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Claude Bernard

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A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism….to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.

 
Claude Bernard

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You don't need something more to get something more. That's what emergence means. Life can emerge from physics and chemistry plus a lot of accidents. The human mind can arise from neurobiology and a lot of accidents, the way the chemical bond arises from physics and certain accidents. Doesn't diminish the importance of these subjects to know they follow from more fundamental things plus accidents.

 
Murray Gell-Mann
 

The moment juries or judges go beyond their functions, and take upon themselves to lay down the law or find the facts, not according to the law as it is, but according to the law as they think it ought to be, then the certainty of the law is at an end; there is nothing to rely upon; we are left to the infinite variety and uncertainty of human opinion; to caprice which may at any moment influence the best of us, to feelings and prejudices, perhaps excellent in themselves, but which may distort or disturb our judgment, and distract our minds from the single simple operation of ascertaining whether the facts proved bring the case within the law as we are bound to take it.

 
John Coleridge
 

Evolution is all about processes that almost never happen. Every birth in every lineage is a potential speciation event, but speciation almost never happens, not once in a million births. Mutation in DNA almost never happens -- not once in a trillion copyings -- but evolution depends on it. Take the set of infrequent accidents -- things that almost never happen -- and sort them into the happy accidents, the neutral accidents, and the fatal accidents; amplify the effects of the happy accidents -- which happens automatically when you have replication and competition -- and you get evolution.

 
Daniel C. Dennett
 

The case for individual freedom rests chiefly on the recognition of the inevitable and universal ignorance of all of us concerning a great many of the factors on which the achievement of our ends and welfare depend. It is because every individual knows so little and, in particular, because we rarely know which of us knows best that we trust the independent and competitive efforts of many to induce the emergence of what we shall want when we see it.
Humiliating to human pride as it may be, we must recognize that the advance and even the preservation of civilization are dependent upon a maximum of opportunity for accidents to happen. These accidents occur in the combination of knowledge and attitudes, skills and habits, acquired by individual men and also when qualified men are confronted with the particular circumstances which they are equipped to deal with. Our necessary ignorance of so much means that we have to deal largely with probabilities and chances.
Of course, it is true of social as of individual life that favorable accidents usually do not just happen. We must prepare for them.

 
Friedrich Hayek
 

God, who prepares His work for the ages, accomplishes it by the feeblest instruments. It is the method of His providence to produce great results from inconsiderable means. The law which prevades the kingdom of nature is discerned in the history of mankind. Truth makes silent progress, like the water that trickles behind the rocks, and loosens them from the mountain on which they rest. Suddenly the hidden operation is revealed, and a single day suffices to lay bare the work of years, if not of ages.

 
John Lanahan
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