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Limitation and limits (the Industrial
Revolution, supermarkets, factory farming, mobile phones, warfare, versatility)
Quantum mechanics
Linkage schemata
Surveys
Framing
Isolation and abstraction
Isolation and the 'Whole
Truth' (Mahler)
Isolation and distortion
Kant and the limits of knowledge
Logic
Allowing and disallowing
Technical comments
I make use of these concepts very extensively. These are two modes of {restriction}. Limitation is free: Here, {restriction} is freely chosen, self-imposed. Limits are bound.
Some examples of limitation (some of these are described in other parts of the site but are brought together here.)
The industrial revolution was surely not a disastrous interruption to an idyllic pre-industrial life but a development which has brought massive benefits as well as massive disadvantages. The benefits include medical advances (and veterinary advances), sanitation systems, systems for the supply of drinking water, transportation systems which allow distant communities to be fed rather than to starve...and many others. Huge factories and warehouses and computerized distribution networks are an intrinsic and necessary part of the modern industrial world. But the tendency has been to apply these systems to areas where it can be argued that they aren't appropriate, or even morally harmful. Massive supermarkets are the industrial system applied to retailing. Only aspects of the industrial system are appropriate, not the industrial system applied mechanically. Battery chicken sheds, intensive broiler sheds and intensive pig units, factory farming in general, are the industrial system applied to retailing.
Mobile phones have their uses - life-saving uses in some cases - but to use them without any limitation - in trains, on buses, imposing private conversations on other people in a public space, and in many other circumstances, is, I claim, wrong. When mobile-phone users switch off their mobile phones before going into a concert, or in a library where mobile phones are banned, then they are recognizing, on the other hand, limits.
Over long periods of time, warfare has been unrestricted. When besieged cities surrendered, all the inhabitants were put to the sword, or some were slaughtered and the rest sold into slavery. Enemy combatants who surrendered were killed. No attempt was made to treat wounded enemy combatants. Grotius in the seventeenth century made important contributions to establishing international law. Eventually, with the Geneva conventions, measures were taken to impose {restriction}, on warfare: for example to lay down rules for the protection of non-combatants, to protect combatants who had surrendered or were wounded, to impose {restriction} on the kinds of weapons which could be used, banning the use of poison gas, for example. I have played a part in opposing the use of anti-personnel mines. As is commonly known, these can kill non-combatants long after a conflict has ended. There are very good arguments, I think, for extending the {restriction} of weapons by banning the manufacture of anti-personnel mines. Achieving that as a practicable objective would not be easy.
The philosopher Bertrand Russell opposed involvement in the First World War but supported the need for military action in the Second World War. I think that there can be legitimate disagreements about the First World War, but he was surely correct in supporting military action in the Second World War. This is to apply limitation - to work for a world order which makes the maintenance of peace more likely This amounts to a large number of separate responsibilities, and is not the same as working for a 'world government,' which I think is a futile objective. To anticipate the possibility that there may be war in the future needs adequate expenditure on the armed forces in time of peace. I'm a wholehearted critic of so many aspects of life in this country, including political life, but I think that its armed forces are cause for overwhelming pride.
Some examples of limits.
The inescapable limits to achievement, accomplishment, experience, involving the need to choose. By practising a musical instrument intensively, to that extent the time is lost for any number of other activities. Commitment to a very demanding job entails the sacrifice of some time with family, friends, commitment to a good cause. Full commitment to a humanitarian cause may cause atrophy - partial, not full, it's to be hoped - of some aspects of the personality. Time given to natural beauty is time not given to the plight of people whose lives have been blighted.
The obvious limits to energy use imposed by finite resources, of non-renewable sources. The limits of renewable resources, each of which has its disadvantages.
The kinetic energy of a rigid rotator in classical physics isn't subject to {restriction}, unlike a quantized rotator, which is subject to {/quantum restriction} on angular momentum. The quantum number for rotation is subject to {restriction}. It can only have integer values.
{/quantum restriction} on vibrational energy can be calculated by solving the time independent Schroedinger equation in one dimension.
One of the simplest systems illustrating quantization is the particle which is confined to a one dimensional box. When the Schroedinger equation is solved, it's found that there is {restriction}, since there are well-behaved solutions only for certain energy values, the equation which gives these energy values including the quantum number for the system, an integer. Here, the theorist (not the experimenter) confining the particle in the one-dimensional box constitutes {/free restriction}. The fact that values for the quantum number are integral constitutes {/bound restriction}.
{/free restriction}, unlike {/bound restriction} in scientific investigations, involves a teleological component: the scientist is practising {/free restriction} in order to corroborate or falsify a theory.
{restriction} is applied to the content of content brackets []in linkage schemata when only certain ontological entities are considered for inclusion, such as structural universals, abstract particulars, assertions of possibility and necessity in possible-worlds semantics, subjects or predicates, concrete objects, persons, and obviously many other entities.
{/intrinsic restriction}, in the terminology I use, is applied to the content of linkage brackets <>as a result of excluding entities which belong to content brackets. Otherwise, {/extrinsic restriction} is applied by choosing for inclusion linkages such as the mathematical 'equals' sign, logical connectives, membership of a mathematical set, and obviously many more.
A survey is more often than not subject to {restriction}, that is, {restriction} has surveys within its sphere of application, or, more concisely, {restriction}: surveys. This {restriction}: surveys can be evaluated. It may be inevitable, since it would be impractical to give a survey not subject to {restriction}, or the survey may include all the survey-items which are necessary for an understanding, interpretation, analysis, practical decision or whatever may be the purpose of the survey. In this case, we have a positive evaluation, {restriction}ev+ However, a survey may omit one or more survey-items which are highly relevant, indispensable to the purposes of the survey, leading to {distortion}. In this case, we have {restriction}ev- If, as may well be the case, there are complexities which make it difficult to decide upon the evaluation, then {resolution} may be carried out to break down the matter into separate components, allowing a decision to be made for each of these components or reservations may be listed - there are a number of methods which can remove the problem.
'The rhetoric of the frame: essays on the boundaries of the artwork,' edited by Paul Duro is a comprehensive and exceptionally interesting treatment of the concept applied to visual art. The concept also has an established use in literary studies. For example, a framed narrative is a 'narrative within a narrative,' or one with various levels of narrative. Derrida uses the terms 'parergon' (such as the frame enclosing the artwork) and 'ergon,' an artwork or text which is enclosed.
My use of {/framing} has no connotations of enclosure. As a sub-theme of {restriction}, it's applied only to the setting of a boundary. {/framing}has {limitation} and {/limitation} has {free restriction}. Obviously, {/framing} also has {separation}. Paul Duro, in 'Containment and Transgression in French Seventeenth-Century Painting' (from the work cited), writes in connection with a remark of Poussin, "the principal function of the frame is to separate the objects it represents from those not crucial to the representation." Paul Duro writes of the extent of the world beyond the bounds established by the frame." These 'bounds' (and the 'containment' of the title of this essay) are instances of {restriction.}And, also: "The frame permits the operation of distinction, setting its limits and the conditions under which history painting may operate." Obviously, using my terminology, these 'limits' constitute {limitation}, as free rather than bound.
{restriction} has {/isolation}. {isolation} is a necessary part of scientific analysis. A concrete problem to do with the momentum of the particular car involves subjecting the elements of the problem to {isolation}, (the elements being only those entities which are relevant to the solution of the problem by the methods of mechanics.)
Isolation and the 'Whole Truth'
Aldous Huxley, in 'Music at Night,' distinguishes between [gives {separation} to] 'tragedy' and 'the Whole Truth:' "To make a tragedy the artist must isolate a single element out of the totality of human experience and use that exclusively as his material. Tragedy is something that is separated out from the Whole Truth, distilled from it...chemically pure...It is because of its chemical purity that tragedy so effectively performs its function of catharsis...in recent times literature has become more and more acutely conscious of the Whole Truth - of the great ocean of irrelevant things, events and thoughts stretching away endlessly in every direction..."
This is quoted in Deryck Cooke, 'Gustav Mahler.' He writes of Mahler's music, "For Mahler, music had to include the trivialities and absurdities of everyday life." And, "Any assessment of it as 'pure music' by Beethovenian standards is meaningless: if Beethoven's symphonies are lie perfect poetic odes or taut classical dramas, Mahler's are like roomy, discursive volumes of autobiography. But though they are 'impure', they are none the less essentially on the tragic plane." (Page 17, 18).
To use considerations such as these as a 'mechanical' way of arriving at the conclusion that Mahler is a great composer would be mistaken, though. This would be to avoid the use of judgement. I agree with this opinion on Mahler's music, taken from an internet discussion:
[Why is Mahler thought of as a great composer?] "Beats me. Perhaps because he reminds some of movie music from the '30's. Movie music seems to be the touchstone for entry into what some think of as "classical" music - loud, fragmented, pointlessly emotional, with lots of noisy climaxes and off the wall pathos...To me Mahler's symphonies sound like the work of a great orchestrator who's convinced himself he can - and must - prove himself greater than Beethoven but who has absolutely nothing to say and can't tell the difference between vulgarity and profundity." I prefer the less characteristic symphonies of Mahler such as the First and the Fourth to the more characteristic symphonies such as the Sixth or the Ninth. The Ninth has its moments, such as the opening of the second movement (its orchestration is good but no more than good - violas playing with bassoons), but it's increasingly overtaken by whimsicality and empty gestures that only have volume. This becomes the dominant emphasis once the 'meno mosso' section begins.
The focus is upon one aspect, excluding other aspects which are relevant. To give just one example, focussing attention only upon the real risks to health of smoking, and ignoring aspects of the person other than the person's willingness to risk health.
Kant and the limits of knowledge
In the section of the 'Critique of Pure Reason' he called 'Transcendental Dialectic,' Kant maintained (translating into my own terminology) that a priori knowledge has as its only legitimate 'sphere of application' objects of possible experience, and that {restriction} makes it impossible to have knowledge of the nature of the soul or the cosmos, or the existence of God. These are things which transcend possible experience and can't be matters of knowledge.
In natural language, 'none, some, most, all' show a gradient of {restriction} from most restricted to least restricted. In a gradient of {restriction}, {ordering}:- {restriction}. This can be shown as:
== 'none' > == 'some' > == 'most' == 'all'
In quantificational logic, the existential quantifier is more restricted in effect than the universal operator:
> 
The scope of a quantifier can also be understood in terms of {restriction}. The scope of the quantifier is more restricted in
( y) Fy 
Gy than in
( y) (Fy
Gy).
The scope of a quantifier is the complete expression following it.
Gödel's Theorem has as its sphere of application deduction from theorems. It finds {restriction} in axiomatic systems- there are undecidable propositions (Gödel propositions) within the system or true propositions which can't be derived from the axioms.
I use these terms in connection with the {restriction}of diversification. Examples:
(1) Childhood traumas may be extenuating circumstances in cases of a murder conviction - so that the death penalty, which I oppose, should be all the more unthinkable - OR, by diversification, they may not. The more severe the traumas, the greater the likelihood of that they do amount to extenuating circumstances. This is how I see the matter. Unswerving supporters of the death penalty - I refer to them as 'primitive' people - may well disallow any of these extenuating circumstances. For them, there are no cruelties inflicted upon a baby or child which could make a death sentence unthinkable. And so, in the United States, there have gone to the execution chamber people such as Johnny Garrett (in the primitive state of Texas), a juvenile offender who was treated in an unspeakable way as a child (when he was a baby, he was put on the burner of a cooker, for example.)
Kant allowed the contrast between analytic and synthetic statements. Quine disallowed the contrast, imposing a {restriction} on diversification. There are separate contrasts analytic-synthetic and a posteriori-a priori, giving, by {diversification}, four theoretical forms. Kant disallowed one of these, the analytic-a posteriori form. He allowed the synthetic-a posteriori and the analytic-a priori forms, although he believed that they were without interest. The synthetic-a priori form, of course, he regarded as very significant.
{separation} has {/restriction}. {restriction} has {/isolation}+ev and {/isolation}-ev. {isolation}+ve often entails the exclusion of elements or factors which are irrelevant to a consideration or solution of a problem. {isolation}-ve often involves the exclusion of elements or factors which are relevant to a consideration or solution of a problem, by, for example, {restriction}ev- of a survey.
