“Should my notion be true, a vast mass of technicalities may be swept from our logical text-books, and yet the small remaining part of logical doctrine will prove far more useful than all the learning of the Schoolmen.”

— William Stanley Jevons

Preface
The Substitution of Similars, The True Principles of Reasoning (1869)
Context: The new and wonderful results of the late Dr. Boole's mathematical system of Logic appear to develop themselves as most plain and evident consequences of the self-same process of substitution, when applied to the Primary Laws of Thought. Should my notion be true, a vast mass of technicalities may be swept from our logical text-books, and yet the small remaining part of logical doctrine will prove far more useful than all the learning of the Schoolmen.

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William Stanley Jevons 69

English economist and logician 1835–1882

Edward Abbey (1927–1989) American author and essayist

Source: The Journey Home (1977), p. 121
Context: As for the "solitary confinement of the mind," my theory is that solipsism, like other absurdities of the professional philosopher, is a product of too much time wasted in library stacks between the covers of a book, in smoke-filled coffeehouses (bad for brains) and conversation-clogged seminars. To refute the solipsist or the metaphysical idealist all that you have to do is take him out and throw a rock at his head: if he ducks he's a liar. His logic may be airtight but his argument, far from revealing the delusions of living experience, only exposes the limitations of logic.

“Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 3
1900s

“Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics…. The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible…. I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s “Algebra” published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.”

James Whitbread Lee Glaisher (1848–1928) English mathematician and astronomer

Source: "Presidential Address British Association for the Advancement of Science," 1890, p. 466 : On the need of text-books on higher mathematics

“If someone doesn't value evidence, what evidence are you going to provide to prove that they should value it? If someone doesn’t value logic, what logical argument could you provide to show the importance of logic?”

Sam Harris (1967) American author, philosopher and neuroscientist

Sam Harris, "Is the Foundation of Morality Natural or Supernatural? – William Lane Craig vs. Sam Harris http://www.reasonablefaith.org/is-the-foundation-of-morality-natural-or-supernatural-the-craig-harris, University of Notre Dame, Notre Dame, Indiana, United States – April 2011 http://www.youtube.com/watch?v=pk7jHJRSzhM&t=1m10s
2010s

“The logic now in use serves rather to fix and give stability to the errors which have their foundation in commonly received notions than to help the search for truth. So it does more harm than good.”

Francis Bacon book Novum Organum

Aphorism 7
Novum Organum (1620), Book I

“Since my logic aims to teach and instruct the understanding, not that it may with the slender tendrils of the mind snatch at and lay hold of abstract notions (as the common logic does), but that it may in very truth dissect nature, and discover the virtues and actions of bodies, with their laws as determined in matter; so that this science flows not merely from the nature of the mind, but also from the nature of things.”

Francis Bacon book Novum Organum

Aphorism 52
Novum Organum (1620), Book II

“A frequent source of misunderstanding has to do with the interpretation of fuzzy logic. The problem is that the term fuzzy logic has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FLw is almost synonymous with the theory of fuzzy sets. In this context, what is important to recognize is that: (a) FLw is much broader than FLn and subsumes FLn as one of its branches; (b) the agenda of FLn is very different from the agendas of classical multivalued logics; and (c) at this juncture, the term fuzzy logic is usually used in its wide rather than narrow sense, effectively equating fuzzy logic with FLw</sub”

Lotfi A. Zadeh (1921–2017) Electrical engineer and computer scientist

Zadeh (1995) in Foreword of George J. Klir Fuzzy sets and fuzzy logic: theory and applications.
1990s

“In my field, Wikipedia is more reliable than the text-books.”

Harold Kroto (1939–2016) British chemist

Citation

“And there will be, and will ever remain, an impassable gulf between the religious consciousness and the logical, unless the logical consciousness reaches up to embrace the religious, and learns to state the absolute Is in terms of the absolute Ought.”

George Holmes Howison (1834–1916) American philosopher

Source: The City of God and the True God as its Head (In Royce’s “The Conception of God: a Philosophical Discussion Concerning the Nature of the Divine Idea as a Demonstrable Reality”), p.124

“Logic tends to reduce everything to identities and genera, to each representation having no more than one self-same content in whatever place, time or relation it may occur to us. And there is nothing that remains for two successive moments of its existence.”

Miguel de Unamuno (1864–1936) 19th-20th century Spanish writer and philosopher

The Tragic Sense of Life (1913), V : The Rationalist Dissolution
Context: A terrible thing is intelligence. It tends to death as memory tends to stability. The living, the absolutely unstable, the absolutely individual, is strictly unintelligible. Logic tends to reduce everything to identities and genera, to each representation having no more than one self-same content in whatever place, time or relation it may occur to us. And there is nothing that remains for two successive moments of its existence. My idea of God is different each time that I conceive it. Identity, which is death, is the goal of the intellect. The mind seeks what is dead, for what is living escapes it; it seeks to congeal the flowing stream in blocks of ice; it seeks to arrest it. In order to analyze a body it is necessary to extenuate or destroy it. In order to understand anything it is necessary to kill it, to lay it out rigid in the mind.

“Should my notion be true, a vast mass of technicalities may be swept from our logical text-books, and yet the small remaining part of logical doctrine will prove far more useful than all the learning of the Schoolmen.”

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William Stanley Jevons 69

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