Semantics And The Semantics Of Necessity

In the first two sections I present and motivate a formal semantics program that is modeled after the application of numbers in measurement (e.g., of length). Then, in the main part of the paper, I use the suggested framework to give an account of the semantics of necessity and possibility: (i) I show thatthe measurement theoretic framework is consistent with a robust (non-Quinean) view of modal logic, (ii) I give an account of the semantics of the modal notions within this framework, and (iii) I defend the suggested account against various objections.     

Anything is possible

This paper criticises necessitarianism, the thesis that there is at least one necessary truth; and defends possibilism, the thesis that all propositions are contingent, or that anything is possible. The second section maintains that no good conventionalist account of necessity is available, while the third section criticises model theoretic necessitarianism. The fourth section sketches some recent technical work on nonclassical logic, with the aim of weakening necessitarian intuitions and strengthening possibilist intuitions. The fifth section considers several a prioristic attempts at demonstrating that there is at least one necessary proposition and finds them inadequate. The final section emphasises the epistemic aspect of possibilism.     

A semantical investigation on Brouwer-Zadeh logic

Conclusion In the standard approach to quantum mechanics, closed subspaces of a Hilbert space represent propositions. In the operational approach, closed subspaces are replaced by effects that represent a mathematical counterpart for properties which can be measured in a physical system. Effects are a proper generalization of closed subspaces. Effects determine a Brouwer-Zadeh poset which is not a lattice. However, such a poset can be embedded in a complete Brouwer-Zadeh lattice. From an intuitive point of view, one can say that these structures represent a natural logical abstraction from the structure of propositions of a quantum system. The logic that arises in this way is Brouwer-Zadeh logic. This paper shows that such a logic can be characterized by means of an algebraic and a Kripkean semantics. Finally, a strong completeness theorem for BZL is proved.     

“Four-Valued” Semantics for the Relevant Logic R

This paper sets out two semantics for the relevant logic R based on Dunn's four-valued semantics for first-degree entailments. Unlike Routley's semantics for weak relevant logics, they do not use two ternary accessibility relations. Unlike Restall's semantics, they capture all of R. But there is a catch. Both of the present semantics are neighbourhood semantics, that is, they include sets of propositions in the specification of their frames.     

Husserl on Meaning,Grammar, and the Structure of Content

Husserl’s Logical Grammar is intended to explain how complex expressions can be constructed out of simple ones so that their meaning turns out to be determined by the meanings of their constituent parts and the way they are put together. Meanings are thus understood as structured contents and classified into formal categories to the effect that the logical properties of expressions reflect their grammatical properties. As long as linguistic meaning reduces to the intentional content of pre-linguistic representations, however, it is not trivial to account for how semantics relates to syntax in this context. In this paper, I analyze Husserl’s Logical Grammar as a system of recursive rules operating on representations and suggest that the syntactic form of representations (both mental and linguistic) contributes to their semantics because it carries information about semantic role. I further discuss Husserl’s syntactic account of the unity of propositions and argue that, on this  account, logical form supervenes on syntactic form. In the last section I draw some implications for the phenomenology of thought and conjecture that the structural features it displays are likely to convey the syntactic structures of an underlying language-like representational system.     

Uncertainty and Persistence: a Bayesian Update Semantics for Probabilistic Expressions

This paper presents a general-purpose update semantics for expressions of subjective uncertainty in natural language. First, a set of desiderata are established for how expressions of subjective uncertainty should behave in dynamic, update-based semantic systems; then extant implementations of expressions of subjective uncertainty in such models are evaluated and found wanting; finally, a new update semantics is proposed. The desiderata at the heart of this paper center around the contention that expressions of subjective uncertainty express beliefs which are not persistent (i.e. beliefs that won’t necessarily survive the addition of new information that is compatible with all previous information), whereas propositions express beliefs that are persistent. I argue that if we make the move of treating updates in a dynamic semantics as Bayesian updates, i.e. as conditionalization, then expressions of subjective uncertainty will behave the way we want them to without altering the way propositions behave.     

Let Us Investigate! Dynamic Conjecture-Making as the Formal Logic of Abduction

We present a dynamic approach to Peirce’s original construal of abductive logic as a logic of conjecture making, and provide a new decidable, contraction-free and cut-free proof system for the dynamic logic of abductive inferences with neighborhood semantics. Our formulation of the dynamic logic of abduction follows the philosophical and scientific track that led Peirce to his late, post-1903 characterization of abductive conclusions as investigands, namely invitations to investigate propositions conjectured at the level of pre-beliefs.     

The Application of Constraint Semantics to the Language of Subjective Uncertainty

This paper develops a compositional, type-driven constraint semantic theory for a fragment of the language of subjective uncertainty. In the particular application explored here, the interpretation function of constraint semantics yields not propositions but constraints on credal states as the semantic values of declarative sentences. Constraints are richer than propositions in that constraints can straightforwardly represent assessments of the probability that the world is one way rather than another. The richness of constraints helps us model communicative acts in essentially the same way that we model agents’ credences. Moreover, supplementing familiar truth-conditional theories of epistemic modals with constraint semantics helps capture contrasts between strong necessity and possibility modals, on the one hand, and weak necessity modals, on the other.     

状态相似性与流量限制模型

在可能世界语义中,如果根据是否含有模态算子而将一个点上为真的公式分为两类,那么可以认为不含模态算子的公式描述的是当前点的信息,其它公式描述的是其它点的信息,以及当前点与其它点的关系。通过对不同点上命题真值指派的比较,我们可以在可能世界语义模型上定义出一种状态相似性。本文构造了三类刻画状态相似性的模型,并给出了分别刻画其中两类模型的完全的系统。本文最后讨论这些模型在时态逻辑和信念逻辑中的应用。     

A Formal Reconstruction of Buridan's Modal Syllogism

In this paper, we provide a historical exposition of John Buridan's theory of divided modal propositions. We then develop a semantic interpretation of Buridan's theory which pays particular attention to Buridan's ampliation of modal terms. We show that these semantics correctly capture his syllogistic reasoning.     

Buridan's Consequentia: Consequence and Inference Within a Token-Based Semantics

I examine the theory of consequentia of the medieval logician, John Buridan. Buridan advocates a strict commitment to what we now call proposition-tokens as the bearers of truth-value. The analysis of Buridan's theory shows that, within a token-based semantics, amendments to the usual notions of inference and consequence are made necessary, since pragmatic elements disrupt the semantic behaviour of propositions. In my reconstruction of Buridan's theory, I use some of the apparatus of modern two-dimensional semantics, such as two-dimensional matrices and the distinction between the context of formation and the context of evaluation of utterances.     

Why Propositions Cannot be Sets of Truth-supporting Circumstances

No semantic theory satisfying certain natural constraints can identify the semantic contents of sentences (the propositions they express), with sets of circumstances in which the sentences are true–no matter how fine-grained the circumstances are taken to be. An objection to the proof is shown to fail by virtue of conflating model-theoretic consequence between sentences with truth-conditional consequence between the semantic contents of sentences. The error underlines the impotence of distinguishing semantics, in the sense of a truth-based theory of logical consequence, and semantics, in the sense of a theory of meaning.     

The Problem with Token-reflexivity

This essay presents an argument against the token-reflexive approach to the semantics for indexical languages. After some preliminary remarks in section one, sections two and three explain why some traditional arguments against token-reflexivity are ultimately ineffective. Section four puts forth a more persuasive argument, to the effect that token-reflexive views overgenerate with respect to results of analyticity. However, as section five explains, defenders of the alternative, type-oriented view have all too often wasted the advantage offered by their approach: the unmotivated, independent restriction of semantic evaluation to so-called ‘proper’ indexes is responsible for undesirable conclusions, similar to those to which token- reflexive theorists are committed.     

What Tipper is Ready for: A Semantics for Incomplete Predicates

This paper presents a precise semantics for incomplete predicates such as “ready”. Incomplete predicates have distinctive logical properties that a semantic theory needs to accommodate. For instance, “Tipper is ready” logically implies “Tipper is ready for something”, but “Tipper is ready for something” does not imply “Tipper is ready”. It is shown that several approaches to the semantics of incomplete predicates fail to accommodate these logical properties. The account offered here defines contexts as structures containing an element called a proposition set, which contains atomic propositions and negations of atomic propositions. The condition under which “Tipper is ready” is true in a context is defined in terms of the contents of the proposition set for the context. On this account, the content of the context pertinent to a conversation must be determined not by what speakers have in mind but by relations of objective relevance.     

The Normal Distribution Derived from Qualitative Conditions

The normal distribution is characterized in a measurement theoretic framework. The qualitative conditions guarantee that representations can be regarded as random variables. Additional axioms, also qualitative in the measurement sense, yield the normal. One characterization draws on a limit theorem. The main result derives the normal distribution from conjoint measurement axioms. This approach consists of formulating properties of a linear model as a component structure with error as one component. The normal distribution of errors is shown to be a consequence of the measurement theoretic assumptions. The possible impact of these results on statistical models is discussed. Copyright 2001 Academic Press.     

What Incompleteness Arguments are and What They are Not

Cappelen and Lepore (2005) maintain that Incompleteness Arguments for context sensitivity are fallacious. In their view, Incompleteness Arguments are non sequitur fallacies whose conclusions are not logically related to premises. They affirm that the conclusions of Incompleteness Arguments are metaphysical claims about the existence of entities that might be constituents of propositions, while their premises concern psychological data about speakers' dispositions to truth evaluate sentences in contexts of utterance. Cappelen and Lepore reject Incompleteness Arguments because psychological data have no bearing on metaphysical issues. I do not dispute Cappelen and Lepore's claim that psychological data have no relevance to metaphysics. Nonetheless, I argue that Cappelen and Lepore's criticism is vitiated by a misunderstanding of the nature of Incompleteness Arguments that makes them overlook the link between semantics and linguistic competence. I try to shed light on the real nature of Incompleteness Arguments by pointing at the failure of Cappelen and Lepore's criticism. My aim is not to defend Semantic Contextualism, but to bring to attention the link between semantics and linguistic competence that should never be overlooked in debates in the field of semantics.     

Truth,Partial Logic and Infinitary Proof Systems

In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an \(\omega \)-rule.     

A Way to Interpret Łukasiewicz Logic and Basic Logic

Fuzzy logics are in most cases based on an ad-hoc decision about the interpretation of the conjunction. If they are useful or not can typically be found out only by testing them with example data. Why we should use a specific fuzzy logic can in general not be made plausible. Since the difficulties arise from the use of additional, unmotivated structure with which the set of truth values is endowed, the only way to base fuzzy logics on firm ground is the development of alternative semantics to all of whose components we can associate a meaning. In this paper, we present one possible approach to justify ex post Łukasiewicz Logic as well as Basic Logic. The notion of ambiguity is central. Our framework consists of a Boolean or a Heyting algebra, respectively, endowed with an equivalence relation expressing ambiguity. The quotient set bears naturally the structure of an MV- or a BL-algebra, respectively, and thus can be used to interpret propositions of the mentioned logics.