Intuitive theory

The purpose of this research was to explore the representation, manipulation, and utilization of strategic knowledge in organic synthesis planning. The method we decided to explore was to create an axiomatic theory to replace our intuitive theory about chemical synthesis. This formal method of reasoning is very powerful in that it completely eliminates any questions about the method used to reach a conclusion. Since any conclusions reached would be theorems of the axiomatic theory, the acceptability of the conclusions rests completely on the acceptability of the postulates and not upon the method of reasoning. We are then free to focus on the chemical principles which are provided as postulates. 

Definition of Axiomatic Theories. An axiomatic theory is an attempt to formalize an intuitive theory. Geometry was intuitive before Euclid wrote "The Elements . An intuitive theory is defined as a body of knowledge which attempts to express relationships and causality between objects, but is not formal. Most modern science is still intuitive, even though it may represent many of it s findings in exact mathematical formulae. As long as the entire corpus of knowledge is not expressed in a single formal system, it will remain intuitive. 

In modern axiomatic theory, postulates and axioms are defined simply as given statements. By the definition of an axiomatic theory the concept of truth is not considered relevant to its construction. If we can derive a theory which seems to mirror reality as reported by our current experimental knowledge, then we consider the postulates to be successful in some sense of the word. If the theory derived from the postulates clash drastically with our observations, the postulates can be thrown away as non-relevant . If the differences are slight, or if the theory predicts new experiments which should show differences from what the intuitive theory would predict, we can even call the axiomatic theory interesting . 

D Van Dyck, M Op de Beeck. A simple intuitive theory for electron diffraction. Ultramicroscopy 64 99 - 107,1996. 

Brands are abstract objects comprising a cluster of related concepts interlinked via various intuitive theories. The number and nature of these concepts and the associated intuitive theories determine the brand s conceptual structure. A successful brand is hkely to be rich in conceptual content that has the capacity to trigger rewarding emotional outcomes that determine behaviour. 

Of course, children or lay people do not always frame their ideas in these exact words. But it is a small step from If he wanted to keep moving along he would have to keep pushing (an example of what a child actually said, cf Gunstone Watts) to Sustained motion needs a continuous force . So, it is plausible to assume that the child would have assented to the latter sentence. If children and lay people can be said to hold the intuitive theory in this sense, what follows ... 

According to many researchers the intuitive theory is at variance with the principles of Newtonian mechanics (McCloskey, 1983). I agree that Sustained motion needs a continuous force seems to be contradictory to Newton s first law, and that to have a force is meaningless in Newtonian mechanics. But does it follow that the intuitive theory contradicts Newtonian mechanics I think not. Consider ... 

The above exemplifies two related issues (ef. Davidson, 2001, essays 9 to 12). First, the interdependence of belief and meaning what someone believes when she assents to some sentence depends on what the sentence means for her. Second, the associated problem of interpretation if we only know which sentences someone assents to, and we cannot assume identity of meaning, then how are we to find out what her sentences mean and what she believes My methodological criticism of a lot of research into children s thinking is that this problem of interpretation, despite quite common implicit recognition, is hardly ever explicitly mentioned, let alone properly solved. Reports in which intuitive theories are formulated, without further clarification, in terms fliat are also in use in science, cannot be expected to have solved the problem. 

The adhesion between two solid particles has been treated. In addition to van der Waals forces, there can be an important electrostatic contribution due to charging of the particles on separation [76]. The adhesion of hematite particles to stainless steel in aqueous media increased with increasing ionic strength, contrary to intuition for like-charged surfaces, but explainable in terms of electrical double-layer theory [77,78]. Hematite particles appear to form physical bonds with glass surfaces and chemical bonds when adhering to gelatin [79]. 

We have already mentioned that real-world data have drawbacks which must be detected and removed. We have also mentioned outliers and redundancy. So far, only intuitive definitions have been given. Now, aimed with information theory, we are going firom the verbal model to an algebraic one. 

When we talk about knowledge of the physical world, we generally refer to facts derived from systematic observation, study, and experimentation as well as the concepts and theories based on these facts. This is contrasted with belief (faith, intuition) in the spiritual or supernatural. 

To a first approximation, the activation energy can be obtained by subtracting the energies of the reactants and transition structure. The hard-sphere theory gives an intuitive description of reaction mechanisms however, the predicted rate constants are quite poor for many reactions. 

Thus certainty factors express the intuitive notion that the certainty of a conclusion should be lower than the certainty of the data and knowledge involved in arriving at the conclusion. Certainty factor theory also allows for combining the CFs of conjunctions, disjunctions, and negations ... 

The importance of inherent flaws as sites of weakness for the nucleation of internal fracture seems almost intuitive. There is no need to dwell on theories of the strength of solids to recognize that material tensile strengths are orders of magnitude below theoretical limits. The Griffith theory of fracture in brittle material (Griflfith, 1920) is now a well-accepted part of linear-elastic fracture mechanics, and these concepts are readily extended to other material response laws. 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

The EMT analysis indicated that the stress relaxes in proportion to the number of bonds removed. The initial linear decrease of E/Eq with is intuitively appealing and is the basis for many linear constitutive theories of polymers. An example is the Doi-Edwards theory of viscoelasticity of linear polymer melts [49] in which... 

In the early days of alloy theory, Lifshitz argued on intuitive grounds that one can calculate the properties of a disordered alloy from one sufficiently large sample," and referred to this property of a large sample as self-averaging. It can be seen most easily in exact... 

Explained in such general terms as maximizing the good, ntilitarianisni is an intuitively plausible ethical theory. Disagreements occur when defenders attempt to specify the content and meaning of the... 

The problem is to articulate this intuition formally to define a measure that not only captures our intuitive feel for what distinguishes the complex from the simple but also provides an objective basis for formulating conjectures and theories about complexity. While a universally accepted measure has yet to be defined, a number of interesting proposals have been made in recent years. All such measures of complexity fall into two general classes ... 

How can we predict whether a given cycloaddition reaction will occur with suprafacial or with antarafacial geometry According to frontier orbital theory, a cycloaddition reaction takes place when a bonding interaction occurs between the HOMO of one reactant and the LUMO of the other. An intuitive explanation of this rule is to imagine that one reactant donates electrons to the other. As with elec-trocyclic reactions, it s the electrons in the HOMO of the first reactant that are least tightly held and most likely to be donated. But when the second reactant accepts those electrons, they must go into a vacant, unoccupied orbital—the LUMO. 

Despile the convincing support for the atomic theory provided by chemical evidence, there is intuitive appeal to evidence that is closer to the direct vision type. From such experiments comes a much more detailed view of the atom and its make-up. 

It has been possible to develop axiomatic theories for complete and partial ignorance that, by studying the sets of acts and states, yield a better understanding of the choice of criteria, and are in harmony with logical formalization of intuitively acceptable notions. We have treated in a rudimentary fashion a subject that is deep, novel, and promising. 

By a brilliant physical intuition B. van der Pol succeeded finally (1920) in establishing his equation (which is given in Section 6.11) but, not having any mathematical theory at his disposal, he determined the nature of Ike solution by the graphical method of isoclines. It became obvious that the problem, which was a real stumbling block for many years, had been finally solved, at least in principle. 

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