"We have three principal means: observation of nature, reflection, and experiment. Observation gathers the facts reflection combines them, experiment verifies the result of the combination. It is essential that the observation of nature be assiduous, that reflection be profound, and that experimentation be exact. Rarely does one see these abilities in combination. And so, creative geniuses are not common." (Denis Diderot, "On the Interpretation of Nature", 1753)
"It will seem not a little paradoxical to ascribe a great importance to observations even in that part of the mathematical sciences which is usually called Pure Mathematics, since the current opinion is that observations are restricted to physical objects that make impression on the senses. As we must refer the numbers to the pure intellect alone, we can hardly understand how observations and quasi-experiments can be of use in investigating the nature of the numbers. Yet, in fact, as I shall show here with very good reasons, the properties of the numbers known today have been mostly discovered by observation, and discovered long before their truth has been confirmed by rigid demonstrations. There are even many properties of the numbers with which we are well acquainted, but which we are not yet able to prove; only observations have led us to their knowledge. Hence we see that in the theory of numbers, which is still very imperfect, we can place our highest hopes in observations; they will lead us continually to new properties which we shall endeavor to prove afterwards. The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such a discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful. (Leonhard Euler, "Specimen de usu observationum in mathesi pura" , Novi Commentarii academiae scientiarum Petropolitanae 6, 1756/57)
"He who has not made the experiment, or who is not accustomed to require rigorous accuracy from himself, will scarcely believe how much a few hours take from certainty of knowledge, and distinctness of imagery; how the succession of objects will be broken, how separate parts will be confused, and how many particular features and discriminations will be compressed and conglobated into one gross and general idea." (Samuel Johnson, "A Journey to the Western Islands of Scotland", 1775)
"As dangerous as is the desire to systematize in the physical sciences, it is, nevertheless, to be feared that in storing without order a great multiplicity of experiments we obscure the science rather than clarify it, render it difficult of access to those desirous of entering upon it, and finally, obtain at the price of long and tiresome work only disorder and confusion." (Antoine L Lavoisier, "Mémoires de l’Académie Royale des Sciences", 1777)
"Facts, observations, experiments - these are the materials of a great edifice, but in assembling them we must combine them into classes, distinguish which belongs to which order and to which part of the whole each pertains." (Antoine L Lavoisier, "Mémoires de l’Académie Royale des Sciences", 1777)
"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 de Lavoisier, cca. 1790)
"We must trust to nothing but facts: These are presented to us by Nature, and cannot deceive. We ought, in every instance, to submit our reasoning to the test of experiment, and never to search for truth but by the natural road of experiment and observation." (Antoin-Laurent de Lavoisiere, "Elements of Chemistry", 1790)
"We ought, in every instance, to submit our reasoning to the test of experiment, and never to search for truth but by the natural road of experiment and observation." (Antoine-Laurent Lavoisier, "Elements of Chemistry in a New Systematic Order", 1790)
"Extravagant theories, however, in those parts of philosophy, where our knowledge is yet imperfect, are not without their use; as they encourage the execution of laborious experiments, or the investigation of ingenious deductions, to conform or refute them." (Erasmus Darwin, "The botanic garden: A poem, in two parts", 1793)
"Conjecture may lead you to form opinions, but it cannot produce knowledge. Natural philosophy must be built upon the phenomena of nature discovered by observation and experiment." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)
"Conjectures in philosophy are termed hypotheses or theories; and the investigation of an hypothesis founded on some slight probability, which accounts for many appearances in nature, has too often been considered as the highest attainment of a philosopher. If the hypothesis (sic) hangs well together, is embellished with a lively imagination, and serves to account for common appearances - it is considered by many, as having all the qualities that should recommend it to our belief, and all that ought to be required in a philosophical system." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)
"Mankind are always ready to adopt or reject what accords with pre-conceived opinions, to make reason subservient to prejudice, and to reject without examination, whatever is discordant with a received system; thus closing the door of science, and excluding themselves from the benefit of light." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)
"Most of our philosophical instruments are measures of effects. The progress made in natural philosophy increases every day by the number of these measures; by these it still continues to be improved." (George Adams, Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)
"It is an acknowledged truth in philosophy that a just theory will always be confirmed by experiment." (Thomas R Malthus, "An Essay on The Principle of Population", 1798)
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