“Heisenberg now approached the problem from a new philosophical angle. He discarded all models, pictures and parables, and made a clear distinction between sure knowledge we gain from observation of nature and the conjectural knowledge we introduce when we use models, pictures and parables. Sure knowledge… can only be numerical, so that Heisenberg's results were inevitably mathematical in form, and could not disclose anything about the true nature of physical properties or entities.”

Physics and Philosophy (1942)

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James Jeans54

British mathematician and astronomer 1877–1946

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“The final truth about a phenomenon resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge of the phenomenon is complete. We go beyond the mathematical formula at our own risk; we may find a model or a picture which helps us understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault. The making of models or pictures to explain mathematical formulas and the phenomena they describe is not a step towards, but a step away from reality; it is like making a graven image of a spirit.”

James Jeans book The Mysterious Universe

The Mysterious Universe (1930)

“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.”

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

Source: The Principles of Science: A Treatise on Logic and Scientific Method (1874) Vol. 1, p. 14

“Philosophical knowledge is the knowledge gained by reason from concepts; mathematical knowledge is the knowledge gained by reason from the construction of concepts.”

Immanuel Kant book Critique of Pure Reason

A 713, B 741
Critique of Pure Reason (1781; 1787)

“Intelligence has two parts, which we shall call the epistemological and the heuristic. The epistemological part is the representation of the world in such a form that the solution of problems follows from the facts expressed in the representation. The heuristic part is the mechanism that on the basis of the information solves the problem and decides what to do.
[…]
The right way to think about the general problems of metaphysics and epistemology is not to attempt to clear one's own mind of all knowledge and start with 'Cogito ergo sum' and build up from there. Instead, we propose to use all of our knowledge to construct a computer program that knows. The correctness of our philosophical system will be tested by numerous comparisons between the beliefs of the program and our own observations and knowledge.”

John McCarthy (1927–2011) American computer scientist and cognitive scientist

John McCarthy and Patrick J. Hayes. " Some Philosophical Problems from the Standpoint of Artificial Intelligence http://www-formal.stanford.edu/jmc/mcchay69.html", Sect. 2.1, Machine Intelligence 4, ed. Donald Michie (Elsevier, 1969), p. 463 ff., ISBN 0444197443 <br class="br">1960s

“Knowledge is encoded in models. Models are synthetic sets of rules, and pictures, and algorithms providing us with useful representations of the world of our perceptions and of their patterns.”

Didier Sornette (1957) French scientist

Source: Why Stock Markets Crash - Critical Events in Complex Systems (2003), Chapter 5, Modeling Financial Bubbles And Market Crashes, p. 134.

“Once we recognize that all historical knowledge is relational knowledge, and can only be formulated with reference to the position of the observer, we are faced, once more, with the task of discriminating between what is true and what is false in such knowledge.”

Karl Mannheim (1893–1947) Hungarian sociologist

Ideology and Utopia (1929)

“It is absurd to suppose we can think of nature as a system apart from knowledge, for it is knowledge that is increasingly determining the course of nature”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1960s, Beyond Economics: Essays on Society, 1968, p. 141 as cited in John Laurent (2003) Evolutionary Economics and Human Nature. p. 175

“An artist needs knowledge and the power of observation only so that he can tell from what he is abstaining, and to be sure that his abstention will not appear artificial or false.”

Andrei Tarkovsky (1932–1986) Soviet and Russian film-maker, writer, film editor, film theorist, theatre and opera director

Journal entry (7 July 1980); published in Time Within Time: The Diaries 1970-1986 (1989)

“Heisenberg’s starting point was the philosophical judgment, that a physical theory should not concern itself with things like electron orbits in atoms that can never be observed. This is a risky assumption, but in this case it served Heisenberg well.”

Steven Weinberg (1933) American theoretical physicist

Source: Lectures on Quantum Mechanics (2012, 2nd ed. 2015), Ch. 1: Historical Introduction

“Understanding human nature is the highest knowledge, and only by knowing it can we know God. It is also a fact that the knowledge of God is the highest knowledge, and only by knowing God can we understand human nature.”

Swami Vivekananda (1863–1902) Indian Hindu monk and phylosopher

Pearls of Wisdom

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