The role of logical and nonlogical factors in making inferences about category membership

Three postulates are proposed concerning the manner in which persons infer the validity of propositions that do not necessarily follow logically from the information available. These postulates assume that subjects first attempt to identify the propositions that are most and least likely to follow from the information given. They then use their beliefs in these propositions as anchors, relative to which the validity of other propositions is evaluated on the basis of both logical and nonlogical criteria. Two experiments are reported in which these postulates are used successfully to diagnose the logical and nonlogical factors that underlie inferences based upon both single statements and sets of syllogistically related propositions. The implications of the proposed postulates for existing formulations of social inference and cognitive organization are discussed.     

The development of young children's awareness of logical inconsistencies

Research by Markman (1979) suggests that children up to 12 years of age do not spontaneously detect logical inconsistencies. The present study was directed to factors which may limit children's ability to recognize their failures to understand. A task was devised which involved materials that were clearly based on children's experiences, and which involved premises and conclusions which were presented contiguously, rather than being interspersed among other sentences. Ninety-six 5-, 6-, and 7-year-old children were asked to judge the acceptability of eight three-sentence “stories” told by a puppet, and were asked to justify their responses. The stories differed in whether they were consistent or inconsistent, and in whether the principle upon which a story's consistency depended was implicitly or explicitly stated. The results showed developmental differences. By Age 7 years, most children were quite capable of evaluating sentences for their logical consistency. Five-year-olds, however, did not perform as well on the task, especially when the information upon which the logical cohesiveness of the stories rested was implicitly, rather than explicitly, stated. An examination of the justifications provided by these children revealed that they tended to question the empirical validity of individual sentences, rather than integrate the story as a whole and examine its overall logical structure.     

The logic of logical revision formalizing dummett's argument

Neil Tennant and Joseph Salerno have recently attempted to rigorously formalize Michael Dummett's argument for logical revision. Surprisingly, both conclude that Dummett commits elementary logical errors, and hence fails to offer an argument that is even prima facie valid. After explicating the arguments Salerno and Tennant attribute to Dummett, I show how broader attention to Dummett's writings on the theory of meaning allows one to discern, and formalize, a valid argument for logical revision. Then, after correctly providing a rigorous statement of the argument, I am able to delineate four possible anti-Dummettian responses. Following recent work by Stewart Shapiro and Crispin Wright, I conclude that progress in the anti-realist's dialectic requires greater clarity about the key modal notions used in Dummett's proof.     

Are children any more logical than monkeys on the five-term series problem?

Six-year-old children were tested on several versions of the five-term transitivity problem as used by B. O. McGonigle and M. Chalmers (1977, Nature (London), 267, 694–696) with squirrel monkeys as subjects. Both binary and triadic versions of the tests were administered in both verbal and nonverbal modes to help determine whether or not any major procedural differences between the monkey version and that used conventionally in research with children might account for the monkey's apparently nonlogical solution of the problem. The main result is that children showed very similar response profiles to that of monkeys in all the conditions used. In addition, “labeling”, direct seriation, and “association” post-tests suggest that nonlogical strategies can underwrite ostensibly impeccable transitive “reasoning” in child as well as monkey.     

Russellian and Wittgensteinian Atomism

One difference between Russell's logical atomism in The Philosophy of Logical Atomism and Wittgenstein's in the Tractatus is that Russell's doctrine is explicitly epistemological, whereas Wittgenstein's is not; another difference is that Wittgenstein gives an a priori argument for the doctrine of logical atomism whereas Russell gives no such argument. I argue that these two differences are instructively connected: Russell's focus on epistemology prevents him from being able to give a motivated argument for the truth of logical atomism. Furthermore, I argue that this is not just a contingent failure of Russell's system: no primarily epistemological atomism can avail itself of Wittgenstein's style of a priori argument for the truth of atomism. An important suggestion of the argument, illuminating with respect to the subsequent history of analytic philosophy, is that Russell's logical atomism already contains the seeds of verificationism in a nascent form, whereas Wittgenstein's atomism has no tendency toward verification.     

Elementary schoolchildren know a logical argument when they see one

Both empirical data and theoretical approaches suggest that argumentation is an important component of development of reasoning skills. We argue that if argumentation does have a primary role, then children should be able to distinguish more from less logical justifications even when they are incapable of determining the correct conclusion by themselves. We asked 8- and 11-year-old children to choose one of two conclusions for abstract reasoning problems, based on justifications from authority (friends and teacher) or logical ones (probability and counterexamples). Although there was a clear age-related increase, even the younger children considered logical justifications to be better than authority, irrespective of the specific conclusion endorsed. Thus, children can distinguish logical and non-logical justifications even when they cannot easily arrive at the correct conclusion by themselves.     

The logic of the medical research article

As do all forms of science, medical theories have a factual as well as a logical basis. New information is presented in medical research articles. These papers have three separate arguments: the argument of the hypothesis, the argument of the experimental protocol, and the argument of the hypothesis's judgment. These arguments may be examples of the hypothetico-deductive or confirmational model of scientific inference. The logical form of these arguments are informal and inductive rather than formal and deductive. Understanding the nature of the logic of the medical research article may help avoid erroneous conclusions.     

I. Psychologism,Functionalism, and the modal status of logical Laws

In a recent article (Inquiry, Vol. 19 [1976]), J. W. Meiland addresses the issue of psychologism in logic, which holds that logic is a branch of psychology and that logical laws (such as the Principle of Non‐Contradiction) are contingent upon the nature of the mind. Meiland examines Husserl's critique of psychologism, argues that Husserl is not convincing, and offers two new objections to the psychologistic thesis. In this paper I attempt to rebut those objections. In question are the acceptable criteria for determining the possibility or impossibility of systems of logic significantly different from our own. I argue that a criteriological application of our accepted laws of logic to this question commits a circular fallacy. I then argue that, even if we accept logical consistency as a criterion for possibility, a plausible argument for the possibility of valid alternative logics can be constructed by using the functionalist analogy between minds and automata. Finally, I attempt to rebut the claim that in logic the only changes possible are conceptual changes that would not permit a proposition to be both true and false.     

A note on mathematical pluralism and logical pluralism

Mathematical pluralism notes that there are many different kinds of pure mathematical structures—notably those based on different logics—and that, qua pieces of pure mathematics, they are all equally good. Logical pluralism is the view that there are different logics (consequence relations), which are, in an appropriate sense, equally good. Some, such as Shapiro (Varieties of logic, Oxford University Press, Oxford, 2014), have argued that mathematical pluralism entails logical pluralism. In this brief note I argue that this does not follow. There is a crucial distinction to be drawn between the preservation of truth (simpliciter) and the preservation of truth-in-a-structure; and once this distinction is drawn, this suffices to block the argument. The paper starts by clarifying the relevant notions of mathematical and logical pluralism. It then explains why the argument from the first to the second does not follow. A final section considers a few objections.

     

因果条件中儿童社会信息推理的发展

采用因果条件性逻辑推理研究的一般模式,研究了儿童社会信息因果推理发展状况。实验结果表明：(1)儿童社会信息推理能力呈年级性递增。(2)社会信息的内容会影响儿童社会信息推理的能力。(3)儿童四种逻辑形式推理能力之间的差异显著．AC、DA在年级水平上差异都十分显著,但MP和MT在年级水平上差异不显著,儿童在各个年级四种推理能力之间的差异都显著,确定型和非确定型逻辑推理能力之间的差异显著。(4)逻辑形式的难度、儿童的年龄影响儿童合理化解释的类型。     

The logical form of universal generalizations

First order logic does not distinguish between different forms of universal generalization; in this paper I argue that lawlike and accidental generalizations (broadly construed) have a different logical form, and that this distinction is syntactically marked in English. I then consider the relevance of this broader conception of lawlikeness to the philosophy of science.     

Representing logical and semantic structure of knowledge acquired from discourse

A network model of logical and semantic structures from which speakers or writers generate linguistic messages at the discourse level is presented. While linguistic structures were considered in developing the model, the semantic and logical networks are defined without reference to linguistic structures and thus may be used to represent knowledge structures acquired from both linguistic and nonlinguistic sources. A second problem addressed is that of determining what logical and semantic information is acquired when a text is understood. To assess acquired knowledge, a procedure is presented for coding a subject's verbal reconstruction of knowledge acquired from a presented text (or other input) against the logical and semantic structure from which the text (or other input) was derived. The procedures are illustrated using data obtained from children who were asked to “retell” simple narrative stories.     

A defense of contingent logical truths

A formula is a contingent logical truth when it is true in every model M but, for some model M, false at some world of M. We argue that there are such truths, given the logic of actuality. Our argument turns on defending Tarski’s definition of truth and logical truth, extended so as to apply to modal languages with an actuality operator. We argue that this extension is the philosophically proper account of validity. We counter recent arguments to the contrary presented in Hanson’s ‘Actuality, Necessity, and Logical Truth’ (Philos Stud 130:437–459, 2006).     

The contribution of logical reasoning to the learning of mathematics in primary school

It has often been claimed that children's mathematical understanding is based on their ability to reason logically, but there is no good evidence for this causal link. We tested the causal hypothesis about logic and mathematical development in two related studies. In a longitudinal study, we showed that (a) 6‐year‐old children's logical abilities and their working memory predict mathematical achievement 16 months later; and (b) logical scores continued to predict mathematical levels after controls for working memory, whereas working memory scores failed to predict the same measure after controls for differences in logical ability. In our second study, we trained a group of children in logical reasoning and found that they made more progress in mathematics than a control group who were not given this training. These studies establish a causal link between logical reasoning and mathematical learning. Much of children's mathematical knowledge is based on their understanding of its underlying logic.     

Children’s solutions of logical versus empirical problems: What’s missing and what develops?

This research examined the development of the ability to differentiate logical from empirical problems and the different ways in which children solve these problems. Thirty-two 4- and 5-year-olds, thirty-four 8- and 9-year-olds, and thirty-five 11- and 12-year-olds were given five questions regarding an imaginary character’s predictions as to where a ball would land after being dropped through a ‘tautology machine’. The questions examined encoding and recall of problems, children’s understanding of when evidence was necessary, and children’s evaluation of form and evidence. Data were analyzed in two ways: (1) by comparing differences across participants on component questions and (2) an individual analysis examining the consistency of responses to component questions across the problem set. Overall, the results indicated that: (1) sixth graders tended to differentiate logical from empirical problems while preschool and third grade children rarely did; (2) young children tend to ignore both the logical connective and the second half of problems-termed a ‘cut;’ (3) these cuts are less frequent when a problem is compatible with one empirical possibility; (4) cuts do not stem from encoding or recall errors, but seem to be the product of incomplete problem processing and (5) from third to sixth grade, children’s understanding of logical form increased as the rate of cuts decreased.     

Reassessing logical hylomorphism and the demarcation of logical constants

The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in particular of the vexed issue of demarcating the class of logical constants. I begin with a characterization of currently widespread views on form and matter in logic, which I refer to as ‘logical hylomorphism as we know it’—LHAWKI, for short—and argue that the hylomorphism underlying LHAWKI is mereological. Next, I sketch an overview of the historical developments leading from Aristotelian, non-mereological metaphysical hylomorphism to mereological logical hylomorphism (LHAWKI). I conclude with a reassessment of the prospects for the combination of hylomorphism and logic, arguing in particular that LHAWKI is not the only and certainly not the most suitable version of logical hylomorphism. In particular, this implies that the project of demarcating the class of logical constants as a means to define the scope and nature of logic rests on highly problematic assumptions.     

Reconstruction of arbitrary versus logical sequences by preschool children

The ability of preschool children to construct and reconstruct ordered sequences was examined in a series of four experiments. In Expt. 1, the task was to copy, with the model present or absent, the order of items pegged on a clothesline. In Expts. 2–4, the subjects were required to reconstruct ordered series of pictures from memory. In all experiments, the orders were either logical or arbitrary. Reconstruction of an arbitrary series of events is within the problem solving capacity of 4-yr-old children if (a) reconstruction takes place in the presence of the model or follows immediately upon the removal of the model and (b) the original sequence is presented simultaneously. If, however, the lag between viewing and reconstruction is increased and/or the original set is not viewed simultaneously, as a unit, performance declines. The provision of an inherent order to the items within a set, either by introducing a connective narrative, or a depicted logical sequence, is sufficient to maintain that order over time and to provide a unifying cohesion to the items when viewed successively.     

Conjunctive bias in memory representations of logical connectivesa

The paper presents the conjunctive bias in memory-a novel phenomenon that helps to clarify representations of logical connectives. The conjunctive bias is a tendency toward more accurate recall and recognition of conjunctive forms than of forms based on other logical connectives and a tendency to recall and recognize other logical forms as if they were conjunctions. Three experiments, in which participants' memory representations associated with different logical connectives were examined, were conducted to test the conjunctive bias hypothesis. In Experiment 1, participants learned picture-proposition pairs involving either conjunctions or disjunctions and then had to recall each proposition when cued with its picture. In Experiments 2 and 3, recognition memory for conjunctions, disjunctions, and conditionals was examined with an old/new recognition procedure. The findings of these experiments provide evidence for the conjunctive bias. Furthermore, the results of Experiment 3 suggest that corjunctive bias is not simply a pragmatically caused preference for conjunctions. The discussion focuses on the implications of these findings for current theories of deductive reasoning.     

Validity and Effectiveness of Ambiguity: A Famous Argument by Socrates

An argument can be superficially valid and rhetorically effective even if what is plausibly meant, what is derived from what, and how it is derived is not at all clear. An example of such an argument is provided by Socrates??s famous refutation of Euthyphro??s second definition of holy, which is generally regarded as clearly valid and successful. This paper provides a stricter logical analysis than the ones in the literature. In particular, it is shown that the argument contains a syntactically ambiguous expression, a passage that needs to be read charitably, and a previously unnoticed but crucial shift between two notions of unholy. Different analyses may be provided, depending on how these interpretation problems are solved. The conditions under which the refutation is valid and successful are far from obvious, and are here explicitly specified.