But we are interested in understanding the world and whether claims about more serious matters are true, such as:
Does a personal god exist?
What was the origin of the universe?
Is there life after death?
Does mathematics really describe the physical world?
Obviously, then, the need to learn how to deal with such questions as, "What color is the pencil?" becomes a serious matter.
The analytical thinker is aware not only that concepts are given their meanings in terms of their relationship to each other but also of the limitations of those meanings.
To use a simple example viewed as a problem of science: I am at rest as I sit in my chair. The "educated" person knows that I am moving at approximately 1000 miles per hour around the "axis" of the earth, 18 miles a second around the sun, and 250 miles a second around the center of our galaxy, not to mention the movements of the Sun within the galaxy and the galaxy itself.
The astronauts, repairing the Hubble telescope are "at rest" relative to the telescope but, are moving five miles a second over our heads.
The analytical thinker comparing those motions in his mind's eye comes to understand, assuming the scientific data to be accurate, that even those motions may be deceptive in their interpretations depending on, among other things, their relative positions in space.
After all, as Einstein has shown, the astronauts overhead may be "at rest" and we, all the inhabitants on Earth, may be moving at 18,000 miles an hour beneath them.
Children in the pre-high school grades are taught times tables and other mathematical concepts by rote.
If, as they reach the higher grades, they have not been taught that mathematics is a form of deductive logic, and that mathematical concepts, i.e., numbers, points, lines, planes, etc., do not actually describe the physical world, then the teachers, the colleges, and universities are not teaching the students to think analytically.
Mathematical concepts have no physically existential status.
The teacher is not asking the student such questions as:
What is a number?
Do numbers, in fact, exist?"
Would there be numbers if intelligent beings did not exist?
Does conceiving the idea of numbers bring them into existence?
What does "exist" mean in the claim, "Numbers, i.e., mathematical concepts, exist (autonomously?)?"
Why, when a mathematician says, "There are as many points on an infinitely small leg of a Pythagorean right triangle as there are on its infinitely long hypotenuse," should it be accepted as true when common sense would strongly suggest otherwise?
If a teacher does not explain to his students (as in the case of teaching times tables) that "a point has no dimensions" (to cite one definition), is equivalent to saying it is nothing; i.e.; it is only an idea (i.e.; there are as many ideas on the small leg as there are on the long hypotenuse.), then he is not teaching the student to think analytically.
I have, here, referred mainly to mathematical and philosophical concepts.
However, the same kind of examination of ideas (a la Socrates) applies to all kinds of language: mathematical, scientific, theistic, ordinary -- to cite only a few -- with which we make claims to having truth and knowledge.
We must never accept language at face value.
There are certain PRINCIPLES, rules, facts, information we must be aware of.
Otherwise, it is impossible to become an analytical thinker sufficient to protecting ourselves against the abuse of language that is and will be foisted upon us all our lives.
To the degree that one examines language and defines terms and distinguishes between DESCRIPTIVE and PRESCRIPTIVE, FALSIFIABLE and UNFALSIFIABLE statements, he is well on the road to becoming an analytical thinker and, hence, a clear and critical thinker.
SEE FILE 21: PERENNIAL QUESTIONS