Claudio
Gutierrez 
Translated from Spanish by Inés Gutiérrez
Claudio
Gutierrez
This work follows an exposition order which strictly corresponds to the second unit, “logic”, of the official syllabus for the “Elements of Philosophy” course. Each of the chapters corresponds to an item in the program, and can be explained approximately over a three-lesson week, as anticipated by the high school curriculum.
The system of logic and special symbols utilized are the author's creation. We have preferred them over more classical systems because they are clearer and simpler, making them more appropriate at to this level of teaching. The natural deduction version presented, though, lacks the technical attribute of completeness within the general logic of first order. Given the elementary character of the course and following what is costumary, we have decided ourselves in favor of an incomplete system, since it is more easily understandable and teachable than a complete one. This limitation does not affect the technical attribute of consistency or the trustworthiness of its deductions. Finally, given the objectives of the course, we have tried to reduce formal techniques to a very minimum.
Due to the practical nature that a basic course of logic should have, we recommend that this text be used in combination with Exercises for "Elements of Logic", by Gutiérrez and Coronado. The professor giving the course should make a weekly assignment from that booklet, since logic can only be learned through practice.
Those parts of the text not essential for continuous reading have been marked by indentation, their purpose being only emphasis or amplification. They are not necessary for understanding the rest of the material, but are important for the overall presentation. A professor would do well in not including these parts in the tests.
We have been especially careful when choosing our examples, so that they do not turn out to be anodyne, as often happens in logic texts. We have tried to select examples on important issues, with social and civic implications. The premises used in these examples do not necessarily correspond to the author’s thoughts, nor does the student have to accept them. As the student will have to use what is learned here when confronting problems in real life, it seemed appropriate to use examples giving rise to discussion instead of undisputable statements from traditional logic, such as “Socrates is mortal”. Nevertheless, efforts have been made to avoid examples with a high emotional content, which can cloud dispassionate reflection. We hope to have succeeded in finding the point of balance between the anodyne and the passionate. The reader will be the final judge.
The author wishes to express his gratitude to various members of the Faculty of Philosophy at
the University of Costa Rica, who have examined parts of the text and contributed to its improvement. Imperfections should be attributed solely to deficiencies of the author.
Completeness:
All theorems of a system can be proven according to the given rules. Theorems which cannot be demonstrated within the system are not necessarily the most important or the most useful, though.
Consistency:
It is impossible to prove a statement and its contradiction within the same system. An inconsistent system is practically useless.
Kurt Gödel, a distinguished meta-mathematician from the beginning of the XX century, demonstrated conclusively that a system of logic, complex enough to contain the rules of elementary mathematics, must be inconsistent unless it is incomplete.
It would be hard to expect a lapse of 32 years not to have changed a person, and this author is no
exception. And the change can be all the more intense if the first edition occurred in the
year 1968, year of the “Revolution of the Imagination” in Paris and the struggle against the
Vietnam War in the United States (the author resided for three years in the country during that
tumultuous decade); on the other hand, the second edition occurred in the year 2000, the age of
economical
and cultural globalization, a decade after the fall of the Berlin Wall and the collapse of the
Soviet Union. We think the reader will enjoy the contrast between the examples from the
original version and the critical footnotes from 2000. Especially in the
cases where the 1968 author illustrates a fallacy… using an example which the 2000
author criticizes as fallacious, applying material from the same text! We think that this
confrontation magnifies the text’s educational value, by including historical perspective and
underlining the social and moral conditioning of logic discourse and –more generally– of any
comprehensive human thought.
Finally, we have by and large respected the anachronism of the examples, for the sake of authenticity. Nevertheless, in cases where history seems to be repeating itself, we have not been able to resist calling the attention of the reader to the contemporary counterpart. For the sake of educational value.