Principle of insufficient reason

The idea of equal probabilities has been elevated by Laplace510 to the rank of a philosophical principle, called principle of insufficient reason . Like many philosophical principles it leaves the essential question unanswered How do I select the elementary events to which equal a priori probabilities are to be assigned In textbook problems about tossing dice or drawing cards it is obvious what the author has in mind. One knows that he is concerned with the mathematics of step b and that the dice and cards merely serve as a ritual way of defining an a priori distribution. In actual applications, however, step a cannot be dismissed so cavalierly. 

In certain cases, probabilities can be assigned by the so-called principle of insufficient reason. Thus, suppose we are involved in the vice of coin tossing. Consider the two mutually exclusive propositions... 

Many cases occur, however, in which the principle of insufficient reason is insufficient for the assignment of probabilities. That is, we are not able to reduce the problem to a statement of mutually exclusive, exhaustive, and equally likely propositions. As an example, consider the disintegration of a radioactive nucleus. We choose this example since it is similar to the processes mentioned in the text. ... 

The Laplace principle, sometimes known as the principle of insufficient reason, assumes that the probabilities of future events occurring are equal. That is, in the absence of any information to the contrary, it is assumed that all future outcomes are equally likely to occur. The expected cost (or profit/revenue) of each alternative is then computed, and the alternative that yields the minimum expected cost (or maximum expected profit/revenue) is selected. The mathematical expression for this principle is... 

Flere we derive the functional form of the entropy function, S = -k Zi Pi In Pi from a Principle of Fair Apportionment. Coins and dice have intrinsic symmetries in their possible outcomes. In unbiased systems, heads is equivalent to tails, and every number on a die is equivalent to every other. The Principle of Fair Apportionment says that if there is such an intrinsic symmetry, and if there is no constraint or bias, then all outcomes will be observed with the same probability. That is, the system treats each outcome fairly in comparison with every other outcome. The probabilities will tend to be apportioned between those outcomes in the most uniform possible way, if the number of trials is large enough. Throughout a long history, the idea that every outcome is equivalent has gone by various names. In the 1700s, Bernoulli called it the Principle of Insufficient Reason in the 1920s, Keynes called it the Principle of Indifference 1. ... 

Despite this, the principle of the fuel cell was not able to be developed into a technically mature process for a long time. The main reasons, apart from insufficient knowledge of the electrochemical processes involved, were material problems. Around the turn of the century, the dynamo generator (1866, Siemens), combustion... 

It can be seen that the CE and AAS results before dialysis differ strongly but reach a very similar level after purification by dialysis. One reason for these differences lies in the principle of CE itself. The demand for electroneutrality in the buffer system requires the replacement of the released sodium cations in the buffer and the polyelectrolyte environment by buffer cations, i.e. imidazolium ions. This replacement is an equilibrium reaction whose kinetics can lead to insufficient ion exchange during analysis, resulting in the observed variations. However, in all cases the recovery rate is no-... 

Instruction sets (programming), 71 Instrumentation (automatic control system), 158 Instrument Society of America (ISA), 1772 Insufficient reason principle, 2380 Insurance industry ... 

The basic principles of some generally accepted gas cleaning processes for solvent removal are given in Table 22.1.2. For more than 70 years adsorption processes using activated carbon, in addition to absorption and condensation processes, have been used in adsorptive removal and recovery of solvents. The first solvent recovery plant for acetone was commissioned for economic reason in 1917 by Bayer. In the decades that followed solvent recovery plants were built and operated only if the value of the recovered solvents exceeded the operation costs and depreciation of the plant. Today sueh plants are used for adsorptive purification of exhaust air streams, even if the return is insufficient, to meet environmental and legal requirements. 

Having established a SIL target it is insufficient merely to assess that the design will meet the Maximum Tolerable Risk target. It is necessary to establish whether further improvements are justified and thus the principle of ALARP (as low as reasonably practicable) is called for as good practice. In the UK this is also arguably necessary in order to meet safety legislation ( all that is reasonably practicable is called for in the Health Safety at Work Act 1974). 

Polyethylene is processed by a wide variety of techniques, most of which were outlined briefly in Chapter 8. There is insufficient space here to deal adequately with the principles and practice of these processes or even with the particular characteristics of polyethylene being fabricated by these processes. For this reason a list of books giving further details Is given at the end of Chapter 8. 

Measurement caused by concurrent reactions or incomplete reaction processes in the case of chemical principles, and by instrumental deviations and wrong adjustment in the case of physical methods. A frequently encountered reason for the occurrence of systematic deviations is erroneous calibration due to unsuitable calibration standards, matrix effects, or insufficient methodical or theoretical foundation. 

Eorthis reason, the Substitution Principle cannot be implemented to its full and necessary effect simply as a general policy statement within the regulatory framework, since this will be an insufficient driver for change. Instead it needs a clear mandatory imperative to drive it. Within REACH, this means that the Substitution Principle needs to be written into the authorisation procedure so that the availability of a safer alternative is sufficient grounds for an authorisation to be refused. 

The WTO Members have the right to establish their own level of protection, which means that they may choose their own sanitary measures necessary for the protection of life or health, provided they are not inconsistent with the provisions of the SPS Agreement. Such measures applied shall be based on scientific principles and may not be maintained without sufficient scientific evidence, except in the case where relevant scientific evidence is insufficient. Then measures may be taken on a provisional basis, on the basis of available pertinent information, and they shall reviewed within a reasonable period of time. These provisions in the SPS Agreement are often referred to as the precautionary principle . 

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