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 to Be a Humean Interventionist

This paper aims to provide Humean metaphysics for the interventionist theory of causation. This is done by appealing to the hierarchical picture of causal relations as being realized by mechanisms, which in turn are identified with lower‐level causal structures. The modal content of invariances at the lowest level of this hierarchy, at which mechanisms are reduced to strict natural laws, is then explained in terms of projectivism based on the best‐system view of laws.     

Healing elements of therapeutic conversation: dialogue as an embodiment of love

From our Bakhtinian perspective, understanding requires an active process of talking and listening. Dialogue is a precondition for positive change in any form of therapy. Using the perspectives of dialogism and neurobiological development, we analyze the basic elements of dialogue, seeking to understand why dialogue becomes a healing experience in a network meeting. From the perspective of therapist as dialogical partner, we examine actions that support dialogue in conversation, shared emotional experience, creation of community, and creation of new shared language. We describe how feelings of love, manifesting powerful mutual emotional attunement in the conversation, signal moments of therapeutic change.     

Quantum Logic as a Fragment of Independence-Friendly Logic

The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation ¬ over and above the dual (strong) negation . Then in a Hilbert space turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension of a logical space. The received Birkhoff and von Neumann quantum logic can be interpreted by taking their disjunction to be ¬(A & B). Their logic can thus be mapped into a Boolean structure to which an additional operator has been added.     

Information-seeking dialogues: Some of their logical properties

The dialogical games introduced in Jaakko Hintikka, Information-Seeking Dialogues: A Model, (Erkenntnis, vol. 14, 1979) are studied here to answer the question as to what the natural logic or the logic of natural language is. In a natural language certain epistemic elements are not explicitly indicated, but they determine which inference rules are valid. By means of dialogical games, the question is answered: all classical first-order rules have to be modified in the same way in which some of them are modified in the transition to intuitionistic logic. (Furthermore, in some cases quantificational rules have to be modified further.) The rules that are left unmodified by intuitionists are applicable only to the output of certain game rules, but not to others. In. this sense, neither classical nor yet intuitionistic logic is the logic of natural language. We need a new type of nonclassical logic, justified by our information-seeking dialogues.