Non-Adjunctive Inference and Classical Modalities

The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A∧B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, 1980). The unified semantical characterization in terms of neighborhoods permits comparisons between different forms of non-adjunctive inference. For example, we show that the non-adjunctive logic proposed in (Schotch and Jennings, 1980) is not adequate in general for representing the logic of high probability operators. An alternative interpretation of the forcing relation of Schotch and Jennings is derived from the proposed unified semantics and utilized in order to propose a more fine-grained measure of epistemic coherence than the one presented in (Schotch and Jennings, 1980). Finally we propose a syntactic translation of the purely implicative part of Jaśkowski's system D₂ into a classical system preserving all the theorems (and non-theorems) explicilty mentioned in (Jaśkowski, 1969). The translation method can be used in order to develop epistemic semantics for a larger class of non-adjunctive (discursive) logics than the ones historically investigated by Jaśkowski.     

Thomason’s Paradox for Belief,and Two Consequence Relations

Thomason (1979/2010)’s argument against competence psychologism in semantics envisages a representation of a subject’s competence as follows: he understands his own language in the sense that he can identify the semantic content of each of its sentences, which requires that the relation between expression and content be recursive. Then if the scientist constructs a theory that is meant to represent the body of the subject’s beliefs, construed as assent to the content of the pertinent sentences, and that theory satisfies certain ‘natural assumptions’, then it implies that the subject is inconsistent if the beliefs include arithmetic. I challenge the result by insisting that the motivation for Thomason’s principle (ii), via Moore’s Paradox, leads to a more complex representation, in which stating the facts and expressing one’s beliefs are treated differently. Certain logical connections among expressions of assent, and between expression and statement, are a matter of consequence on pain of pragmatic incoherence, not consequence on pain of classical logical inconsistency. But while this salvages the possibility that a modification of the above sort of representation could be adequate, Thomason’s devastating conclusion returns if the scientist identifies himself as the subject of that representation, even when paying heed to the requirement of pragmatic coherence of the sort highlighted by Moore’s Paradox.     

New Foundations for a Relational Theory of Theory-revision

AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions ‘J is a contraction of K with respect to A’ and ‘J is a revision of K with respect to A’. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds of theory-change (expansion, contraction and revision). The new theory is stated by means of introduction and elimination rules for the relational notions. In this new setting one can re-examine the relationship between contraction and revision, using the appropriate versions of the so-called Levi and Harper identities. Among the positive results are the following. One can derive the extensionality of contraction and revision, rather than merely postulating it. Moreover, one can demonstrate the existence of revision-functions satisfying a principle of monotonicity. The full set of AGM-postulates for revision-functions allow for completely bizarre revisions. This motivates a Principle of Minimal Bloating, which needs to be stated as a separate postulate for revision. Moreover, contractions obtained in the usual way from the bizarre revisions, by using the Harper identity, satisfy Recovery. This provides a new reason (in addition to several others already adduced in the literature) for thinking that the contraction postulate of Recovery fails to capture the Principle of Minimal Mutilation. So the search is still on for a proper explication of the notion of minimal mutilation, to do service in both the theory of contraction and the theory of revision. The new relational formulation of AGM-theory, based on principal-case analysis, shares with the original, functional form of AGM-theory the idealizing assumption that the belief-sets of rational agents are to be modelled as consistent, logically closed sets of sentences. The upshot of the results presented here is that the new relational theory does a better job of making important matters clear than does the original functional theory. A new setting has been provided within which one can profitably address two pressing questions for AGM-theory: (1) how is the notion of minimal mutilation (by both contractions and revisions) best analyzed? and (2) how is one to rule out unnecessary bloating by revisions?     

Reflections on the revolution at Stanford

We inquire into the question whether the Aristotelian or classical ideal of science has been realised by the Model Revolution, initiated at Stanford University during the 1950s and spread all around the world of philosophy of science—salute Suppes. The guiding principle of the Model Revolution is: a scientific theory is a set of structures in the domain of discourse of axiomatic set-theory, characterised by a set-theoretical predicate. We expound some critical reflections on the Model Revolution; the conclusions will be that the philosophical problem of what a scientific theory is has not been solved yet—pace Suppes. While reflecting critically on the Model Revolution, we also explore a proposal of how to complete the Revolution and briefly address the intertwined subject of scientific representation, which has come to occupy center stage in philosophy of science over the past decade.     

A Dynamic-Logical Perspective on Quantum Behavior

In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators previously used to model various forms of classical information flow: the “test” operator from Dynamic Logic, the “announcement” operator from Dynamic Epistemic Logic and the “revision” operator from Belief Revision theory. The main points stressed in our investigation are the following: (1) The perspective and the techniques of “logical dynamics” are useful for understanding quantum information flow. (2) Quantum mechanics does not require any modification of the classical laws of “static” propositional logic, but only a non-classical dynamics of information. (3) The main such non-classical feature is that, in a quantum world, all information-gathering actions have some ontic side-effects. (4) This ontic impact can affect in its turn the flow of information, leading to non-classical epistemic side-effects (e.g. a type of non-monotonicity) and to states of “objectively imperfect information”. (5) Moreover, the ontic impact is non-local: an information-gathering action on one part of a quantum system can have ontic side-effects on other, far-away parts of the system.     

Proof Systems Combining Classical and Paraconsistent Negations

New propositional and first-order paraconsistent logics (called L _ω and FL _ω , respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding theorems of L _ω and FL _ω into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple semantics for L _ω and FL _ω are proved. The cut-elimination theorems for L _ω and FL _ω are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems. Presented by Yaroslav Shramko and Heinrich Wansing     

GAKhN: an aesthetics of ruins,or Aleksej Losev’s failed project

In the course of his collaboration with GAKhN, whose task was to create a systemic ‘scientific’ theory of art, Losev undertook a systematic interpretation of German classical aesthetics as the historical presupposition for his own Christian, Platonist doctrine of art conceived as a dialectical universe comprising totalizing connections at all levels. This interpretation was concealed in a masterful way within the ‘Commentaries’ to Dialektika khudožestvennoj formy. Independently of the significant results achieved by this revival of the classical tradition, Losev’s mythologized theory of art called forth a critical reaction on the part of his GAKhN colleagues and brought to light some of the broader theoretical attitudes present among GAKhN’s collaborators.     

Tracking, Epistemic Dispositions and the Conditional Analysis

According to Nozick’s tracking theory of knowledge, an agent a knows that p just in case her belief that p is true and also satisfies the two tracking conditionals that had p been false, she would not have believed that p, and had p been true under slightly different circumstances, she would still have believed that p. In this paper I wish to highlight an interesting but generally ignored feature of this theory: namely that it is reminiscent of a dispositional account of knowledge: it invites us to think of knowledge as a manifestation of a cognitive disposition to form true beliefs. Indeed, given a general account of dispositions in terms of subjunctive conditionals, the two tracking conditionals are satisfied just in case the belief in question results from some cognitive disposition to form true beliefs. Recently, such a conditional account of dispositions has, however, been criticised for its vulnerability to so-called ‘masked’, ‘mimicked’ and ‘finkish’ counterexamples. I show how the classical counterexamples to Nozick’s theory divide smoothly into four corresponding categories of counterexamples from epistemic masking, mimicking and finkishness. This provides strong evidence for the thesis that satisfaction of the two tracking conditionals is symptomatic of knowledge and that knowledge is instead constituted by a dispositional capability to form true beliefs. The attempt to capture such a cognitive, dispositional capability in terms of the tracking conditionals, although providing a good approximation in a wide variety of cases, still comes apart from the real thing whenever the epistemic layout is characterised by masking-, mimicking- and finkish mechanisms. In the last part of the paper I explore the prospect of improving the tracking theory in the light of these findings.     

The 10-Item Positive and Negative Affect Schedule for Children, Child and Parent Shortened Versions: Application of Item Response Theory for More Efficient Assessment

The Positive and Negative Affect Schedule for Children (PANAS-C/P; child and parent versions) yield positive affect (PA) and negative affect (NA) scales that are clinically useful for identifying youth with anxiety and mood problems. Despite the advantages that item response theory (IRT) offers relative to classical test theory with respect to shortening test instruments, no studies to date have applied IRT methodology to the PANAS-C/P scales. In the present study, we thus applied IRT methodology using a school-based development sample (child sample: N = 799; parent sample: N = 553) and developed a shortened 5-item PA scale (joyful, cheerful, happy, lively, proud) and a 5-item NA scale (miserable, mad, afraid, scared, sad) for the sake of simultaneously increasing the assessment efficiency of the PANAS-C/P scales while improving the psychometric properties of the scales. The reduced PA and NA child scales classified relevant diagnostic groups in a separate clinic-referred validation sample (N = 662) just as well as the original PANAS-C child scales and may be used to help identify youth with internalizing disorders in need of mental health services.     

Modal logic and model theory

We propose a first order modal logic, theQS4E-logic, obtained by adding to the well-known first order modal logicQS4 arigidity axiom schemas:A → □A, whereA denotes a basic formula. In this logic, thepossibility entails the possibility of extending a given classical first order model. This allows us to express some important concepts of classical model theory, such as existential completeness and the state of being infinitely generic, that are not expressibile in classical first order logic. Since they can be expressed in -logic, we are also induced to compare the expressive powers ofQS4E and . Some questions concerning the power of rigidity axiom are also examined.     

SHUTTING DRETSKE’S DOOR

Dretske proposes a theory of knowledge in terms of a theory of information, but wishes to deny that empirical knowledge settles the large question of scepticism. This leads him to deny the closure of knowledge under known entailment. In a recent paper J?ger argues that Dretske’s theory of information entails closure for knowledge, ‘at least for the kind of propositions here at issue’ (J?ger 2004:194). If J?ger is right, Dretske is seriously embarrassed and must give something up. In this paper I show that there are two flaws in J?ger’s argument. The principle of informational closure considered by J?ger is incompatible with Dretske’s theory of information, and J?ger’s argument that Dretske is committed to a certain kind of substitution instance of that principle of informational closure is invalid. I propose adequacy conditions on signalled information and use them to motivate a formulation of a general closure principle for signalled information. I show that Dretske’s account of information satisfies the adequacy conditions, but in a way which commits him to an instance of the general closure principle. I argue that Dretske is consequently committed to closure for some cases of knowledge for which he wishes to deny closure. Finally, I sketch how, on the basis of the closure principle to which Dretske is committed, J?ger’s broader argument may yet go through.     

Misrepresenting consciousness

An important objection to the “higher-order” theory of consciousness turns on the possibility of higher-order misrepresentation. I argue that the objection fails because it illicitly assumes a characterization of consciousness explicitly rejected by HO theory. This in turn raises the question of what justifies an initial characterization of the data a theory of consciousness must explain. I distinguish between intrinsic and extrinsic characterizations of consciousness, and I propose several desiderata a successful characterization of consciousness must meet. I then defend the particular extrinsic characterization of the HO theory, the “transitivity principle,” against its intrinsic rivals, thereby showing that the misrepresentation objection conclusively falls short.     

A Hobbesian derivation of the principle of universalization

In this article, I derive a weak version of Kant’s categorical imperative within an informal game-theoretic framework. More specifically, I argue that Hobbesian agents would choose what I call the weak principle of universalization, if they had to decide on a rule of conflict resolution in an idealized but empirically defensible hypothetical decision situation. The discussion clarifies (i) the rationality requirements imposed on agents, (ii) the empirical conditions assumed to warrant the conclusion, and (iii) the political institutions that are necessary to implement the derived principle. The analysis demonstrates the moral significance of the weak principle of universalization and its epistemic advantage over the categorical imperative.     

If Logic, Definitions and the Vicious Circle Principle

In a definition (∀x)((xєr)↔D[x]) of the set r, the definiens D[x] must not depend on the definiendum r. This implies that all quantifiers in D[x] are independent of r and of (∀x). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence requirements are what created the typical paradoxes of set theory. Poincaré’s Vicious Circle Principle was intended to bar such violations. Russell nevertheless misunderstood the principle; for him a set a can depend on another set b only if (bєa) or (b ⊆ a). Likewise, the truth of an ordinary first-order sentence with the G?del number of r is undefinable in Tarki’s sense because the quantifiers of the definiens depend unavoidably on r.     

How Truth Behaves When There’s No Vicious Reference

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth “its consequence that truth behaves like an ordinary classical concept under certain conditions—conditions that can roughly be characterized as those in which there is no vicious reference in the language.” To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of “no vicious reference” generated both by revision theories of truth and by fixed-point theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard.     

Pragmatic concepts of valid inference and of implication

Summary The paper gives a tentative reconstruction of the classical theory of so called fallacious arguments. Its title refers to the following observations. One of the fallacies listed in traditional logic ispetitio principii. It seem natural to add to the list another, similar fallacy. An argumentationArg ⁺ considered as a part of a theoretical contextC commits this fallacy relatively toC, if it contains an inference such that the principle of this inference has not been proved inC. By principle of a given inference the conditional is meant whose antecedent and consequent are the conjuction of all the premisses and the conclusion of the inference respectively. If the principle of a given inference has been proved in a given contextC, the inference is valid relatively toC and the premisses are implying the conclusion relatively toC. Both these concepts, of valid inference and of implication do involve the concept of an effectively performed proof; hence they are pragmatic concepts.     

The structure of lexical concepts

Jerry Fodor (Concepts: Where cognitive science went wrong. New York: Oxford University Press, 1998) famously argued that lexical concepts are unstructured. After examining the advantages and disadvantages of both the classical approach to concepts and Fodor’s conceptual atomism, I argue that some lexical concepts are, in fact, structured. Roughly stated, I argue that structured lexical concepts bear a necessary biconditional entailment relation to their structural constituents. I develop this account of the structure of lexical concepts within the framework of Pavel Tichy’s (The foundations of Frege’s logic. Berlin, New York: De Gruyter, 1988) theory of constructions. I argue that concepts are constructions which can be combined by way of Tichy’s construction-forming operations of composition and closure and an additional operation, simplification, which I propose in section 6. The last of these construction-forming operations plays a central role in my account of lexical concept structure. Stated generally, structured lexical concepts are a result of simplifying their structural constituents.