Exercises for “Element of Logic”
Chapter I

Concept of Logic, Logic and Psychology, Logic and Rhetoric

Claudio Gutierrez and Luis G. Coronado

Translated from Spanish by Inés Gutiérrez

  1. Distinguish the word “logic” or “logical” used in a technical sense from the word used in the ordinary sense.

    1. The tax-reform measures proposed for the immediate future are totally logical, inasmuch as they acknowledge the national reality and are the result of in-depth study.

    2. Logic is a study of the methods and principles used to distinguish between correct and incorrect reasoning.

    3. The explanation offered by Mr. Quiros concerning the way in which the crime was carried out was the most logical, due to its consistency and the intimate connection between the statements and the conclusion.

    4. We can say that the attitude assumed by the board of directors is logical, since it prevented the aggravation of the present situation.

    5. The statement made by the Minister before the parliamentary commission was commendable for its logic, since it provided much light on the issue under discussion.

  2. Indicate what, from the following paragraphs, would be of interest to psychology and what to logic.

    1. Where do thoughts originate? The mind is usually associated with man’s nervous system, which differs solely from that of the animal kingdom by its wide diversity; and if we descend in the zoological scale we find the amoeba and other unicellular species, in which each cell performs all vital functions: feeding and assimilation, breathing and oxidation, excretion, sensitiveness and reproduction. (Wolff, Introduction to Psychology)

    2. Mathematics as a science began when someone for the first time –probably a Greek– proved propositions about anything or something, without specifying the particular things intended. These propositions were first stated by the Greeks for geometry and, consequently, geometry was the great mathematical Greek science. After the appearance of geometry, many centuries went by before algebra acquired a really effective impulse, notwithstanding some timid advances by the last Greek mathematicians. (Whitehead, Principia Mathematica)

    3. The origins of mathematical invention are a problem which must inspire great interest… It is the act in which the human spirit most dispenses with its external world, where it works for itself and itself only, so that by studying the processes of geometrical thought, we can hope to attain its most essential elements…. A first event should surprise us –or rather would surprise us if we were not so accustomed to it. How is it that there are people who do not understand mathematics? If mathematics invoke no more than the laws of logic accepted by all focused spirits; if its evidence is based upon the principles common to all men and which no one in his right mind could deny, how is it possible that there are so many people refractory to it? (Poincaré, Science and Method)

  3. In relation with these three conflicts, to what extent can logic contribute to their solution? What other methods apart from logic can help to resolve them?
    1. In response to the watchful attitude of university students concerning national issues, Mr. X affirms that this is due to the extremist currents which have infiltrated the University, while Mr. Z maintains that this attitude implies a new and deep awareness of their position as university students.

    2. Mr. A stated, when interviewed, that heart transplants would be contrary to medical ethics, so long as what is technically understood by “death” is not defined. On the other hand, Mr. B affirmed, on being interviewed, that he only considers this kind of transplant from a scientific point of view, and thus confers thereon a greater importance and usefulness.

    3. There are some who affirm that the problem of birth control is a false problem, inasmuch as new sources of production can be exploited and a possibility exists for technical progress in the means of production. On the other hand, others maintain that the problem is a real one: if demographic growth is not limited, future generations –and in some cases the current generation– will be deeply affected by serious problems, such as a food shortage, health, education, the distribution of wealth, employment, etc.

      Copyright © 1968-2006 Claudio Gutierrez and Luis G. Coronado