Trivalent Semantics and the Vaguely Vague

Michael Tye responds to the problem of higher-order vagueness for his trivalent semantics by maintaining that truth-value predicates are “vaguely vague”: it’s indeterminate, on his view, whether they have borderline cases and therefore indeterminate whether every sentence is true, false, or indefinite. Rosanna Keefe objects (1) that Tye’s argument for this claim tacitly assumes that every sentence is true, false, or indefinite, and (2) that the conclusion is any case not viable. I argue – contra (1) – that Tye’s argument needn’t make that assumption. A version of her objection is in fact better directed against other arguments Tye advances, though Tye can absorb this criticism without abandoning his position’s core. On the other hand, Keefe’s second objection does hit the mark: embracing ‘vaguely vague’ truth-value predicates undermines Tye’s ability to support validity claims needed to defend his position. To see this, however, we must develop Keefe’s remarks further than she does.     

Vagueness,Kant and Topology: a Study of Formal Epistemology

In this paper we propose an approach to vagueness characterised by two features. The first one is philosophical: we move along a Kantian path emphasizing the knowing subject’s conceptual apparatus. The second one is formal: to face vagueness, and our philosophical view on it, we propose to use topology and formal topology. We show that the Kantian and the topological features joined together allow us an atypical, but promising, way of considering vagueness.     

Second-Order Quantifier Elimination in Higher-Order Contexts with Applications to the Semantical Analysis of Conditionals

Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing second-order variables to appear within higher-order contexts. Then we focus on a semantical analysis of conditionals, using the introduced technique and Gabbay’s semantics provided in [10] and substantially using a third-order accessibility relation. The analysis is done via finding correspondences between axioms involving conditionals and properties of the underlying third-order relation. Presented by Wojciech Buszkowski     

The Genesis of Hi-Worlds: Towards a Principle-Based Possible World Semantics

A Leibnizian semantics proposed by Becker in 1952 for the modal operators has recently been reviewed in Copeland’s paper The Genesis of Possible World Semantics (Copeland in J Philos Logic 31:99–137, 2002), with a remark that “neither the binary relation nor the idea of proving completeness was present in Becker’s work”. In light of Frege’s celebrated Sense-Determines-Reference principle, we find, however, that it is Becker’s semantics, rather than Kripke’s semantics, that has captured the true spirit of Frege’s semantic program. Furthermore, for Kripke’s possible world semantics to fit in Frege’s framework of senses, worlds and referents, it will have to be thoroughly reformulated. By introducing the notion of a hi-world into the picture, we manage to keep the key ingredients of Becker’s semantics intact, while at the same time solve a fatal problem that used to shadow Becker’s original semantics—it had not been able to make sense of inhomogeneous modality. The resulting generalized Beckerian semantics provides, in effect, a Beckerian analysis of the Kripkean possible worlds. It reveals the subtle hierarchical internal structure of a Kripkean world that has not been discovered before.     

A Generic Framework for Adaptive Vague Logics

In this paper, we present a generic format for adaptive vague logics. Logics based on this format are able to (1) identify sentences as vague or non-vague in light of a given set of premises, and to (2) dynamically adjust the possible set of inferences in accordance with these identifications, i.e. sentences that are identified as vague allow only for the application of vague inference rules and sentences that are identified as non-vague also allow for the application of some extra set of classical logic rules. The generic format consists of a set of minimal criteria that must be satisfied by the vague logic in casu in order to be usable as a basis for an adaptive vague logic. The criteria focus on the way in which the logic deals with a special ⊡-operator. Depending on the kind of logic for vagueness that is used as a basis for the adaptive vague logic, this operator can be interpreted as completely true, definitely true, clearly true, etc. It is proven that a wide range of famous logics for vagueness satisfies these criteria when extended with a specific ⊡-operator, e.g. fuzzy basic logic and its well known extensions, cf. [7], super- and subvaluationist logics, cf. [6], [9], and clarity logic, cf. [13]. Also a fuzzy logic is presented that can be used for an adaptive vague logic that can deal with higher-order vagueness. To illustrate the theory, some toy-examples of adaptive vague proofs are provided.     

A Professor’s Moral Thinking at the Abstract Level Versus The Professor’s Moral Thinking in the Real Life Situation (Consistency Problem)

We conducted an on-line survey to investigate the professor’s idea of “morality” and then to compare their moral thinking at the abstract level with their moral thinking in the real life situations by sampling 257 professors from the University of Novi Sad. We constructed questionnaire based on related theoretical ethical concepts. Our results show (after we performed exploratory factor analysis) that the professor’s idea of “morality” consists of the three moral thinking patterns which are simultaneously activated during the process of their abstract moral thinking. We have identified these patterns in the following manner: deontological, formal and subjective pattern. In addition, our results show that of the three, the subjective pattern is more activated than the other two during their process of the moral thinking at the abstract level. We also discovered that there is a statistically significant difference between professor’s moral thinking patterns activation level at the abstract level and their moral thinking patterns activation level in the real life situation.     

A Grim Semantics For Logics of Belief

Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics, and we suggest that the condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for K4 and KD4.     

Linguistic communication and the semantics/pragmatics distinction

Most people working on linguistic meaning or communication assume that semantics and pragmatics are distinct domains, yet there is still little consensus on how the distinction is to be drawn. The position defended in this paper is that the semantics/pragmatics distinction holds between (context-invariant) encoded linguistic meaning and speaker meaning. Two other ‘minimalist’ positions on semantics are explored and found wanting: Kent Bach’s view that there is a narrow semantic notion of context which is responsible for providing semantic values for a small number of indexicals, and Herman Cappelen and Ernie Lepore’s view that semantics includes the provision of values for all indexicals, even though these depend on the speaker’s communicative intentions. Finally, some implications are considered for the favoured semantics/pragmatics distinction of the fact that there are linguistic elements (lexical and syntactic) which do not contribute to truth-conditional content but rather provide guidance on pragmatic inference.     

The Two-Dimensional Content of Consciousness

In this paper I put forward a representationalist theory of conscious experience based on Robert Stalnaker’s version of two-dimensional modal semantics. According to this theory the phenomenal character of an experience correlates with a content equivalent to what Stalnaker calls the diagonal proposition. I show that the theory is closely related both to functionalist theories of consciousness and to higher-order representational theories. It is also more compatible with an anti-Cartesian view of the mind than standard representationalist theories.     

Temporal Parts and Time Travel

This paper argues that, in light of certain scenarios involving time travel, Sider’s definition of ‘instantaneous temporal part’ cannot be accepted in conjunction with a semantic thesis that perdurantists often assume. I examine a rejoinder from Sider, as well as Thomson’s alternative definition of ‘instantaneous temporal part’, and show how neither helps. Given this, we should give up on the perdurantist semantic thesis. I end by recommending that, once we no longer accept such semantics, we should accept a new set of definitions, which are superior in certain respects to Sider’s original set.     

Multi-valued Semantics: Why and How

According to Suszko’s Thesis, any multi-valued semantics for a logical system can be replaced by an equivalent bivalent one. Moreover: bivalent semantics for families of logics can frequently be developed in a modular way. On the other hand bivalent semantics usually lacks the crucial property of analycity, a property which is guaranteed for the semantics of multi-valued matrices. We show that one can get both modularity and analycity by using the semantic framework of multi-valued non-deterministic matrices. We further show that for using this framework in a constructive way it is best to view “truth-values” as information carriers, or “information-values”.     

A Pinch of Salt for Frege

Michael Dummett has argued that a formal semantics for our language is inadequate unless it can be shown to illuminate to our actual practice of speaking and understanding. This paper argues that Frege’s account of the semantics of predicate expressions according to which the reference of a predicate is a concept (a function from objects to truth values) has exactly the required characteristics. The first part of the paper develops a model for understanding the distinction between objects and concepts as an ontological distinction. It argues that, ontologically, we can take a Fregean function to be generated by a property detection device that can register for any object the presence or absence of that property. This provides a direct connection between the semantics of sentences and the structure of perceptual judgment. The second part of the paper deals with arguments that have been mounted against the coherence of Frege’s semantics. It argues that some of these are question begging, while others are correct in so far as Frege’s claim is untenable if we assume that the syntactic categories singular term and predicate are primary, and the ontological categories are simply projections of these syntactic categories. However, the objections dissipate once we recognize that an independent ontological characterization of the distinction is available.     

Color,context, and compositionality

Color adjectives have played a central role in work on language typology and variation, but there has been relatively little investigation of their meanings by researchers in formal semantics. This is surprising given the fact that color terms have been at the center of debates in the philosophy of language over foundational questions, in particular whether the idea of a compositional, truth-conditional theory of natural language semantics is even coherent. The challenge presented by color terms is articulated in detail in the work of Charles Travis. Travis argues that structurally isomorphic sentences containing color adjectives can shift truth value from context to context depending on how they are used and in the absence of effects of vagueness or ambiguity/polysemy, and concludes that a deterministic mapping from structures to truth conditions is impossible. The goal of this paper is to provide a linguistic perspective on this issue, which we believe defuses Travis’ challenge. We provide empirical arguments that color adjectives are in fact ambiguous between gradable and nongradable interpretations, and that this simple ambiguity, together with independently motivated options concerning scalar dimension within the gradable reading accounts for the Travis facts in a simpler, more constrained, and thus ultimately more successful fashion than recent contextualist analyses such as those in Szabó (Perspectives on semantics, pragmatics and discourse: A festschrift for Ferenc Kiefer, 2001) or Rothschild and Segal (Mind Lang, 2009).     

Comparing Fixed-Point and Revision Theories of Truth

In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. (Martin and Woodruff independently developed this semantics, but not to the same extent as Kripke.) Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting theories of truth, and establishes the resulting relationships among these theories. The point is to get a sense of the lay of the land amid a variety of options. Our results will also provide technical fodder for the methodological remarks of the companion paper to this one.     

Client Uncertainty and the Process of Change in Psychotherapy: The Impact of Individual Differences in Self-concept Clarity and Intolerance of Uncertainty

We describe a number of ways in which two major components of client uncertainty, namely, self-concept clarity and intolerance of uncertainty may either facilitate or impede change in psychotherapy. Clients with low self-concept clarity find it much more difficult to clearly identify and understand their problematic thoughts, emotions, and behaviors; thus slowing down their progress through the various stages identified in Prochaska’s model of psychotherapeutic change. To illustrate, they may engage in much more contemplation prior to action, as they struggle to increase their awareness and insight. Clients with high intolerance of uncertainty experience substantial discomfort when faced with uncertainty, causing them to be highly motivated to avoid or minimize any aspects of psychotherapy that focus on change. This may cause them to avoid confronting their problems during the action stage of therapy. We further suggest that it would be beneficial to assess these two components of client uncertainty very early on in the therapeutic process, in order to facilitate a given client’s progress. Finally, we indicate a need for much more research that explores the role of these two individual difference constructs during therapy. This might include, for example, studies that directly examine how self-concept clarity and intolerance of uncertainty may relate to progress through each stage of change, or the selective use of avoidance strategies. Authorship of this paper is equal. A special thanks to Joan Olinger for her many helpful comments on this paper. This paper won the 2007 Wilfred Quaytman Award for Innovations in Psychotherapy, jointly sponsored by the Long Island Consultation Center and International Scientific Comminucations, Inc. to commemorate the spirit and dedication of Dr. Wil Quaytman, psychologist, psychotherapist, and founding editor of the Journal of Contemporary Psychotherapy.     

Free Semantics

Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic focussed upon, but the results extend to MC. The semantics is called ‘free semantics’ since it is disjunctively and existentially free in that no disjunctive or existential witnesses are produced, unlike in truth-functional semantics. Such ‘witnesses’ are only assumed in generality and are not necessarily actual. The paper sets up the free semantics in a truth-functional style and gives a natural deduction interpetation of the meta-logical connectives. We then set out a familiar tableau-style system, but based on natural deduction proof rather than truth-functional semantics. A proof of soundness and completeness is given for a reductio system, which is a transform of the tableau system. The reductio system has positive and negative rules in place of the elimination and introduction rules of Brady’s normalized natural deduction system for DW. The elimination-introduction turning points become closures of threads of proof, which are at the points of contradiction for the reductio system.     

Inexact Knowledge with Introspection

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality.