Time and Tradition as Reflected in the Etz Hayim Torah Commentary

At the beginning of the twenty‐first century, the Conservative Movement in North America published a Torah commentary reflecting its historical and theological elucidation of Judaism. This commentary, Etz Hayim, evinces a number of features that the following essay subjects to critical comment and analysis. These include: the commentary’s emphasis on historical context as critical to deciphering the Torah narratives and its laws; the presupposition that Judaism functions as an organism constantly in flux, open to patterns of progress and decline, with an aptitude for rebirth and self‐renewal; and that the pivotal rubrics of belonging, believing, and behaving are quintessential features of Jewish identity. While these characteristics are relatively uncontroversial, the same cannot be said for the editorial decision to divide, on the same page, the commentary’s 'historical' and 'homiletical' segments – a feature which effectively drives underground the option to integrate spiritual values and lessons using the tools of modern critical scholarship. Another unfortunate feature of Etz Hayim is that its two essays on Jewish law (Halakha) offer contrasting, competitive interpretations of how the halakhic process actually works in the minds of Conservative decisors. Yet these alternate approaches are not sufficiently delineated for the lay reader. Finally, while Etz Hayim does highlight value concepts that function as goads to ritual observance, the various contributors to the commentary and to the appended essays never fully engage why Conservative Jews ought to become serious practitioners of Jewish tradition. These shortcomings notwithstanding, Etz Hayim does offer a template of hope and expectation: through its historical‐religious experiences, the Jewish people facilitates an ethical worldview of particular, and of universal, merit.     

A Lambek Automaton

We define an automata-theoretic counterpart of (type-logical)grammars based on the (associative) Lambek-calculus L, a prominentformalism in computational linguistics. While the usual push-downautomaton (PDA) has the same weak generative power as the L-basedgrammars (Pentus, 1995), there is no direct relationship betweenthe computations of a PDA for some language L and the derivationsof an L-based grammar for L. In the Lambek-automaton, on theother hand, there is a tight relation (1-1) between automatoncomputations and grammar derivations. The automaton exhibitsa novel mode of operation, using hypothetical steps, directlyinspired by the hypothetical reasoning embodied by L.     

Defeasible inheritance systems and reactive diagrams

Inheritance diagrams are directed acyclic graphs with two typesof connections between nodes: x y (read x is a y) and x y(read as x is not a y). Given a diagram D, one can ask the formalquestion of "is there a valid (winning) path between node xand node y?" Depending on the existence of a valid path we cananswer the question "x is a y" or "x is not a y". The answer to the above question is determined through a complexinductive algorithm on paths between arbitrary pairs of pointsin the graph. This paper aims to simplify and interpret such diagrams andtheir algorithms. We approach the area on two fronts. (1) Suggest reactive arrows to simplify the algorithms for the winningpaths. (2) We give a conceptual analysis of (defeasible or nonmonotonic)inheritance diagrams, and compare our analysis to the "small"and "big sets" of preferential and related reasoning. In our analysis, we consider nodes as information sources andtruth values, direct links as information, and valid paths asinformation channels and comparisons of truth values. This resultsin an upward chaining, split validity, off-path preclusion inheritanceformalism of a particularly simple type. We show that the small and big sets of preferential reasoninghave to be relativized if we want them to conform to inheritancetheory, resulting in a more cautious approach, perhaps closerto actual human reasoning. We will also interpret inheritance diagrams as theories of prototypicalreasoning, based on two distances: set difference, and informationdifference. We will see that some of the major distinctions between inheritanceformalisms are consequences of deeper and more general problemsof treating conflicting information. It is easily seen that inheritance diagrams can also be analysedin terms of reactive diagrams - as can all argumentation systems. AMS Classification: 68T27, 68T30 Received for publication 15 March 2007.     

Comparing Computational Power

It is common practice to compare the computational power ofdifferent models of computation. For example, the recursivefunctions are strictly more powerful than the primitive recursivefunctions, because the latter are a proper subset of the former(which includes Ackermann's function). Side-by-side with this"containment" method of measuring power, it is also standardto base comparisons on "simulation". For example, one says thatthe (untyped) lambda calculus is as powerful—computationallyspeaking—as the partial recursive functions, because thelambda calculus can simulate all partial recursive functionsby encoding the natural numbers as Church numerals. The problem is that unbridled use of these two distinct waysof comparing power allows one to show that some computationalmodels (sets of partial functions) are strictly stronger thanthemselves! We argue that a better definition is that modelA is strictly stronger than B if A can simulate B via some encoding,whereas B cannot simulate A under any encoding. We show thatwith this definition, too, the recursive functions are strictlystronger than the primitive recursive. We also prove that therecursive functions, partial recursive functions, and Turingmachines are "complete", in the sense that no injective encodingcan make them equivalent to any "hypercomputational" model.¹     

Ternary Exclusive Or

Ternary exclusive or is the (two valued) truth function thatis true just in case exactly one of its three arguments is true.This is an interesting truth function, not definable in termsof the binary exclusive or alone, although the binary case isdefinable in terms of the ternary case. This article investigatesthe types of truth functions that can be defined by ternaryexclusive or, and relates these findings to the seminal workof Emil Post.     

A road careened into the woods: Comments on Dr. Morrison's commentary

Morrison's commentary on the paper entitled “Social Competence as a Developmental Construct” E. Waters & L. A. Sroufe Developmental Review 1983 3 79–97 focused primarily on the relevance of grand theory to contemporary issues in developmental psychology. The present comments reiterate central themes in the Waters and Sroufe paper that were either misconstrued or not discussed in the commentary. Waters and Sroufe offered (1) a definitional sketch rather than a grand theory, (2) a discussion of the need to employ diverse measures in order to assess a single construct at different ages, (3) much more extensive reference to empirical evidence than indicated in the commentary, and (4) a detailed discussion of assessment strategies common to various projects in which the coherence of individual development has been most evident in empirical data.     

Satisfiability Decay along Conjunctions of Pseudo-Random Clauses

k-SAT is a fundamental constraint satisfaction problem. It involvesS(m), the satisfaction set of the conjunction of m clauses,each clause a disjunction of k literals. The problem has manytheoretical, algorithmic and practical aspects. When the clauses are chosen at random it is anticipated (butnot fully proven) that, as the density parameter m/n (n thenumber of variables) grows, the transition of S(m) to beingempty, is abrupt: It has a "sharp threshold", with probability1 – o(1). In this article we replace the random ensemble analysis by apseudo-random one: Derive the decay rule for individual sequencesof clauses, subject to combinatorial conditions, which in turnhold with probability 1 – o(1). This is carried out under the big relaxation that k is not constantbut k = log n , or even r log log n . Then the decay of S isslow, "near-perfect" (like a radioactive decay), which entailssharp thresholds for the transition-time of S below any givenlevel, down to S = .     

'The Doers of the Law Will Be Justified': The Exegetical Origins of Martin Bucer's Triplex Iustificatio

This essay seeks to sketch the profile of Martin Bucer's viewson the doctrine of justification as developed in his 1536 commentaryon Romans, focusing in particular on his idiosyncratic languageof ‘threefold justification’ in his comments onRom. 2:13. This text is taken as a vantage point from whichto survey the history of interpretation of the Pauline conceptof justification within the Augustinian tradition, giving extendedconsideration to exegesis by Augustine and Thomas Aquinas. Bucer'sinitial discussion of the Pauline usage of o in the praefatato his commentary is examined next, and it is concluded thathis understanding of justification falls more or less withinthe trajectory charted by previous medieval interpreters. Turningthen to Bucer's comments on Rom. 2:13, it is argued that thenotion of ‘threefold justification’ arises as anattempt to integrate the early evangelical appropriation ofthe Scotist language of ‘divine acceptation’ withina traditional Augustinian account of justification as both eventand process. The resulting formula collapses predestinationinto justification, making the latter the unifying concept inBucer's soteriology. It is hoped that this essay will contributeto deepening our understanding of an oft-neglected reformerwhile at the same time broadening our understanding of earlyevangelical teaching on a central doctrinal locus.     

A task‐ and role‐based perspective on super‐recognizers: Commentary on ‘Super‐recognizers: From the lab to the world and back again’

This article provides a commentary on recent work by Ramon et al. (2019, British Journal of Psychology) on super‐recognizers. The commentary advocates a task‐ and role‐based approach to SR research and greater collaboration between researchers and the applied community.     

'At that Time the Group Around Maximian was Enjoying Imperial Power': an Interpolation in Gregory of Nyssa's Homily in Praise of Theodore

The sentence ‘For at that time the group around Maximianwas enjoying imperial power’, the only chronological indicatorin Gregory of Nyssa's In Theodorum, may be identified on literarygrounds as a scribal interpolation. When this is recognized,the Passio Theodori (BHG 1761) becomes the oldest evidence forthe dating of Theodore's martyrdom.     

Mary's Virginity in partu and Tertullian's anti-Docetism in De Carne Christi Reconsidered

Astute scholars have already pointed to the fact that it isTertullian's vehement anti-docetism that best explains his rejectionof the notion that Mary's virginity did not relate only to thequestion of the conception of Jesus. Insistence on Mary's virginityin the act of giving birth (in partu) or thereafter (post partum)would, for Tertullian, weaken the argument that Jesus was possessedof true humanity in his flesh. This important question in historicaltheology is revisited from the literary perspective of rhetoricalcriticism. I wish to argue that it is really Tertullian's handlingof Scripture as an evidential tool in the construction of arhetorical position that allows him to use reference to Mary'svirginity as part of his anti-docetic position. A close examinationof the rhetoric of Tertullian's De Carne Christi will illustratethis point.     

On the Consistency of Q-Matrix Estimation: A Rejoinder

This rejoinder responds to the commentary by Liu (Psychometrika, 2015) entitled “On the consistency of Q-matrix estimation: A commentary” on the paper “A general method of empirical Q-matrix validation” by de la Torre and Chiu (Psychometrika, 2015). It discusses and addresses three concerns raised in the commentary, namely the estimation accuracy when a provisional Q-matrix is used, the consistency of the Q-matrix estimator, and the computational efficiency of the proposed method.     

The Origins of the Anaphoral Benedictus

This paper presents evidence for the Benedictus following theSanctus having been introduced first in Jerusalem in the Liturgyof St James. The structure and variety of the Benedictus areexamined, along with theories of Jewish and Antiochene originin relation to the Apostolic Constitutions. A fifth-centuryJerusalem homily provides the first evidence for the Mattheanform, subsequently contained in all versions of the Liturgyof St James and which becomes normative for nearly all eucharistictraditions. The conclusion distinguishes between the originsof the idea of the anaphoral Benedictus and the origins of itsform. The idea of a ‘blessed be’ acclamation afterthe Sanctus may well lie in Jewish traditions, but the originsof its form lie in the Palm Sunday acclamation of fourth-centuryJerusalem.     

Naming and Diagonalization, from Cantor to Godel to Kleene

We trace self-reference phenomena to the possibility of namingfunctions by names that belong to the domain over which thefunctions are defined. A naming system is a structure of theform (D, type( ),{ }), where D is a non-empty set; for everya D, which is a name of a k-ary function, {a}: D^k D is thefunction named by a, and type(a) is the type of a, which tellsus if a is a name and, if it is, the arity of the named function.Under quite general conditions we get a fixed point theorem,whose special cases include the fixed point theorem underlyingGödel's proof, Kleene's recursion theorem and many othertheorems of this nature, including the solution to simultaneousfixed point equations. Partial functions are accommodated byincluding "undefined" values; we investigate different systemsarising out of different ways of dealing with them. Many-sortednaming systems are suggested as a natural approach to generalcomputatability with many data types over arbitrary structures.The first part of the paper is a historical reconstruction ofthe way Gödel probably derived his proof from Cantor'sdiagonalization, through the semantic version of Richard. Theincompleteness proof–including the fixed point construction–resultfrom a natural line of thought, thereby dispelling the appearanceof a "magic trick". The analysis goes on to show how Kleene'srecursion theorem is obtained along the same lines.     

Generalizing from Case Studies: A Commentary

This commentary responds to the articles assembled for the thematic issue Self-identity on the move: methodological elaborations (IPBS, 51 (2), June 2017). The issue points in two directions. Firstly, the articles investigate the way individual self-identity develops in changing social and cultural environments, specifically in the contexts of family, youth and migration. Secondly, the special issue is also interested in methodological elaboration, more specifically the question of how one can generalize from individual case studies, especially when looking at complex, multiscale, semiotic processes. This commentary particularly addresses the second point and uses the various cases in this issue (i) to better understand something of the larger intellectual debate around the question of ‘generalizing from case studies’, and (ii) to reflect on writing as a tool for indexing generalization. The commentary highlights five textual moves the authors use to make their findings relevant beyond the specifics of the local study.     

In Defense of Mainstream Conservatism: A Response to Crouse and Stalker

This article provides a response to Crouse and Stalker's reply to my commentary (Thomas, 2013) on their article titled “Do Right‐Wing Authoritarian Beliefs Originate from Psychological Conflict?” (Psychoanalytic Psychology, 24, 25–44). The authors' critical remarks regarding my commentary are addressed, and recommendations are offered for a more cautious use of psychoanalytic theory and results derived from The Right‐Wing Authoritarianism Scale (Altemeyer, 1998) for labeling persons with mainstream conservative political beliefs as being “psychopathological” or “right‐wing authoritarians.” Such assertions regarding the personality characteristics of political conservatives are particularly troubling, since the authors' conclusions were purely speculative, and they collected neither clinical nor empirical data on patients or research subjects with so‐called right‐wing authoritarian personalities to support their speculations.     

The Basic Constructive Logic for a Weak Sense of Consistency defined with a Propositional Falsity Constant

The logic B_Kc1 is the basic constructive logic in the ternaryrelational semantics (without a set of designated points) adequateto consistency understood as the absence of the negation ofany theorem. Negation is introduced in B_Kc1 with a negationconnective. The aim of this paper is to define the logic B_Kc1F.In this logic negation is introduced via a propositional falsityconstant. We prove that B_Kc1 and B_Kc1F are definitionally equivalent.     

Scientific Thought

Using Pritchard's technique, the frequency and duration of total disappearance of stabilized images were compared using two reporting procedures: i.e., (a) a running commentary and (b) only “off” or “on.” Two target figures were employed: a simple triangle and a five-by-five grid of squares. The incidence and duration of complete disappearance was (a) less with the commentary than with the off-on procedure and (b) less with the grid than with the triangle. Hypotheses to account for the differences are discussed.