On Plurality (1900-1949)

"[...] there is a universal principle, operating in every department of nature and at every stage of evolution, which is conservative, creative and constructive. [...] I have at last fixed upon the word synergy, as the term best adapted to express its twofold character of ‘energy’ and ‘mutuality’ or the systematic and organic ‘working together’ of the antithetical forces of nature. [...] Synergy is a synthesis of work, or synthetic work, and this is what is everywhere taking place. It may be said to begin with the primary atomic collision in which mass, motion, time, and space are involved, and to find its simplest expression in the formula for force, which implies a plurality of elements, and signifies an interaction of these elements." (Lester F Ward, "Pure Sociology", 1903)

"Reduced to their most pregnant difference, empiricism means the habit of explaining wholes by parts, and rationalism means the habit of explaining parts by wholes. Rationalism thus preserves affinities with monism, since wholeness goes with union, while empiricism inclines to pluralistic views. No philosophy can ever be anything but a summary sketch, a picture of the world in abridgment, a foreshortened bird's-eye view of the perspective of events. And the first thing to notice is this, that the only material we have at our disposal for making a picture of the whole world is supplied by the various portions of that world of which we have already had experience. We can invent no new forms of conception, applicable to the whole exclusively, and not suggested originally by the parts." (William James, "A Pluralistic Universe", 1908)

"Classes and concepts may, however, also be conceived as real objects, namely classes as 'pluralities of things' or as structures consisting of a plurality of things and concepts as the properties and relations of things existing independently of our definitions and constructions. It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence. They are in the same sense necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions." (Kurt Gödel, "The Philosophy of Bertrand Russell", 1944)

"The only possible alternative is simply to keep to immediate experience that consciousness is a singular of which the plural is unknown; that there is only one thing and that what seems to be a plurality is merely a series of different aspects of this one thing, produced by a deception (the Indian MAJA); the same illusion is produced in a gallery of mirrors, and in the same way Gaurisankar and Mt Everest turned out to be the same peak seen from different valleys." (Erwin Schrödinger, "What Is Life?", 1944)

"A set is a unity of which its elements are the constituents. It is a fundamental property of the mind to comprehend multitudes into unities. Sets are multitudes which are also unities. A multitude is the opposite of a unity. How can anything be both a multitude and a unity? Yet a set is just that. It is a seemingly contradictory fact that sets exist. It is surprising that the fact that multitudes are also unities leads to no contradictions: this is the main fact of mathematics. Thinking a plurality together seems like a triviality: and this appears to explain why we have no contradiction. But 'many things for one' is far from trivial." (Kurt Gödel)

On Plurality (-1899)

"If simple unity could be adequately perceived by the sight or by any other sense, then, there would be nothing to attract the mind towards reality any more than in the case of the finger [...] But when it is combined with the perception of its opposite, and seems to involve the conception of plurality as much as unity, then thought begins to be aroused within us, and the soul perplexed and wanting to arrive at a decision asks 'What is absolute unity?' This is the way in which the study of the one has a power of drawing and converting the mind to the contemplation of reality." (Plato, "Republic", cca. 380 BC)

"In all things which have a plurality of parts, and which are not a total aggregate but a whole of some sort distinct from the parts, there is some cause." (Aristotle, "Metaphysics", cca. 335-323 BC)

"What is one is indivisible whatever it may be, e.g. a man is one man, not many. Number on the other hand is a plurality of 'ones' and a certain quantity of them. Hence number must stop at the indivisible: for 'two' and 'three' are merely derivative terms, and so with each of the other numbers." (Aristotle, "Physics", cca. 4th-century BC)

"There can only be one wisdom. For if it were possible that there be several wisdoms, then these would have to be from one. Namely, unity is prior to all plurality." (Nicholas of Cusa, "De Pace Fidei" ["The Peace of Faith"], 1453)

"Numquam ponenda est pluralitas sine necessitate."
"Plurality is never to be posited without necessity." (William of Occam,"Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi", 1495)

"The essence of the 'Truth' most glorious and mose exalted is nothing but Being His Being is not subject to defect or diminution. He is untouched by change or variation, and is exempt from plurality and multiplicity, He transcends all manifestations, and is unknowable and invisible, Every 'how' and 'why' have made their appearance through Him, but in Himself He transcends every 'how' and 'why'. Everything is perceived by Him, while he is beyond perception. They outwaid eye is too dull to behold His beauty, and the eye of the heart is dimmed by the contemplation of His perfection." (Nūr ad-Dīn 'Abd ar-Rahmān Jāmī, "Lawāih", 15th century)

"The view of things [called Pantheism] [...] - that all plurality is only apparent, that in the endless series of individuals, passing simultaneously and successively into and out of life, generation after generation, age after age, there is but one and the same entity really existing, which is present and identical in all alike; [...] Now if plurality and difference belong only to the appearance-form; if there is but one and the same Entity manifested in all living things: it follows that, when we obliterate the distinction between the ego and the non-ego, we are not the sport of an illusion. Rather are we so, when we maintain the reality of individuation, — a thing the Hindus call Maya, that is, a deceptive vision, a phantasma. The former theory we have found to be the actual source of the phaenomenon of Compassion; indeed Compassion is nothing but its translation into definite expression. This, therefore, is what I should regard as the metaphysical foundation of Ethics, and should describe it as the sense which identifies the ego with the non-ego, so that the individual directly recognises in another his own self, his true and very being. From this standpoint the profoundest teaching of theory pushed to its furthest limits may be shown in the end to harmonise perfectly with the rules of justice and loving-kindness, as exercised; and conversely, it will be clear that practical philosophers, that is, the upright, the beneficent, the magnanimous, do but declare through their acts the same truth as the man of speculation wins by laborious research [...] He who is morally noble, however deficient in mental penetration, reveals by his conduct the deepest insight, the truest wisdom; and puts to shame the most accomplished and learned genius, if the latter's acts betray that his heart is yet a stranger to this great principle, - the metaphysical unity of life." (Arthur Schopenhauer, "On the Basis of Morality", 1840)

"Even with the examples of the infinite considered so far it could not escape our notice that not all infinite multitudes are to be regarded as equal to one another in respect of their plurality, but that some of them are greater (or smaller) than others, i.e. another multitude is contained as a part in one multitude (or on the contrary one multitude occurs in another as a mere part).This also is a claim which sounds to many paradoxical." (Bernard Bolzano, "Paradoxes of the Infinite", 1851)

"But rather they are able, in spite of that relationship between them that is the same for both of them, to have a relationship of inequality in their pluralities, so that one of them can be presented as a whole, of which the other is a part. An equality of these pluralities may only be concluded if some other reason is added, such as that both multitudes have exactly the same determining grounds, e.g. they have exactly the same way of being formed." (Bernard Bolzano, "Paradoxien des Unedlichen" ["Paradoxes of the Infinite"], 1851)

"Therefore both multitudes have one and the same plurality, as one can also say, equal plurality. Obviously this conclusion becomes void as soon as the multitude of things in A is an infinite multitude, for now not only do we never reach, by counting, the last thing in A, but rather, by virtue of the definition of an infinite multitude, in itself there is no last thing in A, i.e. however many have already been designated, there are always others to designate." (Bernard Bolzano, "Paradoxien des Unedlichen" ["Paradoxes of the Infinite"], 1851)

On Plurality (1950-)

"A social system consists in a plurality of individual actors interacting with each other in a situation which has at least a physical or environmental aspect, actors who are motivated in terms of a tendency to the 'optimization of gratification' and whose relation to their situations, including each other, is defined and mediated in terms of a system of culturally structured and shared symbols." (Talcott Parsons, "The Social System", 1951)

"A social system is a mode of organization of action elements relative to the persistence or ordered processes of change of the interactive patterns of a plurality of individual actors." (Talcott Parsons, "The Social System", 1951) 

"Relativity is inherently convergent, though convergent toward a plurality of centers of abstract truths. Degrees of accuracy are only degrees of refinement and magnitude in no way affects the fundamental reliability, which refers, as directional or angular sense, toward centralized truths. Truth is a relationship." (R Buckminster Fuller, "The Designers and the Politicians", 1962)

"A set is formed by the grouping together of single objects into a whole. A set is a plurality thought of as a unit. If these or similar statements were set down as definitions, then it could be objected with good reason that they define idem per idemi or even obscurum per obscurius. However, we can consider them as expository, as references to a primitive concept, familiar to us all, whose resolution into more fundamental concepts would perhaps be neither competent nor necessary." (Felix Hausdorff, "Set Theory", 1962)

"Science is imagination in the service of the verifiable truth and that service is indeed communal. It cannot be rigidly planned. Rather, it requires freedom and courage and the plural contributions of many different kinds of people who must maintain their individuality while giving to the group." (Gerald M Edelman, [Nobel Prize] 1972)

"What is so remarkable in all these theories and doctrines is their implicit monism, the claim that behind the obvious multiplicity of the world’s appearances and, even more pertinently to our context, behind the obvious plurality of man’s faculties and abilities, there must exist a oneness - the old hen pan, 'the all is one' - either a single source or a single ruler." (Hannah Arendt, "The Life of the Mind", 1977)

"[...] the plurality that we perceive is only an appearance; it is not real." (Erwin Schrödinger, 'The Mystic Vision', 1984 )

"There are a variety of swarm topologies, but the only organization that holds a genuine plurality of shapes is the grand mesh. In fact, a plurality of truly divergent components can only remain coherent in a network. No other arrangement-chain, pyramid, tree, circle, hub-can contain true diversity working as a whole. This is why the network is nearly synonymous with democracy or the market." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"It is part of the lore of science that the most parsimonious explanation of observed facts is to be preferred over convoluted and long-winded theories. Ptolemaic epicycles gave way to the Copernican system largely on this premise, and in general, scientific inquiry is governed by the oft-quoted dictum of the medieval cleric William of Occam that 'nunquam ponenda est pluralitas sine necesitate' , which may be paraphrased as 'choose the simplest explanation for the observed facts' ." (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

"Complementary to the principle of multidimensionality and parallel to it is the concept of plurality. Plurality of function, structure, and process, as we will see later on, is at the core of systems theory of development. It makes the high/high a possibility and choice a reality. Plurality simply maintains that systems can have multiple structures and multiple functions and be governed by multiple processes; it denies the classical view of a single structure with a single function in a single cause-and-effect relationship." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)

"Singularity refers to theories in which a particular structure, function, or process is considered fixed and/or primary in all environments. Plurality refers to theories that consider structure, function, or process to be multiple and/or variable in the same or different environments." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)