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.
Interpretation
Logic alone cannot capture the entirety of reality; intuition plays a crucial role in understanding the whole.
Henri Poincaré's quote emphasizes the limitations of pure logic in grasping the complete essence of reality. While logic can break down complex demonstrations into correct, elementary operations, it falls short of providing a holistic view. This broader understanding relies on intuition, suggesting that human perception and instinct are equally important in comprehending the unity of existence, which cannot be fully articulated through logical reasoning alone.
In practice
This quote can be used in a discussion about the limitations of scientific reasoning in philosophy.
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.
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.
Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
Multiply, vary, let the strongest live and the weakest die.
To be black and an intellectual in America is to live in a box. On the box is a label, not of my own choosing.
Against the suffering which may come upon one from human relationships the readiest safeguard is voluntary isolation, keeping oneself aloof from other people. The happiness which can be achieved along this path is, as we see, the happiness of quietness. Against the dreaded external world one can only defend oneself by some kind of turning away from it, if one intends to solve the task by oneself.
If the Holy Spirit was withdrawn from the church today, 95 percent of what we do would go on and no one would know the difference. If the Holy Spirit had been withdrawn from the New Testament church, 95 percent of what they did would stop, and everybody would know the difference.
Mankind will endure when the world appreciates the logic of diversity.
The word 'ivory' rang in the air, was whispered, was sighed. You would think they were praying to it. A taint of imbecile rapacity blew through it all, like a whiff from some corpse. By Jove! I've never seen anything so unreal in my life. And outside, the silent wilderness surrounding this cleared speck on the earth struck me as something great and invincible, like evil or truth, waiting patiently for the passing away of this fantastic invasion.
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