But the episode underscores America's propensity for incommensurable and excessive punishment for people of color.
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Rawaa Nancy Albilal, president and chief executive of the Support Center, said that travel loans put refugee families under incommensurable stress.
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Once upon a time, the self was hermetically sealed off from the selves around it; now it is cultures that are mutually incommensurable.
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Jio undid the tyranny of flatness by introducing gradated tones into his bands, thereby melding two seemingly incommensurable vocabularies: volumetric surfaces with flat ones.
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These two presentations exemplified the kind of relationship that any democracy worthy of that name must foster and protect — one between individuals who are incommensurable, but simultaneously interdependent and equal.
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This debut novel, 12 years in the writing, is a welcome example of how fiction can have urgency, how it's still one of the greatest forms for tackling the incommensurable.
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Second, that language has become incommensurable with the Amazon-worker's experience, because she is engaged in a kind of labor so alienated from ordinary existence that it cannot really be described.
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Space serves as the transcendental horizon of what is both incommensurable and terrifying about human life; cosmological time as a structure becomes a metaphor for our own desire to outlive the Earth and, with it, our own history.
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Gowdy, the South Carolina Republican, likes to tell Gabbard that she is "the most Christlike member of Congress," a complicated sort of compliment that says something about the way we try to reconcile spiritual traditions that are ultimately incommensurable.
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From the days of Copernicus to our own time, scientists have tried to teach us humility: that our minuscule species is only a speck on a tiny planet in one of the least important galaxies of the seemingly incommensurable universe.
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Thus my own experience writing this piece has connected me to a network of writers and thinkers who help to convey these (implicit) black bodies across the thresholds of market valuation while also identifying their incommensurable cultural and aesthetic worth.
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Harping on the fact that this is what Trump is doing — that his campaign is about fear of the other, not "economic anxiety" — is true and important, but it simply reiterates the point that campaigns are in part clashes of incommensurable values.
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Taking what curators describe as the "diverse, ambiguous and often incommensurable manifestations" of art and politics, the exhibition panders to zombie millennials, confused and bewildered by the lack of alternatives under capitalism, completely tone deaf to what is clearly an emergent and divisive culture war.
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" Describing her plots as "always haunting, hypnotic, incommensurable and strange," the essayist Scott Bradfield wrote in a tribute to Ms. Wilhelm in The Los Angeles Times after her death that her books pose "deep questions about the efficacy of science, the fugue states of dreaming, the vast bland conformity of social life, and the ways that a desire for power infiltrates every human relationship.
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But this equilibrium of incommensurable interests depends on certain conditions being right: that China continues to get richer, confirming its leaders' optimism; that people on each side of the strait do not come to see each other as enemies; that Asia remains more or less stable, so the sides do not get caught up in other conflicts; and that, if the worst comes to the worst, America's armed forces will step in to keep the peace.
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His quote from the TLS (found on the Guggenheim's exhibition site for ZERO: Countdown to Tomorrow) reads in full: From the beginning we looked upon the term [ZERO] not as an expression of nihilism—or as a dada-like gag, but as a word indicating a zone of silence and of pure possibilities for a new beginning as at the countdown when rockets take off—zero is the incommensurable zone in which the old state turns into the new.
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She began the book by acknowledging: I must constantly choose among competing and apparently incommensurable goods and that circumstances may force me to a position in which I cannot help being false to something or doing something wrong; that an event that simply happens to me may, without my consent, alter my life; that it is equally problematic to entrust one's good to friends, lovers, or country and to try to have a good life without them—all these I take to be not just the material of tragedy, but everyday facts of practical wisdom.
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"Incommensurable Ontologies and the Return of the Witness in Neil Gaiman's 1602." ImageTexT 4.1.
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It is an assumption that comes from the necessity of establishing a peaceful coexistence amongst diverse and, sometimes, incommensurable identities.
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Ahui, together with aheia, ahi and ahu, belongs to a group of words that express incommensurable joy, esteem and similar positive attitudes.
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A more general notion of incommensurability has been applied to the sciences at the meta-level in two significant ways. Eric Oberheim and Paul Hoyningen-Huene argue that realist and anti-realist philosophies of science are also incommensurable, thus scientific theories themselves may be meta-incommensurable. Similarly, Nicholas Best describes a different type of incommensurability between philosophical theories of meaning. He argues that if the meaning of a first-order scientific theory depends on its second-order theory of meaning, then two first order theories will be meta-incommensurable if they depend on substantially different theories of meaning.
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One must not, however, use different possible referential objects in the same translation, because they are incommensurable and the resulting translation hypothesis would contain logical fallacies.
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In each right triangle, Pythagoras's theorem establishes the length of the hypotenuse in terms of this unit. If a hypotenuse is related to the unit by the square root of a positive integer that is not a perfect square, it is a realization of a length incommensurable with the unit, such as , , . For more detail, see Quadratic irrational. Incommensurable lengths conflicted with the Pythagorean school's concept of numbers as only whole numbers.
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That is, there is a common unit of length in terms of which a and b can both be measured; this is the origin of the term. Otherwise the pair a and b are incommensurable.
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He proved that no two concepts or products could be the same because of their different histories. He called this the "No Doppelgangers" clause or edict. Later he reflected "Time is incommensurable for Actors".Gordon Pask (1996).
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If a particular paradigm cannot solve an anomaly, a crisis in science may result. An existing paradigm may be superseded by a rival paradigm. There may be no common measure for assessing the competing scientific theories. They are 'incommensurable'.
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Analytic geometry continues to be a mainstay of pre-calculus and calculus curriculum. Another important area of application is number theory. In ancient Greece the Pythagoreans considered the role of numbers in geometry. However, the discovery of incommensurable lengths contradicted their philosophical views.
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He gathered a group of students around him to study mathematics, music, and philosophy, and together they discovered most of what high school students learn today in their geometry courses. In addition, they made the profound discovery of incommensurable lengths and irrational numbers.
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Br. with a monograph, Hermeneutics Between Philosophy and Theology: The Imperative to Think the Incommensurable. After obtaining a venia legendi in Philosophy of Religion, Wiercinski was 2007-2012 Privatdozent before becoming in 2012 ausserplanmäßiger Professor (Professor extra numerum) of Philosophy of Religion at the Albert-Ludwigs-Universität Freiburg, Germany.
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The spiral of Theodorus: A construction for line segments with lengths whose ratios are the square root of a positive integer One of the consequences of the Pythagorean theorem is that line segments whose lengths are incommensurable (so the ratio of which is not a rational number) can be constructed using a straightedge and compass. Pythagoras's theorem enables construction of incommensurable lengths because the hypotenuse of a triangle is related to the sides by the square root operation. The figure on the right shows how to construct line segments whose lengths are in the ratio of the square root of any positive integer. Each triangle has a side (labeled "1") that is the chosen unit for measurement.
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"Jean Francois Lyotard." Key contemporary social theorists. 2003. Malden, MA: Blackwell Publishers, 211. In Lyotard's works, the term 'language games', sometimes also called 'phrase regimens', denotes the multiplicity of communities of meaning, the innumerable and incommensurable separate systems in which meanings are produced and rules for their circulation are created.
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The Pythagorean school dealt with proportions by comparison of integer multiples of a common subunit. According to one legend, Hippasus of Metapontum (ca. 470 B.C.) was drowned at sea for making known the existence of the irrational or incommensurable. ; Hippasus was on a voyage at the time, and his fellows cast him overboard.
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The Pythagoreans are credited with the proof of the existence of irrational numbers. When the ratio of the lengths of two line segments is irrational, the line segments themselves (not just their lengths) are also described as being incommensurable. A separate, more general and circuitous ancient Greek doctrine of proportionality for geometric magnitude was developed in Book V of Euclid's Elements in order to allow proofs involving incommensurable lengths, thus avoiding arguments which applied only to a historically restricted definition of number. Euclid's notion of commensurability is anticipated in passing in the discussion between Socrates and the slave boy in Plato's dialogue entitled Meno, in which Socrates uses the boy's own inherent capabilities to solve a complex geometric problem through the Socratic Method.
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From the point of view of Planck units, this is comparing apples with oranges, because mass and electric charge are incommensurable quantities. Rather, the disparity of magnitude of force is a manifestation of the fact that the charge on the protons is approximately the unit charge but the mass of the protons is far less than the unit mass.
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This allowed scientists, policy makers, and others of cultural influence to promulgate a belief in the gender binary under a veil of positivism and scientific enlightenment. Since the eighteenth century, the dominant view of sexual difference has been that of two stable, incommensurable, and opposite sexes on which the political, economic, and cultural lives of men and women are based and social order is sustained. Contrary to modern day, "the dominant discourse construed the male and female bodies as hierarchically, vertically, ordered versions of one sex" rather than as "horizontally ordered opposites, as incommensurable." In fact, it wasn't until the second half of the eighteenth century that the idea of two distinct sexes was established and, through the politics of the day, generated new ways of understanding people and social reality.
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This provides a value of π ≈ = 3.1416, using it to calculate an approximation of the Earth's circumference. Aryabhata stated that his result "approximately" (' "approaching") gave the circumference of a circle. His 15th-century commentator Nilakantha Somayaji (Kerala school of astronomy and mathematics) has argued that the word means not only that this is an approximation, but that the value is incommensurable (irrational).
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Kuhn's Structure provides important accounts related to the concept representation, and the key conceptual changes that occur during a scientific revolution. Kuhn sought to determine ways of representing concepts and taxonomies by frames.Barker, Peter, Xiang Chen and Hanne Andersen (2003) "Kuhn on Concepts and Categorization" in Thomas Kuhn, edited by Thomas Nickles, Cambridge University Press Kuhn's work attempts to show that incommensurable paradigms can be rationally compared by revealing the compatibility of attribute lists of say a species outlined in a pre- Darwinian and a post-Darwinian milieu accounted for in two incommensurable taxonomies, and that this compatibility is the platform for rational comparison between rival taxonomies. With a view to comparing normal science to revolutionary science, Kuhn illustrates his theory of paradigms and theory of concepts within the history of electricity, chemistry and other disciplines.
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Both Haugen and Weinreich considered the use of phonemes beyond a single language to be inappropriate when phonemic systems between languages were incommensurable with each other. reiterates this point when he says, > "Since each state is a system consisting of members solely defined by their > mutual relations, any two non-identical systems must necessarily be > incommensurable, for no element in one can be identified with any element in > the other. ...structurally we cannot identify or even compare any Spanish > vowel-phoneme with any Italian vowel-phoneme, because a member of a 5-vowel > system is intrinsically different from a member of a 7-term system." Similarly, , argues that phonemic representations may lead to confusion when dealing with phonological interference and remarks that narrow phonetic transcription can be cumbersome, especially when discussing other grammatical features like syntax and morphology.
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The part which nature has in any work of man, is > indefinite and incommensurable. It is impossible to decide that in any one > thing nature does more than in any other. One cannot even say that labour > does less. Less labour may be required; but if that which is required is > absolutely indispensable, the result is just as much the product of labour, > as of nature.
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If physical quantities have different dimensions (such as length vs. mass), they cannot be expressed in terms of similar units and cannot be compared in quantity (also called incommensurable). For example, asking whether a kilogram is larger than an hour is meaningless. Any physically meaningful equation (and any inequality) will have the same dimensions on its left and right sides, a property known as dimensional homogeneity.
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The Elements ( Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics.
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However, the philosopher Donald Davidson published a highly regarded essay in 1974, "On the Very Idea of a Conceptual Scheme" (Proceedings and Addresses of the American Philosophical Association, Vol. 47, (1973-1974), pp. 5–20) arguing that the notion that any languages or theories could be incommensurable with one another was itself incoherent. If this is correct, Kuhn's claims must be taken in a weaker sense than they often are.
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There seems to be a radical fault in the very notion of a contest that can not by its nature be won or lost. (Gray, 1999, p. 96) #Any assertion that "essentially contested" concepts are incommensurable made at the same time as an assertion that "they have any common subject-matter" is incoherent; and, also, it reveals an "inconsistency in the idea of essential contestability".Gray (1999), p. 96.
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This approximation is the seventh in a sequence of increasingly accurate approximations based on the sequence of Pell numbers, which can be derived from the continued fraction expansion of . Despite having a smaller denominator, it is only slightly less accurate than the Babylonian approximation. Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational.
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He argues that different knowledges are connected with different livelihoods and lifestyles and should therefore be treated equally. Cognitive justice is a critique on the dominant paradigm of modern scienceSantos, Boaventura de Sousa (ed) (2007). "Cognitive Justice in a Global World: Prudent knowledges for a decent life". Lanham: Lexington and promotes the recognition of alternative paradigms or alternative sciences by facilitating and enabling dialogue between, often incommensurable, knowledges.
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The analytic method is ascribed to Plato, while a formula for obtaining Pythagorean triples bears his name. Eudoxus (408–c. 355 BC) developed the method of exhaustion, a precursor of modern integration and a theory of ratios that avoided the problem of incommensurable magnitudes. The former allowed the calculations of areas and volumes of curvilinear figures, while the latter enabled subsequent geometers to make significant advances in geometry.
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The 20th century philosopher Martin Heidegger suggested that subjective experience and activity (i.e. the "mind") cannot be made sense of in terms of Cartesian "substances" that bear "properties" at all (whether the mind itself is thought of as a distinct, separate kind of substance or not). This is because the nature of subjective, qualitative experience is incoherent in terms of – or semantically incommensurable with the concept of – substances that bear properties. This is a fundamentally ontological argument.
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According to this school of thought, each ethnic group has a distinct worldview that is incommensurable with the worldviews of other groups. Although more inclusive than earlier views, this approach to culture still allowed for distinctions between "civilized" and "primitive" or "tribal" cultures. In 1860, Adolf Bastian (1826–1905) argued for "the psychic unity of mankind." He proposed that a scientific comparison of all human societies would reveal that distinct worldviews consisted of the same basic elements.
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Tidal constituents combine to give an endlessly varying aggregate because of their different and incommensurable frequencies: the effect is visualized in an animation of the American Mathematical Society illustrating the way in which the components used to be mechanically combined in the tide-predicting machine. Amplitudes of tidal constituents are given below for six example locations: Eastport, Maine (ME), Biloxi, Mississippi (MS), San Juan, Puerto Rico (PR), Kodiak, Alaska (AK), San Francisco, California (CA), and Hilo, Hawaii (HI).
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In the second appendix of Against Method (p. 114), Feyerabend states, "I never said... that any two rival theories are incommensurable... What I did say was that certain rival theories, so-called 'universal' theories, or 'non-instantial' theories, if interpreted in a certain way, could not be compared easily." Incommensurability did not concern Feyerabend greatly, because he believed that even when theories are commensurable (i.e. can be compared), the outcome of the comparison should not necessarily rule out either theory.
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To rephrase: when theories are incommensurable, they cannot rule each other out, and when theories are commensurable, they cannot rule each other out. Assessments of (in)commensurability, therefore, don't have much effect in Feyerabend's system, and can be more or less passed over in silence. In Against Method Feyerabend claimed that Imre Lakatos's philosophy of research programmes is actually "anarchism in disguise", because it does not issue orders to scientists. Feyerabend playfully dedicated Against Method to "Imre Lakatos: Friend, and fellow-anarchist".
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Kuhn pointed out that it could be difficult to assess whether a particular paradigm shift had actually led to progress, in the sense of explaining more facts, explaining more important facts, or providing better explanations, because the understanding of "more important", "better", etc. changed with the paradigm. The two versions of reality are thus incommensurable. Kuhn's version of incommensurability has an important psychological dimension; this is apparent from his analogy between a paradigm shift and the flip-over involved in some optical illusions.
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Therefore, opponents of GPI claim that GPI cannot function to measure the goals of a diverse, plural society. Supporters of GDP as a measure of societal well-being claim that competing measures such as GPI are more vulnerable to political manipulation. Finnish economists Mika Maliranta and Niku Määttänen write that the problem of alternative development indexes is their attempt to combine things that are incommensurable. It is hard to say what they exactly indicate and difficult to make decisions based on them.
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Whose Justice? Which Rationality?, 361–362. MacIntyre's account also defends three further theses: first, that all rational human inquiry is conducted whether knowingly or not from within a tradition; second, that the incommensurable conceptual schemes of rival traditions do not entail either relativism or perspectivism; third, that although the arguments of the book are themselves attempts at universally valid insights they are nevertheless given from within a particular tradition (that of Thomist Aristotelianism) and that this need not imply any philosophical inconsistency.
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Thelema roughly means "will" in Greek. The phrase True Will does not appear in The Book of the Law, the central sacred text of Thelema. Nevertheless, Aleister Crowley's various commentaries on the Book routinely postulate that each individual has a unique and incommensurable True Will that determines his or her proper course in life. Crowley's invention appears to be an attempt to explain how some actions may be wrong (or "false") when "There is no law beyond Do what thou wilt".
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Foam in an egg carton which simulates the atomic surface structure of graphite, commensurable due to alignment in this photo Incommensurable due to twisting, so the valleys and hills don't line up Superlubricity is a regime of motion in which friction vanishes or very nearly vanishes. What is a "vanishing" friction level is not clear, which makes the term superlubricity quite vague. As an ad hoc definition, a kinetic coefficient of friction less than 0.01 can be adopted. This definition also requires further discussion and clarification.
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5–20) in 1974 arguing that the notion that any languages or theories could be incommensurable with one another was itself incoherent. If this is correct, Kuhn's claims must be taken in a weaker sense than they often are. Furthermore, the hold of the Kuhnian analysis on social science has long been tenuous, with the wide application of multi-paradigmatic approaches in order to understand complex human behaviour (see for example John Hassard, Sociology and Organization Theory: Positivism, Paradigm and Postmodernity. Cambridge University Press, 1993, ).
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Theodorus had explored the theory of incommensurable quantities, and Theaetetus continued those studies with great enthusiasm; specifically, he classified various forms of irrational numbers according to the way they are expressed as square roots. This theory is presented in great detail in Book X of Euclid's Elements. Theaetetus was one of the few Greek mathematicians who was actually a native of Athens. Most Greek mathematicians of antiquity came from the numerous Greek cities scattered around the Ionian coast, the Black Sea and the whole Mediterranean basin.
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The most basic rule of dimensional analysis is that of dimensional homogeneity. :: Only commensurable quantities (physical quantities having the same dimension) may be compared, equated, added, or subtracted. However, the dimensions form an abelian group under multiplication, so: :: One may take ratios of incommensurable quantities (quantities with different dimensions), and multiply or divide them. For example, it makes no sense to ask whether 1 hour is more, the same, or less than 1 kilometre, as these have different dimensions, nor to add 1 hour to 1 kilometre.
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Further, every resultant is clearly traceable in > its components, because these are homogeneous and commensurable. It is > otherwise with emergents, when, instead of adding measurable motion to > measurable motion, or things of one kind to other individuals of their kind, > there is a co-operation of things of unlike kinds. The emergent is unlike > its components insofar as these are incommensurable, and it cannot be > reduced to their sum or their difference. In 1999, economist Jeffrey Goldstein provided a current definition of emergence in the journal Emergence.
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An apple and an orange Apples and Oranges, by Paul Cézanne. A comparison of apples and oranges occurs when two items or groups of items are compared that cannot be practically compared. The idiom, comparing apples and oranges, refers to the apparent differences between items which are popularly thought to be incomparable or incommensurable, such as apples and oranges. The idiom may also be used to indicate that a false analogy has been made between two items, such as where an apple is faulted for not being a good orange.
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The space that is to be established anew between philosophy and theology thanks to the contemplation of the incommensurable is an invitation to hermeneutics. That which happens in the no-man’s land between the two disciplines is hermeneutics and can only be hermeneutics. It is a hermeneutics between the courage to inquire and the humility to listen. Wiercinski claims no final judgment regarding the single proper connection of philosophy and theology, but attempts rather to show another way, a way that is to negotiate between the two disciplines.
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The proof that the square root of 2 () is irrational (i.e. cannot be expressed as a fraction of two whole numbers) was discovered by the ancient Greeks, and is perhaps the earliest known example of a proof by infinite descent. Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational. Little is known with certainty about the time or circumstances of this discovery, but the name of Hippasus of Metapontum is often mentioned.
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In ethics, value pluralism (also known as ethical pluralism or moral pluralism) is the idea that there are several values which may be equally correct and fundamental, and yet in conflict with each other. In addition, value-pluralism postulates that in many cases, such incompatible values may be incommensurable, in the sense that there is no objective ordering of them in terms of importance. Value pluralism is opposed to value monism. Value- pluralism is a theory in metaethics, rather than a theory of normative ethics, or a set of values in itself.
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Using this model it can be shown, for example, that the origin of the unusual ground insulating ferromagnetic state of a solid like K2CuF4 can be traced to its orbital ordering. Even when starting from a relatively high-symmetry structure the combined effect of exchange interactions, spin-orbit coupling, orbital- ordering and crystal deformations activated by the JTE can lead to very low symmetry magnetic patterns with specific properties. For example, in CsCuCl3 an incommensurable helicoidal pattern appears both for the orbitals and the distortions along the z-axis. Moreover, many of these compounds show complex phase diagrams when varying temperature or pressure.
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If lattices are incommensurable, friction was not observed, however, if the surfaces are commensurable, friction force is present. At the atomic level, these tribological properties are directly connected with superlubricity. An example of this is given by solid lubricants, such as graphite, MoS2 and Ti3SiC2: this can be explained with the low resistance to shear between layers due to the stratified structure of these solids. Even if at the macroscopic scale friction involves multiple microcontacts with different size and orientation, basing on these experiments one can speculate that a large fraction of contacts will be in superlubric regime.
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Political Liberalism. Columbia University Press, 1993, pp. 134–49. The overlapping consensus could in sum be said to “depend, in effect, on there being a morally significant core of commitments common to the ‘reasonable’ fragment of each of the main comprehensive doctrines in the community”D'Agostino, Fred, "Original Position", The Stanford Encyclopedia of Philosophy (Summer 2003 Edition), Edward N. Zalta (ed.). It has been argued that reasonable forms of religious and moral public education may be agreed by considering which common values and principles may be determined through overlapping consensus between those of otherwise incommensurable comprehensive doctrines (e.g.
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These earlier Greek ideas of numbers were later upended by the discovery of the irrationality of the square root of two. Hippasus, a disciple of Pythagoras, showed that the diagonal of a unit square was incommensurable with its (unit-length) edge: in other words he proved there was no existing (rational) number that accurately depicts the proportion of the diagonal of the unit square to its edge. This caused a significant re- evaluation of Greek philosophy of mathematics. According to legend, fellow Pythagoreans were so traumatized by this discovery that they murdered Hippasus to stop him from spreading his heretical idea.
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48–50 Eudoxus introduced the idea of non-quantified mathematical magnitude to describe and work with continuous geometrical entities such as lines, angles, areas and volumes, thereby avoiding the use of irrational numbers. In doing so, he reversed a Pythagorean emphasis on number and arithmetic, focusing instead on geometrical concepts as the basis of rigorous mathematics. Some Pythagoreans, such as Eudoxus's teacher Archytas, had believed that only arithmetic could provide a basis for proofs. Induced by the need to understand and operate with incommensurable quantities, Eudoxus established what may have been the first deductive organization of mathematics on the basis of explicit axioms.
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In the 1920s, Neurath debated these matters with leading Social Democratic theoreticians (such as Karl Kautsky, who insisted that money is necessary in a socialist economy). While serving as a government economist during the war, Neurath had observed that "As a result of the war, in-kind calculus was applied more often and more systematically than before.... war was fought with ammunition and with the supply of food, not with money" i.e. that goods were incommensurable. This convinced Neurath of the feasibility of economic planning in terms of amounts of goods and services, without use of money.
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In Morgenthau's early career, the book review of his dissertation by Carl Schmitt had a lasting and negative effect on Morgenthau. Schmitt had become a leading juristic voice for the rising Nazi movement in Germany and Morgenthau came to see their positions as incommensurable, although it has been argued that Schmitt and Morgenthau engaged in a "hidden dialogue" in which they influenced each other.See W. Scheuerman, "Carl Schmitt and Hans Morgenthau: Realism and Beyond" (see note 3). See also Hans-Karl Pichler, "The Godfathers of 'Truth': Max Weber and Carl Schmitt in Morgenthau's Theory of Power Politics," Review of International Studies, 1998, v.
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Frank Ninkovich writes: :As for the two cold wars thesis, the chief problem is that the two periods are incommensurable. To be sure, they were joined together by enduring ideological hostility, but in the post-World War I years Bolshevism was not a geopolitical menace. After World War II, in contrast, the Soviet Union was a superpower that combined ideological antagonism with the kind of geopolitical threat posed by Germany and Japan in the Second World War. Even with more amicable relations in the 1920s, it is conceivable that post-1945 relations would have turned out much the same.
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To explain this phenomenon Kerner developed a microscopic theory of the S → F instability. None of the classical traffic flow theories and models incorporate the S → F instability of the three-phase theory. The basic result of the three-phase theory about the nucleation nature of traffic breakdown (F → S transition) shows that the three-phase theory is incommensurable with all earlier traffic flow theories and models (see explanations below). As mentioned, the main reason of Kerner’s three-phase traffic theory is the explanation of the empirical nucleation nature of traffic breakdown (F → S transition) at the bottleneck.
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Simmel's outlook, while gloomy, is not wholly negative. As money and transactions increase, the independence of an individual decreases as he or she is drawn into a holistic network of exchange governed by quantifiable monetary value. Paradoxically, this results in greater potential freedom of choice for the individual, as money can be deployed toward any possible goal, even if most people's sheer lack of money renders that potential quite low much of the time. Money's homogenizing nature encourages greater liberty and equality and melts away forms of feudalism and patronage, even as it minimizes exceptional, incommensurable achievements in art and love.
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It is also suggested that Aryabhata (5th century AD), in calculating a value of pi to 5 significant figures, used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). Later, in their treatises, Indian mathematicians wrote on the arithmetic of surds including addition, subtraction, multiplication, rationalization, as well as separation and extraction of square roots. Mathematicians like Brahmagupta (in 628 AD) and Bhāskara I (in 629 AD) made contributions in this area as did other mathematicians who followed. In the 12th century Bhāskara II evaluated some of these formulas and critiqued them, identifying their limitations.
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These claims of relativism are, however, tied to another claim that Kuhn does at least somewhat endorse: that the language and theories of different paradigms cannot be translated into one another or rationally evaluated against one another—that they are incommensurable. This gave rise to much talk of different peoples and cultures having radically different worldviews or conceptual schemes—so different that whether or not one was better, they could not be understood by one another. However, the philosopher Donald Davidson published the highly regarded essay "On the Very Idea of a Conceptual Scheme" (Proceedings and Addresses of the American Philosophical Association, Vol. 47, (1973–1974), pp.
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This interpretation is supported by Whorf's subsequent statement that "No individual is free to describe nature with absolute impartiality, but is constrained by certain modes of interpretation even when he thinks himself most free". Similarly the statement that observers are led to different pictures of the universe has been understood as an argument that different conceptualizations are incommensurable making translation between different conceptual and linguistic systems impossible. Neo-Whorfians argue this to be a misreading since throughout his work one of his main points was that such systems could be "calibrated" and thereby be made commensurable, but only when we become aware of the differences in conceptual schemes through linguistic analysis.
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The scientists reinterpret ambiguous data, discard anomalous data, and try to stuff nature into the box of their shared paradigm—a theoretical matrix or fundamental view of nature—until compatible data become scarce, anomalies accumulate, and scientific "crisis" ensues. Newly training, some young scientists defect to revolutionary science, which, simultaneously explaining both the normal data and the anomalous data, resolves the crisis by setting a new "exemplar" that contradicts normal science. Kuhn explains that rival paradigms, having incompatible languages, are incommensurable. Trying to resolve conflict, scientists talk past each other, as even direct observations—for example, that the Sun is "rising"—get fundamentally conflicting interpretations.
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"The Incommensurability of Scientific Theories" in The Stanford Encyclopedia of Philosophy. "...he had developed his notion of the incommensurability of scientific theories more than ten years prior to the appearance of Kuhn's Structure of Scientific Revolutions (1962)" which lays the foundation for much of his philosophy of science. He first presented his notion of incommensurability in 1952 to Karl Popper's London School of Economics seminar and to a gathering of illustrious Wittgensteinians (Elizabeth Anscombe, Peter Geach, H. L. A. Hart and Georg Henrik von Wright) in Anscombe's Oxford flat. Feyerabend argued that frameworks of thought, and thus scientific paradigms, can be incommensurable for three reasons.
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While the foundation of Narrative Identity Theory is the holding together of life experiences in a unified structure, Internarrative Identity Theory celebrates what have previously been considered problematic areas of experience - conflict, marginalization, disruption, subversion, deviation - as places of possibility for self creation. Internarrative Identity Theory locates the solution of narrative conflict within the problem itself. Existence in-between authoritarian discourses and dominant cultures enables an extended form of agency wherein a subject is able to undermine traditional associations, assumptions, concepts, and at the same time, create links between otherwise incommensurable world views. Rather than being a passive recipient of dominant discourses the Internarrative subject is uniquely able to subvert regulatory identity practices.
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This leads to there being a fundamental, incremental, and referential structure of development which is not relative but again, fundamental. :From these remarks, one thing is however certain: Kuhn is not saying that incommensurable theories cannot be compared - what they can’t be is compared in terms of a system of common measure. He very plainly says that they can be compared, and he reiterates this repeatedly in later work, in a (mostly in vain) effort to avert the crude and sometimes catastrophic misinterpretations he suffered from mainstream philosophers and post-modern relativists alike.Sharrock. W., Read R. Kuhn: Philosopher of Scientific Revolutions But Thomas Kuhn denied the accusation of being a relativist later in his postscript.
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The change in focus by Eudoxus stimulated a divide in mathematics which lasted two thousand years. In combination with a Greek intellectual attitude unconcerned with practical problems, there followed a significant retreat from the development of techniques in arithmetic and algebra. The Pythagoreans had discovered that the diagonal of a square does not have a common unit of measurement with the sides of the square; this is the famous discovery that the square root of 2 cannot be expressed as the ratio of two integers. This discovery had heralded the existence of incommensurable quantities beyond the integers and rational fractions, but at the same time it threw into question the idea of measurement and calculations in geometry as a whole.
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But, if we come across a theory T' in which Class S is empty then the theories are incommensurable with each other. However, Feyerabend clarifies this by stating that, incommensurability between T and T' will depend on the interpretation given to the theories. If this is instrumental, every theory that refers to the same language of observation will be commensurable. In the same way, if a realist perspective is sought then it will favour a unified position which employs the most highly abstracted terms of whatever theory is being considered in order to describe both theories, giving a significance to the observational statements as a function of these terms, or, at least to replace the habitual use they are given.
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"The three dimensions of sensorial volume", Gleizes would write in 1925, "left open the field for the introduction of the time factor".Albert Gleizes, "Cubisme", Vers une conscience plastique, Essai de généralisation, 1925, in Bulletin de l'Effort Moderne, 22–32, February 1926–Feb 1927. Also published in La Vie des Lettres et des Arts, May 1925 (written as part of the Bauhaus book, Kubismus). See too Peter Brooke, Albert Gleizes: For and Against the Twentieth Century, 2001, "The diversity of the relations of line to line must be indefinite;" write Gleizes and Metzinger, "on this condition it incorporates quality, the incommensurable sum of the affinities perceived between that which we discern and that which pre-exists within us: on this condition a work of art is able to move us".
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In mathematics and theoretical physics, quasiperiodic motion is in rough terms the type of motion executed by a dynamical system containing a finite number (two or more) of incommensurable frequencies. That is, if we imagine that the phase space is modelled by a torus T (that is, the variables are periodic like angles), the trajectory of the system is modelled by a curve on T that wraps around the torus without ever exactly coming back on itself. A quasiperiodic function on the real line is the type of function (continuous, say) obtained from a function on T, by means of a curve :R -> T which is linear (when lifted from T to its covering Euclidean space), by composition. It is therefore oscillating, with a finite number of underlying frequencies.
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Unlike some analytic philosophers who try to generate moral consensus on the basis of rationality, MacIntyre uses the historical development of ethics to circumvent the modern problem of "incommensurable" moral notions, whose merits cannot be compared in any common framework. Following Hegel and Collingwood, he offers a "philosophical history" (as opposed to analytical and phenomenological approaches) in which he concedes from the beginning that "there are no neutral standards available by appeal to which any rational agent whatsoever could determine" the conclusions of moral philosophy.After Virtue, 3, xiii. In his most famous work, After Virtue, he deprecates the attempt of Enlightenment thinkers to deduce a universal rational morality independent of teleology, whose failure led to the rejection of moral rationality altogether by successors such as Friedrich Nietzsche, Jean-Paul Sartre, and Charles Stevenson.
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Commensurability is a concept in the philosophy of science whereby scientific theories are commensurable if scientists can discuss them using a shared nomenclature that allows direct comparison of theories to determine which theory is more valid or useful. On the other hand, theories are incommensurable if they are embedded in starkly contrasting conceptual frameworks whose languages do not overlap sufficiently to permit scientists to directly compare the theories or to cite empirical evidence favoring one theory over the other. Discussed by Ludwik Fleck in the 1930s,Ludwik Fleck (Stanford Encyclopedia of Philosophy); Fleck's term for incommensurability was "niewspółmierność". and popularized by Thomas Kuhn in the 1960s, the problem of incommensurability results in scientists talking past each other, as it were, while comparison of theories is muddled by confusions about terms, contexts and consequences.
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The party declared its will to participate in the elections but only whilst keeping its "revolutionary purpose" of overthrowing "bourgeois democracy" well in mind.Mihael Sobolevski, Luciano Giuricin, Il Partito Comunista di Fiume, (1921–1924): Documenti-Građa, Centro di ricerche storiche Rovigno, Fiume: Centar za historiju radničkog pokreta i NOR-a Istre, 1982, p. 24. Simon declared that the Socialist Party ceased to exist and in its place the Communist Party of the Free State of Fiume (Partito Comunista dello Stato libero di Fiume) was constituted. The unitarian socialists were put on a defensive: although they accepted the 21 points and promised not to infringe the unity of the United Proletarian Front, given the "incommensurable difficulties" of organizing a proletarian party in a bilingual environment, the name Socialist Party had to be retained.
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Some valid knowledge is lost through the passage of time, and other knowledge is gained, with the result that the non-science fields do not make scientific progress towards understanding their subject areas. From the 18th century through late 20th century, the history of science, especially of the physical and biological sciences, was often presented as a progressive accumulation of knowledge, in which true theories replaced false beliefs. Some more recent historical interpretations, such as those of Thomas Kuhn, tend to portray the history of science in terms of competing paradigms or conceptual systems in a wider matrix of intellectual, cultural, economic and political trends. These interpretations, however, have met with opposition for they also portray the history of science as an incoherent system of incommensurable paradigms, not leading to any scientific progress, but only to the illusion of progress.
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Thomas Samuel Kuhn (; July 18, 1922 – June 17, 1996) was an American philosopher of science whose 1962 book The Structure of Scientific Revolutions was influential in both academic and popular circles, introducing the term paradigm shift, which has since become an English-language idiom. Kuhn made several claims concerning the progress of scientific knowledge: that scientific fields undergo periodic "paradigm shifts" rather than solely progressing in a linear and continuous way, and that these paradigm shifts open up new approaches to understanding what scientists would never have considered valid before; and that the notion of scientific truth, at any given moment, cannot be established solely by objective criteria but is defined by a consensus of a scientific community. Competing paradigms are frequently incommensurable; that is, they are competing and irreconcilable accounts of reality. Thus, our comprehension of science can never rely wholly upon "objectivity" alone.
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Along with a number of mid-20th century philosophers (most notably, Wilfrid Sellars, Willard Van Orman Quine, and Richard Rorty), Feyerabend was influential in the development of eliminative materialism, a radical position in the philosophy of mind that holds that our ordinary, common-sense understanding of the mind (what materialist monists call "folk psychology") is false. It is succinctly described by a modern proponent, Paul Churchland, as follows: : "Eliminative materialism is the thesis that our commonsense conception of psychological phenomena constitutes a radically false theory, a theory so fundamentally defective that both the principles and the ontology of that theory will eventually be displaced, rather than smoothly reduced, by completed neuroscience." In three short papers published in the early sixties, Feyerabend sought to defend materialism against the supposition that the mind cannot be a physical thing. Feyerabend suggested that our commonsense understanding of the mind was incommensurable with the (materialistic) scientific view, but that nevertheless we ought to prefer the materialistic one on general methodological grounds.
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Wiercinski has generated research accomplishments in his subject areas that demonstrate his scholarly expertise both in the range of his works as well as in their broad, contentful composition. He understands hermeneutics as a specific mind-set of openness that admits of neither a priori nor apodictic demarcations between domains of knowledge, but instead sits decidedly between them in order to overcome the compartmentalization of knowledge forms from each other. Despite the postmodern format of this hermeneutic in-between — which of course will not be raised to a trans- regional, conceptually achievable absolutism — Wiercinski positions hermeneutics within the horizon of man’s unmistakable ability to attain truth, which actualizes itself in the history of knowledge and its forms. He understands philosophy of religion as the hermeneutic mediation between the incommensurable knowledge forms of religion/theology and philosophy, which are not separated off from one another but rather allude to one another both genealogically and constitutively.
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If two material things are combined, the dual Measures of the one are added to those of the other. The degree to which they exhibit self- preservation is registered in the internal Measure—weight in this case—which ends up being equal, after combination, to the sum of the original two Measures; the degree to which they exhibit Qualitative alteration is registered in the external Measure—space in this case—which does not necessarily result in a sum equal to its parts, but often in the case of material substances exhibits a diminution in overall volume. If we adopt the constant of one specific Real Measure as our Unit, the constants of other Real Measures can be brought into relation to it as Amounts in a (b) series of Measure relations. Since it is arbitrary which one Real Measure in such a series will serve as the Unit, there are as many incommensurable series of Measure relations as there are individual Real Measures.
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However, when two Real Measures, which are themselves ratios, are combined, the result is a new ratio of those ratios, itself designated by a constant in the form of a Quantum. If this constant is adopted as the Unit, instead of an individual Real Measure, then what were two incommensurable series are now made commensurable with each other in a common denominator. Since each Real Measure within a series forms such a constant with every other member in that series, any individual series in which a particular Real Measure serves as the Unit can be made commensurable with any other series with a different Real Measure as Unit. Since it is a thing’s Real Measure that determines its specific Quality, and since that Real Measure is in turn derived from the Quantitative relation it has with other Real Measures in the form of a series of constants, it would appear that, as in Determinate Being above, Quality is only relative and externally determined.
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Fish discussed Nelson's concepts within the framework of changing viewpoints on free speech through varying mediums of communication including online fora and speech in other venues: "How to weigh these elements also figures in Nelson's consideration of the Internet with its capacity for international communications—how to weigh the intent of an Internet speaker against an unintended hostile foreign audience shielded by its own local laws or even remote, but culturally distinctive, domestic audiences for that matter". He posits that Nelson's plurality theory contains elements which would impact free speech in the future: "What Nelson terms 'incommensurable values' embedded in remote legal cultures not perceived by the speaker requires close attention to context, speaker's intention or lack thereof, and 'uptake' on the part of distant audiences. His is indeed a theory fraught with possibilities both favorable and unfavorable to an expanded scope for the contents of free speech". Professor Steven B. Lichtman of the department of political science at the University of Vermont reviewed the book for the Law and Politics Book Review, and identified Nelson's pluralist theory as a significant contribution.
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A whole number of just perfect fifths will never add up to a whole number of octaves, because they are incommensurable (see Fundamental theorem of arithmetic). If a stacked-up whole number of perfect fifths is to close with the octave, then one of the intervals that is enharmonically equivalent to a fifth must have a different width than the other fifths. For example, to make a 12-note chromatic scale in Pythagorean tuning close at the octave, one of the fifth intervals must be lowered ("out-of-tune") by the Pythagorean comma; this altered fifth is called a wolf fifth because it sounds similar to a fifth in its interval size and seems like an out-of-tune fifth. However, it really is a Pythagorean diminished sixth (or an augmented third instead of a fourth), say the interval between C and E. Wolf intervals are an artifact of keyboard design. This can be shown most easily using an isomorphic keyboard, such as that shown in Figure 2. Fig.
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Heath, p. 112 The Pythagoreans' conception of number included only what would today be called rational numbers, casting doubt on the validity of the theory in geometry where, as the Pythagoreans also discovered, incommensurable ratios (corresponding to irrational numbers) exist. The discovery of a theory of ratios that does not assume commensurability is probably due to Eudoxus of Cnidus. The exposition of the theory of proportions that appears in Book VII of The Elements reflects the earlier theory of ratios of commensurables.Heath, p. 113 The existence of multiple theories seems unnecessarily complex to modern sensibility since ratios are, to a large extent, identified with quotients. However, this is a comparatively recent development, as can be seen from the fact that modern geometry textbooks still use distinct terminology and notation for ratios and quotients. The reasons for this are twofold: first, there was the previously mentioned reluctance to accept irrational numbers as true numbers, and second, the lack of a widely used symbolism to replace the already established terminology of ratios delayed the full acceptance of fractions as alternative until the 16th century.
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In a symposium in Studies in Emergent Order devoted to the book, Skoble added: "Chartier's argument demonstrates not only that natural law theory is compatible with spontaneous order theory, but also that what this confluence points to is a voluntary, polycentric legal order. The book is thus valuable not only for offering a robust defense of polycentrism, but for doing so in a way that ties together two important threads from the liberal tradition, natural law and spontaneous order, and in doing so, enhances our understanding of both."Aeon J. Skoble, "Natural Law and Spontaneous Order in the Work of Gary Chartier ," Studies in Emergent Order 7 (2014): 311-12. Also writing in the symposium, Jason Brennan criticized Chartier's reliance on the controversial new natural law theory and objected to his embrace of the theory's view that basic aspects of well being are incommensurable, a view Brennan suggested led to counterintuitive, implausible conclusions.Jason Brennan, "Controversial Ethics as a Foundation for Controversial Political Theory ," Studies in Emergent Order 7 (2014): 299-306; cp.
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Given his changing definition of incommensurability Pérez Ransanz has identified three phases in Kuhn's work, or at least in how it deals with this concept. As we have seen above the first phase was seen in The Structure of Scientific Revolutions (SSR) and it is characterized by an overall vision that is applied to paradigms. This perspective was replaced in the 1970s by a localist and semanticist vision in which incommensurability is now defined as the relationship between two theories that are articulated in two languages that are not completely interchangeable, as Kuhn states in the following extract: The above only prohibits one type of comparison, that which is carried out between the statements of these two theories in a one-to-one relationship. An idea that underlies this formulation is that translation implies symmetry and transitivity so that if theory T is translatable with theory T', then T' can be translated to T, and furthermore if there is a third theory T and this can be translated to T', then theories T and T' cannot be incommensurable, as long as the transitive relationship and the symmetrical relationship assures that their statements can be compared one to another.
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