Mental representation of logical connectives

Logical connectives, such as “AND”, “OR”, “IF . . . THEN”, and “IF AND ONLY IF” are ubiquitous in both language and cognition; however, reasoning with logical connectives is error-prone. We argue that some of these errors may stem from people's tendency to minimize the number of possibilities compatible with logical connectives and to construct a “minimalist” one-possibility representation. As a result, connectives denoting a single possibility (e.g., conjunctions) are likely to be represented correctly, whereas connectives denoting multiple possibilities (e.g., disjunctions or conditionals) are likely to be erroneously represented as conjunctions. These predictions were tested and confirmed in three experiments using different paradigms. In Experiment 1, participants were presented with a multiple-choice task and asked to select all and only those possibilities that would indicate that compound verbal propositions were true versus false. In Experiment 2, a somewhat similar task was used, except that participants were asked later to perform a cued recall of verbal propositions. Finally, Experiment 3 used an old/new recognition paradigm to examine participants' ability to accurately recognize different logical connectives. The results of the three experiments are discussed in relation to theories of representation of possibilities and theories of reasoning.     

The escape-to-Israel syndrome: Variations on the geographic cure

The author conceptualizes a pattern of thought and behavior that can be called the escape-to-Israel syndrome. This pattern is a contemporary variety, appearing primarily in the Jewish population, of the geographic cure: that is, one can solve one's personal dilemmas by moving from one place to another. The syndrome is characterized by a tendency to idealize life in Israel. This idealization, and the viewers' fantasy of their own future in Israel, deflect solid confrontation with genuine personal problems. If, in fact, they do move to Israel, they may experience shock and trauma at the gap between expected reality and the discovered one. This may only compound their emotional difficulties.The author wishes to express his gratitude to Professor Shamai Davidson, Clinical Director of the Shalvata Mental Health Center, Hod HaSharon, Israel, for his critical comments during the preparation of this article.     

Strict embedding of the elementary ontology into the monadic second-order calculus of predicates admitting the empty individual domain

There is given the proof of strict embedding of Leniewski's elementary ontology into monadic second-order calculus of predicates providing a formalization of the class of all formulas valid in all domains (including the empty one). The elementary ontology with the axiom S (S S) is strictly embeddable into monadic second-order calculus of predicates which provides a formalization of the classes of all formulas valid in all non-empty domains.     

The development of socialization skills in an electively mute child

In a booth designed especially for work with both autistic and electively mute children, a 4-yr-old girl named Dolly, who had no communicative speech or imitative skills, was given a preliminary session in which her verbal output was assessed. To elicit sounds from Dolly, an instrument called a “color organ” was used as a positive reinforcer. After this baseline assessment, in 40 half-hour sessions, Dolly was taught to make eye contact with E, and to obey instructions—although it was first necessary to extinguish her disruptive behavior, particularly her opérant crying. In addition, she learned non-verbal imitative behavior, such as hand clapping; and verbal imitative behavior, such as saying “Hi!” Social (play) sessions were begun after session 21, and continued for the remaining time. These were helpful in generalizing Dolly's learned skills to an environment other than the booth; and to other tasks, such as singing “Ee-eye-ee-eye-oh” in the refrain of the song, “Old McDonald”; and pointing to E's eyes, saying “ice”.     

Wisdom as Parental Teaching in Proverbs 1–9

It is the contention of this article that Proverbs chs. 1–9 is a literary unity in which wisdom has the denotation of the parental household teaching. Teachings which have other contexts in other parts of the Old Testament have in Pr. 1–9 a parental teaching context. Besides denoting the parental teaching, personified speaking Wisdom has the personal features of a teacher. Both Wisdom's features and her message serve to reinforce the parental teaching. Personified Wisdom also denotes the teaching of the entire Book of Proverbs. Through the device of personified Wisdom, the wisdom of Solomon enshrined in the Book of Proverbs is re-located from the royal court to the individual Israelite household. This is evident in the literary design of the book. It also reflects the situation of the book's redaction in post-exilic Judaism.     

Internal approach to external sets and universes

A problem which enthusiasts ofIST, Nelson's internal set theory, usually face is how to treat external sets in the internal universe which does not contain them directly. To solve this problem, we considerBST,bounded set theory, a modification ofIST which is, briefly, a theory for the family of thoseIST sets which are members of standard sets.We show thatBST is strong enough to incorporate external sets in the internal universe in a way sufficient to develop the most advanced applications of nonstandard methods. In particular, we define inBST an enlargement of theBST universe which satisfies the axioms ofHST, an external theory close to a theory introduced by Hrbaek. HST includes Replacement and Saturation for all formulas but contradicts the Power Set and Choice axioms (either of them is incompatible with Replacement plus Saturation), therefore to get an external universe which satisfies all ofZFC minus Regularity one has to pay by a restriction of Saturation. We prove thatHST admits a system of subuniverses which modelZFC (minus Regularity but with Power Set and Choice) and Saturation in a form restricted by a fixed but arbitrary standard cardinal.Thus the proposed system of set theoretic foundations for nonstandard mathematics, based on the simple and natural axioms of the internal theoryBST, provides the treatment of external sets sufficient to carry out elaborate external constructions.Partially supported by AMS grants in 1993 and 1994 and DFG grant in 1994.Presented byRobert Goldblatt