"The art of war teaches us to rely not on the likelihood of the enemy's not coming, but on our own readiness to receive him; not on the chance of his not attacking, but rather on the fact that we have made our position unassailable.” (Sun Tzu, “The Art of War”, 5th century BC)
“No human being will ever know the Truth, for even if they happen to say it by chance, they would not even known they had done so.” (Xenophanes, 5th century BC)
“God's dice always have a lucky roll.” (Sophocles, 5th century BC)
“Nothing occurs at random, but everything for a reason and by necessity” (Leucippus, 5th century BC)
“Everything existing in the universe is the fruit of chance.” (Democritus, 4th century BC)
“For that which is probable is that which generally happens.” (Aristotle, “The Art of Rhetoric”, 4th century BC)
“I know too well that these arguments from probabilities are imposters, and unless great caution is observed in the use of them, they are apt to be deceptive.” (Plato,” Phaedo” [On the Soul], 4th century BC)
“All human actions have one or more of these seven causes: chance, nature, compulsions, habit, reason, passion, desire.” (Aristotle, 4th century BC)
“If in a discussion of many matters […] we are not able to give perfectly exact and self-consistent accounts, do not be surprised: rather we would be content if we provide accounts that are second to none in probability.” (Plato, “Timaeus”, cca. 360 BC)
“A likely impossibility is always preferable to an unconvincing possibility. The story should never be made up of improbable incidents; there should be nothing of the sort in it.” (Aristotle, “Poetics”, cca. 335 BC)
“How often things occur by the mearest chance.” (Terence, “Phormio”, 2nd century BC)
“Suam habet fortuna rationem.’
“Chance has its reasons.” (Gaius Petronius, “Satryicon liber” [“The Book of Satyrlike Adventures”], 1st century BC)
"Probability is the very guide of life." (Cicero, “De Natura Deorum” [“On the Nature of the Gods”], 45 BC)
“Valor is of no service, chance rules all, and the bravest often fall by the hands of cowards.” (Cornelius Tacitus, cca. 69-100 AD)
"A wide knowledge of probabilities constitutes a master key whose use is universal." (John of Salisbury, "Metalogicon", 1159)
"The method of demonstration is therefore generally feeble and ineffective with regard to facts of nature (I refer to corporeal and changeable things). But it quickly recovers its strength when applied to the field of mathematics. For whatever it concludes in regard to such things as numbers, proportions and figures is indubitably true, and cannot be otherwise. One who wishes to become a master of the science of demonstration should first obtain a good grasp of probabilities. Whereas the principles of demonstrative logic are necessary; those of dialectic are probable." (John of Salisbury, "Metalogicon", 1159)
“Thus, joining the rigor of demonstrations in mathematics with the uncertainty of chance, and conciliating these apparently contradictory matters, it can, taking its name from both of them, with justice arrogate the stupefying name: The Mathematics of Chance.” (Blaise Pascal, [Address to the Academie Parisienne de Mathematiques] 1654)
“As a Foundation to the following Proposition, I shall take Leave to lay down this Self-evident Truth: That any one Chance or Expectation to win any thing is worth just such a Sum, as wou’d procure in the same Chance and Expectation at a fair Lay.“ (Christiaan Huygens, “De ratiociniis in ludo aleae”, 1657)
“The good or evil of an event should be considered in view of the event's likelihood of occurrence.” (Antoine Amauld & Pierre Nicole, “The Art of Thinking: Port-Royal Logic”, 1662)
“Take away probability, and you can no longer please the world; give probability, and you can no longer displease it.” (Blaise Pascal, “Thoughts“, 1670)
“In practical life we are compelled to follow what is most probable; in speculative thought we are compelled to follow truth. […] we must take care not to admit as true anything, which is only probable. For when one falsity has been let in, infinite others follow.” (Baruch Spinoza, [letter to Hugo Boxel], 1674)
“Probability is a degree of possibility.” (Gottfried W Leibniz, “On estimating the uncertain”, 1676)
“Probability, however, is not something absolute, [it is] drawn from certain information which, although it does not suffice to resolve the problem, nevertheless ensures that we judge correctly which of the two opposites is the easiest (facilius) given the conditions known to us.” (Gottfried W Leibniz, “Forethoughts for an encyclopaedia or universal science”, cca. 1679)
“Consider however (imitating Mathematicians) certainty or truth to be like the whole; and probabilities [to be like] parts, such that probabilities would be to truths what an acute angle [is] to a right [angle].” (Gottfried W Leibniz, [ to Vincent Placcius] 1687)
“The probable is something which lies midway between truth and error” (Christian Thomasius, “Institutes of Divine Jurisprudence”, 1688)
“Probability is the appearance of agreement upon fallible proofs. As demonstration is the showing the agreement or disagreement of two ideas by the intervention of one or more proofs, which have a constant, immutable, and visible connexion one with another; so probability is nothing but the appearance of such an agreement or disagreement by the intervention of proofs, whose connexion is not constant and immutable, or at least is not perceived to be so, but is, or appears for the most part to be so, and is enough to induce the mind to judge the proposition to be true or false, rather than the contrary.” (John Locke, “An Essay Concerning Human Understanding”, Book IV, 1689)
“Probability is likeliness to be true, the very notation of the word signifying such a proposition, for which there be arguments or proofs to make it pass, or be received for true. […] The grounds of probability are two: conformity with our own experience, or the testimony of others' experience. Probability then, being to supply the defect of our knowledge and to guide us where that fails, is always conversant about propositions whereof we have no certainty, but only some inducements to receive them for true.” (John Locke, “An Essay Concerning Human Understanding”, Book IV, 1689)
“It is impossible for a Die, with such determin’d force and direction, not to fall on such a determin’d side, only I don’t know the force and direction which makes it fall on such a determin’d side, and therefore I call that Chance, which is nothing but want of Art…” (John Arbuthnot, “Of the Laws of Chance”, 1692)
"To understand the theory of chance thoroughly, requires a great knowledge of numbers, and a pretty competent one of Algebra." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1700)
“We define the art of conjecture, or stochastic art, as the art of evaluating as exactly as possible the probabilities of things, so that in our judgments and actions we can always base ourselves on what has been found to be the best, the most appropriate, the most certain, the best advised; this is the only object of the wisdom of the philosopher and the prudence of the statesman.” (Jacob Bernoulli, “Ars Conjectandi”, 1713)
“Probability is a degree of certainty and it differs from certainty as a part from a whole.” (Jacob Bernoulli, “Ars Conjectandi”, 1713)
“The probability of an Event is greater, or less, according to the number of Chances by which it may Happen, compar’d with the number of all the Chances, by which it may either Happen or Fail. […] Therefore, if the Probability of Happening and Failing are added together, the Sum will always be equal to Unit.” (Abraham De Moivre, “The Doctrine of Chances”, 1718)
"Events are independent when the happening of any one of them does neither increase nor abate the probability of the rest." (Thomas Bayes, "An Essay towards solving a Problem in the Doctrine of Chances", 1763)
"the probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon it's happening." (Thomas Bayes, "An Essay towards solving a Problem in the Doctrine of Chances", 1763)
“If an event can be produced by a number n of different causes, the probabilities of the existence of these causes, given the event (prises de l'événement), are to each other as the probabilities of the event, given the causes: and the probability of each cause is equal to the probability of the event, given that cause, divided by the sum of all the probabilities of the event, given each of the causes.” (Pierre-Simon Laplace, "Mémoire sur la Probabilité des Causes par les Événements", 1774)
“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.” (Pierre-Simon Laplace, "Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres", 1783)
“[…] determine the probability of a future or unknown event not on the basis of the number of possible combinations resulting in this event or in its complementary event, but only on the basis of the knowledge of order of familiar previous events of this kind” (Marquis de Condorcet, “Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix”, 1785)
“The art of drawing conclusions from experiments and observations consists in evaluating probabilities and in estimating whether they are sufficiently great or numerous enough to constitute proofs. This kind of calculation is more complicated and more difficult than it is commonly thought to be […]” (Antoine-Laurent Lavoisier, cca. 1790)
“Probability has reference partly to our ignorance, partly to our knowledge [..] The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all cases possible is the measure of this probability, which is thus simply a fraction whose number is the number of favorable cases and whose denominator is the number of all cases possible.” (Pierre-Simon Laplace, “Philosophical Essay on Probabilities”, 1814)
“One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth - induction and analogy - are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay.” (Pierre-Simon Laplace, “Philosophical Essay on Probabilities”, 1814)
“The probability of an event is the reason we have to believe that it has taken place, or that it will take place.” (Siméon-Denis Poisson, “'Règles générales des probabilités”, 1837)
“The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen).” (Siméon-Denis Poisson, “'Règles générales des probabilités”, 1837)
“I consider the world probability as meaning the state of mind with respect to an assertion, a coming event, or any other matter on which absolute knowledge does not exist.” (Augustus De Morgan, “Essay on Probability”, 1838)
"The determination of the average man is not merely a matter of speculative curiosity; it may be of the most important service to the science of man and the social system. It ought necessarily to precede every other inquiry into social physics, since it is, as it were, the basis. The average man, indeed, is in a nation what the centre of gravity is in a body; it is by having that central point in view that we arrive at the apprehension of all the phenomena of equilibrium and motion." (Adolphe Quetelet, "A Treatise on Man and the Development of his Faculties", 1842)
“The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore, the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man's mind." (James C Maxwell, 1850)
“[…] probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.” (George Boole, “The Laws of Thought”, 1854)
“If an event can be produced by a number n of different causes, the probabilities of the existence of these causes, given the event (prises de l'événement), are to each other as the probabilities of the event, given the causes: and the probability of each cause is equal to the probability of the event, given that cause, divided by the sum of all the probabilities of the event, given each of the causes.” (Pierre-Simon Laplace, "Mémoire sur la Probabilité des Causes par les Événements", 1774)
“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.” (Pierre-Simon Laplace, "Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres", 1783)
“[…] determine the probability of a future or unknown event not on the basis of the number of possible combinations resulting in this event or in its complementary event, but only on the basis of the knowledge of order of familiar previous events of this kind” (Marquis de Condorcet, “Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix”, 1785)
“The art of drawing conclusions from experiments and observations consists in evaluating probabilities and in estimating whether they are sufficiently great or numerous enough to constitute proofs. This kind of calculation is more complicated and more difficult than it is commonly thought to be […]” (Antoine-Laurent Lavoisier, cca. 1790)
“Probability has reference partly to our ignorance, partly to our knowledge [..] The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all cases possible is the measure of this probability, which is thus simply a fraction whose number is the number of favorable cases and whose denominator is the number of all cases possible.” (Pierre-Simon Laplace, “Philosophical Essay on Probabilities”, 1814)
“One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth - induction and analogy - are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay.” (Pierre-Simon Laplace, “Philosophical Essay on Probabilities”, 1814)
“The probability of an event is the reason we have to believe that it has taken place, or that it will take place.” (Siméon-Denis Poisson, “'Règles générales des probabilités”, 1837)
“The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen).” (Siméon-Denis Poisson, “'Règles générales des probabilités”, 1837)
“I consider the world probability as meaning the state of mind with respect to an assertion, a coming event, or any other matter on which absolute knowledge does not exist.” (Augustus De Morgan, “Essay on Probability”, 1838)
"The determination of the average man is not merely a matter of speculative curiosity; it may be of the most important service to the science of man and the social system. It ought necessarily to precede every other inquiry into social physics, since it is, as it were, the basis. The average man, indeed, is in a nation what the centre of gravity is in a body; it is by having that central point in view that we arrive at the apprehension of all the phenomena of equilibrium and motion." (Adolphe Quetelet, "A Treatise on Man and the Development of his Faculties", 1842)
“The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore, the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man's mind." (James C Maxwell, 1850)
“[…] probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.” (George Boole, “The Laws of Thought”, 1854)
"There is no more remarkable feature in the mathematical theory of probability than the manner in which it has been found to harmonize with, and justify, the conclusions to which mankind have been led, not by reasoning, but by instinct and experience, both of the individual and of the race. At the same time it has corrected, extended, and invested them with a definiteness and precision of which these crude, though sound, appreciations of common sense were till then devoid." (Morgan W Crofton, "Probability", Encyclopaedia Britannica 9th Ed,, 1885)
“One can hardly give a satisfactory definition of probability.” (Henri Poincaré, “Calcul des Probabilités”, 1912)
“Nature prefers the more probable states to the less probable because in nature processes take place in the direction of greater probability. Heat goes from a body at higher temperature to a body at lower temperature because the state of equal temperature distribution is more probable than a state of unequal temperature distribution.” (Max Planck, “The Atomic Theory of Matter”, 1909)
"Part of our knowledge we obtain direct; and part by argument. The Theory of Probability is concerned with that part which we obtain by argument, and it treats of the different degrees in which the results so obtained are conclusive or inconclusive." (John M Keynes, "A Treatise on Probability", 1921)
“We know that the probability of well-established induction is great, but, when we are asked to name its degree we cannot. Common sense tells us that some inductive arguments are stronger than others, and that some are very strong. But how much stronger or how strong we cannot express.” (John M Keynes, “A Treatise on Probability”, 1921)
“There can be no unique probability attached to any event or behaviour: we can only speak of ‘probability in the light of certain given information’, and the probability alters according to the extent of the information.” (Sir Arthur S Eddington, “The Nature of the Physical World”, 1928)
“Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.” (Bertrand Russell, 1929)
“When an observation is made on any atomic system that has been prepared in a given way and is thus in a given state, the result will not in general be determinate, i.e. if the experiment is repeated several times under identical conditions several different results may be obtained. If the experiment is repeated a large number of times it will be found that each particular result will be obtained a definite fraction of the total number of times, so that one can say there is a definite probability of its being obtained any time that the experiment is performed. This probability the theory enables one to calculate.” (Paul A M Dirac, “The Principles of Quantum Mechanics”, 1930)
“The theory of probability as a mathematical discipline can and should be developed from axioms in exactly the same way as geometry and algebra.” (Andrey Kolmogorov, “Foundations of the Theory of Probability”, 1933)
“Starting from statistical observations, it is possible to arrive at conclusions which not less reliable or useful than those obtained in any other exact science. It is only necessary to apply a clear and precise concept of probability to such observations. “ (Richard von Mises, “Probability, Statistics, and Truth”, 1939)
“Probabilities must be regarded as analogous to the measurement of physical magnitudes; that is to say, they can never be known exactly, but only within certain approximation.” (Emile Borel, “Probabilities and Life”, 1943)
“The conception of chance enters in the very first steps of scientific activity in virtue of the fact that no observation is absolutely correct. I think chance is a more fundamental conception that causality; for whether in a concrete case, a cause-effect relation holds or not can only be judged by applying the laws of chance to the observation.” (Max Born, 1949)
"Historically, Statistics is no more than State Arithmetic, a system of computation by which differences between individuals are eliminated by the taking of an average. It has been used - indeed, still is used - to enable rulers to know just how far they may safely go in picking the pockets of their subjects." (Michael J Moroney, "In Facts from Figures", 1951)
"It is never possible to predict a physical occurrence with unlimited precision.” (Max Planck, “The Meaning of Causality in Physics”, 1953)
“The epistemological value of probability theory is based on the fact that chance phenomena, considered collectively and on a grand scale, create non-random regularity.” Andrey Kolmogorov, “Limit Distributions for Sums of Independent Random Variables”, 1954)
“Starting from statistical observations and applying to them a clear and precise concept of probability it is possible to arrive at conclusions which are just as reliable and ‘truth-full’ and quite as practically useful as those obtained in any other exact science.” (Richard von Mises, “Probability, Statistics, and Truth”2nd Ed., 1957)
“Probability is a mathematical discipline with aims akin to those, for example, of geometry or analytical mechanics. In each field we must carefully distinguish three aspects of the theory: (a) the formal logical content, (b) the intuitive background, (c) the applications. The character, and the charm, of the whole structure cannot be appreciated without considering all three aspects in their proper relation.” (William Feller, “An Introduction to Probability Theory and Its Applications”, 1957)
“The mathematician, the statistician, and the philosopher do different things with a theory of probability. The mathematician develops its formal consequences, the statistician applies the work of the mathematician and the philosopher describes in general terms what this application consists in. The mathematician develops symbolic tools without worrying overmuch what the tools are for; the statistician uses them; the philosopher talks about them. Each does his job better if he knows something about the work of the other two.“ (I.J. Good, “Kinds of Probability”, Science Vol. 129, 1959)
“In its efforts to learn as much as possible about nature, modem physics has found that certain things can never be ‘known’ with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities.” (Richard P Feynman, “The Feynman Lectures on Physics”, 1964)
“The probability concept used in probability theory has exactly the same structure as have the fundamental concepts in any field in which mathematical analysis is applied to describe and represent reality.” (Richard von Mises, “Mathematical Theory of Probability and Statistics”, 1964)
“After all, without the experiment - either a real one or a mathematical model - there would be no reason for a theory of probability.” (Thornton C Fry, “Probability and Its Engineering Uses”, 1965)
“[I]n probability theory we are faced with situations in which our intuition or some physical experiments we have carried out suggest certain results. Intuition and experience lead us to an assignment of probabilities to events. As far as the mathematics is concerned, any assignment of probabilities will do, subject to the rules of mathematical consistency.” (Robert Ash, “Basic probability theory”, 1970)
“Of course, we know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?” (Albert Claude, “The Coming of Age of the Cell”, Science, 1975)
“The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.” (Benoit Mandelbrot, “The Fractal Geometry of Nature”, 1977)
“Events may appear to us to be random, but this could be attributed to human ignorance about the details of the processes involved.” (Brain S Everitt, “Chance Rules”, 1999)
“One can hardly give a satisfactory definition of probability.” (Henri Poincaré, “Calcul des Probabilités”, 1912)
“Nature prefers the more probable states to the less probable because in nature processes take place in the direction of greater probability. Heat goes from a body at higher temperature to a body at lower temperature because the state of equal temperature distribution is more probable than a state of unequal temperature distribution.” (Max Planck, “The Atomic Theory of Matter”, 1909)
"Part of our knowledge we obtain direct; and part by argument. The Theory of Probability is concerned with that part which we obtain by argument, and it treats of the different degrees in which the results so obtained are conclusive or inconclusive." (John M Keynes, "A Treatise on Probability", 1921)
“We know that the probability of well-established induction is great, but, when we are asked to name its degree we cannot. Common sense tells us that some inductive arguments are stronger than others, and that some are very strong. But how much stronger or how strong we cannot express.” (John M Keynes, “A Treatise on Probability”, 1921)
“There can be no unique probability attached to any event or behaviour: we can only speak of ‘probability in the light of certain given information’, and the probability alters according to the extent of the information.” (Sir Arthur S Eddington, “The Nature of the Physical World”, 1928)
“Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.” (Bertrand Russell, 1929)
“When an observation is made on any atomic system that has been prepared in a given way and is thus in a given state, the result will not in general be determinate, i.e. if the experiment is repeated several times under identical conditions several different results may be obtained. If the experiment is repeated a large number of times it will be found that each particular result will be obtained a definite fraction of the total number of times, so that one can say there is a definite probability of its being obtained any time that the experiment is performed. This probability the theory enables one to calculate.” (Paul A M Dirac, “The Principles of Quantum Mechanics”, 1930)
“The theory of probability as a mathematical discipline can and should be developed from axioms in exactly the same way as geometry and algebra.” (Andrey Kolmogorov, “Foundations of the Theory of Probability”, 1933)
“Starting from statistical observations, it is possible to arrive at conclusions which not less reliable or useful than those obtained in any other exact science. It is only necessary to apply a clear and precise concept of probability to such observations. “ (Richard von Mises, “Probability, Statistics, and Truth”, 1939)
“Probabilities must be regarded as analogous to the measurement of physical magnitudes; that is to say, they can never be known exactly, but only within certain approximation.” (Emile Borel, “Probabilities and Life”, 1943)
“The conception of chance enters in the very first steps of scientific activity in virtue of the fact that no observation is absolutely correct. I think chance is a more fundamental conception that causality; for whether in a concrete case, a cause-effect relation holds or not can only be judged by applying the laws of chance to the observation.” (Max Born, 1949)
"Historically, Statistics is no more than State Arithmetic, a system of computation by which differences between individuals are eliminated by the taking of an average. It has been used - indeed, still is used - to enable rulers to know just how far they may safely go in picking the pockets of their subjects." (Michael J Moroney, "In Facts from Figures", 1951)
"It is never possible to predict a physical occurrence with unlimited precision.” (Max Planck, “The Meaning of Causality in Physics”, 1953)
“The epistemological value of probability theory is based on the fact that chance phenomena, considered collectively and on a grand scale, create non-random regularity.” Andrey Kolmogorov, “Limit Distributions for Sums of Independent Random Variables”, 1954)
“Starting from statistical observations and applying to them a clear and precise concept of probability it is possible to arrive at conclusions which are just as reliable and ‘truth-full’ and quite as practically useful as those obtained in any other exact science.” (Richard von Mises, “Probability, Statistics, and Truth”2nd Ed., 1957)
“Probability is a mathematical discipline with aims akin to those, for example, of geometry or analytical mechanics. In each field we must carefully distinguish three aspects of the theory: (a) the formal logical content, (b) the intuitive background, (c) the applications. The character, and the charm, of the whole structure cannot be appreciated without considering all three aspects in their proper relation.” (William Feller, “An Introduction to Probability Theory and Its Applications”, 1957)
“The mathematician, the statistician, and the philosopher do different things with a theory of probability. The mathematician develops its formal consequences, the statistician applies the work of the mathematician and the philosopher describes in general terms what this application consists in. The mathematician develops symbolic tools without worrying overmuch what the tools are for; the statistician uses them; the philosopher talks about them. Each does his job better if he knows something about the work of the other two.“ (I.J. Good, “Kinds of Probability”, Science Vol. 129, 1959)
“In its efforts to learn as much as possible about nature, modem physics has found that certain things can never be ‘known’ with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities.” (Richard P Feynman, “The Feynman Lectures on Physics”, 1964)
“The probability concept used in probability theory has exactly the same structure as have the fundamental concepts in any field in which mathematical analysis is applied to describe and represent reality.” (Richard von Mises, “Mathematical Theory of Probability and Statistics”, 1964)
“After all, without the experiment - either a real one or a mathematical model - there would be no reason for a theory of probability.” (Thornton C Fry, “Probability and Its Engineering Uses”, 1965)
“[I]n probability theory we are faced with situations in which our intuition or some physical experiments we have carried out suggest certain results. Intuition and experience lead us to an assignment of probabilities to events. As far as the mathematics is concerned, any assignment of probabilities will do, subject to the rules of mathematical consistency.” (Robert Ash, “Basic probability theory”, 1970)
“Of course, we know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?” (Albert Claude, “The Coming of Age of the Cell”, Science, 1975)
“The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.” (Benoit Mandelbrot, “The Fractal Geometry of Nature”, 1977)
“Events may appear to us to be random, but this could be attributed to human ignorance about the details of the processes involved.” (Brain S Everitt, “Chance Rules”, 1999)
"The objectivist view is that probabilities are real aspects of the universe - propensities of objects to behave in certain ways - rather than being just descriptions of an observer’s degree of belief. For example, the fact that a fair coin comes up heads with probability 0.5 is a propensity of the coin itself. In this view, frequentist measurements are attempts to observe these propensities. Most physicists agree that quantum phenomena are objectively probabilistic, but uncertainty at the macroscopic scale - e.g., in coin tossing - usually arises from ignorance of initial conditions and does not seem consistent with the propensity view." (Stuart J Russell & Peter Norvig, "Artificial Intelligence: A Modern Approach", 2010)
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