The art of concluding from experience and observation consists in evaluating probabilities, in estimating if they are high or numerous enough to constitute proof. This type of calculation is more complicated and more difficult than one might think. It demands a great sagacity generally above the power of common people. The success of charlatans, sorcerors, and alchemists—and all those who abuse public credulity—is founded on errors in this type of calculation.
Antoine Lavoisier and Benjamin Franklin, Rapport des commissaires chargés par le roi de l'examen du magnétisme animal (Imprimerie royale, 1784), trans. Stephen Jay Gould, "The Chain of Reason versus the Chain of Thumbs", Bully for Brontosaurus (W.W. Norton, 1991), p. 195
Here, then: a revolution [in science and chemistry] has taken place in an important part of human knowledge since your departure from Europe... I will consider this revolution to be well advanced and even completely accomplished if you range yourself with us. ...After having brought you up to date on what is happening in chemistry, it would be well to speak to you about our political revolution. We regard it as done and without any possibility of return to the old order.
When I began the following Work, my only object was to extend and explain more fully the Memoir which I read at the public meeting of the Academy of Sciences in the month of April 1787, on the necessity of reforming and completing the Nomenclature of Chemistry. While engaged in this employment, I perceived, better than I had ever done before, the justice of the following maxims of the Abbé de Condillac, in his System of Logic, and some other of his works. "We think only through the medium of words.—Languages are true analytical methods.—Algebra, which is adapted to its purpose in every species of expression, in the most simple, most exact, and best manner possible, is at the same time a language and an analytical method.—The art of reasoning is nothing more than a language well arranged."
Thus, while I thought myself employed only in forming a Nomenclature, and while I proposed to myself nothing more than to improve the chemical language, my work transformed itself by degrees, without my being able to prevent it, into a treatise upon the Elements of Chemistry.
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.
We may lay it down as an incontestible axiom, that, in all the operations of art and nature, nothing is created; an equal quantity of matter exists both before and after the experiment; the quality and quantity of the elements remain precisely the same; and nothing takes place beyond changes and modifications in the combination of these elements. Upon this principle the whole art of performing chemical experiments depends: We must always suppose an exact equality between the elements of the body examined and those of the products of its analysis.
Now Mayow, like Boyle, conceived the air as made up of minute particles, while he restricted himself to two varieties, those, namely, which are necessary to life, called by him "spiritus igno-aereus," and those incapable of supporting respiration or combustion, which are left after the removal of this "spiritus." Since a mixture of saltpetre and sulphur continued burning even under water, he assumed that his igno-aereal particles must also be contained in the salt. Acids too contained the new principle. ...Mayow died in 1679 at the age of thirty-four years; had he lived but a little longer, it can scarcely be doubted that he would have forestalled the revolutionary work of Lavoisier, and stifled the theory of phlogiston at its birth. As it was, his work, though rendered in one of the most luminous and convincing scientific publications of the period, was immediately forgotten, and so proved of little effect on the evolution of our modern chemical system.
Francis Paul Armitage, A History of Chemistry (1906) p.23
Though Lavoisier generally gets credit for the authorship of this principle [ conservation of mass ], others had conceived it before him, The seventeenth century chemysts, notably Helmont, Starkey, and Boyle, had a dawning awareness of the importance of weighing and measuring materials before and after an experimental process, though their methods and measurement devices were not so precise. In 1623, Francis Bacon declared, "..when they percieve that a body which was before manifest to the senses has escaped and disappeared, they should not admit or liquidate the account before it has been shown to them where the body has gone to and into what it has been received." And as early as 450 B.C., Anaxagoras argued, "Wrongly do the Greeks suppose that aught begins or ceases to be; for nothing comes into being or is destroyed; but all is an aggregation or secretion of preexisting things; so that all becoming might more correctly be called becoming mixed, and all corruption, becoming separate."
One of the most fundamental principles of Lavoisier's chemistry was the use of numbers, notably in relation to what we often call today the principle of conservation of mass... The principle implies that the experimenter must not only keep account of all the reacting solids and liquids, but also the gases—that is, all of the products. ...This rule led to quantitative experiments. Lavoisier was not the first person to use numbers in chemistry but he was a pioneer in using such numerical measurements as the basis of his system of chemistry. ...When Lavoisier first announced this law, chemists generally believed in... "phlogiston" which supposedly entered into chemical reactions (such as combustion) but had no weight. It was a radical step, therefore, for Lavoisier to base a system of chemistry on a balance of weights and to maintain that chemistry is not concerned with weightless "substances." ...this was indeed a chemical revolution.
I. Bernard Cohen, The Triumph of Numbers: How Counting Shaped Modern Life (2005)
In 1774 he [ Joseph Priestley ] thought he had obtained nitrous oxide... in 1775 he saw the gas as dephlogisticated air... If we refuse the palm to Priestley, we cannot award it to Lavoisier for the work of 1775... Lavoisier insisted that oxygen was an atomic "principle of acidity"… formed only when that "principle" united with "caloric"... Ignoring Scheele, we can safely say that oxygen had not been discovered before 1774, and we would probably say that it had been discovered by 1777 or shortly thereafter. But... any attempt to date the discovery must inevitably be arbitrary because discovering a new sort of phenomenon is necessarily a complex event, one which involves recognizing both that something is and what it is.
We are... bound to attach the greatest importance to the preliminary step taken by Lavoisier, who is even more justly called the father of modern chemistry than Kepler is called the father of modern astronomy. The exact claims of Lavoisier to this important place in the history of chemistry have been variously stated: ...since his time, and greatly through his labours, the quantitative method has been established as the ultimate test of chemical facts; the principle of this method being the rule that in all changes of combination and reaction, the total weight of the various ingredients—be they elementary bodies or compounds—remains unchanged. The science of chemistry was thus established upon an exact, a mathematical basis. By means of this method Lavoisier, utilising and analysing the results gained by himself and others before him, notably those of Priestley, Cavendish, and Black, succeeded in destroying the older theory of combustion, the so-called phlogistic theory.
The extension of Black's method by the physicist Lavoisier led to the downfall of the purely qualitative theory of phlogiston, and gave to chemistry the true methods of investigation, and its first great quantitative law—the law of conservation of matter.
The law of conservation of mass was first put into definite form by Lavoisier, in the eighties of the eighteenth century. In considering the fermentation of fruit-juices, wherein carbonic acid gas and alcohol are produced, Lavoisier said:—"We must evidently have a complete knowledge of the analyses and the nature of the substances which can be fermented; for nothing is created, either in the operations of art, or in those of nature, and it may be laid down as a principle that, in every operation there is an equal quantity of matter before and after the operation; ...there is nothing but certain changes, certain modifications. The whole art of experimenting in chemistry rests on this principle; in all experiments one is obliged to assume an actual equality between the principles [that is, elements] of the substances examined and those obtained by the analysis of these substances. Thus, inasmuch as grape-juice yields carbonic acid gas and alcohol, I can affirm that grape juice=carbonic acid gas+alcohol."