"The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics. (Galileo Galilei, "The Assayer", 1623)
"We think only through the medium of words. Languages are true analytical methods. Algebra, which is adapted to its purpose in every species of expression, in the most simple, most exact, and best manner possible, is at the same time a language and an analytical method. The art of reasoning is nothing more than a language well arranged." (Abbé de Condillac, "System of Logic", cca. 1781)
"Language is the express image and picture of human thoughts; and, from the picture, we may often draw very certain conclusions with regard to die original. (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)
"Nothing more readily gives the conception of a thing than the seeing an image of it. Hence, by a figure common in language, conception is called an image of the thing conceived. But to shew that it is not a real but a metaphorical image, it is called an image in the mind. We know nothing that is properly in the mind but thought; and, when anything else is said to be in the mind, the expression must be figurative, and signify some kind of thought." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)
"We think only through the medium of words. Languages are true analytical methods. Algebra, which is adapted to its purpose in every species of expression, in the most simple, most exact, and best manner possible, is at the same time a language and an analytical method. The art of reasoning is nothing more than a language well arranged." (Antoine-Laurent Lavoisier, "Elements of Chemistry", 1790)
"Languages are true analytical methods." (Antoine-Laurent Lavoisier, "Elements of Chemistry", 1790)
"For language is the armory of the human mind; and at once contains the trophies of its past, and the weapons of its future conquests." (Samuel T Coleridge," Biographia Literaria", 1817)
"The best part of human language, properly so called, is derived from reflection on the acts of the mind itself." (Samuel T Coleridge," Biographia Literaria", 1817)
"Metaphor [...] may be said to be the algebra of language." (Charles C Colton, "Lacon", 1820)
"The diversity of languages is not a diversity of signs and sounds but a diversity of views of the world." (Wilhelm von Humboldt, 1820)
"Every word in language serves to designate an idea and some of them even complete propositions. Therefore, it is only natural to suppose that each idea is composed of at least as many parts as there are words in its expression." (Bernard Bolzano, "Wissenschaftslehre" ["Theory of Science"], 1837)
"Language has time as its element; all other media have space as their element." (Søren Kierkegaard, "Either/Or: A Fragment of Life", 1843)
"A successful attempt to express logical propositions by symbols, the laws of whose combinations should be founded upon the laws of the mental processes which they represent, would, so far, be a step towards a philosophical language." (George Boole, "The Mathematical Analysis of Logic", 1847)
"Accuracy of language is one of the bulwarks of truth." (Anna B Jameson, "A Commonplace Book of Thoughts, Memories, and Fancies", 1854)
"To deduce the laws of the symbols of Logic from a consideration of those operations of the mind which are implied in the strict use of language as an instrument of reasoning." (George Boole, "An Investigation of the Laws of Thought", 1854)
"The language of mathematics, permitting great sharpness and accuracy of definition, conduces largely to their power of drawing necessary conclusions. Language is not only a means of recording the results of our thinking; it is an instrument of thought, and that of the highest value." (Thomas Hill, "The Imagination in Mathematics", The North American Review Vol. 85 (176), 1857)
"The figure of speech or of thought by which we transfer the language and ideas of a familiar science to one with which we are less acquainted may be called Scientific Metaphor." (James C Maxwell, British Association for the Advancement of Science, 1871)
"The various languages placed side by side show that with words it is never a question of truth, never a question of adequate expression; otherwise, there would not be so many languages. The ‘thing in itself’ (which is precisely what the pure truth, apart from any of its consequences, would be) is likewise something quite incomprehensible to the creator of language and something not in the least worth striving for. This creator only designates the relations of things to men, and for expressing these relations he lays hold of the boldest metaphors. To begin with, a nerve stimulus is transferred into an image: first metaphor. The image, in turn, is imitated in a sound: second metaphor. And each time there is a complete overleaping of one sphere, right into the middle of an entirely new and different one." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)
"Language is a system of interdependent terms in which the value of each term results solely from the simultaneous presence of the others. (Ferdinand de Saussure, "Course in general linguistics", 1915)
"Language is a purely human and non-instinctive method of communicating ideas, emotions and desires by means of a system of voluntarily produced symbols." (Edward Sapir, "Language", 1921)
"The essence of language lies, not in the use of this or that special means of communication, but in the employment of fixed associations (however these may have originated) in order that something now sensible - a spoken word, a picture, a gesture, or what not — may call up the 'idea' of something else. Whenever this is done, what is now sensible may be called a 'sign' or 'symbol', and that of which it is intended to call up the 'idea' may be called its 'meaning'. This is a rough outline of what constitutes 'meaning'." (Bertrand Russell, "Analysis of Mind", 1921)
"But how can we avoid the use of human language? The [...] symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason - only thus may we hope to build mathematics on the solid foundation of logic." (Tobias Dantzig, "Number: The Language of Science", 1930)
"Language is the communicative process par excellence in every known society, and it is exceedingly important to observe that whatever may be the shortcomings of a primitive society judged from the vantage point of civilization its language inevitably forms as sure, complete and potentially creative an apparatus of referential symbolism as the most sophisticated language that we know of." (Edward Sapir, "Communication", 1931)
"A language is like a map; it is not the territory represented, but it may be a good map or a bad map. If the map shows a different structure from the territory represented-for instance, shows the cities in a wrong order, or some places east of others while in the actual territory they are west - then the map is worse than useless, as it misinforms and leads astray. One who made use of it could never be certain of reaching his destination. The use of ellanguage to represent events which operate as-a-whole is, at least, equally misguiding and semantically dangerous." (Alfred Korzybski, "Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics", 1933)
"Any organism must be treated as-a-whole; in other words, that an organism is not an algebraic sum, a linear function of its elements, but always more than that. It is seemingly little realized, at present, that this simple and innocent-looking statement involves a full structural revision of our language […]" (Alfred Korzybski, "Science and Sanity", 1933)
"Every language having a structure, by the very nature of language, reflects in its own structure that of the world as assumed by those who evolved the language. In other words, we read unconsciously into the world the structure of the language we use." (Alfred Korzybski, "Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics", 1933)
"By the logical syntax of a language, we mean the formal theory of the linguistic forms of that language - the systematic statement of the formal rules which govern it together with the development of the consequences which follow from these rules. A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for examples, the words) or to the sense of the expressions (e. g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are constructed." (Rudolf Carnap, "Logical Syntax of Language", 1934)
"A symbol is language and yet not language." (Robin G Collingwood, "The Principles of Art", 1938)
"Thus the use of language itself is based on the principle that any symbolism which works has objective validity; and it is illegitimate to use words to contradict this principle." (Kenneth Craik, "The Nature of Explanation", 1943)
"The words of the language, as they are written or spoken, do not seem to play any role in any mechanism of thought. The physical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced or combined. […] But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought - before there is any connection with logical construction in words or other kinds of signs which can be communicated to others. The above-mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will. " (Albert Einstein, [letter to Hadamard, in (Jacques Hadamard, "The Psychology of Invention in the Mathematical Field, 1945)])
"[The information of a message can] be defined as the 'minimum number of binary decisions which enable the receiver to construct the message, on the basis of the data already available to him.' These data comprise both the convention regarding the symbols and the language used, and the knowledge available at the moment when the message started." (Dennis Gabor, "Optical transmission" in Information Theory : Papers Read at a Symposium on Information Theory, 1952)
"For a large class of cases - though not for all - in which we employ the word 'meaning' it can be defined thus: the meaning of a word is its use in language." (Ludwig Wittgenstein, "Philosophical investigations", 1953)
"Like everything metaphysical the harmony between thought and reality is to be found in the grammar of the language." (Ludwig Wittgenstein, "Philosophical Investigations", 1953)
"The forms of a person’s thoughts are controlled by inexorable laws of pattern of which he is unconscious. These patterns are the unperceived intricate systematizations of his own language - shown readily enough by a candid comparison and contrast with other languages, especially those of a different linguistic family." (Benjamin L Whorf, 1956)
"We are always looking for metaphors in which to express our ideas of life, for our language is inadequate for all its complexities. Life is a labyrinth.[...] Life is a machine.[...] Life is a laboratory.[...] It is but a metaphor. When we speak of ultimate things we can, maybe, speak only in metaphors. Life is a dance, a very elaborate and complex dance [...]." (Charles Singer, "A Short History of Scientific Ideas to 1900", 1959)
"[a pictorial representation] is not a faithful record of a visual experience, but the faithful construction of a relational model […] Such a model can be constructed to any required degree of accuracy . What is decisive here is clearly the word 'required'. The form of a representation cannot be divorced from its purpose and the requirements of the society in which the given visual language gains currency." (Ernst H Gombrich," Art and illusion", 1960)
"By a symbol I do not mean an allegory or a sign, but an image that describes in the best possible way the dimly discerned nature of the spirit. A symbol does not define or explain; it points beyond itself to a meaning that is darkly divined yet still beyond our grasp, and cannot be adequately expressed in the familiar words of our language." (Carl G Jung, "The Structure And Dynamics Of The Psyche", 1960)
"Language, in its origin and essence, is simply a system of signs or symbols that denote real occurrences or their echo in the human soul." (Carl G Jung, "The Structure And Dynamics Of The Psyche", 1960)
"[Human] communication is rendered more complex by the use of differing sets of sound-symbols, called languages and by the fact that a given set of symbols tends to change with the passage of years to become an entirely new language." (Howard L Myers, "The Creatures of Man", 1968)
"In practice, let us note, the determination of sets by means of characterizing criteria runs into difficulty because of the ambiguity of our language. The task of separating the objects belonging to a set from those that do not is often made difficult by the large number of objects of intermediate type." (Naum Ya. Vilenkin, "Stories about Sets", 1968)
"Learning a language represents training in the delusions of that language." (Frank Herbert, "The Bureau of Sabotage: Whipping Star", 1969)
"Images apparently occupy a curious position somewhere between the statements of language, which are intended to convey a meaning, and the things of nature, to which we only can give a meaning." (Ernst Gombrich, "Symbolic Images", 1972)
"The unconscious reveals its meaning imaginatively, through symbols and images, and it speaks [...] a basically mythological language." (Morton Kelsey, "Myth, History & Faith", 1974)
"Without a constant misuse of language, there cannot be any discovery, any progress." (Paul K Feyerabend,"Against Method: Outline of an Anarchistic Theory of Knowledge", 1975)
"A higher-level formal language is an abstract machine." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation", 1976)
"[…] semantic nets [are defined] as graphical analogues of data structures representing 'facts' in a computer system for understanding natural language." (Lenhart K Schubert," "Extending the Expressive Power of Semantic Networks", Artificial Intelligence 7, 1976)
"[...] much of the information on which human decisions are based is possibilistic rather than probabilistic in nature, and the intrinsic fuzziness of natural languages - which is a logical consequence of the necessity to express information in a summarized form - is, in the main, possibilistic in origin." (Lotfi A Zadeh, "Fuzzy Sets as the Basis for a Theory of Possibility", Fuzzy Sets and Systems, 1978)
"Clever metaphors die hard. Their tenacity of life approaches that of the hardiest micro-organisms. Living relics litter our language, their raisons d’etre forever past, ignored if not forgotten, and their present fascination seldom impaired by the confusions they may create." (James R Moore, "The Post-Darwinian Controversies", 1979)
"[...] language is the medium through which new conceptual metaphors are created." (George Lakoff and Mark Johnson, "Metaphors We Live By", 1980)
"Metaphor is for most people a device of the poetic imagination and the rhetorical flourish - a matter of extraordinary rather than ordinary language. Moreover, metaphor is typically viewed as characteristic of language alone, a matter of words rather than thought or action. For this reason, most people think they can get along perfectly well without metaphor. We have found, on the contrary, that metaphor is pervasive in everyday life, not just in language but in thought and action. Our ordinary conceptual system, in terms of which we both think and act, is fundamentally metaphorical in nature." (George Lakoff & Mark Johnson, "Metaphors we Live by", 1980)
"New metaphors are capable of creating new understandings and, therefore, new realities. This should be obvious in the case of poetic metaphor, where language is the medium through which new conceptual metaphors are created." (George Lakoff and Mark Johnson, "Metaphors We Live By", 1980)
"The essence of metaphor is understanding and experiencing one kind of thing in terms of another. […] Metaphor is pervasive in everyday life, not just in language but in thought and action. Our ordinary conceptual system, in terms of which we both think and act, is fundamentally metaphorical in nature." (George Lakoff & Mark Johnson, "Metaphors We Live By", 1980)
"Language cannot be studied in isolation from the investigation of ‘rationality’. It cannot afford to neglect our everyday assumptions concerning the total behavior of a reasonable person. […] An integrational linguistics must recognize that human beings inhabit a communicational space which is not neatly compartmentalized into language and nonlanguage. […] It renounces in advance the possibility of setting up systems of forms and meanings which will ‘account for’ a central core of linguistic behavior irrespective of the situation and communicational purposes involved." (Roy Harris, "The Language Myth", 1981)
"The test of the intelligibility of any statement that overwhelms us with its air of profundity is its translatability into language that lacks the elevation and verve of the original statement but can pass muster as a simple and clear statement in ordinary, everyday speech. Most of what has been written about beauty will not survive this test. In the presence of many of the most eloquent statements about beauty, we are left speechless - speechless in the sense that we cannot find other words for expressing what we think or hope we understand." (Mortimer J Adler, Six Great Ideas, 1981)
"Language is the most formless means of expression. Its capacity to describe concepts without physical or visual references carries us into an advanced state of abstraction." (Ian Wilson, "Conceptual Art", 1984)
"What makes people smarter than machines? They certainly are not quicker or more precise. Yet people are far better at perceiving objects in natural scenes and noting their relations, at understanding language and retrieving contextually appropriate information from memory, at making plans and carrying out contextually appropriate actions, and at a wide range of other natural cognitive tasks. People are also far better at learning to do these things more accurately and fluently through processing experience." (James L McClelland et al, "The appeal of parallel distributed processing", 1986)
"Modeling underlies our ability to think and imagine, to use signs and language, to communicate, to generalize from experience, to deal with the unexpected, and to make sense out of the raw bombardment of our sensations. It allows us to see patterns, to appreciate, predict, and manipulate processes and things, and to express meaning and purpose. In short, it is one of the most essential activities of the human mind. It is the foundation of what we call intelligent behavior and is a large part of what makes us human. We are, in a word, modelers: creatures that build and use models routinely, habitually – sometimes even compulsively – to face, understand, and interact with reality." (Jeff Rothenberg, "The Nature of Modeling. In: Artificial Intelligence, Simulation, and Modeling", 1989)
"[Language comprehension] involves many components of intelligence: recognition of words, decoding them into meanings, segmenting word sequences into grammatical constituents, combining meanings into statements, inferring connections among statements, holding in short-term memory earlier concepts while processing later discourse, inferring the writer’s or speaker’s intentions, schematization of the gist of a passage, and memory retrieval in answering questions about the passage. [… The reader] constructs a mental representation of the situation and actions being described. […] Readers tend to remember the mental model they constructed from a text, rather than the text itself." (Gordon H Bower & Daniel G Morrow, 1990)
"The concepts of science, in all their richness and ambiguity, can be presented without any compromise, without any simplification counting as distortion, in language accessible to all intelligent people." (Stephen J Gould, "Wonderful Life: The Burgess Shale and the Nature of History", 1990)
"[For] us to be able to speak and understand novel sentences, we have to store in our heads not just the words of our language but also the patterns of sentences possible in our language. These patterns, in turn, describe not just patterns of words but also patterns of patterns. Linguists refer to these patterns as the rules of language stored in memory; they refer to the complete collection of rules as the mental grammar of the language, or grammar for short." (Ray Jackendoff, "Patterns in the Mind", 1994)
"[...] images are probably the main content of our thoughts, regardless of the sensory modality in which they are generated and regardless of whether they are about a thing or a process involving things; or about words or other symbols, in a given language, which correspond to a thing or process. Hidden behind those images, never or rarely knowable by us, there are indeed numerous processes that guide the generation and deployment of those images in space and time. Those processes utilize rules and strategies embodied in dispositional representations. They are essential for our thinking but are not a content of our thoughts." (Antonio R Damasio,"Descartes' Error. Emotion, Reason, and the Human Brain", 1994)
"The mental model, in turn, can be considered as a syntactic language of thought whose semantic interpretation is provided by the actual world. In this sense, a person's beliefs are true to the extent that they correspond to the world." (William J Rapaport, "Understanding Understanding: Syntactic Semantics and Computational Cognition", Philosophical Perspectives Vol. 9, 1995)
"To talk about sensemaking is to talk about reality as an ongoing accomplishment that takes form when people make retrospective sense of the situations in which they find themselves and their creations. There is a strong reflexive quality to this process. People make sense of things by seeing a world on which they already imposed what they believe. In other words, people discover their own inventions. This is why sensemaking can be understood as invention and interpretations understood as discovery. These are complementary ideas. If sensemaking is viewed as an act of invention, then it is also possible to argue that the artifacts it produces include language games and texts." (Karl E Weick, "Sensemaking in Organizations", 1995)
"Artificial intelligence comprises methods, tools, and systems for solving problems that normally require the intelligence of humans. The term intelligence is always defined as the ability to learn effectively, to react adaptively, to make proper decisions, to communicate in language or images in a sophisticated way, and to understand." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)
"Metaphor, the life of language, can be the death of meaning. It should be used in moderation, like vodka. Writers drunk on metaphor can forget they are conveying information and ideas." (Robert Fulford, 1996)
"The purpose of a conceptual model is to provide a vocabulary of terms and concepts that can be used to describe problems and/or solutions of design. It is not the purpose of a model to address specific problems, and even less to propose solutions for them. Drawing an analogy with linguistics, a conceptual model is analogous to a language, while design patterns are analogous to rhetorical figures, which are predefined templates of language usages, suited particularly to specific problems." (Peter P Chen [Ed.], "Advances in Conceptual Modeling", 1999)
"Abstraction is itself an abstract word and has no single meaning. […] Every word in our language is abstract, because it represents something else." (Eric Maisel, "The Creativity Book: A Year's Worth of Inspiration and Guidance", 2000)
"In the language of mental models, such past experience provided the default assumptions necessary to fill the gaps in the emerging and necessarily incomplete framework of a relativistic theory of gravitation. It was precisely the nature of these default assumptions that allowed them to be discarded again in the light of novel information - provided, for instance, by the further elaboration of the mathematical formalism - without, however, having to abandon the underlying mental models which could thus continue to function as heuristic orientations." (Jürgen Renn, "Before the Riemann Tensor: The Emergence of Einstein’s Double Strategy", [in "The Universe of General Relativity"] 2000)
"A symbol is a mental representation regarding the internal reality referring to its object by a convention and produced by the conscious interpretation of a sign. In contrast to signals, symbols may be used every time if the receiver has the corresponding representation. Symbols also relate to feelings and thus give access not only to information but also to the communicator’s motivational and emotional state. The use of symbols makes it possible for the organism using it to evoke in the receiver the same response it evokes in himself. To communicate with symbols is to use a language." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"Those who violate the rules of a language do not enter new territory; they leave the domain of meaningful discourse. Even facts in these circumstances dissolve, because they are shaped by the language and subjected to its limitations." (Paul K Feyerabend,"Conquest of Abundance", 2001)
"When we acquire a language we don’t simply learn how to use the correct words, grammar and conventions for speaking appropriately in context, we also acquire a ‘world view’: an implicit set of assumptions and presuppositions regarding how to understand the world, who and what we are within it, and everything else that is entailed in categorising our experience." (Michael Forrester," Psychology of the Image", 2000)
"It is not so much that particular languages evolve and then cause us to see the world in a given way, but that language and worldview develop side by side to the point where language becomes so ingrained that it constantly supports a specific way of seeing and structuring the world. In the end it becomes difficult to see the world in any other light." (F David Peat, "From Certainty to Uncertainty", 2002)
"A person thinking in the nonverbal mode is actually thinking with the meaning of the language in the form of mental pictures of the concepts and ideas it contains. Nonverbal thought doesn't require literacy. An illiterate person can communicate without knowing what the symbols look like. [...] Literacy, then, is established as the person learns how the symbols look and becomes able to recognize them as representing certain things or concepts." (Ronald D Davis & Eldon M Braun, "The Gift of Learning", 2003)
"A symbol is an object, act, or event that conveys meaning to others. Symbols can be considered a rich, non-verbal language that vibrantly conveys the organization’s important values concerning how people relate to one another and interact with the environment." (Richard L Daft & Dorothy Marcic, "Understanding Management" 5th Ed., 2006)
"Human language is a vehicle of truth but also of error, deception, and nonsense. Its use, as in the present discussion, thus requires great prudence. One can improve the precision of language by explicit definition of the terms used. But this approach has its limitations: the definition of one term involves other terms, which should in turn be defined, and so on. Mathematics has found a way out of this infinite regression: it bypasses the use of definitions by postulating some logical relations (called axioms) between otherwise undefined mathematical terms. Using the mathematical terms introduced with the axioms, one can then define new terms and proceed to build mathematical theories. Mathematics need, not, in principle rely on a human language. It can use, instead, a formal presentation in which the validity of a deduction can be checked mechanically and without risk of error or deception." (David Ruelle,"The Mathematician's Brain", 2007)
"A modeling language is usually based on some kind of computational model, such as a state machine, data flow, or data structure. The choice of this model, or a combination of many, depends on the modeling target. Most of us make this choice implicitly without further thinking: some systems call for capturing dynamics and thus we apply for example state machines, whereas other systems may be better specified by focusing on their static structures using feature diagrams or component diagrams. For these reasons a variety of modeling languages are available." (Steven Kelly & Juha-Pekka Tolvanen, "Domain-specific Modeling", 2008)
"When the words are used without mental image or concrete objects, we label them as metaphor. […] While concepts are being internalised, language is not only appropriated but metaphorised." (Lynne Cameron, "Metaphor in the construction of a learning environment", 2008)
"Symbolic reasoning falls short not only in modeling low level behaviors but is also difficult to ground "into real world interactions and to scale upon dynamic environments […] This has lead many […] to abandon symbolic systems […] and […] focus on parallel distributed, entirely sub-symbolic approaches […] well suited for many learning and control tasks, but difficult to apply [in] areas such as reasoning and language." (Joscha Bach, "Principles of Synthetic Intelligence PSI: An Architecture of Motivated Cognition", 2009)
"Language accelerates learning and creation by permitting communication and coordination. A new idea can be spread quickly if someone can explain it and communicate it to others before they have to discover it themselves. But the chief advantage of language is not communication but autogeneration. Language is a trick that allows the mind to question itself; a magic mirror that reveals to the mind what the mind thinks; a handle that turns a mind into a tool."
"Language is a tool of social intercourse to such an extent that it is newly reinvented every time it is absent." (Mario Bunge, "Matter and Mind: A Philosophical Inquiry", 2010)
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