What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
Interpretation
A good definition should be precise and logical for philosophers and scientists, but it must also be comprehensible for students in education.
Henri Poincare emphasizes that while a good definition in scientific or philosophical terms should adhere strictly to logical principles, in the realm of education, the primary focus should be on clarity and understandability for learners. This highlights the importance of tailoring definitions to the audience, ensuring that knowledge is accessible and meaningful for students.
In practice
A teacher might use this quote to highlight the importance of clear definitions in lesson planning.
When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.
It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.
A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.
Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
I love working with kids, talking with them and listening to them. I always encourage kids to reach beyond their dreams. Don't try to be like me. Be better than me.
Oh, magic hour, when a child first knows she can read printed words.
One of the many interesting and surprising experiences of the beginner in child analysis is to find in even very young children a capacity for insight which is often far greater than that of adults.
A book has but one voice, but it does not instruct everyone alike.
Instead of being presented with stereotypes by age, sex, color, class, or religion, children must have the opportunity to learn that within each range, some people are loathsome and some are delightful.
Some are bewildered in the maze of schools, And some made coxcombs nature meant but fools.
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