Induction Quotes
In every science, after having analysed the ideas, expressing the more complicated by means of the more simple, one finds a certain number that cannot be reduced among them, and that one can define no further. These are the primitive ideas of the science; it is necessary to acquire them through experience, or through induction; it is impossible to explain them by deduction.
Giuseppe Peano
It is possible to express the laws of thermodynamics in the form of independent principles, deduced by induction from the facts of observation and experiment, without reference to any hypothesis as to the occult molecular operations with which the sensible phenomena may be conceived to be connected; and that course will be followed in the body of the present treatise. But, in giving a brief historical sketch of the progress of thermodynamics, the progress of the hypothesis of thermic molecular motions cannot be wholly separated from that of the purely inductive theory.
William John Macquorn Rankine
Science sometimes improves hypotheses and sometimes disproves them. But proof would be another matter and perhaps never occurs except in the realms of totally abstract tautology. We can sometimes say that if such and such abstract suppositions or postulates are given, then such and such abstract suppositions or postulates are given, then such and such must follow absolutely. But the truth about what can be perceived or arrived at by induction from perception is something else again.
Gregory Bateson
Twenty-eight years ago, I created my first game on an Apple II in my bedroom closet at a time when the interactive entertainment industry was taking its first baby steps. Today the games business has grown to a multi-billion dollar industry and we are just at the tip of the iceberg. I'm thrilled to have been a part of this successful journey and I'm extremely honored by the Academy's Hall of Fame induction.
Richard Garriott
Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.
David Hilbert
To find themselves utterly alone at night where company is desirable and expected makes some people fearful; but a case more trying by far to the nerves is to discover some mysterious companionship when intuition, sensation, memory, analogy, testimony, probability, induction - every kind of evidence in the logician's list - have united to persuade consciousness that it is quite in isolation.
Thomas Hardy
The idea of not having a Deity that he could not comprehend had long been one of Roswell Gardiner's favourite rules of faith. He did not understand by this pretending dogma, that he was, in any respect, of capacity equal to comprehend with that of the Divine Being, but simply that he was not to be expected or required to believe in any theory which manifestly conflicted with his knowledge and experience, as both were controlled by the powers of induction he had derived directly from his Creator. In a word, his exception was one of the most obvious of the suggestions of the pride of reason, and just so much in direct opposition to the great law of regeneration, which has its very gist in the converse of this feeling --Faith.
James Fenimore Cooper
Induction was shown to be untenable as a scientific method by Popper in The Logic of Scientific Discovery (1959). Instead, advances in scientific understanding come ideally from hypothetico-deductivism: firstly, development of a hypothesis in relation to a problem situation, and secondly, its testing in relation to all relevant knowledge and furthermore by its great explanatory power.
John Carew Eccles
By induction we gain no certain knowledge; but by observation, and the inverse use of deductive reasoning, we estimate the probability that an event which has occurred was preceded by conditions of specified character, or that such conditions will be followed by the event. ...I have no objection to use the words cause and causation, provided they are never allowed to lead us to imagine that our knowledge of nature can attain to certainty. ...We can never recur too often to the truth that our knowledge of the laws and future events of the external world are only probable.
William Stanley Jevons
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
We tend to believe the premises because we can see that their consequences are true, instead of believing the consequences because we know the premises to be true. But the inferring of premises from consequences is the essence of induction; thus the method in investigating the principles of mathematics is really an inductive method, and is substantially the same as the method of discovering general laws in any other science.
Bertrand Russell
There is no constitutional or legal requirement that the President shall take the oath of office in the presence of the People but there is so manifest an appropriateness in the public induction to office of the chief executive officer of the nation that from the beginning of the Government the people to whose service the official oath consecrates the officer, have been called to witness the solemn ceremonial.
Benjamin Harrison
![[T]he human reason discovers new relations between things not by deduction, but by that unpredictable blend of speculation and insight... induction, which-like other forms of imagination-cannot be formalized. (Jacob Bronowski)](https://cdn.quotesdtb.com/img/quotes_images_webp/71/jacob-bronowski-blend-deduction-422571.webp)
After the elections, Dr Singh did try to be more assertive, taking a view on who would be in his Cabinet and who would not, and resisting the induction of the DMK's A. Raja and T.R. Baalu, for their unsavoury reputations. Watching from the sidelines, I had hoped he would not buckle under pressure. Dr Singh stood his ground for a day, managed to keep Baalu out, but had to yield ground on Raja under pressure from his own party. To me, it was a reiteration of the message that the victory was not his but the Family's.
Manmohan Singh
Mill, in speaking of Hume's celebrated principle, "that nothing is credible which is contradictory to experience, or at variance with the laws of nature," calls it a very plain and harmless proposition, being, in effect, nothing more than that whatever is contradictory to a complete induction is incredible. Admit the existence of a Deity, and the possibility of a miracle is the natural consequence. No doubt our examination of the evidence which sustains an unusual phenomenon should be most carefully conducted; but we must not measure the credibility or incredibility of an event by the narrow sphere of our own experience, nor forget that there is a Divine energy which overrides what we familiarly call the laws of nature.
Charles Babbage
It is not unreasonable nor derogatory to the attributes of Omnipotence, to imagine that some general laws may be observed in the creation of new worlds; and if man could witness the birth of such worlds, he might reason by induction upon the origin of his own. But in the absence of such data, an attempt has been made to fancy some analogy between the agents now employed to destroy, renovate, and perpetually vary the earth's surface, and those whereby the first chaotic mass was formed, and brought by supposed nascent energy from the embryo to the habitable state.
Charles Lyell