Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.
Interpretation
The quote suggests that extreme beliefs, whether doubt or certainty, eliminate the necessity for deep thinking.
Henri Poincare highlights that both doubt and blind belief are shortcuts that lead to a lack of critical thinking and self-reflection. By relying on either extremity, one avoids the nuanced understanding and contemplation that come with truly engaging with ideas and beliefs. The emphasis is on the importance of reflective thinking over simplistic binaries.
In practice
In a discussion about critical thinking at a seminar.
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.
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.
Don’t underestimate the value of irony—it is extremely valuable.
Age brings a freedom. When you're young, you're much more subject to the idea of what feminine is or how you should look or how you should behave.
No sanction can stand against ignited minds.
Would you rather live your life according to the approval of others or aligned with your truth and your dreams?
Circumstances are beyond human control, but our conduct is in our own power.
When you are on a great horse, you have the best seat you will ever have.
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