A B S T R A C T<\/span><\/strong><\/p>\n Giuseppe Primiero in his remarks entitled „Computational Hypotheses and Computational experiments” expresses a thought-provoking idea: The analogy between the scientific method and the problem-solving process underlying computing still is a tempting proposition.<\/em><\/p>\n Before going into details, let me sum up the vein of my comment. I do not endorse the view about a sharp demarcation between empirical and\u00a0 mathematical (including mathematical logic) theories, as claimed in the standard classifications of sciences. My point is like that of Quine, G\u00f6del, Tarski, etc. that the difference is rather in degree of reliability. It is the greatest with logical and\u00a0 mathematical theories, but even these do not enjoy absolute reliability.<\/p>\n Let us call computational sciences<\/em>\u00a0 those in which mechanical procedures serve as problem-solving devices. I suggest to distinguish between most reliable<\/em> mechanical procedures from those less reliable which I am to call tentative<\/em>. The latter are just\u00a0 tentative for possible deficiencies either of observational data or of conceptualization (i.e., a creative concept-formation). As a case study to exemplify the latter, I take Aristotle’s model of the universe, since its deficient conceptualization, e.g.\u00a0 its idea of motion, hampered the development of astronomy.<\/p>\n When using the term „algorithm”, we mean a problem solving device that is based either on a mathematical theory, or on some empirical knowledge, e.g. culinary experiments to result in pedantic recipes in a Cookbook. The latter proves to be the case in various domains of\u00a0 technology.<\/p>\n In the case of mathematical theories as Boolean algebra, arithmetic, etc., respective algorithms do not need to be tested as to their reliability, since such a merit is warranted by an underlying mathematical theory. However, we may need to inquire into their\u00a0 effectiveness.<\/p>\n Such a need can be nicely exemplified in the case of arithmetic. In my text I give some tips in this direction. For instance, algorithms based on the first-order Peano arithmetic are more efficient in mathematical practice than those based on Presburger arithmetic, while less efficient than in he case of second-order Peano arithmetic. Such increases of effectiveness are due to ever more sophisticated conceptualizations, same as in empirical\u00a0 theories (e.g. as in comparing Newton’s mechanics with that of Aristotle).<\/p>\n","protected":false},"excerpt":{"rendered":" A B S T R A C T Giuseppe Primiero in his remarks entitled „Computational Hypotheses and Computational experiments” expresses a thought-provoking idea: The analogy between the scientific method and the problem-solving process underlying computing still is a tempting proposition. … Czytaj dalej