A Completeness Proof of Kiczuk’s Logic of Physical Change

In this paper the class of minimal models C ^ZI for Kiczuk’s system of physical change ZI is provided and soundness and completeness proofs of ZI with respect to these models are given. ZI logic consists of propositional logic von Wright’s And Then and six specific axioms characterizing the meaning of unary propositional operator “Zm”, read “there is a change in the fact that”. ZI is intended to be a logic which provides a formal account for describing two kinds of process change: the change from one state of the process to its other state (e.g., transmitting or absorbing energy with greater or less than the usual intensity) and the perishing of the process (e.g., cessation of the energetic activity of the sun).     

A Simplified Proof of the Church–Rosser Theorem

Takahashi translation * is a translation which means reducing all of the redexes in a λ-term simultaneously. In [4] and [5], Takahashi gave a simple proof of the Church–Rosser confluence theorem by using the notion of parallel reduction and Takahashi translation. Our aim of this paper is to give a simpler proof of Church–Rosser theorem using only the notion of Takahashi translation.     

A New Proof of the McKinsey–Tarski Theorem

It is a landmark theorem of McKinsey and Tarski that if we interpret modal diamond as closure (and hence modal box as interior), then \(\mathsf S4\) is the logic of any dense-in-itself metrizable space. The McKinsey–Tarski Theorem relies heavily on a metric that gives rise to the topology. We give a new and more topological proof of the theorem, utilizing Bing’s Metrization Theorem.     

Satisfying Predicates: Kleene's Proof of the Hilbert–Bernays Theorem

The Hilbert–Bernays Theorem establishes that for any satisfiable first-order quantificational schema S, one can write out linguistic expressions that are guaranteed to yield a true sentence of elementary arithmetic when they are substituted for the predicate letters in S. The theorem implies that if L is a consistent, fully interpreted language rich enough to express elementary arithmetic, then a schema S is valid if and only if every sentence of L that can be obtained by substituting predicates of L for predicate letters in S is true. The theorem therefore licenses us to define validity substitutionally in languages rich enough to express arithmetic. The heart of the theorem is an arithmetization of Gödel's completeness proof for first-order predicate logic. Hilbert and Bernays were the first to prove that there is such an arithmetization. Kleene established a strengthened version of it, and Kreisel, Mostowski, and Putnam refined Kleene's result. Despite the later refinements, Kleene's presentation of the arithmetization is still regarded as the standard one. It is highly compressed, however, and very difficult to read. My goals in this paper are expository: to present the basics of Kleene's arithmetization in a less compressed, more easily readable form, in a setting that highlights its relevance to issues in the philosophy of logic, especially to Quine's substitutional definition of logical truth, and to formulate the Hilbert–Bernays Theorem in a way that incorporates Kreisel's, Mostowski's, and Putnam's refinements of Kleene's result.     

Giles’s Game and the Proof Theory of Łukasiewicz Logic

In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Łukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof system. In particular, such strategies mirror derivations in a hypersequent calculus developed in recent work on the proof theory of Łukasiewicz logic. Presented by Daniele Mundici     

Proof of situational sensitivity of mood states and dynamic traits—ergs and sentiments—to disturbing stimuli

A separation of state and trait factors, and an allocation of modulation values to situations, was attempted by giving the Eight State Battery (8SQ) and the Motivation Analysis Test (MAT) to two groups, each under two situations, one aversive. The difference scores between a pre- and postexposure to the mild and the severe aversive situations were significant on all 8SQ factors but mainly on ergs, not sentiments, in the MAT. The state changes, notably on Anxiety, Regression, Depression and Guilt, were greater on the more shocking stimulus, while Fear rose and Narcism fell significantly on the MAT. Changes were greater on unintegrated than integrated motivational components, confirming hypotheses by others.     

Decomposition Proof Systems for Gödel-Dummett Logics

The main goal of the paper is to suggest some analytic proof systems for LC and its finite-valued counterparts which are suitable for proof-search. This goal is achieved through following the general Rasiowa-Sikorski methodology for constructing analytic proof systems for semantically-defined logics. All the systems presented here are terminating, contraction-free, and based on invertible rules, which have a local character and at most two premises.     

Does Reductive Proof Theory Have A Viable Rationale?

The goals of reduction andreductionism in the natural sciences are mainly explanatoryin character, while those inmathematics are primarily foundational.In contrast to global reductionistprograms which aim to reduce all ofmathematics to one supposedly ``universal' system or foundational scheme, reductive proof theory pursues local reductions of one formal system to another which is more justified in some sense. In this direction, two specific rationales have been proposed as aims for reductive proof theory, the constructive consistency-proof rationale and the foundational reduction rationale. However, recent advances in proof theory force one to consider the viability of these rationales. Despite the genuine problems of foundational significance raised by that work, the paper concludes with a defense of reductive proof theory at a minimum as one of the principal means to lay out what rests on what in mathematics. In an extensive appendix to the paper,various reduction relations betweensystems are explained and compared, and arguments against proof-theoretic reduction as a ``good' reducibilityrelation are taken up and rebutted.     

Proof vs Provability: On Brouwer’s Time Problem

Is a mathematical theorem proved because provable, or provable because proved? If Brouwer’s intuitionism is accepted, we’re committed, it seems, to the latter, which is highly problematic. Or so I will argue. This and other consequences of Brouwer’s attempt to found mathematics on the intuition of a move of time have heretofore been insufficiently appreciated. Whereas the mathematical anomalies of intuitionism have received enormous attention, too little time, I’ll try to show, has been devoted to some of the temporal anomalies that Brouwer has invited us to introduce into mathematics.     

Al-Ghazali’s Position on the ‘Second Proof’ of the ‘Philosophers’ for the Eternity of the World,in the First Discussion of the Incoherence of the Philosophers

In the Incoherence of the Philosophers, Abu Hamid al-Ghazali (1058-1111) raised objections against the doctrine of the ‘philosophers’ (represented chiefly by al-Farabi and Ibn Sina) on 20 specific points. In the first, and longest discussion, he examines and rebuts four of their proofs of the pre-eternity of the world—that is, that the universe as a whole had no beginning but extends perpetually into the past. Al-Ghazali rejects that doctrine. But his own position on the issue does not become clear until he discusses the philosophers’ ‘second proof.’ In this paper, I will examine the relevant text of the Incoherence of the Philosophers, in order to clarify the nature of Al-Ghazali’s position in relation to the second proof. I will explain why Al-Ghazali cannot adopt what I refer to as the ‘naïve’ theological position, according to which God temporally preceded the world. Instead, Al-Ghazali concurs with the philosophers that time is the measure of motion, but he asserts that time was created with the world, both having a beginning before which there was no time. God, on the other hand, is not temporally prior to the world, but neither is he simultaneous, as the second proof supposes. As timelessly eternal, God bears no temporal relation to the world at all. In conclusion, I describe what I refer to as a naïve philosophical position, which is entailed by the second proof, but distinct from both Al-Ghazali’s position and that adopted by Ibn Rushd in his critique of Al-Ghazali in the Incoherence of the Incoherence. I argue that this naïve philosophical position (and thus, the second proof) is incoherent.     

The Philosophy for Children Curriculum: Resisting ‘Teacher Proof’ Texts and the Formation of the Ideal Philosopher Child

The philosophy for children curriculum was specially written by Matthew Lipman and colleagues for the teaching of philosophy by non-philosophically educated teachers from foundation phase to further education colleges. In this article I argue that such a curriculum is neither a necessary, not a sufficient condition for the teaching of philosophical thinking. The philosophical knowledge and pedagogical tact of the teacher remains salient, in that the open-ended and unpredictable nature of philosophical enquiry demands of teachers to think in the moment and draw on their own knowledge and experience of academic philosophy. Providing specialist training or induction in the P4C curriculum cannot and should not replace undergraduate and postgraduate degrees in academic philosophy at universities. However, although for academic philosophers the use of the P4C curriculum could be beneficial, I will argue that its use poses the risk of wanting to form children into the ideal ‘abnormal’ child, the thinking child—the adult philosopher’s child positioned as such by the Lipman novels. The notion of narrativity is central in my argument. With the help of two picturebooks—The Three Pigs (2001) by David Weisner and Voices in the Park (1998) by Anthony Browne—I illustrate my claim that philosophy as ‘side-shadowing’ or meta-thinking can only be generated in the space ‘in between’ text, child and educator, thereby foregrounding a ‘pedagogy of exposure’ (Biesta 2011) rather than ‘teacher proof’ texts.     

Correction to: Improved Parent–Child Interactions Predict Reduced Internalizing Symptoms Among the Offspring of Parents with Bipolar Disorder Undergoing a Prevention Program: A Proof‑of‑Concept Study

Research on Child and Adolescent Psychopathology - Correction to: Journal of Abnormal Child Psychology     

The Proof is in the Pudding: Commentary on Papers Updating Anna Freud’s Diagnostic Profile

ABSTRACT

This fine collection of articles documents efforts to bring Anna Freud’s diagnostic profile (1965) up to date by integrating more recent theory and research in attachment theory, inter-subjective theory, and theories deriving from the work of Bion on the process of “containing” (Bion, 1988). While some of the articles present the theoretical context for this integrative effort, Melandri’s (this issue) thoughtful and comprehensive clinical case shows us how an updated diagnostic profile can be put to work in the consulting room.     

Indian Rational Theology: Proof,Justification, and Epistemic Liberality in Nyāya's Argument for God

In classical India, debates over rational theology naturally become the occasion for fundamental questions about the scope and power of inference itself. This is well evinced in the classical proofs for God by the Hindu Nyāya tradition and the opposing arguments of classical Buddhists and Mīmā?sā philosophers. This paper calls attention to, and provides analysis of, a number of key nodes in these debates, particularly questions of inferential boundaries and whether inductive reasoning has the power to support inferences to wholly unique entities (like God). Further questions probed involve the supposed connection between structured objects and agential creators, and the status of examples used in traditional inference. Further, it calls attention to and defends what may be called an epistemological liberalism, championed—paradoxically perhaps—by Nyāya, and opposed by Buddhists and Mīmā?sakas.     

Severity of Types of Violations of Research Ethics: Perception of Iranian Master’s Students of Translation

Violations of research ethics including a varieties of plagiarism by students in Iran is a concern which has lately called promising levels of attention as rules are updated and better enforced and more awareness is being raised. As to deal with any problem, a full understanding of its nature is necessary, the current study focused on how a sample of Iranian students construe this phenomenon. To collect the necessary data, an original questionnaire with 34 closed-ended items included the most common instances of violations of research ethics was designed. The items included were mainly varieties of plagiarism identified in the literature. The items were narrowed down with reference to the qualitative data from focus group interviews with a purposive sample of Iranian graduate students. In the main phase of the study, using the questionnaire, quantitative data were obtained from the responses of 274 graduate students of translation studying in various Iranian universities. The findings revealed the participants did not have a fully accurate perception and appreciation of research ethics violation as they failed to distinguish ethically acceptable from unethical conducts. The contributing sample showed indifference to most ethical issues in scholarly publication. Translating a text and presenting it as one’s own in addition to text recycling were identified as the most severe instances perceived. The types, fraudulence, unacknowledged use, duplicate publication, misreferencing, excessive overuse were perceived the most severe to the least severe according to the sample. The typology and the findings on the severity of the types and instances were recommended to be used as an empirically supported guideline for curriculum design of academic writing courses in graduate programs in Iranian universities or similar contexts.