Intuitionistic Theory Research Articles

Neue Erkenntnisse im Bereich der Wissenswissenschaften

We commented on the emergence of knowledge science, including epistemology, knowledge engineering, management science with knowledge management, sociological (soft) systems science, technology management, and technological (hard) systems science. As opposed to philosophic macro-theories of knowledge creation on long historical scale, many new micro-theories of knowledge creation for today and tomorrow emerged since 1990. All such micro-theories take into account the interplay of intuitive and emotional, tacit aspects of knowledge with rational and explicit aspects. A contemporary theory of intuition explains rationally why intuitive and emotive aspects are much stronger sources of creative ideas. There is a qualitative difference between group-oriented organizational processes of knowledge creation in industrial and market organizations and individual-oriented academic processes of knowledge creation; the latter can be described by a Triple Helix of academic knowledge creation. Combining both organizational and academic processes of knowledge creation is the prescriptive Nanatsudaki model of seven creative processes. The importance of diverse elements of these models was empirically supported by the results of a survey of creativity conditions in a Japanese university, using multiple criteria decision making for knowledge acquisition from large data bases.

Conceptual Change and Education

In order to understand the advanced, scientific concepts of the various disciplines, students cannot rely on the simple memorization of facts. They must learn how to restructure their naive, intuitive theories based on everyday experience and lay culture. In other words, they must undergo profound conceptual change. This type of conceptual change cannot be achieved without systematic instruction that takes into consideration both individual, constructivist and sociocultural factors. Teachers must find ways to enhance individual students’ motivation by creating a social classroom environment that supports the creation of intentional learners who can engage in the deep and enduring comprehension activities required for the revision of conceptual knowledge.

The Psychophysiology Of Intuition: A Quantum-Holographic Theory Of Nonlocal Communication

This work seeks to explain intuitive perception—those perceptions that are not based on reason or logic or on memories or extrapolations from the past, but are based, instead, on accurate foreknowledge of the future. Often such intuitive foreknowledge involves perception of implicit information about nonlocal objects and/or events by the body's psychophysiological systems. Recent experiments have shown that intuitive perception of a future event is related to the degree of emotional significance of that event, and a new study shows that both the brain and the heart are involved in processing a pre-stimulus emotional response to the future event. Drawing on this research and on the principles of quantum holography, I develop a theory of intuition that views the perception of things remote in space or ahead in time (nonlocal communication) as involving processes of energetic resonance connecting the body's psychophysiological systems to the quantum level. The theory explains how focused emotional attention directed to the nonlocal object of interest attunes the bio-emotional energy generated by the body's psychophysiological systems to a domain of quantum-holographical information, which contains implicit information about the object. The body's perception of such implicit information about things distant in space/time is experienced as an intuition.

The Good in the Right: A Theory of Intuition and Intrinsic Value

The Good in the Right: A Theory of Intuition and Intrinsic Value

Review of The Right In the Good: A Theory of Intuition and Intrinsic Value, by Robert Audi

Review of The Right In the Good: A Theory of Intuition and Intrinsic Value, by Robert Audi

De Jongh and Glivenko theorems for equality theories ★

This paper is concerned with the logical structure of intuitionistic equality theories. We prove that De Jongh theorem holds for the theory of decidable equality, but uniform De Jongh theorem fails even for the theory of weakly decidable equality. We also show that the theory of weakly decidable equality is the weakest equality theory which enjoys Glivenko theorem.

Modelling as a way of organising knowledge

The paper is motivated by the need of to address a new the old topic of operational research and hard (but also soft) systems science: what is the role of mathematical modelling, how does it relate to knowledge, to creativity, to human concerns? Such a need arises because of the great change observed today, of informational revolution, of transition towards knowledge-based economy, towards networked organization of our social and economic life. During last 50 years operational research, mathematical modelling and computerised techniques of model analysis and optimisation contributed essentially to the change of perception of contemporary world, characteristic for the current informational revolution indicating the change of civilisation eras. These contributions have been noted during these years inside operational research, but analysed mostly from so-called soft systems thinking perspective. Main contributions to the actual formation of the new era, however, came from the hard systems research, in particular, as we shall show, from mathematical modelling in applications to the development of technological systems. The new civilisation era of information and knowledge-based economy started around 1980. It is a long duration historical era, characterised by a new way of understanding the world. This understanding is systemic and chaotic; in particular, it assumes the emergence of qualitatively new properties of complex systems on higher layers of complexity, which cannot be reduced to the properties of system components. On this background, it is necessary to reflect a new on the theory of knowledge. The paper presents a discussion of the concept of knowledge from several perspectives, such as the perspective of operational research, of systems science, of mathematical modelling, of knowledge-based economy, of knowledge engineering and knowledge management, of interactive model-based decision support. The human-centred development of informational technology necessitates a re-appraisal of soft systems approaches; their values and limitations are discussed. Additionally, a rational theory of intuition is recalled to show its relation with the concept of tacit knowledge, of knowledge creation and with harmonious approaches to knowledge characterising Far East philosophy as well as Japanese approaches to knowledge management and creation. Epistemological conclusions from the rational theory of intuition are discussed, including a new concept of micro-theories of knowledge creation and the concept of Creative Space.

Intuitive rules in science and mathematics: a reaction time study

It has been observed that students react in similar ways to mathematics and science tasks that differ with regard either to their content area and/or to the type of reasoning required, but share some common, external features. Based on these observations, the Intuitive Rules Theory was proposed. In this present study the framework of this theory was employed and the reaction times of two types of responses were measured: those that are regarded as intuitive and those that are viewed as counter-intuitive. The motivation behind this study was to empirically address the immediacy characteristics of intuitive responses in the context of science and mathematics. The focus was on the comparison of area and perimeter of geometrical shapes, in the context of the intuitive rule more A – more B. The main findings showed that the reaction times of intuitive responses were, indeed, shorter than reaction times of counter-intuitive ones.

Intuitive Economics: The Role of Power and Knowledge in the Dismal Science

Recent disputes over the epistemological nature of social science inquiry, often referred to as “Science Wars”, display many of the hallmarks of a much older, largely forgotten quarrel in social science: The Methodenstreit of Economics ‐ pitting the Austrian School of Economics against the German Historical School in the 1880s ‐ has largely remained unresolved to date, despite several attempts to overcome it. Yet, curiously, these e orts seem overlooked and outside of the current battlefield of the science wars, where much of the debate is shaped by contemporary political theory. While critical theory, poststructuralism and postmodernism are leaving distinct marks on the sociological research agenda, mainstream economic theory seems impervious to similar much-needed developments. Revisiting Edgar Salin’s concept of Anschauliche Theorie (intuitive theory) and putting it into context with power and knowledge presents a useful starting point for rekindling this debate in the dismal science. Indeed, a recasting of these ideas in the form of intuitive economics might constitute a central element in a broader framework aimed at overcoming the lack of vision in contemporary economic theory.

The Good in the Right: A Theory of Intuition and Intrinsic Value

The Good in the Right: A Theory of Intuition and Intrinsic Value

Are Intuitive Rules Universal?

This paper presents a cross-cultural study on the intuitive rules theory. The study was conducted in Australia (with aboriginal children) in Taiwan and in Israel. Our findings indicate that Taiwanese and Australian Aboriginal students, much like Israeli ones, provided incorrect responses, most of which were in line with the intuitive rules. Also, developmental trends were found to be similar yet differences were found with regard to the rate of developmental change.

Preservation theorems for bounded formulas

In this paper we naturally define when a theory has bounded quantifier elimination, or is bounded model complete. We give several equivalent conditions for a theory to have each of these properties. These results provide simple proofs for some known results in the model theory of the bounded arithmetic theories like CPV and PV1. We use the mentioned results to obtain some independence results in the context of intuitionistic bounded arithmetic. We show that, if the intuitionistic theory of polynomial induction on strict \(\Pi_2^{b}\) formulas proves decidability of \(\Sigma_1^b\) formulas, then P=NP. We also prove that, if the mentioned intuitionistic theory proves \({\rm LMIN}(\Sigma_{1}^{b})\), then P=NP.

Theory-based Bayesian models of inductive learning and reasoning

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.

An Independence Result for Intuitionistic Bounded Arithmetic

It is shown that the intuitionistic theory of polynomial induction on positive Π1b (coNP) formulas does not prove the sentence ¬¬∀x, yz ≤ y(x ≤ |y| → x = |z|). This implies the unprovability of the scheme ¬¬PIND(Σ1b+) in the mentioned theory. However, this theory contains the sentence ∀x, y¬¬z ≤ y(x ≤ |y| → x = |z|). The above independence result is proved by constructing an ω-chain of submodels of a countable model of S2 + Ω3 + ¬exp such that none of the worlds in the chain satisfies the sentence, and interpreting the chain as a Kripke model.

Towards a Semantics Based on the Notion of Justification

Suppose we want to take seriously the neoverificationist idea that an intuitionistic theory of meaning can be generalized in such a way as to be applicable not only to mathematical but also to empirical sentences. The paper explores some consequences of this attitude and takes some steps towards the realization of this program. The general idea is to develop a meaning theory, and consequently a formal semantics, based on the idea that knowing the meaning of a sentence is tantamount to having a criterion for establishing what is a justification for it. Section 1 motivates a requirement of epistemic transparency imposed onto justifications conceived as mental states. In Section 2, the formal notion of justification for an atomic formula is defined, in terms of the notion of cognitive state. In Section 3, the definition is extended to logically complex formulas. In Section 4, the notion of truth-ground is introduced and is used to give a definition of logical validity.

Connectionist computations of intuitionistic reasoning

The construction of computational models with provision for effective learning and added reasoning is a fundamental problem in computer science. In this paper, we present a new computational model for integrated reasoning and learning that combines intuitionistic reasoning and neural networks. We use ensembles of neural networks to represent intuitionistic theories, and show that for each intuitionistic theory and intuitionistic modal theory there exists a corresponding neural network ensemble that computes a fixed-point semantics of the theory. This provides a massively parallel model for intuitionistic reasoning. In our model, the neural networks can be trained from examples to adapt to new situations using standard neural learning algorithms, thus providing a unifying foundation for intuitionistic reasoning, knowledge representation, and learning.

Book ReviewsRobert Audi, . The Good in the Right: A Theory of Intuition and Intrinsic Value.Princeton, NJ: Princeton University Press, 2004. Pp. 244. $45.00 (cloth).

Previous articleNext article No AccessBook Reviews Robert Audi, . The Good in the Right: A Theory of Intuition and Intrinsic Value.Princeton, NJ: Princeton University Press, 2004. Pp. 244. $45.00 (cloth).Sean D. McKeeverSean D. McKeeverDavidson College Search for more articles by this author Davidson CollegePDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Ethics Volume 116, Number 2January 2006 Article DOIhttps://doi.org/10.1086/498542 Views: 36Total views on this site Permission to reprint a book review printed in this section may be obtained only from the author.PDF download Crossref reports no articles citing this article.

Explanation and understanding.

The study of explanation, while related to intuitive theories, concepts, and mental models, offers important new perspectives on high-level thought. Explanations sort themselves into several distinct types corresponding to patterns of causation, content domains, and explanatory stances, all of which have cognitive consequences. Although explanations are necessarily incomplete--often dramatically so in laypeople--those gaps are difficult to discern. Despite such gaps and the failure to recognize them fully, people do have skeletal explanatory senses, often implicit, of the causal structure of the world. They further leverage those skeletal understandings by knowing how to access additional explanatory knowledge in other minds and by being particularly adept at using situational support to build explanations on the fly in real time. Across development and cultures, there are differences in preferred explanatory schemes, but rarely are any kinds of schemes completely unavailable to a group.

Completeness and Cut-elimination in the Intuitionistic Theory of Types

In this paper we define a model theory and give a semantic proof of cut-elimination for ICTT, an intuitionistic formulation of Church's theory of types defined by Miller et al. and the basis for the λProlog programming language. Our approach, extending techniques of Takahashi and Andrews and tableaux machinery of Fitting, Smullyan, Nerode and Shore, is to prove a completeness theorem for the cut-free fragment and show semantically that cut is a derived rule. This allows us to generalize a result of Takahashi and Schutte on extending partial truth valuations in impredicative systems. We extend Andrews' notion of Hintikka sets to intuitionistic higher-order logic in a way that also defines tableau-provability for intuitionistic type theory. In addition to giving a completeness theorem without using cut we then show, using cut, how to establish completeness of more conventional term models. These models give a declarative semantics for the logic underlying the λProlog programming language.

On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.