The mind has its illusions as the sense of sight; and in the same manner that the sense of feeling corrects the latter, reflection and calculation correct the former.
Truth and justice are the immutable laws of social order.
The weight of evidence for an extraordinary claim must be proportioned to its strangeness.
His last words, according to De Morgan: Man follows only phantoms.
I have lived long enough to know what I did not at one time believe – that no society can be upheld in happiness and honor without the sentiment of religion.
Do you believe in god? I have no need for that hypothesis, he may be around though.
It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.
What we know here is very little, but what we are ignorant of is immense.
Nature laughs at the difficulties of integration.
The simplicity of nature is not to be measured by that of our conceptions. Infinitely varied in its effects, nature is simple only in its causes, and its economy consists in producing a great number of phenomena, often very complicated, by means of a small number of general laws.
The theory of probabilities is basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it.
What we know is not much. What we don’t know is enormous.
Man follows only phantoms.
The telescope sweeps the sky without finding God.
The word ‘chance’ then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge.
Your Highness, I have no need of this hypothesis.
Napoleon: You have written this huge book on the system of the world without once mentioning the author of the universe. Laplace: Sire, I had no need of that hypothesis. Later when told by Napoleon about the incident, Lagrange commented: Ah, but that is a fine hypothesis. It explains so many things.
The most important questions of life are indeed, for the most part, really only problems of probability.
Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories.
Read Euler, read Euler. He is the master of us all.