“In a certain sense all knowledge is inductive. We can only learn the laws and relations of things in nature by observing those things. But the knowledge gained from the senses is knowledge only of particular facts, and we require some process of reasoning by which we may collect out of the facts the laws obeyed by them. Experience gives us the materials of knowledge: induction digests those materials, and yields us general knowledge. When we possess such knowledge, in the form of general propositions and natural laws, we can usefully apply the reverse process of deduction to ascertain the exact information required at any moment. In its ultimate foundation, then, all knowledge is inductive—in the sense that it is derived by a certain inductive reasoning from the facts of experience.”

Opera Omnia, ser. 1, vol. 2, p. 459 Spcimen de usu observationum in mathesi pura, as quoted by George Pólya, Induction and Analogy in Mathematics Vol. 1, Mathematics and Plausible Reasoning (1954)
Context: It will seem 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 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 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 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.

Annotations to Sir Joshua Reynolds's Discourses, pp. xvii–xcviii (c. 1798–1809)
1790s

Paul Cilliers (2005: 263) as quoted in: Vikki Bell (2007) Culture and Performance: The Challenge of Ethics, Politics and Feminist Theory. p. 8

Pearls of Wisdom

On Contradiction (1937)
Original: (zh-CN) 就人类认识运动的秩序说来，总是由认识个别的和特殊的事物，逐步地扩大到认识一般的事物。人们总是首先认识了许多不同事物的特殊的本质，然后才有可能更进一步地进行概括工作，认识诸种事物的共同的本质。

Ideology and Utopia (1929)

Introduction
Popular Astronomy: A Series of Lectures Delivered at Ipswich (1868)

Physics and Philosophy (1942)

Source: Course of Experimental Philosophy, 1745, p. v: Preface
Context: All the knowledge we have of nature depends upon facts; for without observations and experiments our natural philosophy would only be a science of terms and an unintelligible jargon. But then we must call in Geometry and Arithmetics, to our Assistance, unless we are willing to content ourselves with natural History and conjectural Philosophy. For, as many causes concur in the production of compound effects, we are liable to mistake the predominant cause, unless we can measure the quantity and the effect produced, compare them with, and distinguish them from, each other, to find out the adequate cause of each single effect, and what must be the result of their joint action.