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.
The human heart is a factory of idols...Everyon e of us is, from his mother's womb, expert in inventing idols.
It is always the false that makes you suffer, the false desires and fears, the false values and ideas, the false relationships between people. Abandon the false and you are free of pain; truth makes happy, truth liberates.
If what I say resonates with you, it's merely because we're branches of the same tree.
I would rather be a man of paradoxes than a man of prejudices.
Penal law was not created by the common people, nor by the peasantry, nor by the proletariat, but entirely by the bourgeoisie as an important tactical weapon in this system of divisions which they wished to introduce.
When a work appears to be ahead of its time, it is only the time that is behind the work.
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