Demonstratio longe optima est experientia.
By far the best proof is experience.

En un mot, pour tirer la loi de l'expérience, if faut généraliser; c'est une nécessité qui s'impose à l'observateur le plus circonspect.
In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.

Common sense is the measure of the possible; it is composed of experience and prevision; it is calculation applied to life. (26 Dec 1852)

Experience of actual fact either teaches fools or abolishes them.

I grew up to be indifferent to the distinction between literature and science, which in my teens were simply two languages for experience that I learned together.

It must be conceded that a theory has an important advantage if its basic concepts and fundamental hypotheses are 'close to experience,' and greater confidence in such a theory is certainly justified. There is less danger of going completely astray, particularly since it takes so much less time and effort to disprove such theories by experience. Yet more and more, as the depth of our knowledge increases, we must give up this advantage in our quest for logical simplicity in the foundations of physical theory...

Let us suppose the mind to be, as we say, white paper, void of all characters, without any ideas; how comes it to be furnished? Whence comes it by that vast store which the busy and boundless fancy of man has painted on it with an almost endless variety? Whence has it all the materials of reason and knowledge? To this I answer, in one word, from experience.

Men are wise in proportion, not to their experience, but to their capacity for experience.

Much is said about the progress of science in these centuries. I should say that the useful results of science had accumulated, but that there had been no accumulation of knowledge, strictly speaking, for posteriry; for knowledge is to be aquired only by corresponding experience. How can be know what we are told merely? Each man can interpret another's experience only by his own.

Science is a progressive activity. The outstanding peculiarity of man is that he stumbled onto the possibility of progressive activities. Such progress, the accumulation of experience from generation to generation, depended first on the development of language, then of writing and finally of printing. These allowed the accumulation of tradition and of knowledge, of the whole aura of cultural inheritance that surrounds us. This has so conditioned our existence that it is almost impossible for us to stop and examine the nature of our culture. We accept it as we accept the air we breathe; we are as unconscious of our culture as a fish, presumably, is of water.

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. An Introduction to the Study of Experimental Medicine (1865), trans. Henry Copley Green (1957), 11.

The most beautiful experience we can have is the mysterious—the fundamental emotion which stands at the cradle of true art and true science.

We receive experience from nature in a series of messages. From these messages we extract a content of information: that is, we decode the messages in some way. And from this code of information we then make a basic vocabulary of concepts and a basic grammar of laws, which jointly describe the inner organization that nature translates into the happenings and the appearances we meet.

You look at science (or at least talk of it) as some sort of demoralising invention of man, something apart from real life, and which must be cautiously guarded and kept separate from everyday existence. But science and everyday life cannot and should not be separated. Science, for me, gives a partial explanation for life. In so far as it goes, it is based on fact, experience and experiment.