A Quote by Jean Piaget
Logic and mathematics are nothing but specialised linguistic structures.
Quote Topics
Quote Author
Related Quotes
Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.
Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.
We live in a world populated by structures - a complex mixture of geological, biological, social, and linguistic constructions that are nothing but accumulations of materials shaped and hardened by history
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures.
The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.
One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.
Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.
Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative problems in a much broader sense than was suspected to be possible.
Well it was not exactly a dissertation in logic, at least not the kind of logic you would find in Whitehead and Russell's Principia Mathematica for instance. It looked more like mathematics; no formalized language was used.
There is a logic of language and a logic of mathematics.
Language is inherently not concerned with logic. As an expression of the psychological activities of humankind, it simply follows a linear process as it seeks actualisation. Moreover, it does not obey the objective concepts of time and space that belong to the physical world. When the discussion of time and space is imported into linguistic art from scientific aims and research methods, that linguistic art is entirely reduced to trifling pseudo-philosophical issues.
...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.
We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.
Art's supposed to build logic structures.
I started my professional life as a philosopher of language and for several years took the orthodox line that meaning is an essentially linguistic phenomenon. Whether as a result of simply listening to everyday talk about meaning, or reading books of anthropology, sociology and art history, it dawned on me that there is nothing at all privileged or central about linguistic meaning.
Related Authors
Abraham Maslow Quotes
American
Psychologist
Carl Jung Quotes
Swiss
Psychologist
Daniel Kahneman Quotes
Israeli
Psychologist
Edward de Bono Quotes
English
Psychologist
Erich Fromm Quotes
American
Psychologist
James Hillman Quotes
American
Psychologist
M. Scott Peck Quotes
American
Psychologist
Mihaly Csikszentmihalyi Quotes
Hungarian
Psychologist
Nathaniel Branden Quotes
American
Psychologist
Ram Dass Quotes
American
Psychologist
Rollo May Quotes
American
Psychologist
Sigmund Freud Quotes
Austrian
Psychologist
Tara Brach Quotes
American
Psychologist
Viktor E. Frankl Quotes
Austrian
Psychologist
Wayne Dyer Quotes
American
Psychologist