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I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.
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"Solution of a Question in the Theory of Probabilities" (30 November 1853) published in The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science?? (January 1854), p. 32

 

George Boole

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Science Of Energetics. Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodynamics with that of ordinary mechanics, still it is to be remembered that the science of thermodynamics is by no means dependent for its certainty on that or any other hypothesis, having been now reduced, to a system of principles, or general facts, expressing strictly the results of experiment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, applicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the science of energetics, — a science comprehending, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena.

 

William John Macquorn Rankine

 

The first question we should face is: What is the aim of a physical theory? To this question diverse answers have been made, but all of them may be reduced to two main principles:
"A physical theory," certain logicians have replied, "has for its object the explanation of a group of laws experimentally established."
"A physical theory," other thinkers have said, "is an abstract system whose aim is to summarize and classify logically a group of experimental laws without claiming to explain these laws...
Now these two questions — Does there exist a material reality distinct from sensible appearances? and What is the nature of reality? — do not have their source in experimental method, which is acquainted only with sensible appearances and can discover nothing beyond them. The resolution of these questions transcends the methods used by physics; it is the object of metaphysics.
Therefore, if the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics...
Now, to make physical theories depend on metaphysics is surely not the way to let them enjoy the privilege of universal consent.

 

Pierre Duhem

 

Allow me to define more specifically the inherent limitations of our numerical knowledge which are so often overlooked. I want to do this to avoid giving the impression that I generally reject the mathematical method in economics. I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation. We could scarcely have achieved that comprehensive picture of the mutual interdependencies of the different events in a market without this algebraic technique. It has led to the illusion, however, that we can use this technique for the determination and prediction of the numerical values of those magnitudes; and this has led to a vain search for quantitative or numerical constants.

 

Friedrich Hayek

 

Both induction and deduction, reasoning from the particular and the general, and back again from the universal to the specific, form the essence to scientific thinking.

 

Hans Christian von Baeyer

 

Previous to the time of Pascal, who would have thought of measuring doubt and belief? Who could have conceived that the investigation of petty games of chance would have led to the most sublime branch of mathematical science - the theory of probabilities?

 

William Stanley Jevons