Logical certainty

Prediction Simulation Fuzzy Logic Certainty Factors... 

The short summary here of Popper s and Kuhn s contributions to the philosophy of science is based, in the case of Popper, only on his early work, which emphasized logic and classified psychology as not scientific. It should be emphasized that the later work of Popper, particularly in the last two decades, demonstrates his broad and deep ideas covering much more than the philosophy of science in a narrow sense. An excellent example is his opinion on precision, as published in Popper s autobiography (1982, p. 24) The quest for precision is analogous to the quest for certainty, and both should be abandoned. .. One should never try to be more precise than the problem demands. .. It is always undesirable to make an effort to increase precision for its own sake — especially linguistic precision — since this usually leads to loss of clarity. ... 

Because the rules or procedures in expert systems are heuristic they are often not well-defined in a logical sense. Nevertheless, they are used to draw conclusions. A conclusion can be uncertain because the truth of the rules deriving it cannot be established with 100% certainty or because the facts or evidence on which the rule is based are uncertain. Some measure of reliability of the obtained conclusions is therefore useful. There are different approaches used in expert systems to model uncertainty. They can be divided into methods that are based on... 

Nowadays, the library has a great collection of books by philosopher Bertrand Russell (1872-1970). Russell was many things a mathematician, a logician, an atheist, a champion of peace, a controversial political figure, and a recipient of the Nobel Prize in literature. Russell so impressed Einstein that in 1931 Einstein wrote to him, The clarity, certainty, and impartiality you apply to the logical, philosophical, and human issues in your books are unparalleled in our generation. ... 

In so far as the input parameters in a risk analysis try to describe reality, they are not known with certainty, and in so far they are known with certainty, that is, they can be expressed by a single-point value, they do not refer to reality. This reminds ns that risk considerations on uncertainty evaluation becomes a key variable that cannot be neglected. The nse of fuzzy logic to evaluate solvents is innovative. This section will only develop these concepts briefly, allowing more rigorous texts to explain it in detail (Ronvray, 1997). 

On first reaction, this would seem to be wholly good in that logically performance tests on the product should give the greatest certainty that it will be satisfactory in service. However, it is extremely difficult and expensive in most cases to devise adequate simulation rigs. The pressures of standardisation are to demand that they are produced quickly and almost inevitably without any obvious source of funding. The most expedient route often has to be taken and rarely are there the resources to properly evaluate and refine the methods decided on. 

While there is no certainty in this particular matter, it would have been logical to attach at the location where the columns had been some framework at the bottom of the gas chamber ceiling, and pour some concrete in the holes, and thus restore the slab. ... 

The second variety of certainty, so-called derivative certainty, will necessarily be less certain than the first variety because it is based on a process of deduction or inference. Typically, to demonstrate the validity of a derivative certainty, a foundational statement has to be posited, the truth of which is taken to be self-evident. This statement is then used as the starting point in a chain of logical reasoning that eventually leads to the derivative certainty. Such a method of arriving at certainties is clearly open to several objections. The foundational statement itself may be suspect, in which case one or more additional statements will be required to support... 

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