In these researches I followed the principles of the experimental method that we have established, i.e., that, in presence of a well-noted, new fact which contradicts a theory, instead of keeping the theory and abandoning the fact, I should keep and study the fact, and I hastened to give up the theory.

It is that which we do know which is the great hindrance to our learning not that which we do not know.

Observation is a passive science, experimentation is an active science.

Speaking concretely, when we say “making experiments or making observations,” we mean that we devote ourselves to investigation and to research, that we make attempts and trials in order to gain facts from which the mind, through reasoning, may draw knowledge or instruction.
Speaking in the abstract, when we say “relying on observation and gaining experience,” we mean that observation is the mind's support in reasoning, and experience the mind's support in deciding, or still better, the fruit of exact reasoning applied to the interpretation of facts. It follows from this that we can gain experience without making experiments, solely by reasoning appropriately about well-established facts, just as we can make experiments and observations without gaining experience, if we limit ourselves to noting facts.
Observation, then, is what shows facts; experiment is what teaches about facts and gives experience in relation to anything.

The goal of scientific physicians in their own science … is to reduce the indeterminate. Statistics therefore apply only to cases in which the cause of the facts observed is still indeterminate.

We must remain, in a word, in an intellectual disposition which seems paradoxical, but which, in my opinion, represents the true mind of the investigator. We must have a robust faith and yet not believe.
[Often seen summarized as: The investigator should have a robust faith—and yet not believe.]

When entering on new ground we must not be afraid to express even risky ideas so as to stimulate research in all directions. As Priestley put it, we must not remain inactive through false modesty based on fear of being mistaken.