Class and conditional reasoning in children and adolescents

The development of the ability to comprehend and reason with class and conditional logic statements was examined in the light of Piaget's claim that prior to the age of 11-12 years children are limited to reasoning in terms of classes and relations but from the age of 11-12 years reasoning in terms of propositions becomes possible. Subjects from 5 years to 17.5 years were presented with several different comprehension and inference tasks with class and conditional logic statements. Evidence of differences in the ability of subjects under 12 years to verify class and conditional logic statements was consistent with Piaget's claim that the logical classification operations of the concrete subject enable him to interpret class inclusion statements but that the conditional interpretation of empirical information requires formal operational thinking. No distinction in performance between class and conditional statements was found on tasks which required an understanding of the logical consequences of the inclusion relation with subjects younger than first year secondary performing poorly on both class and conditional versions of an evaluation task and a syllogistic reasoning task. Significant changes in patterns of response at adolescence on the conditional verification task, the evaluation task and the syllogistic reasoning task supported Piaget's contention that there are qualitative changes in reasoning at adolescence although, as in other studies, errors in reasoning by adolescents indicated that Piaget overestimated the logical abilities of the formal subject and suggested that Piaget's logical model of cognition should be regarded as a model of logical competence

Poythress’s Trinitarian Logic: A Review Essay

Reviewed Title: Vern Sheridan Poythress. Logic: A God-Centered Approach to the Foundation of Western Thought. Crossway, 2013. 733 pp. ISBN: 978-1-4335-3229-0

Quantum Non-Objectivity from Performativity of Quantum Phenomena

We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables which is a consequence of the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on the one hand, the formalism of QM constructed as a mathematical theory is self-consistent, but, on the other hand, quantum phenomena as results of experimenter's performances are not self-consistent. This self-inconsistency is an effect of that the language of QM differs much from the language of human performances. The first is the language of a mathematical theory which uses some Aristotelian and Russellian assumptions (e.g., the assumption that there are logical atoms). The second language consists of performative propositions which are self-inconsistent only from the viewpoint of conventional mathematical theory, but they satisfy another logic which is non-Aristotelian. Hence, the representation of quantum reality in linguistic terms may be different: from a mathematical theory to a logic of performative propositions. To solve quantum self-inconsistency, we apply the formalism of non-classical self-referent logics

Ancient Logic and its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972

Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others. Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic

Logic and implementation in human reasoning: the psychology of syllogisms

This thesis presents a novel account of syllogistic reasoning, based on data from a non-standard reasoning task called the Individuals Task. An abstract logical treatment of the system, based on a modalised Euler Circles system (Stenning & Oberlander 1994, 1995) is presented, and it is shown that this can be implemented in a diverse range of notationally distinct ways. The Individual Identification Algorithm, as this method is called, makes use of a logical distinction between the premisses of the syllogism; one has an existential, assertive role, and is called the source premiss, whereas the function of the other is to license inference, and so it is called the conditional premiss. This distinction is central to the way the IIA employs modal information to make the use of Euler Circles tractable.The empirical parts of the thesis are concerned with relating the distinction between source and conditional premisses to the Figural Effect (Johnson-Laird & Steedman 1978). It is argued that the Figural Effect is reducible to a tendency for the terms from the source premiss to occur before the terms from the conditional premiss in Individual Conclusions. Since these are comprised of all three terms in the syllogism, it is possible to test new hypotheses concerning the role of the middle term in inference, and the results are shown to be incompatible with all existing theories of the Figural Effect.Since the Individuals Task is non-standard, it is necessary to compare perfor¬ mance profiles on this task with those on the Standard Task; one result of this comparison is that a primary cause of error in the Standard Task is selection of an appropriate quantifier for the conclusion, a result which concurs with the con¬ clusions of Ford (1994) and Wetherick & Gilhooly (1990), but contradicts those of Mental Models theory (Johnson-Laird 1983).Certain anomalies in the prediction of term order by the source/conditional distinction lead to the postulation of a second process for conclusion generation, called Minimal Linking. This logically unsound strategy has effects similar to the illicit conversion of A premisses (Chapman &; Chapman 1959, Revlis 1975)

Working memory and human reasoning : an individual differences approach

Experiments 1-3 investigated the relationship between working memory and syllogistic and five-ten-n series spatial inference. A secondary aim was to replicate the findings of Shah and Miyake (1996) who suggested the use of separate central resources of working memory for spatial and verbal ability. The correlational analysis showed that the complex verbal and spatial working memory span tasks were associated together and consistently predicted reasoning performance in both verbal and visual modalities. The confirmatory factor analysis showed that three factors best accounted for the data -a verbal, a spatial, and a general resource. All the span tasks and most of the reasoning tasks significantly and consistently loaded the general factor. Experiments 4-6 investigated the relationship between working memory and a range of reasoning tasks - identified as either propositional. spatial, or quantifiable tasks. These experiments were based on the work of Stanovich and West (1998) who found that a range of reasoning tasks were predicted by cognitive ability and a reasoner's thinking style. The correlational anaylsis showed that the complex verbal and spatial working memory span tasks were associated together and consistently predicted reasoning perforinance. Two clusters of reasoning task emerged from the correlational analysis - one cluster related to the propositional and simple spatial reasoning tasks, whilst the other related to the quantifiable and complex spatial reasoning tasks. The confin-natory factor analysis showed that four factors best accounted for the data -a verbal, a spatial, a general, and a thinking style resource. All the span tasks and the reasoning tasks loaded the general factor, and most of the reasoning tasks further loaded the thinking disposition factor. These results are discussed in light of models of workino memory, theories of reasoning, and how to best characterise factor 3 (executive function) and factor 4 (thinking style) from tile factor analysis.Economic and Social Research Counci

The intersection between Descriptivism and Meliorism in reasoning research: further proposals in support of ‘soft normativism’

The rationality paradox centers on the observation that people are highly intelligent, yet show evidence of errors and biases in their thinking when measured against normative standards. Elqayam and Evans’ (2011) reject normative standards in the psychological study of thinking, reasoning and deciding in favor of a ‘value-free’ descriptive approach to studying high-level cognition. In reviewing Elqayam and Evans’ (2011) position, we defend an alternative to descriptivism in the form of ‘soft normativism,’ which allows for normative evaluations alongside the pursuit of descriptive research goals. We propose that normative theories have considerable value provided that researchers: (1) are alert to the philosophical quagmire of strong relativism; (2) are mindful of the biases that can arise from utilizing normative benchmarks; and (3) engage in a focused analysis of the processing approach adopted by individual reasoners. We address the controversial ‘is–ought’ inference in this context and appeal to a ‘bridging solution’ to this contested inference that is based on the concept of ‘informal reflective equilibrium.’ Furthermore, we draw on Elqayam and Evans’ (2011) recognition of a role for normative benchmarks in research programs that are devised to enhance reasoning performance and we argue that such Meliorist research programs have a valuable reciprocal relationship with descriptivist accounts of reasoning. In sum, we believe that descriptions of reasoning processes are fundamentally enriched by evaluations of reasoning quality, and argue that if such standards are discarded altogether then our explanations and descriptions of reasoning processes are severely undermined

Logical and Spiritual Reflections

Logical and Spiritual Reflections is a collection of six shorter philosophical works, including: Hume’s Problems with Induction; A Short Critique of Kant’s Unreason; In Defense of Aristotle’s Laws of Thought; More Meditations; Zen Judaism; No to Sodom. Of these works, the first set of three constitutes the Logical Reflections, and the second set constitutes the Spiritual Reflections. Hume’s Problems with Induction, which is intended to describe and refute some of the main doubts and objections David Hume raised with regard to inductive reasoning. It replaces the so-called problem of induction with a principle of induction. David Hume’s notorious skepticism was based on errors of observation and reasoning, with regard to induction, causation, necessity, the self and freewill. These are here pointed out and critically analyzed in detail – and more accurate and logical theories are proposed. The present work also includes refutations of Hempel’s and Goodman’s alleged paradoxes of induction. A Short Critique of Kant’s Unreason, which is a brief critical analysis of some of the salient epistemological and ontological ideas and theses in Immanuel Kant’s famous Critique of Pure Reason. It shows that Kant was in no position to criticize reason, because he neither sufficiently understood its workings nor had the logical tools needed for the task. Kant’s transcendental reality, his analytic-synthetic dichotomy, his views on experience and concept formation, and on the forms of sensibility (space and time) and understanding (his twelve categories), are here all subjected to rigorous logical evaluation and found deeply flawed – and more coherent theories are proposed in their stead. In Defense of Aristotle’s Laws of Thought, which addresses, from a phenomenological standpoint, numerous modern and Buddhist objections and misconceptions regarding the basic principles of Aristotelian logic. Many people seem to be attacking Aristotle’s Laws of Thought nowadays, some coming from the West and some from the East. It is important to review and refute such ideas as they arise. More Meditations, which is a sequel to the author’s earlier work, Meditations. It proposes additional practical methods and theoretical insights relating to meditation and Buddhism. It also discusses certain often glossed over issues relating to Buddhism – notably, historicity, idolatry, messianism, importation to the West. Zen Judaism, which is a frank reflection on the tensions between reason and faith in today’s context of knowledge, and on the need to inject Zen-like meditation into Judaism. This work also treats some issues in ethics and theodicy. No to Sodom, which is an essay against homosexuality, using biological, psychological, spiritual, ethical and political arguments

Imaging deductive reasoning and the new paradigm

There has been a great expansion of research into human reasoning at all of Marr’s explanatory levels. There is a tendency for this work to progress within a level largely ignoring the others which can lead to slippage between levels (Chater et al., 2003). It is argued that recent brain imaging research on deductive reasoning—implementational level—has largely ignored the new paradigm in reasoning—computational level (Over, 2009). Consequently, recent imaging results are reviewed with the focus on how they relate to the new paradigm. The imaging results are drawn primarily from a recent meta-analysis by Prado et al. (2011) but further imaging results are also reviewed where relevant. Three main observations are made. First, the main function of the core brain region identified is most likely elaborative, defeasible reasoning not deductive reasoning. Second, the subtraction methodology and the meta-analytic approach may remove all traces of content specific System 1 processes thought to underpin much human reasoning. Third, interpreting the function of the brain regions activated by a task depends on theories of the function that a task engages. When there are multiple interpretations of that function, interpreting what an active brain region is doing is not clear cut. It is concluded that there is a need to more tightly connect brain activation to function, which could be achieved using formalized computational level models and a parametric variation approach

Approximate syllogistic reasoning: a contribution to inference patterns and use cases

In this thesis two models of syllogistic reasoning for dealing with arguments that involve fuzzy quantified statements and approximate chaining are proposed. The modeling of quantified statements is based on the Theory of Generalized Quantifiers, which allows us to manage different kind of quantifiers simultaneously, and the inference process is interpreted in terms of a mathematical optimization problem, which allows us to deal with more arguments that standard deductive ones. For the case of approximate chaining, we propose to use synonymy, as used in a thesaurus, for calculating the degree of confidence of the argument according to the degree of similarity between chaining terms. As use cases, different types of Bayesian reasoning (Generalized Bayes' Theorem, Bayesian networks and probabilistic reasoning in legal argumentation) are analysed for being expressed through syllogisms