Symbolic representation across domains in preschool children

The study examines children's understanding of notational representation. Children 3 to 5 years old were shown a card containing a notation and told what it said. The children were asked to say what was printed on the card 3 times: when it was under a display named by the notation, when it was under a different display, and finally when it had been returned to the original position. In Study 1, the card contained a word or a picture indicating object identity or a numeral or an analogue indicating quantity. All the children could solve the problems containing pictures, numerals, or analogues, but the word condition was difficult and children believed that the word changed when the card moved to the new display. In Study 2, the comparison between object names and quantities was made more equitable by introducing easy and difficult versions of each condition. This time, there was little difference between cards indicating names and those indicating quantities but large differences in children's ability to solve the problem as a function of their familiarity with the notation that was written. The results point to weaknesses in children's understanding of how representations refer to meanings.     

Constructing worlds

You and I can differ in what we say, or believe, even though the things we say, or believe, are logically equivalent. Discussing what is said, or believed, requires notions of content which are finer-grained than sets of (metaphysically or logically) possible worlds. In this paper, I develop the approach to fine-grained content in terms of a space of possible and impossible worlds. I give a method for constructing ersatz worlds based on a theory of substantial facts. I show how this theory overcomes an objection to actualist constructions of ersatz worlds and argue that it naturally gives rise to useful notions of fine-grained content.     

Symbolic representation of the number three: a study with three-year-old children from contrasting socioeconomic environments

The goal of the present study was to compare a range of aspects in children’s symbolic knowledge about the number three among two groups of three-year-olds from contrasting socioeconomic backgrounds. Every child was presented with five tasks that focused on the number three and that had cognitive demands of different complexity: expressing their age, reciting the conventional number series up to three, quantifying a collection of three, and two tasks requiring the use of visually presented quantitative information.The results showed the same order of difficulty of the tasks in both socioeconomic groups and a clear performance difference depending on socioeconomic background. These findings show that symbolic knowledge about the number three does not come in an all or none fashion. Rather, different aspects of this symbolic competence become apparent in response to different tasks, and seem to depend largely on the socioeconomic environment in which children develop.     

Explaining old worlds

This Comment treats each of Spinosa, Flores, and Dreyfus's three subjects ‐entrepreneurship, democratic activity, and cultivation of solidarity ‐ in turn. Though marred by inattention to moral consequences and an accordingly unjustified meliorism, the authors’ insights reaffirm and strengthen a number of convictions obscured in current political‐theory debates. In particular, their account of the virtuous citizen, and of a variant of solidarity which grows out of such citizens’ activity, deserves recognition. The basic contention that humans are ‘at their best’ when self‐consciously engaged in transformative activities is accepted, with the essential caveat that such activity can only be sustained for relatively short periods of time by individuals and polities alike.     

Pleonastic possible worlds

The role of possible worlds in philosophy is hard to overestimate. Nevertheless, their nature and existence is very controversial. This is particularly serious, since their standard applications depend on there being sufficiently many of them. The paper develops an account of possible worlds on which it is particularly easy to believe in their existence: an account of possible worlds as pleonastic entities. Pleonastic entities are entities whose existence can be validly inferred from statements that neither refer to nor quantify over them as a matter of conceptual necessity. Definitions are proposed that ensure that this is the case for possible worlds.     

Take the best versus simultaneous feature matching: probabilistic inferences from memory and effects of representation format

In 4 experiments, the tendency to use the simple heuristic Take The Best (TTB; G. Gigerenzer & D. Goldstein, 1996) was explored for probabilistic multiattribute inferences from memory. In a newly developed procedure, participants first learned attribute patterns that formed the basis for inferences in a second phase. A Bayesian method classified strategies as TTB, compensatory, or guessing. Experiment 1 had a high rate (64%) of participants classified as TTB users when inferences were made from memory. Experiment 2 showed that this was no mere materials effect. In Experiments 3 and 4, the authors examined effects of the representational format of the attribute information. Experiment 4 showed that the representational format may be an important moderating variable for strategy use.     

Branching of possible worlds

The question as to whether some objects are possible worlds that have an initial segment in common, i.e. so that their fusion is a temporal tree whose branches are possible worlds, arises both for those who hold that our universe has the structure of a temporal tree and for those who hold that what there is includes concrete universes of every possible variety. The notion of “possible world” employed in the question is seen to be the notion of an object of a kind such that objects of that kind play a certain theoretical role. Lewis’s discussion of the question is thereby clarified but is nevertheless inadequate; his negative answer is correct but even from his combinatorialist viewpoint the rationale he provides for this answer is misguided. I explain why the combinatorialist advocate of concrete plenitude should hold that no object is a tree of possible worlds. Then I explain that for a different reason the nomic essentialist advocate of concrete plenitude should hold this much too.     

Functionalism about possible worlds

Various writers have proposed that the notion of a possible world is a functional concept, yet very little has been done to develop that proposal. This paper explores a particular functionalist account of possible worlds, according to which pluralities of possible worlds are the bases for structures which provide occupants for the roles which analyse our ordinary modal concepts. It argues that the resulting position meets some of the stringent constraints which philosophers have placed upon accounts of possible worlds, while also trivializing the question what possible worlds are. The paper then discusses a range of problems facing the functionalist position.     

Partial worlds and paradox

Since universal language systems are confronted with serious paradoxical consequences, a semantic approach is developed in whichpartial worlds form the ontological basis. This approach shares withsituation semantics the basic idea that statements always refer to certain partial worlds, and it agrees with the extensional and model-theoretic character ofpossible worlds semantics. Within the framework of the partial worlds conception a satisfactory solution to theLiar paradox can be formulated. In particular, one advantage of this approach over those theories that are based on the totality of possible worlds semantics can be found in the fact that the so-called Strengthened Liar problem is avoided.I would like to thank Dirk Koppelberg for helpful remarks on an earlier draft of this paper. Special thanks to an anonymous referee for detailed comments.