Deductive principles

Hegel, in The Science of Logic, derived the various ontological categories from each other according to certain deductive principles which have resisted analysis to this day. The connection is neither that of cause to effect, nor that of axiom to theorem, nor finally that of given fact to its condition of possibility. The "self-determination of the concept" appears... 

By using the deduction principle, the complete mathematical model of the electrochemical gas sensors with distributed parameters can be transformed to the mathematical models of the specific gas sensors, which is important for organization of their optimal design. 

From this assumption stems the common use of the term "molecular mechanics" to describe the elementary use of empirical functions in conformational analysis. This similarity to macroscopic bodies made of elastic springs created the common impression as if empirical energy functions are "classical". In fact, empirical methods of describing molecular energies are distinct from molecular orbital methods of quantum chemistry not by being "classical", but by their being empirical guesses not based on any deductive principle, whether classical or quantum mechanical. 

The scientific method, as mentioned, involves observation and experimentation (research) to discover or establish facts. These are followed by deduction or hypothesis, establishing theories or principles. This sequence, however, may be reversed. The noted twentieth-century philosopher Karl Popper, who also dealt with science, expressed the view that the scientist s work starts not with collection of data (observation) but with selection of a suitable problem (theory). In fact, both of these paths can be involved. vSignificant and sometimes accidental observations can be made without any preconceived idea of a problem or theory and vice versa. The scientist, however, must have a well-prepared, open mind to be able to recognize the significance of such observations and must be able to follow them through. Science always demands rigorous standards of procedure, reproducibility, and open discussion that set reason over irrational belief. 

Thermodynamics is a deductive science built on the foundation of two fundamental laws that circumscribe the behavior of macroscopic systems the first law of thermodynamics affirms the principle of energy conservation the second law states the principle of entropy increase. In-depth treatments of thermodynamics may be found in References 1—7. 

Of course, most of what I have said so far is well known. Nevertheless, I hope to have given these issues a new perspective by adopting an almost perversely rigorous approach in demanding that every aspect of electronic configurations should be strictly deducible from quantum mechanics. Although I am not in a position to propose a better explanation, I do not think that we should be complacent about what the present explanation achieves. As I have tried to argue, in terms of deduction from theoretical principles, the present semi-empirical explanation is not fully adequate. 

But let me return to the question of whether the periodic table is fully and deductively explained by quantum mechanics. In the usually encountered explanation one assumes that at certain places in the periodic table unexpected orbital begins to fill as in the case of potassium and calcium where the 4s orbital begins to fill before the 3d shell has been completely filled. This information itself is not derived from first principles. It is justified post facto and by some tricky calculations (Melrose, Scerri, 1996 Vanquickenbome, Pierloot, Devoghel, 1994). 

Because of their ease of synthesis and their structural similarity to peptides, many laboratories have used peptoids as the basis for combinatorial drug discovery. Peptoids were among the first non-natural compounds used to establish the basic principles and practical methods of combinatorial discovery [17]. Typically, diverse libraries of relatively short peptoids (< 10 residues) are synthesized by the mix-and-split method and then screened for biological activity. Individual active compounds can then be identified by iterative re-synthesis, sequencing of compounds on individual beads, or indirect deduction by the preparation of positional scanning libraries. 

However, useful as it is, ligand field theory is not a predictive first principles theory. Thus, it cannot be used to predict a priori the Mossbauer parameters of a given compound. Yet, the need to do so arises fi equently in Mossbauer spectroscopy. For example, if a reaction intermediate or some other unstable chemical species has been characterized by freeze quench Mossbauer spectroscopy and its SH parameters become available, then the question arises as to the structure of the unstable species. Mossbauer spectroscopy in itself does not provide enough information to answer this question in a deductive way. However, the more modest question which structures are compatible with the observed Mossbauer parameters can be answered if one is able to reliably predict Mossbauer parameters... 

In this section we state the postulates of quantum mechanics in terms of the properties of linear operators. By way of an introduction to quantum theory, the basic principles have already been presented in Chapters 1 and 2. The purpose of that introduction is to provide a rationale for the quantum concepts by showing how the particle-wave duality leads to the postulate of a wave function based on the properties of a wave packet. Although this approach, based in part on historical development, helps to explain why certain quantum concepts were proposed, the basic principles of quantum mechanics cannot be obtained by any process of deduction. They must be stated as postulates to be accepted because the conclusions drawn from them agree with experiment without exception. 

The dissociation constant Ka or its commonly reported negative logarithmic form pKa is determined in principle by simultaneous measurement or deduction of the ionic and non-ionic concentrations and the pH of the solution. 

Yet it is on the issues of reproducibility and instrumentation that Occult Chemistry failed to persuade, at least outside of Theosophical circles and the small group of scientists in recent years who have been willing to work entirely at the level of theory. Besant and Leadbeater could move beyond older models of science, which based themselves upon deductions from revealed principles (alchemical or scientific deductions from the writings of the Hermetic tradition, for instance, or from the revelations of H. P. Blavatsky), by turning to experimentation. Not surprisingly, their form of experimentation did not admit of reproducibility. In spite of efforts by Stephen Phillips to conduct blind trials using a Buddhist clairvoyant to confirm Besant and Lead-beater s micro-psi visions (1996,48), direct experience is neither convincingly verifiable nor falsifiable. 

Sea cores offer a data base which should in principle allow deduction of the history of the local sea surface temperature immediately above the deposition site of the core, for there is enough organic material in sea cores to provide the necessary samples for isotope measurement at frequent intervals versus depth in the core, but the time resolution is far less accurate than in varves and tree rings because burrowing sea bottom animals smear the record of the layers. 

The change in the NPV using debt financing of assets is known as the principle of leverage. A similar result can often be obtained by leasing equipment because the lease payments are completely deductible as expenses for income tax purposes. 

The table uses a system of symbols for the elements and a system of conventions for atomic weights it employs a classification, or a visual array, that groups the symbols so that their relations and properties are immediately suggested to the viewer who knows the principles of classification and a few facts. Deductions can be made both to the facts that established the table and to the facts that were unknown when the table was first set out. Here is a scheme that is an explanatory and predictive model and an icon in both the semiotic and the popular senses of the word. But its power comes from visual display, from image, not the principles and facts that can be recorded in ordinary or conventional language. 

The second law, like the first law, is a postulate that has not been derived from any prior principles. It is accepted because deductions from the postulate correspond to... 

Seventeen years is a long time between editions of a book. In order to add some of the vast amount of new material which has been published in that time, I have needed to abridge the older edition and in so doing apologise to oldtimers (myself included ) whose work may have been removed or modified. Nevertheless, the approach used is unchanged. In the first three chapters I have dealt with the acquisition of experimental data and discussed use for building up the rate law and in the deduction of mechanism. In the second part of the book, the mechanistic behavior of transition metal complexes of the Werner type is detailed, using extensively the principles and concepts developed in the first part. 

The basic principle of insurance is to spread the risk of losses. This is generally accomplished by a combination of deductibles, direct insurance, and reinsurance. The insured chooses the amount of loss they are willing to retain by setting the deductible and the cost of coverage. When one insurer is notable to provide full coverage, the direct insurance is often shared by a number of direct insurers. In reinsurance, the direct insurers spread their risks to other insurance companies that specialize in reinsurance. 

Causal Trees were developed in an effort to use the principles of deductive logic found in Fault Tree but make it more user-friendly. Originally, private companies developed the Causal Tree Method (CTM) for safety, process safety, and environmental incident investigations applications. Rhone-Poulenc, for example, was an early user.<20.21) Multiple-Cause Systems Oriented Incident Investigation (MCSOfl) is another name for the CTM. At this time, most companies use simplified versions of fault trees for complex incident investigations. 

A new categorizing principle might be deducted from Fig. 26 which formally is the number of projections of the side-chain configurations, which are identical to the direction of the bridge projection. For example, for the combination A-A none of the side-chain projections correlates with the projection of the bridge, whereas for B-B all projections coincide. Formally, a summarized chirality is obtained, for which the chirality of the side-chains is overlapped by atrop-... 

No matter how intrinsically interesting students find the study of organic chemistry, there will usually be one or more hurdles that need to be overcome, the examinations. Examination technique is undoubtedly a skill, and this chapter is aimed at developing such skills for organic chemistry. Throughout the book, we have tried to convince the reader that, by applying principles and deductive reasoning, we can reduce to a minimal level the amount of material that needs be committed to memory. 

The explanation of the periodic system by quantum mechanics, for example, is only partial. The possible lengths of the various periods in the table follow deductively from the solution of the SchrOdinger equation for the hydrogen atom and the relationship between the four quantum numbers, which is also obtained deductively. However, the repetition of all but the first period length remains a source of debate (/). The repetition of all the other period lengths has not been deduced from first principles however (2). Stated more precisely, the empirical order in which the atomic orbitals are filled has not been deduced. If this were possible the explanation for the lengths of successive periods, including the repetitions, would follow trivially. 

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