Rod's_web

Rod Nillsen's web site Go to the home page email: nillsen@uow.edu.au	Igor Kluvánek quotations
	"I would like to finish these general remarks with one which is almost serious." "I am not exaggerating; I have had my experiences." "The further a reality is removed from a direct sensual experience, the less it is accepted. However, human freedoms depend exactly on the acceptance of realities accessible to the human mind only by a process of abstraction." "We should treat students like human beings." "The aesthetic dimension of human life is so important that a full and harmonious development of a personality without the refining influence of art is not possible." "There is the tendency to avoid statements which can be classified as true or false." "A function is a mathematical object, and as such it can be given a name, that is, it can be denoted by a single symbol." "Human knowledge definitely presupposes experience in the form of either direct sense perception or testimony, but it is more than its empirical and experiential concomitants, such as memory and recall." "All truly liberating acts are genuinely altruistic and involve freely accepted renouncement of some freedoms." "The possibility of applications of results of one branch of science in an other one, or of the results of a science in another science. presupposes an internal unity or interdependence among various sciences. I believe....that such a unity and interdependence really exists." "The identification of knowledge with its empirical and experiential concomitants, that is, with mere observation, acquiring and retaining information, recollection and such like, is a sign of positivism. A positivistic idea of human knowledge leads those who embrace it to disregard the connections between phenomena, concepts, ideas. And yet, a person understands some information available to him or her only if he or she grasps the connections, the relationships, between phenomena, concepts and ideas to which the information refers. It can be said that the understanding of information consists precisely in the grasping of such relations." "Positivism reduces human cognitive activity to mere recording of experience, collecting data, noting information and such like." "The student has great difficulties in distinguishing conceptually the notions that he or she experiences as identical." "The discussion [in our culture] on any subject usually reduces to a quarrel about which of two extreme positions to choose or, perhaps, about which point to choose on a line between the two extremes." "If there is no word in a language for a concept, then the users of that language do not form that concept in their minds and so disregard a certain reality. On the other hand, whenever a round form or phrase is found as a more-or-less vivid image of some reality, then the further search for understanding that reality ends." [Describing the consequences of taking knowledge to consist only of facts.] "Training in techniques whose purpose is constantly disregarded can lead to falsification of ideas." "Teaching without objective aims has a tendency to become trivial and useless. If difficulties arise with putting across deep concepts or effective methods arise, there is no reason either to eliminate such concepts and methods from the curriculum, no matter how objectively useful they may be, or to present them in so 'simplified' a form that they become empty." "I do not believe that education in mathematics which aims at mere factual knowledge, be it even extensive factual knowledge, but fails to improve on the student's ability of self-direction, is worth providing." "...someone may say that life is not made miserable for students or their teachers because they do not bother with such silly problems as I am suggesting. My critic may be right, but I have demonstrated sufficiently, I think, what is the cost of an easier life in terms of a lost sense of purpose and falsification of a classical scientific idea." [Referring to the notion of intervals in school mathematics.] "...a mathematician who contributed to the treasure of our knowledge does not need an apology. What a mathematician may need is exegesis. For there may be ideas in the work of a great mathematician that remained unnoticed or not sufficiently explored, but nevertheless could trigger trains of thought leading to new discoveries, especially if they are combined with the knowledge accumulated since his times." "Every form of positivism elevates some facts to the dignity of principles, or axioms, to which all arguments in a given sphere of discussion are reduced. Such facts are thereby removed from among the targets of human cognitional activity. So, for example, if such a fact happens to be an institution, then this institution is made immune against intelligent understanding and criticism. Thus, every form of positivism is a reactionary force; it is both a cause and manifestation of deeply seated conservatism. "He [Professor McShane] gives me an opportunity to put in my usual commercial slogan: 'Vector measures to every household'." "I will skip the commercial about the further possibilities in this approach to the derivative." "It is not necessary, not even desirable, to strive at all costs for the minimal number of primitive concepts. It is well-known, for example, that functions can be defined in terms of sets. While this point is very important in the investigation of the foundations, its uncritical usage in other branches of mathematics can lead to either pedagogical or logical nonsense or to both." "Independent development of these theories [of integration and summability] led to a situation of truly baroque complexity. At least, so it must appear to the bulk of mathematics students and their teachers. But the necessity to cope with this complexity, and the associated inconsistencies, seem to represent a burden even for working mathematicians. For, apparently, the achievements in either of these theories have not stimulated corresponding progress in the other." "The characterization of null sets and functions goes back to F. Riesz. He uses convergence of monotonic sequences though, rather than absolute summability. Riesz used his discovery of the role of null sets with a great advantage in the simplification of integration theory." "A law does not impose or remove a moral obligation by the mere fact that it is supported by a majority of the population and is promulgated by the competent authority." "The freedom of man, as a free gift of the Omnipotent and Omniscient God, is not susceptible to complete rationalization." Go to the home page