"Metaphors do somehow make known what they mean by the comparison they involve. Whenever we use them, we transfer meaning according to some similarity. But statements such as the aforesaid do not make anything known. There is no inherent resemblance to justify calling law ‘a measure’ or ‘an image’ , nor is it customary to refer to it as such. If one says that law is literally ‘a measure’ or ‘an
image’, he is either deceiving or being deceived. An image is something fashioned in the likeness of something else, but such is not an inherent characteristic of law. If, on the other hand, the statement is not made in a literal sense, it is evident that it is obscure, and worse than any metaphorical expression." (Aristotle)
"The greatest thing by far is to be a master of metaphor. It is the one thing that cannot be learnt from others; it is also a sign of genius, since a good metaphor implies an intuitive perception of the similarity in dissimilars." (Aristotle, "Poetics", cca. 335 BC)
"The employment of tropes, just as the use of schemata, is the exclusive privilege of the very learned. The rules governing tropes are also very strict, so that the latitude in which they may be used is definitely limited. For the rules teach that we may not extend figures. One who is studiously imitating the authors by using metaphors and figures, must take care to avoid crude figures that are hard to interpret. What is primarily desirable in language is lucid clarity and easy comprehensibility. Therefore schemata should be used only out of necessity or for ornamentation. Speech was invented as a means of communicating mental concepts; and figures [of speech] are admitted so far as they compensate by their utility for whatever they lack in conformity to the [rules of the grammatical] art." (John of Salisbury, "Metalogicon", 1159)
"Metaphor [...] may be said to be the algebra of language." (Charles C Colton, “Lacon”, 1820)
“The drive toward the formation of metaphors is the fundamental human drive, which one cannot for a single instant dispense with in thought, for one would thereby dispense with man himself.” (Friedrich Nietzsche, “On Truth and Lies in a Nonmoral Sense”, 1873)
“The folly of mistaking a paradox for a discovery, a metaphor for a proof, a torrent of verbiage for a spring of capital truths, and oneself for an oracle, is inborn in us.” (Paul Valéry, “Introduction to the Method of Leonardo da Vinci”, 1895)
"Progress in truth - truth of science and truth of religion - is mainly a progress in the framing of concepts, in discarding artificial abstractions or partial metaphors, and in evolving notions which strike more deeply into the root of reality." (Alfred N Whitehead, "Religion in the Making", 1926)
"Mathematical research can lend its organisational characteristics to poetry, whereby disjointed metaphors take on a universal sense. Similarly, the axiomatic foundations of group theory can be assimilated into a larger moral concept of a unified universe. Without this, mathematics would be a laborious Barbary." (Dan Barbilian, “The Autobiography of the Scientist”, 1940)
"[…] the major mathematical research acquires an organization and orientation similar to the poetical function which, adjusting by means of metaphor disjunctive elements, displays a structure identical to the sensitive universe. Similarly, by means of its axiomatic or theoretical foundation, mathematics assimilates various doctrines and serves the instructive purpose, the one set up by the unifying moral universe of concepts. " (Dan Barbilian, "The Autobiography of the Scientist", 1940)
“At the final stage you teach me that this wondrous and multicolored universe can be reduced to the atom and that the atom itself can be reduced to the electron. All this is good and I wait for you to continue. But you tell me of an invisible planetary system in which electrons gravitate around a nucleus. You explain this world to me with an image. I realize then that you have been reduced to poetry: I shall never know. Have I the time to become indignant? You have already changed theories. So that science that was to teach me everything ends up in a hypothesis, that lucidity founders in metaphor, that uncertainty is resolved in a work of art.” (Albert Camus, “The Myth of Sisyphus”, 1942)
“A metaphor holds a truth and an untruth, felt as inextricably bound up with each other. If one takes it as it is and gives it some sensual form, in the shape of reality, one gets dreams and art; but between these two and real, full-scale life there is a glass partition. If one analyzes it for its rational content and separates the unverifiable from the verifiable, one gets truth and knowledge but kills the feeling.” (Robert Musil, “Man Without Qualities”, 1943)
"A man desiring to understand the world looks about for a clue to its comprehension. He pitches upon some area of commonsense fact and tries to understand other areas in terms of this one. The original area becomes his basic analogy or root metaphor." (Stephen Pepper, "World Hypotheses: A Study in Evidence", 1948)
"[…] theoretical science is essentially disciplined exploitation of metaphor." (Anatol Rapoport, "Operational Philosophy", 1953)
"Metaphor [...] may be said to be the algebra of language." (Charles C Colton, “Lacon”, 1820)
“The drive toward the formation of metaphors is the fundamental human drive, which one cannot for a single instant dispense with in thought, for one would thereby dispense with man himself.” (Friedrich Nietzsche, “On Truth and Lies in a Nonmoral Sense”, 1873)
“The folly of mistaking a paradox for a discovery, a metaphor for a proof, a torrent of verbiage for a spring of capital truths, and oneself for an oracle, is inborn in us.” (Paul Valéry, “Introduction to the Method of Leonardo da Vinci”, 1895)
"Progress in truth - truth of science and truth of religion - is mainly a progress in the framing of concepts, in discarding artificial abstractions or partial metaphors, and in evolving notions which strike more deeply into the root of reality." (Alfred N Whitehead, "Religion in the Making", 1926)
"Mathematical research can lend its organisational characteristics to poetry, whereby disjointed metaphors take on a universal sense. Similarly, the axiomatic foundations of group theory can be assimilated into a larger moral concept of a unified universe. Without this, mathematics would be a laborious Barbary." (Dan Barbilian, “The Autobiography of the Scientist”, 1940)
"[…] the major mathematical research acquires an organization and orientation similar to the poetical function which, adjusting by means of metaphor disjunctive elements, displays a structure identical to the sensitive universe. Similarly, by means of its axiomatic or theoretical foundation, mathematics assimilates various doctrines and serves the instructive purpose, the one set up by the unifying moral universe of concepts. " (Dan Barbilian, "The Autobiography of the Scientist", 1940)
“At the final stage you teach me that this wondrous and multicolored universe can be reduced to the atom and that the atom itself can be reduced to the electron. All this is good and I wait for you to continue. But you tell me of an invisible planetary system in which electrons gravitate around a nucleus. You explain this world to me with an image. I realize then that you have been reduced to poetry: I shall never know. Have I the time to become indignant? You have already changed theories. So that science that was to teach me everything ends up in a hypothesis, that lucidity founders in metaphor, that uncertainty is resolved in a work of art.” (Albert Camus, “The Myth of Sisyphus”, 1942)
“A metaphor holds a truth and an untruth, felt as inextricably bound up with each other. If one takes it as it is and gives it some sensual form, in the shape of reality, one gets dreams and art; but between these two and real, full-scale life there is a glass partition. If one analyzes it for its rational content and separates the unverifiable from the verifiable, one gets truth and knowledge but kills the feeling.” (Robert Musil, “Man Without Qualities”, 1943)
"A man desiring to understand the world looks about for a clue to its comprehension. He pitches upon some area of commonsense fact and tries to understand other areas in terms of this one. The original area becomes his basic analogy or root metaphor." (Stephen Pepper, "World Hypotheses: A Study in Evidence", 1948)
"[…] theoretical science is essentially disciplined exploitation of metaphor." (Anatol Rapoport, "Operational Philosophy", 1953)
"Scientific metaphors are called models. They are made with the full knowledge that the connection between the metaphor and the real thing is primarily in the mind of the scientist. And they are made with a clearly definable purpose - as starting points of a deductive process. […] Like every other aspect of scientific procedure, the scientific metaphor is a pragmatic device, to be used freely as long as it serves its purpose, to be discarded without regrets when it fails to do so." (Anatol Rapoport, "Operational Philosophy", 1954)
“Speaking without metaphor we have to declare that we are here faced with one of these typical antinomies caused by the fact that we have not yet succeeded in elaborating a fairly understandable outlook on the world without retiring our own mind, the producer of the world picture, from it, so that mind has no place in it. The attempt to press it into it, after all, necessarily produces some absurdities.” (Erwin Schrödinger, „Mind and Matter: the Tarner Lectures”, 1956)
"The symbol and the metaphor are as necessary to science as to poetry." (Jacob Bronowski, "Science and Human Values", 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.” (Charles Singer, “A Short History of Scientific Ideas to 1900”, 1959)
"Every metaphor is the tip of a submerged model. […] Use of theoretical models resembles the use of metaphors in requiring analogical transfer of a vocabulary. Metaphor and model-making reveal new relationships; both are attempts to pour new content into old bottles." (Max Black," Models and Metaphors", 1962)
"[Metaphor] is a loose word, at best, and we must beware of attributing to it stricter rules of usage than are usually found in practice." (Max Black, “Models and Metaphors”, 1962)
"Rationality consists [of] the continuous adaptation of our language to our continually expanding world, and metaphor is one of the chief means by which this is accomplished." (Mary B Hesse, "Models and Analogies in Science", 1966)
"[...] one cannot describe reality; only give metaphors that indicate it. All human modes of description (photographic, mathematical, and literary) are metaphorical. Even the most precise scientific description of an object or movement is a tissue of metaphors." (John Fowles, “'Notes on an Unfinished Novel”, 1969)
"Science advances metaphorically. It does not proceed in an orthogenic fashion moving inexorably forward in a straight line. It does not radiate along many branches like a growing tree. It moves from one view to another by a large leap, preceded by a radical shift in the scientist’s mode of thought." (François Jacob, "The Logic of Life: A History of Heredity", 1970)
“Speaking without metaphor we have to declare that we are here faced with one of these typical antinomies caused by the fact that we have not yet succeeded in elaborating a fairly understandable outlook on the world without retiring our own mind, the producer of the world picture, from it, so that mind has no place in it. The attempt to press it into it, after all, necessarily produces some absurdities.” (Erwin Schrödinger, „Mind and Matter: the Tarner Lectures”, 1956)
"The symbol and the metaphor are as necessary to science as to poetry." (Jacob Bronowski, "Science and Human Values", 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.” (Charles Singer, “A Short History of Scientific Ideas to 1900”, 1959)
"Every metaphor is the tip of a submerged model. […] Use of theoretical models resembles the use of metaphors in requiring analogical transfer of a vocabulary. Metaphor and model-making reveal new relationships; both are attempts to pour new content into old bottles." (Max Black," Models and Metaphors", 1962)
"[Metaphor] is a loose word, at best, and we must beware of attributing to it stricter rules of usage than are usually found in practice." (Max Black, “Models and Metaphors”, 1962)
"Rationality consists [of] the continuous adaptation of our language to our continually expanding world, and metaphor is one of the chief means by which this is accomplished." (Mary B Hesse, "Models and Analogies in Science", 1966)
"[...] one cannot describe reality; only give metaphors that indicate it. All human modes of description (photographic, mathematical, and literary) are metaphorical. Even the most precise scientific description of an object or movement is a tissue of metaphors." (John Fowles, “'Notes on an Unfinished Novel”, 1969)
"Science advances metaphorically. It does not proceed in an orthogenic fashion moving inexorably forward in a straight line. It does not radiate along many branches like a growing tree. It moves from one view to another by a large leap, preceded by a radical shift in the scientist’s mode of thought." (François Jacob, "The Logic of Life: A History of Heredity", 1970)
"But metaphor is an indispensable tool of thought and expression - a characteristic of all human communication, even of that of the scientist. The conceptual models of cybernetics and the energy theories of psycho-analysis are, after all, only labeled metaphors." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)
“A metaphor is a word used in an unfamiliar context to give us a new insight; a good metaphor moves us to see our ordinary world in an extraordinary way.” (Sallie McFague, “Speaking in Parables”, 1975)
"The very nature of science is such that scientists need the metaphor as a bridge between old and new theories." (Earl R MacCormac, "Metaphor and Myth in Science and Religion", 1976)
"Catastrophe Theory is-quite likely-the first coherent attempt (since Aristotelian logic) to give a theory on analogy. When narrow-minded scientists object to Catastrophe Theory that it gives no more than analogies, or metaphors, they do not realise that they are stating the proper aim of Catastrophe Theory, which is to classify all possible types of analogous situations." (René F Thom," La Théorie des catastrophes: État présent et perspective", 1977)
“[…] the use of analogies, particularly with metaphor, adds richness and dimension to arguments and descriptions not possible with ordinary discourse or with propositional reasoning.” (Jeanette M Gallagher, “The Future of Formal Thought Research: The Study of Analogy and Metaphor”, 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)
"One should employ a metaphor in science only when there is good evidence that an important similarity or analogy exists between its primary and secondary subjects. One should seek to discover more about the relevant similarities or analogies, always considering the possibility that there are no important similarities or analogies, or alternatively, that there are quite distinct similarities for which distinct terminology should be introduced. One should try to discover what the 'essential' features of the similarities or analogies are, and one should try to assimilate one’s account of them to other theoretical work in the same subject area - that is, one should attempt to explicate the metaphor." (Richard Boyd, "Metaphor and Theory Change: What Is ‘Metaphor’ a Metaphor For?", 1979)
"The use of metaphor is one of many devices available to the scientific community to accomplish the task of accommodation of language to the causal structure of the world." (Richard Boyd, "Metaphor and theory change: what is ‘metaphor’ a metaphor for?", 1979)
"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 typieully 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 and Mark Johnson, Metaphors We Live By, 1980)
“Analogies, metaphors, and emblems are the threads by which the mind holds on to the world even when, absentmindedly, it has lost direct contact with it, and they guarantee the unity of human experience. Moreover, in the thinking process itself they serve as models to give us our bearings lest we stagger blindly among experiences that our bodily senses with their relative certainty of knowledge cannot guide us through.” (Hannah Arendt, “The Life of the Mind”, 1981)
"Metaphors deny distinctions between things: problems often arise from taking structural metaphors too literally. Because unexamined metaphors lead us to assume the identity of unidentical things, conflicts can arise which can only be resolved by understanding the metaphor (which requires its recognition as such), which means reconstructing the analogy on which it is based. […] The unexplained extension of concepts can too often result in the destruction rather than the expansion of meaning." (David Pimm,"Metaphor and Analogy in Mathematics", For the Learning of Mathematics Vol. 1 (3), 1981)
"Metaphor and simile are the characteristic tropes of scientific thought, not formal validity of argument." (Rom Harré, "Varieties of Realism", 1986)
“All great theories are expansive, and all notions so rich in scope and implication are underpinned by visions about the nature of things. You may call these visions ‘philosophy’, or ‘metaphor’, or ‘organizing principle’, but one thing they are surely not – they are not simple inductions from observed facts of the natural world.” (Stephen Jay Gould, “Time’s Arrow, Time’s Cycle”, 1987)
"Metaphor [is] a pervasive mode of understanding by which we project patterns from one domain of experience in order to structure another domain of a different kind. So conceived metaphor is not merely a linguistic mode of expression; rather, it is one of the chief cognitive structures by which we are able to have coherent, ordered experiences that we can reason about and make sense of. Through metaphor, we make use of patterns that obtain in our physical experience to organise our more abstract understanding. “ (Mark Johnson, “The Body in the Mind”, 1987)
"The model is only a suggestive metaphor, a fiction about the messy and unwieldy observations of the real world. In order for it to be persuasive, to convey a sense of credibility, it is important that it not be too complicated and that the assumptions that are made be clearly in evidence. In short, the model must be simple, transparent, and verifiable." (Edward Beltrami, "Mathematics for Dynamic Modeling", 1987)
"[…] mathematics does not come to us written indelibly on Nature’s Tablets, but rather is the product of a controlled search governed by metaphorical considerations, the premier instance being the heuristics of the conservation principles." (Philip Mirowski, "More Heat than Light: Economics as Social Physics: Physics as Nature’s Economics", 1989)
“The metaphor never goes very far, anymore than a curve can long be confused with its tangent.” (Henri Bergson, “A World of Ideas”, 1989)
"Today’s quarks and leptons can be viewed as metaphors of the underlying reality of nature, though metaphors that are objectively and rationally defied and are components of theories that have great predictive power. And that’s the difference between the metaphors of science and those of myth: scientific metaphors work." (Victor J Stenger, "Physics and Psychics: The Search for a World Beyond the Senses", 1990)
“[metaphors] are always open to more than one interpretation. But far from being a defect this essential openness is the reason why a number of those metaphors have had a very long life and have been able to survive great changes both in science and in the social background against which they first appeared.” (Olaf Pedersen, “The Book of Nature”, 1992)
"Metaphor plays an essential role in establishing a link between scientific language and the world. Those links are not, however, given once and for all. Theory change, in particular, is accompanied by a change in some of the relevant metaphors and in the corresponding parts of the network of similarities through which terms attach to nature." (Thomas S Kuhn, "Metaphor in science", 1993)
“People have amazing facilities for sensing something without knowing where it comes from (intuition); for sensing that some phenomenon or situation or object is like something else (association); and for building and testing connections and comparisons, holding two things in mind at the same time (metaphor). These facilities are quite important for mathematics. Personally, I put a lot of effort into ‘listening’ to my intuitions and associations, and building them into metaphors and connections. This involves a kind of simultaneous quieting and focusing of my mind. Words, logic, and detailed pictures rattling around can inhibit intuitions and associations.” (William P Thurston, “On proof and progress in mathematics”, Bulletin of the American Mathematical Society Vol. 30 (2), 1994)
“A metaphor is not an ornament. It is an organ of perception. Through metaphors, we see the world as one thing or another.” (Neil Postman, “The End of Education: Redefining the Value of School”, 1996)
"If we are to have meaningful, connected experiences; ones that we can comprehend and reason about; we must be able to discern patterns to our actions, perceptions, and conceptions. Underlying our vast network of interrelated literal meanings (all of those words about objects and actions) are those imaginative structures of understanding such as schema and metaphor, such as the mental imagery that allows us to extrapolate a path, or zoom in on one part of the whole, or zoom out until the trees merge into a forest." (William H Calvin, "The Cerebral Code", 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 logic of the emotional mind is associative; it takes elements that symbolize a reality, or trigger a memory of it, to be the same as that reality. That is why similes, metaphors and images speak directly to the emotional mind." (Daniel Goleman, "Emotional Intelligence", 1996)
"Ideas about organization are always based on implicit images or metaphors that persuade us to see, understand, and manage situations in a particular way. Metaphors create insight. But they also distort. They have strengths. But they also have limitations. In creating ways of seeing, they create ways of not seeing. There can be no single theory or metaphor that gives an all-purpose point of view, and there can be no simple "correct theory" for structuring everything we do. The challenge facing modern managers is to become accomplished in the art of using metaphor to find new ways of seeing, understanding, and shaping their actions." (Gareth Morgan, ”Imaginization”, 1997)
"Metaphysics in philosophy is, of course, supposed to characterize what is real - literally real. The irony is that such a conception of the real depends upon unconscious metaphors." (George Lakoff, "Philosophy in the Flesh: The Embodied Mind and its Challenge to Western Thought", 1999)
“Metaphors can have profound significance because, as images or figures, they allow the mind to grasp or discover unsuspected ideal and material relationships between objects.” (Giuseppe Del Re, “Cosmic Dance”, 1999)
"[…] philosophical theories are structured by conceptual metaphors that constrain which inferences can be drawn within that philosophical theory. The (typically unconscious) conceptual metaphors that are constitutive of a philosophical theory have the causal effect of constraining how you can reason within that philosophical framework." (George Lakoff, "Philosophy in the Flesh: The Embodied Mind and its Challenge to Western Thought", 1999)
“Metaphor is evidence of the human ability to visualize the universe as a coherent organism. Proof of our capacity, not just to see one thing in another but to change the very nature of things. When a metaphor is accepted as fact, it enters groupthink, taking on an existence in the real world. [...] Metaphor is the default form of thought, providing many angles from which to literally 'see' the world." (Marcel Danesi, "Poetic Logic: The Role of Metaphor in Thought, Language, and Culture", 2004)
“Metaphorizing is a manner of thinking, not a property of thinking. It is a capacity of thought, not its quality. It represents a mental operation by which a previously existing entity is described in the characteristics of another one on the basis of some similarity or by reasoning. When we say that something is (like) something else, we have already performed a mental operation. This operation includes elements such as comparison, paralleling and shaping of the new image by ignoring its less satisfactory traits in order that this image obtains an aesthetic value. By this process, for an instant we invent a device, which serves as the pole vault for the comparison’s jump. Once the jump is made the pole vault is removed. This device could be a lightning-speed logical syllogism, or a momentary created term, which successfully merges the traits of the compared objects.” (Ivan Mladenov, “Conceptualizing Metaphors: On Charles Peirce’s marginalia”, 2006)
"In order to understand how mathematics is applied to understanding of the real world it is convenient to subdivide it into the following three modes of functioning: model, theory, metaphor. A mathematical model describes a certain range of phenomena qualitatively or quantitatively. […] A (mathematical) metaphor, when it aspires to be a cognitive tool, postulates that some complex range of phenomena might be compared to a mathematical construction." (Yuri I Manin," Mathematics as Metaphor: Selected Essays of Yuri I. Manin" , 2007)
"Metaphor is a primary cognitive tool by which we make sense of the world." (Terry Marks-Tarlow, "Psyche's Veil: Psychotherapy, Fractals and Complexity", 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)
“The relationship of math to the real world has been a conundrum for philosophers for centuries, but it is also an inspiration for poets. The patterns of mathematics inhabit a liminal space - they were initially derived from the natural world and yet seem to exist in a separate, self-contained system standing apart from that world. This makes them a source of potential metaphor: mapping back and forth between the world of personal experience and the world of mathematical patterns opens the door to novel connections.” (Alice Major, “Mapping from e to Metaphor”, 2018)
“A metaphor is a word used in an unfamiliar context to give us a new insight; a good metaphor moves us to see our ordinary world in an extraordinary way.” (Sallie McFague, “Speaking in Parables”, 1975)
"The very nature of science is such that scientists need the metaphor as a bridge between old and new theories." (Earl R MacCormac, "Metaphor and Myth in Science and Religion", 1976)
"Catastrophe Theory is-quite likely-the first coherent attempt (since Aristotelian logic) to give a theory on analogy. When narrow-minded scientists object to Catastrophe Theory that it gives no more than analogies, or metaphors, they do not realise that they are stating the proper aim of Catastrophe Theory, which is to classify all possible types of analogous situations." (René F Thom," La Théorie des catastrophes: État présent et perspective", 1977)
“[…] the use of analogies, particularly with metaphor, adds richness and dimension to arguments and descriptions not possible with ordinary discourse or with propositional reasoning.” (Jeanette M Gallagher, “The Future of Formal Thought Research: The Study of Analogy and Metaphor”, 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)
"One should employ a metaphor in science only when there is good evidence that an important similarity or analogy exists between its primary and secondary subjects. One should seek to discover more about the relevant similarities or analogies, always considering the possibility that there are no important similarities or analogies, or alternatively, that there are quite distinct similarities for which distinct terminology should be introduced. One should try to discover what the 'essential' features of the similarities or analogies are, and one should try to assimilate one’s account of them to other theoretical work in the same subject area - that is, one should attempt to explicate the metaphor." (Richard Boyd, "Metaphor and Theory Change: What Is ‘Metaphor’ a Metaphor For?", 1979)
"The use of metaphor is one of many devices available to the scientific community to accomplish the task of accommodation of language to the causal structure of the world." (Richard Boyd, "Metaphor and theory change: what is ‘metaphor’ a metaphor for?", 1979)
"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 typieully 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 and Mark Johnson, Metaphors We Live By, 1980)
“Analogies, metaphors, and emblems are the threads by which the mind holds on to the world even when, absentmindedly, it has lost direct contact with it, and they guarantee the unity of human experience. Moreover, in the thinking process itself they serve as models to give us our bearings lest we stagger blindly among experiences that our bodily senses with their relative certainty of knowledge cannot guide us through.” (Hannah Arendt, “The Life of the Mind”, 1981)
"Metaphors deny distinctions between things: problems often arise from taking structural metaphors too literally. Because unexamined metaphors lead us to assume the identity of unidentical things, conflicts can arise which can only be resolved by understanding the metaphor (which requires its recognition as such), which means reconstructing the analogy on which it is based. […] The unexplained extension of concepts can too often result in the destruction rather than the expansion of meaning." (David Pimm,"Metaphor and Analogy in Mathematics", For the Learning of Mathematics Vol. 1 (3), 1981)
"Metaphor and simile are the characteristic tropes of scientific thought, not formal validity of argument." (Rom Harré, "Varieties of Realism", 1986)
“All great theories are expansive, and all notions so rich in scope and implication are underpinned by visions about the nature of things. You may call these visions ‘philosophy’, or ‘metaphor’, or ‘organizing principle’, but one thing they are surely not – they are not simple inductions from observed facts of the natural world.” (Stephen Jay Gould, “Time’s Arrow, Time’s Cycle”, 1987)
"Metaphor [is] a pervasive mode of understanding by which we project patterns from one domain of experience in order to structure another domain of a different kind. So conceived metaphor is not merely a linguistic mode of expression; rather, it is one of the chief cognitive structures by which we are able to have coherent, ordered experiences that we can reason about and make sense of. Through metaphor, we make use of patterns that obtain in our physical experience to organise our more abstract understanding. “ (Mark Johnson, “The Body in the Mind”, 1987)
"The model is only a suggestive metaphor, a fiction about the messy and unwieldy observations of the real world. In order for it to be persuasive, to convey a sense of credibility, it is important that it not be too complicated and that the assumptions that are made be clearly in evidence. In short, the model must be simple, transparent, and verifiable." (Edward Beltrami, "Mathematics for Dynamic Modeling", 1987)
"[…] mathematics does not come to us written indelibly on Nature’s Tablets, but rather is the product of a controlled search governed by metaphorical considerations, the premier instance being the heuristics of the conservation principles." (Philip Mirowski, "More Heat than Light: Economics as Social Physics: Physics as Nature’s Economics", 1989)
“The metaphor never goes very far, anymore than a curve can long be confused with its tangent.” (Henri Bergson, “A World of Ideas”, 1989)
"Today’s quarks and leptons can be viewed as metaphors of the underlying reality of nature, though metaphors that are objectively and rationally defied and are components of theories that have great predictive power. And that’s the difference between the metaphors of science and those of myth: scientific metaphors work." (Victor J Stenger, "Physics and Psychics: The Search for a World Beyond the Senses", 1990)
“[metaphors] are always open to more than one interpretation. But far from being a defect this essential openness is the reason why a number of those metaphors have had a very long life and have been able to survive great changes both in science and in the social background against which they first appeared.” (Olaf Pedersen, “The Book of Nature”, 1992)
"Metaphor plays an essential role in establishing a link between scientific language and the world. Those links are not, however, given once and for all. Theory change, in particular, is accompanied by a change in some of the relevant metaphors and in the corresponding parts of the network of similarities through which terms attach to nature." (Thomas S Kuhn, "Metaphor in science", 1993)
“People have amazing facilities for sensing something without knowing where it comes from (intuition); for sensing that some phenomenon or situation or object is like something else (association); and for building and testing connections and comparisons, holding two things in mind at the same time (metaphor). These facilities are quite important for mathematics. Personally, I put a lot of effort into ‘listening’ to my intuitions and associations, and building them into metaphors and connections. This involves a kind of simultaneous quieting and focusing of my mind. Words, logic, and detailed pictures rattling around can inhibit intuitions and associations.” (William P Thurston, “On proof and progress in mathematics”, Bulletin of the American Mathematical Society Vol. 30 (2), 1994)
“A metaphor is not an ornament. It is an organ of perception. Through metaphors, we see the world as one thing or another.” (Neil Postman, “The End of Education: Redefining the Value of School”, 1996)
"If we are to have meaningful, connected experiences; ones that we can comprehend and reason about; we must be able to discern patterns to our actions, perceptions, and conceptions. Underlying our vast network of interrelated literal meanings (all of those words about objects and actions) are those imaginative structures of understanding such as schema and metaphor, such as the mental imagery that allows us to extrapolate a path, or zoom in on one part of the whole, or zoom out until the trees merge into a forest." (William H Calvin, "The Cerebral Code", 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 logic of the emotional mind is associative; it takes elements that symbolize a reality, or trigger a memory of it, to be the same as that reality. That is why similes, metaphors and images speak directly to the emotional mind." (Daniel Goleman, "Emotional Intelligence", 1996)
"Ideas about organization are always based on implicit images or metaphors that persuade us to see, understand, and manage situations in a particular way. Metaphors create insight. But they also distort. They have strengths. But they also have limitations. In creating ways of seeing, they create ways of not seeing. There can be no single theory or metaphor that gives an all-purpose point of view, and there can be no simple "correct theory" for structuring everything we do. The challenge facing modern managers is to become accomplished in the art of using metaphor to find new ways of seeing, understanding, and shaping their actions." (Gareth Morgan, ”Imaginization”, 1997)
"Metaphysics in philosophy is, of course, supposed to characterize what is real - literally real. The irony is that such a conception of the real depends upon unconscious metaphors." (George Lakoff, "Philosophy in the Flesh: The Embodied Mind and its Challenge to Western Thought", 1999)
“Metaphors can have profound significance because, as images or figures, they allow the mind to grasp or discover unsuspected ideal and material relationships between objects.” (Giuseppe Del Re, “Cosmic Dance”, 1999)
"[…] philosophical theories are structured by conceptual metaphors that constrain which inferences can be drawn within that philosophical theory. The (typically unconscious) conceptual metaphors that are constitutive of a philosophical theory have the causal effect of constraining how you can reason within that philosophical framework." (George Lakoff, "Philosophy in the Flesh: The Embodied Mind and its Challenge to Western Thought", 1999)
“Metaphor is evidence of the human ability to visualize the universe as a coherent organism. Proof of our capacity, not just to see one thing in another but to change the very nature of things. When a metaphor is accepted as fact, it enters groupthink, taking on an existence in the real world. [...] Metaphor is the default form of thought, providing many angles from which to literally 'see' the world." (Marcel Danesi, "Poetic Logic: The Role of Metaphor in Thought, Language, and Culture", 2004)
“Metaphorizing is a manner of thinking, not a property of thinking. It is a capacity of thought, not its quality. It represents a mental operation by which a previously existing entity is described in the characteristics of another one on the basis of some similarity or by reasoning. When we say that something is (like) something else, we have already performed a mental operation. This operation includes elements such as comparison, paralleling and shaping of the new image by ignoring its less satisfactory traits in order that this image obtains an aesthetic value. By this process, for an instant we invent a device, which serves as the pole vault for the comparison’s jump. Once the jump is made the pole vault is removed. This device could be a lightning-speed logical syllogism, or a momentary created term, which successfully merges the traits of the compared objects.” (Ivan Mladenov, “Conceptualizing Metaphors: On Charles Peirce’s marginalia”, 2006)
"In order to understand how mathematics is applied to understanding of the real world it is convenient to subdivide it into the following three modes of functioning: model, theory, metaphor. A mathematical model describes a certain range of phenomena qualitatively or quantitatively. […] A (mathematical) metaphor, when it aspires to be a cognitive tool, postulates that some complex range of phenomena might be compared to a mathematical construction." (Yuri I Manin," Mathematics as Metaphor: Selected Essays of Yuri I. Manin" , 2007)
"Metaphor is a primary cognitive tool by which we make sense of the world." (Terry Marks-Tarlow, "Psyche's Veil: Psychotherapy, Fractals and Complexity", 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)
“The relationship of math to the real world has been a conundrum for philosophers for centuries, but it is also an inspiration for poets. The patterns of mathematics inhabit a liminal space - they were initially derived from the natural world and yet seem to exist in a separate, self-contained system standing apart from that world. This makes them a source of potential metaphor: mapping back and forth between the world of personal experience and the world of mathematical patterns opens the door to novel connections.” (Alice Major, “Mapping from e to Metaphor”, 2018)
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