Manifestability and Semantic Realism

Abstract: This paper provides a critical discussion of Alexander Miller's recent attack on antirealist arguments against semantic realism that are based on manifestability requirements. Miller attempts to defend semantic realism against Wright-Hale arguments from manifestability. He does so in reliance on a McDowell type assertion-truth platitude. This paper argues in both general terms and in relation to the details of Miller's argument, that attempts to defend semantic realism while accepting a Dummettian-Wittgensteinian framework on theories of meaning, are misconceived and likely to fail, as I believe is true in Miller's case. Semantic realism is best defended within a context of metaphysical realism, and naturalistic-causal theories of meaning and explanation.     

Dual Equivalent Two-valued Under-determined and Over-determined Interpretations for Łukasiewicz’s 3-valued Logic Ł3

?ukasiewicz three-valued logic ?3 is often understood as the set of all 3-valued valid formulas according to ?ukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of ?3: “well-determined” ?3a and “truth-preserving” ?3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for ?3, ?3a and ?3b. The logic ?3 is axiomatized as an extension of Routley and Meyer’s basic positive logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” ?ukasiewicz logics are paraconsistent.     

论牟宗三哲学中的易学研究

牟宗三的易学研究为的是从易学中发见与解析中国哲学、中国思想,旨在抉发中国的玄学与道德哲学,而不是作一种历史的研究。他从哲学上为《周易》的解释提供了一个逻辑符号论的模型,为中国古典思想的现代诠释作出了首开先河的有益尝试;他对易学的“实在论的价值论”或“超越的内在”的价值论的诠释,与康德、维特根斯坦关于道德世界的“超越的外在论”不同;他对易之道德世界的分析与解释也是极其形式化的逻辑的。在这些分析与解释中,《周易》的“逻辑世界”或“符号世界”变成了语义的价值世界,或者说,作为“数理物理”世界的《周易》变成了价值论的道德世界。无论是在叙述方式,或内容的阐释与解析上,牟氏的这项研究都是十分新颖的,为国内所未有。但是,牟氏的易学研究只是他学思的开端起步,相对于他的逻辑研究来说,易学研究构成了他的哲学思想发展进路的前逻辑起点,而非逻辑起点,具有形式的象征意义。     

Order Algebras as Models of Linear Logic

The starting point of the present study is the interpretation of intuitionistic linear logic in Petri nets proposed by U. Engberg and G. Winskel. We show that several categories of order algebras provide equivalent interpretations of this logic, and identify the category of the so called strongly coherent quantales arising in these interpretations. The equivalence of the interpretations is intimately related to the categorical facts that the aforementioned categories are connected with each other via adjunctions, and the compositions of the connecting functors with co-domain the category of strongly coherent quantales are dense. In particular, each quantale canonically induces a Petri net, and this association gives rise to an adjunction between the category of quantales and a category whose objects are all Petri nets.     

Interpretations of intuitionist logic in non-normal modal logics

Historically, it was the interpretations of intuitionist logic in the modal logic S4 that inspired the standard Kripke semantics for intuitionist logic. The inspiration of this paper is the interpretation of intuitionist logic in the non-normal modal logic S3: an S3 model structure can be 'looked at' as an intuitionist model structure and the semantics for S3 can be 'cashed in' to obtain a non-normal semantics for intuitionist propositional logic. This non-normal semantics is then extended to intuitionist quantificational logic.     

Speakable in quantum mechanics

At the 1927 Como conference Bohr spoke the famous words “It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.” However, if the Copenhagen interpretation really adheres to this motto, why then is there this nagging feeling of conflict when comparing it with realist interpretations? Surely what one can say about nature should in a certain sense be interpretation independent. In this paper I take Bohr’s motto seriously and develop a quantum logic that avoids assuming any form of realism as much as possible. To illustrate the non-triviality of this motto, a similar result is first derived for classical mechanics. It turns out that the logic for classical mechanics is a special case of the quantum logic thus derived. Some hints are provided as to how these logics are to be used in practical situations and finally, I discuss how some realist interpretations relate to these logics.     

The Disenchantment of Nonsense: Understanding Wittgenstein's Tractatus

This paper aims to argue against the resolute reading, and offer a correct way of reading Wittgenstein's Tractatus. According to the resolute reading, nonsense can neither say nor show anything. The Tractatus does not advance any theory of meaning, nor does it adopt the notion of using signs in contravention of logical syntax. Its sentences, except a few constituting the frame, are all nonsensical. Its aim is merely to liberate nonsense utterers from nonsense. I argue that these points are either not distinctive from standard interpretations or incorrect. Instead, the Tractarian elucidations help to shed light on the nature of language and logic, and introduce the correct method in philosophy. Philosophy deals with philosophical utterances and Tractarian elucidations by pointing out that they are nonsensical. By doing this, one is helped to see that what they appear to be saying is shown by significant propositions saying something else.     

A Defense of Second-Order Logic

Second-order logic has a number of attractive features, in particular the strong expressive resources it offers, and the possibility of articulating categorical mathematical theories (such as arithmetic and analysis). But it also has its costs. Five major charges have been launched against second-order logic: (1) It is not axiomatizable; as opposed to first-order logic, it is inherently incomplete. (2) It also has several semantics, and there is no criterion to choose between them (Putnam, J Symbol Logic 45:464–482, 1980). Therefore, it is not clear how this logic should be interpreted. (3) Second-order logic also has strong ontological commitments: (a) it is ontologically committed to classes (Resnik, J Phil 85:75–87, 1988), and (b) according to Quine (Philosophy of logic, Prentice-Hall: Englewood Cliffs, 1970), it is nothing more than “set theory in sheep’s clothing”. (4) It is also not better than its first-order counterpart, in the following sense: if first-order logic does not characterize adequately mathematical systems, given the existence of non-isomorphic first-order interpretations, second-order logic does not characterize them either, given the existence of different interpretations of second-order theories (Melia, Analysis 55:127–134, 1995). (5) Finally, as opposed to what is claimed by defenders of second-order logic [such as Shapiro (J Symbol Logic 50:714–742, 1985)], this logic does not solve the problem of referential access to mathematical objects (Azzouni, Metaphysical myths, mathematical practice: the logic and epistemology of the exact sciences, Cambridge University Press, Cambridge, 1994). In this paper, I argue that the second-order theorist can solve each of these difficulties. As a result, second-order logic provides the benefits of a rich framework without the associated costs.     

Moral conflict and the logic of rights

The paper proposes a revised logic of rights in order to accommodate moral conflict. There are often said to be two rival philosophical accounts of rights with respect to moral conflict. Specificationists about rights insist that rights cannot conflict, since they reflect overall deontic conclusions. Generalists instead argue that rights reflect pro tanto constraints on behaviour. After offering an overview of the debate between generalists and specificationists with respect to rights, I outline the challenge of developing a logic of rights-reasoning that is compatible with generalism. I then proceed to offer a new logical framework, which utilizes a simple non-monotonic logic of practical reasoning. Both generalist and specificationist interpretations of the logic are explored. The revised logic shows that traditional characterizations of the debate between specificationists and generalists obscure other relevant philosophical positions.

     

A propositional logic with explicit fixed points

This paper studies a propositional logic which is obtained by interpreting implication as formal provability. It is also the logic of finite irreflexive Kripke Models.A Kripke Model completeness theorem is given and several completeness theorems for interpretations into Provability Logic and Peano Arithmetic.     

Relevant identity

We begin to fill a lacuna in the relevance logic enterprise by providing a foundational analysis of identity in relevance logic. We consider rival interpretations of identity in this context, settling on the relevant indiscernibility interpretation, an interpretation related to Dunn's relevant predication project. We propose a general test for the stability of an axiomatisation of identity, relative to this interpretation, and we put various axiomatisations to this test. We fill our discussion out with both formal and philosophical remarks on identity in relevance logic.     

The Finite Model Property for Logics with the Tangle Modality

The tangle modality is a propositional connective that extends basic modal logic to a language that is expressively equivalent over certain classes of finite frames to the bisimulation-invariant fragments of both first-order and monadic second-order logic. This paper axiomatises several logics with tangle, including some that have the universal modality, and shows that they have the finite model property for Kripke frame semantics. The logics are specified by a variety of conditions on their validating frames, including local and global connectedness properties. Some of the results have been used to obtain completeness theorems for interpretations of tangled modal logics in topological spaces.     

Weak Rejection

Linguistic evidence supports the claim that certain, weak rejections are less specific than assertions. On the basis of this evidence, it has been argued that rejected sentences cannot be premisses and conclusions in inferences. We give examples of inferences with weakly rejected sentences as premisses and conclusions. We then propose a logic of weak rejection which accounts for the relevant phenomena and is motivated by principles of coherence in dialogue. We give a semantics for which this logic is sound and complete, show that it axiomatizes the modal logic KD45 and prove that it still derives classical logic on its asserted fragment. Finally, we defend previous logics of strong rejection as being about the linguistically preferred interpretations of weak rejections.     

What is “the ineffable” exactly? An extensive reading of Wittgenstein’s Tractatus Logico-Philosophicus

The ineffable  in Wittgenstein s Tractatus Logico-Philosophicus is an essential term that has various interpretations. It could be divided into two types, namely, positive and negative, or real and fake. The negative or fake type can be clarified by logical analysis, while the positive or real type can be understood only through philosophical critique. Both the positive and negative types consist of infinity or absoluteness, but the infinity is subject to distinctions in meaning and logic.     

On the Innocence and Determinacy of Plural Quantification

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first‐order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non‐standard (Henkin) interpretations that confronts higher‐order logics on their more traditional, set‐based semantics. We challenge both claims. Our challenge is based on a Henkin‐style semantics for plural logic that does not resort to sets or set‐like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic.     

Semantic memory for metaphor: The conceptual base hypothesis

The idea that people can encode and use an extremely abstract and general form of a complex linguistic (proverb) input-a conceptual base-was examined in two experiments. In Experiment I, each proverb was accompanied by either a conceptually related (good, mediocre, or poor) or an unrelated interpretation. The related interpretations were more effective recall prompts than were the unrelated interpretations, but only for high-imagery proverbs. In Experiment II, subjects wrote interpretations of the proverbs and then received either the proverb subject-noun or a brief story as a prompt. As was the case for the interpretations in Experiment I, the stories did not share any major vocabulary or propositional structure with their proverb source. Nonetheless, the stories were as effective as the nouns. Also, quality of proverb interpretation and of recall performance were positively related, with the correlations involving low-imagery proverbs, and stories, tending to be higher. Both experiments provided support for the conceptual-base notion, and underlined the importance of interpretive context, but more definitive evidence is needed.     

Butter Knives and Screwdrivers: An Intentionalist Defense of Radical Constructivism

Robert Stecker has posed a dilemma for the constructivist theory of interpretation: either interpretations consist of statements with truth values or they do not. Stecker argues that either way, they cannot change the meaning of an artwork. In this article, I argue contra Stecker that if interpretations consist of meaning declarations rather than statements, they can change the meanings of the objects toward which they are directed, where whether they so consist is largely a function of the interpreter's intentions. Hence, the second horn of Stecker's dilemma is defeated.     

Armstrong on Probabilistic Laws of Nature

D. M. Armstrong famously claims that deterministic laws of nature are contingent relations between universals and that his account can also be straightforwardly extended to irreducibly probabilistic laws of nature. For the most part, philosophers have neglected to scrutinize Armstrong’s account of probabilistic laws. This is surprising precisely because his own claims about probabilistic laws make it unclear just what he takes them to be. We offer three interpretations of what Armstrong-style probabilistic laws are, and argue that all three interpretations are incompatible either with some feature of Armstrong’s broader metaphysics or with essential features of his account of laws (or both).     

Reversing how to think about ambiguous figure reversals: spontaneous alternating by uninformed observers

Ambiguous figures are a special class of images that can give rise to multiple interpretations. Traditionally, switching between the possible interpretations of an ambiguous figure, or reversing one's interpretation, has been attributed either to top-down or to bottom-up processes (e.g. attributed to having knowledge of the nature of the ambiguity, or to a form of neuronal fatigue). Here we present evidence that is incompatible with both forms of explanations. Observers aged 5-9 years can reverse ambiguous figures when uninformed about the ambiguity, negating purely top-down explanations. Further, those children who make these 'spontaneous' reversals are more likely to succeed on a high-order theory-of-mind task, negating purely bottom-up explanations.     

Linguistic-pragmatic factors in interpreting disjunctions

' The connective or can be treated as an inclusive disjunction or else as an exclusive disjunction. Although researchers are aware of this distinction, few have examined the conditions under which each interpretation should be anticipated. Based on linguistic-pragmatic analyses, we assume that interpretations are initially inclusive before either (a) remaining so, or (b) becoming exclusive by way of an implicature (but not both). We point to a class of situations that ought to predispose disjunctions to inclusive interpretations and to situations that encourage exclusive interpretations. A disjunction's ultimate interpretation is based on its potential informativeness, where the interpretation of the disjunctive utterance having the smallest number of true conditions is considered most informative. Our investigation leads to five experiments employing arbitrary materials. Among the problems expected to encourage inclusive interpretations are those that present disjunctions in the antecedents of conditionals and in question forms. The best candidates to produce implicatures are those disjunctions that underdetermine an expected conjunctive conclusion, although other disjunctive utterances that are more informative as exclusive are discussed and tested.