“In order to supply the defects of experience, we will have recourse to the probable conjectures of analogy, conclusions which we will bequeath to our posterity to be ascertained by new observations, which, if we augur rightly, will serve to establish our theory and to carry it gradually nearer to absolute certainty.”

— Johann Heinrich Lambert

The System of the World (1800)

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Johann Heinrich Lambert 8

German mathematician, physicist and astronomer 1728–1777

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“In science, conjecture drives both experiment and theory for it is only by forming conjectures (hypotheses) that we can make the direction of our experiments and theories informed. If such and such is true, then I should be able to do this experiment and look for this particular result or I should be able to find this theoretical formulation. Conversely, experiment and theory drive conjecture. One makes a startling observation or has a sudden insight and begins to speculate on its significance and implications and to draw possible conclusions”

Robert Curl (1933) American chemist

conjecture
in his Nobel Lecture http://nobelprize.org/nobel_prizes/chemistry/laureates/1996/curl-lecture.html, December 7, 1996, Dawn of the Fullerenes: Experiment and Conjecture

“Each time new experiments are observed to agree with the predictions the theory survives, and our confidence in it is increased; but if ever a new observation is found to disagree, we have to abandon or modify the theory.”

Stephen Hawking book A Brief History of Time

Source: A Brief History of Time (1988), Ch. 1
Context: Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory. As philosopher of science Karl Popper has emphasized, a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation. Each time new experiments are observed to agree with the predictions the theory survives, and our confidence in it is increased; but if ever a new observation is found to disagree, we have to abandon or modify the theory.

“If, in pursuing this object, we employ our skill in research, not in forming vain conjectures; and if data are to be found, on which Science may form just conclusions, we should not long remain in ignorance with respect to the natural history of this Earth, a subject on which hitherto opinion only, and not evidence, has decided. For in no subject is there naturally less defect of evidence, although philosophers, led by prejudice, or misguided by false theory, have neglected to employ that light by which they should have seen the system of the world.”

Stephen Baxter (1957) author

Source: Ages in Chaos (2003), Chapter 14, “We have now got to the end of our reasoning” (p. 130)

“We experience moments in which we accept ourselves, because we feel that we have been accepted by that which is greater than we. If only more such moments were given us! For it is such moments that make us love our life, that make us accept ourselves, not in our goodness and self-complacency, but in our certainty of the eternal meaning of our life.”

Leslie Weatherhead (1893–1976) English theologian

Source: The Christian Agnostic (1965), p.77-78, (Paul Tillich: The Shaking of the Foundations. 1963. Pelican Books. p. 164

“We must therefore glean up our experiments in this science from a cautious observation of human life, and take them as they appear in the common course of the world, by men’s behaviour in company, in affairs, and in their pleasures. Where experiments of this kind are judiciously collected and compared, we may hope to establish on them a science, which will not be inferior in certainty, and will be much superior in utility to any other of human comprehension.”

David Hume book A Treatise of Human Nature

Introduction
A Treatise of Human Nature (1739-40)

“It makes no sense to expect or claim to 'make the invisible visible', or the unknown known, or the unthinkable thinkable. We can draw conclusions about the invisible; we can postulate its existence with relative certainty. But all we can represent is an analogy, which stands for the invisible but is not it.”

Gerhard Richter (1932) German visual artist, born 1932

undated quotes, The Daily Practice of Painting, Writings (1962-1993)

“Undoubtedly it is our duty, and for our best good, that we occupy and improve the faculties, with which our creator has endowed us, but so far as prejudice, or prepossession of opinion prevails over our minds, in the same proportion, reason is excluded from our theory or practice. Therefore if we would acquire useful knowledge, we must first divest ourselves of those impediments and sincerely endeavor to search out the truth: and draw our conclusions from reason and just argument, which will never conform to our inclination, interest or fancy but we must conform to that if we would judge rightly.”

Ethan Allen (1738–1789) American general

Source: Reason: The Only Oracle Of Man (1784), Ch. XIII Section II - Of The Importance of the Exercise of Reason, and Practice of Morality, in order to the Happiness of Mankind

“We both call in experience to the support of our opinions; but, in your case, the experience is based on vague uncertainties, whilst I, more circumspect, strive never to lose sight of those scientific principles which ought to guide the observer in all his investigations. My aim is not to defend systems, or bolster up theories; I confine myself to the citation of facts, such as society presents to our view. If these facts be legitimately established, it follows that we must accept of and accommodate our reason to them.”

Adolphe Quetelet (1796–1874) Belgian astronomer, mathematician, statistician and sociologist

Preface of M. Quetelet
A Treatise on Man and the Development of His Faculties (1842)

“There is another side to the theory of relativity. We have pointed out in the beginning how the development of science is in the direction to make it less subjective, to separate more and more in the observed facts that which belongs to the reality behind the phenomena, the absolute, from the subjective element, which is introduced by the observer, the relative. Einstein's theory is a great step in that direction. We can say that the theory of relativity is intended to remove entirely the relative and exhibit the pure absolute.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“By induction we gain no certain knowledge; but by observation, and the inverse use of deductive reasoning, we estimate the probability that an event which has occurred was preceded by conditions of specified character, or that such conditions will be followed by the event. …I have no objection to use the words cause and causation, provided they are never allowed to lead us to imagine that our knowledge of nature can attain to certainty. …We can never recur too often to the truth that our knowledge of the laws and future events of the external world are only probable.”

William Stanley Jevons (1835–1882) English economist and logician

Source: The Principles of Science: A Treatise on Logic and Scientific Method (1874) Vol. 1, pp. 257, 260 & 271

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