Extracts about Galileo from Scientific Method: An historical and philosophical introduction by Barry Gower (Routledge, 1997):
Galileo took great pains to ensure that his readers would be persuaded that his conclusions were correct. p. 23
The science of motion was then understood to be a study of the causes of motion, and to be, like any genuine science, a ‘demonstrative’ kind of enquiry. That is to say, experiential knowledge of the facts of motion was superseded by rational knowledge of the causes of those facts, this being accomplished by deductions from fundamental principles, or ‘common notions’, and definitions which were accepted as true. These facts of motion were understood as expressions of common experience rather than as generalisations based upon experiments. This was because the results of the experiments that could be performed were sufficiently uncertain and ambiguous to prevent reliable generalisation; discrepancies between conclusions derived from principles, and experimental results, could be tolerated. The appropriate model of a demonstrative science was Euclidean geometry, where the credibility of a theorem about, say, triangles depends not on how well it fits what we can measure but on its derivability from the basic axioms and definitions of the geometry. p. 23
For Galileo and his contemporaries there was a good reason why demonstration, or proof from first principles, rather than experiment, was required to establish general truths about motion. Any science—scientia—must yield knowledge of what Aristotle had called ‘reasoned facts’, i.e. truths which are both universal and necessary, and such knowledge—philosophical knowledge—can only be arrived at by demonstration. p. 24
there was a long-standing disagreement about the role that mathematics could play in natural philosophy, even though mathematics was able to give certain knowledge. p. 24
In some contexts, notably astronomy and geometry, the more elaborate and intellectually demanding methods of mathematics were often useful and appropriate, but in such contexts it seemed clear that those methods were applicable in so far as what was needed were re-descriptions which could help people formulate accurate predictions. ‘Hypotheses’ which successfully ‘saved the phenomena’, in the sense that they could be used as starting points for derivations of accurate predictions, could meet this need. p. 25
But the status of mathematical astronomy as a demonstrative science was questionable simply because its use of mathematical techniques prevented it from revealing causes; its hypotheses could be no more than ‘likely stories’. Copernicus’s claim that the universe was heliocentric rather than geocentric, for example, was regarded by some as no more than a false hypothesis which happened to be remarkably useful for accurate prediction and calculation. p. 26
[Archimedes] laid the foundation of that part of mechanics we now call statics p. 27
For Galileo, who was familiar with some of Archimedes’ treatises, it was especially important that he had shown that the axiomatic method need not be confined to geometry or arithmetic but could also be used to reach new conclusions in mechanics. p. 27
In the case of the motion displayed by freely falling objects we need, Galileo said, ‘to seek out and clarify the definition that best agrees with that which nature employs’ (Galileo 1989:153). p. 28
Incautious generalisation could easily result in mistakes, and even when it did not there remained the problem of how the certainty of the conclusion could be established, as it must be if the conclusion was to serve as the basis for a science. p. 30
The best he could do was to claim that his definition led to consequences which did have experimental support. p. 30
Experimental discourse lacked the authority it has since acquired, and was commonly regarded as of little relevance to a sound ‘philosophical’ method. p. 30
Natural philosophy, and especially a science of natural motion, was understood to be concerned with universal truths concerning natural phenomena, and there was a danger that erroneous conclusions would be drawn if reliance was placed on a particular experiment concerning artificial phenomena, especially when—as was often the case—the result of such an experiment was ambiguous and the weight to be placed on the testimony of its witnesses was uncertain. p. 31
For with these thought experiments, or experiments performed in the laboratory of the mind, he could avoid some of the disadvantages of real experiments. With them he could provide assurance that observation, albeit observation by the mind’s eye, had some controlling influence in his study of motion, as indeed observation must have in any science. p. 31
For Galileo, then, thought experiments secured a link between the real experiments which had led him to his belief in the principles of a new science of motion, and the common experiences which he would need to appeal to in order to justify those principles to his readers. p. 33
Galileo was able to bring together mathematical and experimental reasoning; it was exactly this which was his chief contribution to the development of scientific method in the seventeenth century. p. 37
What conclusions can we draw about Galileo’s methodology? First, it is clear that Galileo is committed to deductive reasoning. In this respect his views were continuous with those not only of his immediate predecessors but also of classical Greek thinkers such as Aristotle, Euclid and Archimedes. Like them he firmly believed that any science, because it was a type or kind of philosophy, should yield knowledge, and that the only way to achieve this was by employing deductive reasoning from indubitable premisses. Second, the kind of deductive reasoning which Galileo thought most appropriate and useful in natural philosophy was that exemplified in Euclid’s geometry and, more particularly, in Archimedes’ statics. It was this conviction which underlay his famous remark that the book of nature is written in the language of mathematics. p. 37
Third, because of the prominence given to mathematical methods, there is a natural tendency—which begins to be apparent in Galileo—towards a stress on quantitative mathematical discourse. The attempt to move natural philosophy in this direction was certainly contentious. p. 38
Fourth, an examination of the part played by experience in the use of demonstrative methods by Galileo shows that it developed a dual role. On the one hand, there is the concept of universal generalised experience which is expressed and idealised in the principles of a demonstrative science of motion, rather in the same way that such experience is expressed and idealised in Archimedes’ demonstrative science of statics. On the other hand, universal experience—and also particular experiments—can be used to show that the conclusions reached by a demonstrative science are applicable to the real world. p. 38
For, despite the powerful ties with his predecessors, and despite his inability to see where he was going, he succeeded in holding together a way of using reason in science with a reconstituted concept of experience. It would not be right to claim that he canvassed an experimental programme for natural philosophy, but his brilliant use of thought experiments showed that there were ways of broadening the scope of common observation and experience so as to strengthen the foundations of a demonstrative science. p. 38