A Quote by Leonhard Euler

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

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Leonhard Euler
Swiss - Mathematician
April 15, 1707 - September 18, 1783

It is time, therefore, to abandon the superstition that natural science cannot be regarded as logically respectable until philosophers have solved the problem of induction. The problem of induction is, roughly speaking, the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future.

A.J. Ayer

I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them upon the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge - knowledge mingled with ignorance, producing doubt.

William Stanley Jevons

I think the most important work that is going on has to do with the search for very general and abstract features of what is sometimes called universal grammar: general properties of language that reflect a kind of biological necessity rather than logical necessity; that is, properties of language that are not logically necessary for such a system but which are essential invariant properties of human language and are known without learning. We know these properties but we don't learn them. We simply use our knowledge of these properties as the basis for learning.

Noam Chomsky

In philosophy, when we make use of false principles, we depart the farther from the knowledge of truth and wisdom exactly in proportion to the care with which we cultivate them, and apply ourselves to the deduction of diverse consequences from them, thinking that we are philosophizing well, while we are only departing the farther from the truth; from which it must be inferred that they who have learned the least of all that has been hitherto distinguished by the name of philosophy are the most fitted for the apprehension of truth.

Rene Descartes

The Syllogism consists of propositions, propositions consist of words, words are symbols of notions. Therefore if the notions themselves (which is the root of the matter) are confused and over-hastily abstracted from the facts, there can be no firmness in the superstructure. Our only hope therefore lies in a true induction.

Francis Bacon

Sir, Your letter of the 15th is received, but Age has long since obliged me to withhold my mind from Speculations of the difficulty of those of your letter, that their are means of artificial buoyancy by which man may be supported in the Air, the Balloon has proved, and that means of directing it may be discovered is against no law of Nature and is therefore possible as in the case of Birds, but to do this by mechanical means alone in a medium so rare and unassisting as air must have the aid of some principal not yet generally known.

Thomas Jefferson

In experimental philosophy, we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur by which they may either be made more accurate or liable to exceptions.

Isaac Newton

And as this is the obvious appearance of things, it must be admitted, till some hypothesis be discovered, which by penetrating deeper into human nature, may prove the former affections to be nothing but modifications of the latter. All attempts of this kind have hitherto proved fruitless, and seem to have proceeded entirely from that love of simplicity which has been the source of much false reasoning in philosophy.

David Hume

At the heart of science lies discovery which involves a change in worldview. Discovery in science is possible only in societies which accord their citizens the freedom to pursue the truth where it may lead and which therefore have respect for different paths to that truth.

John Charles Polanyi

When philosophic reason is clear and certain by intuition or necessary induction, no subsequent revelation supported by prophecies or miracles can supersede it.

John Adams

It is, however, not necessary, that a man should forbear to write, till he has discovered some truth unknown before; he may be sufficiently useful, by only diversifying the surface of knowledge, and luring the mind by a new appearance to a second view of those beauties which it had passed over inattentively before.

Samuel Johnson

The error of Socrates must be attributed to the false notion of unity from which he starts. Unity there should be, both of the family and of the state, but in some respects only. For there is a point at which a state may attain such a degree of unity as to be no longer a state, or at which, without actually ceasing to exist, it will become an inferior state, like harmony passing into unison, or rhythm which has been reduced to a single foot. The state, as I was saying, is a plurality which should be united and made into a community by education

Aristotle

Ideals are very often formed in the effort to escape from the hard task of dealing with facts, which is the function of science and art. There is no process by which to reach an ideal. There are no tests by which to verify it. It is therefore impossible to frame a proposition about an ideal which can be proved or disproved. It follows that the use of ideals is to be strictly limited to proper cases, and that the attempt to use ideals in social discussion does not deserve serious consideration.

William Graham Sumner

Alchemy is about the generation of a psychic construct, a wholeness, a thing which has many properties, which is paradoxical, which is both mind and matter, which can do anything.

Terence McKenna

Until the seventeenth century there was no concept of evidence with which to pose the problem of induction!

Ian Hacking

The hypotheses which we accept ought to explain phenomena which we have observed. But they ought to do more than this; our hypotheses ought to foretell phenomena which have not yet been observed; ... because if the rule prevails, it includes all cases; and will determine them all, if we can only calculate its real consequences. Hence it will predict the results of new combinations, as well as explain the appearances which have occurred in old ones. And that it does this with certainty and correctness, is one mode in which the hypothesis is to be verified as right and useful.

William Whewell

A Quote by Leonhard Euler

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