Varieties of Monadic Heyting Algebras. Part III

This paper is the concluding part of [1] and [2], and it investigates the inner structure of the lattice (MHA) of all varieties of monadic Heyting algebras. For every n , we introduce and investigate varieties of depth n and cluster n, and present two partitions of (MHA), into varieties of depth n, and into varieties of cluster n. We pay a special attention to the lower part of (MHA) and investigate finite and critical varieties of monadic Heyting algebras in detail. In particular, we prove that there exist exactly thirteen critical varieties in (MHA) and that it is decidable whether a given variety of monadic Heyting algebras is finite or not. The representation of (MHA) is also given. All these provide us with a satisfactory insight into (MHA). Since (MHA) is dual to the lattice NExtMIPC of all normal extensions of the intuitionistic modal logic MIPC, we also obtain a clearer picture of the lattice structure of intuitionistic modal logics over MIPC.     

A content semantics for quantified relevant logics. I

We present an algebraic-style of semantics, which we call a content semantics, for quantified relevant logics based on the weak system BBQ. We show soundness and completeness for all quantificational logics extending BBQ and also treat reduced modelling for all systems containing BB ^d Q. The key idea of content semantics is that true entailments AB are represented under interpretation I as content containments, i.e. I(A)I(B) (or, the content of A contains that of B). This is opposed to the truth-functional way which represents true entailments as truth-preservations over all set-ups (or worlds), i.e. (VaK) (if I(A, a) = T then I(B, a)= T).This paper was presented to the Australasian Association for Logic Conference, held at the University of Auckland from 9–12th July, 1986. I wish to thank those present for some helpful comments. I also wish to thank Kit Fine for some useful discussion on some topics of this paper.     

Graded modalities. I

We study a modal system ¯T, that extends the classical (prepositional) modal system T and whose language is provided with modal operators M inn (nN) to be interpreted, in the usual kripkean semantics, as there are more than n accessible worlds such that.... We find reasonable axioms for ¯T and we prove for it completeness, compactness and decidability theorems.The authors are very indebted to the referee for Ms consideration and appreciation of their work.     

Revolution and the counter-revolution: The conflict over meaning between P. B. Struve and S. L. Frank in 1922

Lecturer in the Lomonossov University, Moscow, specialist in the young Hegel; has also worked quite extensively on Russian prerevolutionary thought. Nikolaj Plotnikov is notably the co-editor of the recently re-published texts,Vekhi, Iz Glubiny in the collection 'Iz istorii oteestvennoj filosofskoj mysli' in conjunction withVoprosy Filosofii.     

Taking Religious Pluralism Seriously. Arguing for an Institutional Turn. Introduction

Discussions of the relations between religions, society, politics, and the state in recent political philosophy are characterized, firstly, by a strong US American bias focusing on limitations of religious arguments in public debate. Even if the restriction or radical exclusion of religious reasons from public debate has recently been extensively criticized, secularist interpretations of liberal-democratic constitutions still prevail. Here it is argued that both strong secularism and weak or second order secularism are counterproductive for many reasons. Secondly, separationist interpretations of state-church relations are predominant, even if the severe wall of separation is criticized more often nowadays. Here it is argued that there are more and more interesting options than either separationism or accommodationism, that we should not exclusively focus at the constitutional relations between state and churches but address the full reciprocal relationship between society, culture, politics, nation, state and (organized) religions, and that we need more historical and comparative perspectives for the required institutionalist turn in political theory in order to overcome the obstacles inherent in predominant American political philosophy. The articles included in this volume are first, modest steps in this new direction.     

Re-visioning resurrection: St. Paul and Swedenborg

St. Paul's spiritual body is envisaged as imaginal body, the wordimaginal standing for the intermediate realm of beings and events in Neoplatonism and Sufism. Swedenborg's world of spirits and angels conforms to this view and so is seen as contributing to a richer understanding of St. Paul in the sense of a good docetism. Crucial in this kind of revisioning the mystery of resurrection is the creative power of visionary imagination, which, in turn, is inseparable from the reality of the soul as thesitus of visionary events.     

On Intermediate Predicate Logics of some Finite Kripke Frames,I. Levelwise Uniform Trees

An intermediate predicate logic L is called finite iff it is characterized by a finite partially ordered set M, i.e., iff L is the logic of the class of all predicate Kripke frames based on M. In this paper we study axiomatizability of logics of this kind. Namely, we consider logics characterized by finite trees M of a certain type (levelwise uniform trees) and establish the finite axiomatizability criterion for this case.     

NEO PI-R Normative Personality Data That Distinguish U.S. Air Force Female Pilots

Female U.S. Air Force (USAF) pilots represent a unique group of women in a challenging, high-risk, and male-dominated profession. Aside from ability and motivation, personality characteristics are considered to play a key role in succeeding as a military pilot (Paullin, Katz, Bruskiewicz, Houston, & Damos, 2006 Paullin, C., Katz, L., Bruskeiwicz, K. T., Houston, J. and Damos, D. 2006. Review of aviator selection (Tech. Rep. No. 1183) Arlington, VA: United States Army Research Institute for the Behavioral Sciences.  [Google Scholar]). This study evaluated psychological baseline test scores from the NEO Personality Inventory–Revised (NEO PI-R) on the current inventory of rated USAF female (n = 512) and male (n = 9630) pilots in an effort to (a) provide modern normative data on the personality traits of current USAF female pilots, (b) identify personality traits that distinguish female pilots from male pilots and non-pilot females in the civilian normative sample, and (c) assess for meaningful personality differences within female pilots across specific airframes (e.g., fighter/bomber, reconnaissance/surveillance, tanker/transport, and helicopter). The results of the study aim to shed light on objective personality traits and differences and assist clinical psychologists with the interpretation of NEO PI-R psychological test scores when evaluating USAF female pilots. A case vignette is provided to illustrate practical application of study findings.     

Social-class indicators differentially predict engagement in prevention vs. detection behaviours

Objective: Few systematic studies have examined the contexts in which social-class variables will predict engagement in health-relevant behaviours. The current research examined whether the impact of social-class on health behaviours depends upon how social-class is assessed and the category of health behaviour under consideration.

Method: Our sample was drawn from the Health Information National Trends Survey in 2012 (N = 3959). Participants reported their income and education as well as their engagement in a variety of prevention and detection behaviours.

Results: Consistent with our hypothesised framework, we found that income predicted engagement in a variety of detection behaviours above and beyond education, whereas education predicted engagement in a variety of prevention behaviours above and beyond income.

Conclusions: Our findings suggest that income and education operate on health behaviours via different pathways and have implications for public health policy and intervention.     

Maturing into Boyhood: James E. Dittes on Men and Meaning

In this essay, I review the progression of James E. Dittes' books on men and men's issues, including The Male Predicament, When Work Goes Sour, Men at Work, and Driven By Hope. Dittes moves from a palpable ambivalence toward men and their attendant griefs in earlier books to an increasingly unconditional affirmation of men in more recent ones. His own professional pilgrimage models his desire that men might mature into boyhood by coming to savor their inherent sense of expectancy as sons.     

The cabinet of Dr. Lacan

Conclusion Obscurity is not the worst failing, and it is philistinism to pretend that it is. In a series of brilliant essays written over the last fifteen years Stanley Cavell has consistently argued that more important than the question whether obscurity could have been avoided is whether it affects our confidence in the author.Confidence raises the issue of intention, and I would have thought that the primary commitment of a psychoanalytic writer was to pass on, and (if he can) to refine while passing on, a particular way of exploring the mind. Indeed this is how Lacan himself proposes that his work should be judged. The aim of my teaching, he writes, has been and still is the training of analysts.For decades now Lacan has been insisting that the nature of this commitment has been systematically obscured, particularly in North America. Training has become routinized, and analysis itself has become distorted into a process of crude social adaptation. There is much here to agree with. Yet two questions must be raised. Has Lacan devised a more effective method of training analysts? And, would one expect this from his writings?Neither question gets a favourable answer. All reports of his training methods, over which he has now brought about three distinct secessions within the French psychoanalytic movement, are horrifying.¹³ It is now, I am told, possible to become a Lacanian analyst after a very few months of Lacanian analysis. And what pedagogic contribution could we expect from a form of prose that has two salient characteristics: it exhibits the application of theory to particular cases as quite arbitrary, and it forces the adherents it gains into pastiche.¹⁴ Lacan's ideas and Lacan's style, yoked in an indissoluble union, represent an invasive tyranny. And it is by a hideous irony that this tyranny should find its recruits among groups that have nothing in common except the sense that they lack a theory worthy of their cause or calling: feminists, cinéastes, professors of literature.Lacan himself offers several justifications for his obscurity, about which he has no false modesty. At times he says that he is the voice, the messenger, the porte-parole, of the unconscious itself. Lacan's claim stirs in my mind the retort Freud made to a similar assult upon his credulity and by someone who had learned from Lacan. It is not the unconscious mind I look out for in your paintings, Freud said to Salvador Dali, it is the conscious.This article originally appeared as a review (The New York Review of Books, January 25, 1979) of the three books listed under References.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

On a certain class ofm-address machines

Conclusion It follows from the proved theorems that ifM =Q, (whereQ={0,q ₁,q ₂,...,q }) is a machine of the classM _F then there exist machinesM _i such thatM _i(1,c)=M (q _i,c) andQ _i={0, 1, 2, ..., +1} (i=1, 2, ..., ).And thus, if the way in which to an initial function of content of memorycC a machine assigns a final onecC is regarded as the only essential property of the machine then we can deal with the machines of the formM ={0, 1, 2, ..., }, and processes (t) (wheret=1,c,cC) only.Such approach can simplify the problem of defining particular machines of the classM _F , composing and simplifying them.Allatum est die 19 Januarii 1970     

A semantical investigation into Leśniewski's axiom of his ontology

A structure A for the language L, which is the first-order language (without equality) whose only nonlogical symbol is the binary predicate symbol , is called a quasi -struoture iff (a) the universe A of A consists of sets and (b) a b is true in A ([p) a = {p } & p b] for every a and b in A, where a(b) is the name of a (b). A quasi -structure A is called an -structure iff (c) {p } A whenever p a A. Then a closed formula in L is derivable from Leniewski's axiom x, y[x y u (u x) u; v(u, v x u v) u(u x u y)] (from the axiom x, y(x y x x) x, y, z(x y z y x z)) iff is true in every -structure (in every quasi -structure).     

Angular homeostasis: IV. Polygonal orbits

Some properties are discussed of regular polygons that may result from angular homeostatic processes in stable orbit. To characterize these homeostatic polygons we need to discuss the winding number, the sidedness (integer, fractional and irrational), multiplicity, envelopes, and density. A regular (i.e., equilateral, equiangular) polygon may be closed in one revolution about its unique center, in multiple revolutions, or not at all. A homeostatic polygon can be generated only if all vertices are included in a single polygon, which occurs if and only if the number of vertices and the number of revolutions required to complete the polygon are relatively prime. For the homeostatic polygon to have a finite number of sides (without repeating itself) the angle subtended by any two successive vertices at the center must be a rational multiple of 2. Biological implications of these properties are illustrated.     

Interpretations of the first-order theory of diagonalizable algebras in peano arithmetic

For every sequence |p _n } _n of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory diagonalizable algebras, we associate a formula ⁰ A, called the value ofA inPA with respect to the interpretation. We show that, ifA is true in every diagonalizable algebra, then, for every, ⁰ A is a theorem ofPA.     

Intuitionistic uniformity principles for propositions and some applications

This note deals with the prepositional uniformity principlep-UP: p x N A (p, x) x N p A (p, x) ( species of all propositions) in intuitionistic mathematics.p-UP is implied by WC and KS. But there are interestingp-UP-cases which require weak KS resp. WC only. UP for number species follows fromp-UP by extended bar-induction (ranging over propositions) and suitable weak continuity. As corollaries we have the disjunction property and the existential definability w.r.t. concrete objects. Other consequences are: there is no non-trivial countable partition of;id is the only injective function from to; there are no many-place injective prepositional functions; card () is incomparable with the cardinality of all metric spaces containing at least three elements.     

On superintuitionistic logics as fragments of proof logic extensions

Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructedIn this diagram the maps, x and are isomorphisms, thereforex ^–1 = ; and the maps and are the semilattice epimorphisms that are not commutative with lattice operation +. Besides, the given diagram is commutative, and the next equalities take place: ^–1 = ^–1 and = ^–1 x. The latter implies in particular that any superintuitionistic logic is a superintuitionistic fragment of some proof logic extension.     

Logics of some kripke frames connected with Medvedev notion of informational types

Intermediate prepositional logics we consider here describe the setI() of regular informational types introduced by Yu. T. Medvedev [7]. He showed thatI() is a Heyting algebra. This algebra gives rise to the logic of infinite problems from [13] denoted here asLM ₁. Some other definitions of negation inI() lead to logicsLM _n (n ). We study inclusions between these and other systems, proveLM _n to be non-finitely axiomatizable (n ) and recursively axiomatizable (n < ). We also show that formulas in one variable do not separateLM from Heyting's logicH, andLM _n (n < ) from Scott's logic (H+S).