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.
The most important aspect of freedom of speech is freedom to learn. All education is a continuous dialogue - questions and answers that pursue every problem on the horizon. That is the essence of academic freedom.
Language is like a road, it cannot be perceived all at once because it unfolds in time, whether heard or read. This narrative or temporal element has made writing and walking resemble each other.
For a lot of us, awareness is merely realizing the extent to which we've been lied to all our lives. You start educating yourself. You become motivated; you follow your muse where it takes you. And you see the world in a different way. You start making decisions based on what you feel is right.
A book is always an emergence above everyday life. A book is expressed life and thus is an addition to life.
When asked, "How do you write?" I invariably answer, "One word at a time," and the answer is invariably dismissed. But that is all it is. It sounds too simple to be true, but consider the Great Wall of China, if you will: one stone at a time, man. That's all. One stone at a time. But I've read you can see that motherfucker from space without a telescope.
I'm of a fearsome mind to throw my arms around every living librarian who crosses my path, on behalf of the souls they never knew they saved.
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