RELAZIONI D’ORDINE E DI EQUIVALENZA

RELAZIONI D’ORDINE E DI EQUIVALENZA

NEGLI ORDINAMENTI GIURIDICI

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1 – L’Ordinamento

Nella logica matematica, un ordinamento è un insieme sul quale sia definita una relazione d’ordine (che produce un ordinamento), o una relazione di equivalenza che produce una ripartizione (in classi).

Mettere in ordine è sicuramente un’attività che consente di organizzare in qualche modo, ed in qualche senso un insieme di oggetti, o di concetti.

La matematica indivisua nell’ordinamento le proprietà che caratterizzano una relazione che produce l’ordinamento stesso, cioè quella proprietà che una relazionee deve possedere perché i collegamenti fre gli elementi dell’insieme, che si vengono a creare, costituiscano un ordinamento dell’insieme stesso. La definizione tecnica per questo tipo di relazioni è definita “relazione d’ordine”.

 

 

 

 

INTRODUCTION TO NOMOLOGY

 

ABSTRACT

 

Nomology is the study of human lawmaking (theorisation) that controls and verifies the correspondence of human laws to a correct theory, i.e. to the respect of the statement of true premises, and of a valid argument. If so, then any conclusion is true, any theory is true, any law must be true.

With such a conclusion we do not want to side neither with Natural Law, nor Positive Law, nor with the polyvalent Logic of Karl Popper. We just want to assume that any human law can intervene if, and only if, it is sure to produce a benefit or en improvement to the natural order; in any contrary case no law (control brought about by enforcing rules) is needed, or can be admitted.

In this work we have tried to investigate the process of codification referred to the major aspects of society, nature, science, and other acts or facts token into consideration by a body of law.

 

 

 

1. Introduction

 

2. Definitions

 

Nomology can be defined as the process, which deals with the study of theories and laws.

The word nomology is a neologism formed by two Greek terms: logos, which indicates ‘the study of’, and nomos, which indicates a theory, a law, the government, or the administration of something.

 

The etymological notion underlying theory is of ‘looking’; only secondarily did it develop via ‘contemplation’ to ‘mental conception’. It comes via late Latin theoria from Greek theörìa ‘contemplation, speculation, theory.’ This was a derivative of theöròs ‘spectator’, which was formed from the base thea- (source also of theàsthai ‘watch, look at,’ from which English gets theatre). Also derived from theoròs was theoreìn ‘look at’, which formed the basis of theorema ‘speculation, intuition, confirmed theory,’ acquired by English via late Latin theorema as theorem.

 

A theorem can be defined as a theory that has been proved, as the Pythagorean Theorem.

 

A law etymologically is that which has been ‘laid’ down. English borrowed the word from Old Norse lagu (replacing the native Old English æ ‘law’), which was the plural of lag ‘laying, good order.’ This came ultimately from th prehistoric Germanic base lag- ‘put’, from which English gets lay. It has no etymologic connection with the semantically similar legal.

English has three words lay. The common verb, ‘cause to lie’ [OE] goes back to the prehistoric Germanic base lag- ‘put,’ a variant of which produces lie. From it was derived lagjan, whose modern descendants are German legen, Dutch leggen, Swedish lägga, Danish lægge, and English lay.

Law comes from the same source, and it is possible that ledge may be an offshoot of lay (which in Middle English was legge). Ledger could well be related too. Lay ‘secular’ comes via Old French lai and Latin laicus from Greek laikòs, a derivative of laòs ‘the people’. And lay ‘ballad’ comes from Old French lai, a word of unknown origin.

The term legal, on the contrary, has a Latin source. The Latin term for ‘law’ was lex. From its stem form leg- come English legal, legislator (which goes back to a Latin compound meaning literally ‘one who proposes a law’), and legitimate. Loyal is a doublet of legal, acquired via Old French rather than directly from Latin. Another derivative of leg- was the Latin verb lēgāre ‘depute, commission, bequeath,’ which has given English collegue, college, delegate, legacy, and legation.

 

A ledger, etymologically, is a book that ‘lies’ in one place. The term was used in 15th and 16th century English with various specific applications, including a ‘large copy of the Breviary’ (the Roman catholic service book), and a ‘large register or record book’ – both big volumes that would not have been moved around much – but it finally settled on the ‘main book in the set of books used for keeping accounts.’ It probably comes from Dutch legger or ligger, agent nouns derived respectively from leggen ‘lay’ and liggen ‘lie’ (relatives of English lay and lie).

 

We said that the Latin term for ‘law’ was lex, defined by G. Devoto as an archaic Indo-European term, which defines the ‘religious law’, and that besides Latin survives only in the Indo-Iranian languages.

 

2.1 Commonly a theory can be:

A set of general principles drawn from any body of facts or abstract thought (as in science).

Principles governing practice (as in a profession of arts, or in an administrative regulation).

A more or less plausible or scientifically acceptable general principle offered to explain observed facts.

Any theory is an argument, i.e. a sequence of sentences (called premises) that leads to a resulting sentence (conclusion).

An argument is a valid argument if the conclusion does follow from the premises. In other words, if an argument is valid, and all its premises are true, then the conclusion must be true.

Any theory is stated through a theorem, which is the logical process by which verity is deducted from the premises of the theory itself by means of mathematical or grammatical rules of logic.

 

2.2 Commonly a law can be:

A rule or principle stating something that always works in the same way under the same conditions.

A rule of conduct or action established by custom or laid down and enforced by a governing authority.

The science that deals with laws and their interpretation and application.

A statement of the observed regularity of nature.

A revelation of a supreme will (as the revelation of the divine will set forth in the Old Testament).

 

2.3 Commonly a law tends to degenerate into:

The control brought about by enforcing rules (forces of law and order).

The imposition of a power.

 

Logic is the activity pertinent to the demonstration process of a statement (Theory or Law), while only the related science is pertinent to demonstrate a premise.

 

The doctrine of Natural Law, Positive Law, and Epistemology are the disciplines that deal with the process of legislation and codification.

In the Natural Law, any theory (or law) comes from the observation of the regularity of nature: i.e., there exists a natural order and any codification process moves to the comprehension of the truth from its observation.

Positive Law (or Positive Right) comes from the induction of experiments, i.e., reasoning from a part to the whole, or from a particular to a general conclusion.

In Epistemology theories and laws are just hypothesis. Scientific revolution in mathematics and physics in the early ‘900 demonstrated that science progresses through deep crises and rearrangements of its conceptual apparatuses. Therefore, in the contemporary Epistemology the problem of the definition of scientific criteria is continuously re-proposed.

Bertrand Russell and Rudolph Carnap consider as scientific a theory when all its items can be connected through rules of ‘correspondence’ to observable data.

Karl R. Popper, introducing the notion of ‘falsificability’, considers as scientific a theory only if it is possible to identify the events whose ascertainment can prove its falsity. In any contrary case, theory will result undemonstrated and just ‘corroborated’ (opinion supported with certain evidence).

 

 

3. Theory and Law in Science

Theory and Law in Science are terms that indicate a same object, i.e. the statement of a more or less plausible scientifically acceptable general principle offered to explain observed facts. Ohm’s law and Ohm’s theory are the same statement of a general principle of electricity.

Therefore, in science law and theory have the same value.

General principles of electricity are accepted because their practical effects are visible, and easy demonstrable in the earth reference system. Nobody can state anything different than that.

General instinct to survival, reproduction, freedom, exchange, and knowledge are needs of nature, therefore they are natural laws, and nobody can state that something coming from nature is unreal, or false. Anyway, their effects are not so easy to be demonstrated as the effects of electricity are, therefore there will always exist someone somewhere who will issue human laws to regulate, by enforcing rules, those activities already regulated by the nature.

In Physics the Theory of Newton, and the Theory of General Relativity move to a similar gravitation theory. That is the principle of correspondence, which indicates the tendency of two physical laws to coincide when they are deducted from at least two different theories.

 

A few Epistemologists arrive to state that the scientific assumption of any term is nothing else than the complex of empiric operations performed when they are used. Once such a condition is satisfied, then it is be possible to state that the theory under examination is scientifically valid.

Therefore, a theory results verified if observable data could be effectively related between them in the same way of the relations of ‘correspondence rules’ terms connected to data. In any contrary case we can say that the theory results counterfeited.

The inconvenient of this theory lays in the presumption that there will always exist rules of correspondence for all the terms of a theory. In the reality that never happens, because it is possible to demonstrate that almost any scientific theory contains terms with no rules of correspondence (the so called ‘theoretic terms’. Epistemologists tried to solve the problem with several modifications to strict Empiricism, looking overall for a shrewdness, which could give scientific sense also to the propositions containing some theoretic terms. Anyway, remains the fact that the verification concept itself is referred to statements with no theoretic term. These doubts are due to the circumstances that no observation, as accurate as possible, will ever allow to verify any authentic scientific law.

In fact, any scientific law states the existence of a certain relationship between variable terms in infinite dominions, so that, in order to verify a law, it should be necessary to verify that the same relationship exists between an infinite number of data (corresponding to variables terms), when it is obvious that data effectively reachable by observation are always a finite number.

Such a difficulty moved the ‘falsification doctrine’ of K. Popper, which states that it is not necessary that a theory results verifiable in order to define a theory as scientific. It is necessary, on the contrary, that its falsity can be proved. In fact, in the act of a theory definition one can indicate a few events whose verification could prove its falsity (potential falsifiers). In any contrary case the theory would not be scientific, but merely metaphysic.

Once the potential falsifiers have been pointed out, scientists will be charged to submit the theory to extreme tests to verify whether it resists to the falsification attempt. If positive, scientists can state that the theory has not been ‘demonstrated’, but just ‘corroborated’.

Therefore, a real science shall be constituted by theories seriously corroborated, and we must note that any corroboration, however serious, will never result as definitive, because nobody can exclude on principle that further proofs could lead to exits in antithesis with the proofs till then performed.

The existence of such a plurality of epistemologies confirms the actuality of the problem about the formulation of a criterion of science, which can give a precise sense to the objectivity of this knowledge, and to its effective superiority in comparison with pre-scientific knowledge, without any further appeal to a presumed absolute metaphysical basis of science.

 

 

4. Civil Law, Common Law, and Social Theory.

How many civil or common laws have currently as same casual links with social theories as law and theory scientifically have?

Any civil or common law must be at least a theory to be real (proved or just corroborated), therefore to be right. If not, any civil or common law will just be a power imposition.

In nature every living being is authorized by natural programs (instinct to survival, reproduction, freedom, exchange, and knowledge) as nature needs to oppose to any power imposition, even if it comes from a process of codification imposed by a Government, an Administration, and/or any presumed or self-styled positive law.

An organism that formulates a lot of codifications and laws is the State, which becomes the highest Institution when it is assumed as a ‘body of law’. ‘Law and Order’ enforce State laws.

Unlike scientific law State law is coercive, even if the case that has to be regulated is not by nature.

Now, if a body of law wants to be a theory -as any scientific statement- it shall contain demonstrability criteria, or the proof that it cannot be forged.  Therefore, to become eligible any law must demonstrate that scientific real premises, a logic argument, and conclusions that come from the premises passed through a coherent (valid) argument, support all its statements. To do that any law must demonstrate that its statements are natural and not forged. In any contrary case the law shall result undemonstrated, therefore false.

 

One of the most frequent objections to the aforementioned definition is that the demonstrability of a State law can take long and hard procedures, while society’s problems need urgent interventions.

That is nonsense, because a law has a sense only when it is able to classify a real order, or when it is able to improve a natural order.

Human society, as any other living being society, has a recognized and accepted natural order that allows applying all instincts for living. Such a natural condition needs no human manipulation or forges to live on. No civil or common law is needed, but to improve technology. Therefore, if human laws want to reach a real improvement, they shall have at the most engineering skills, which shall be the definition of highest organisation levels. In any case, such a manoeuvre- as in all engineering process- must come through a theorem (which has been define as the logical process by which verify is deducted from the premise of the theory itself  by means of mathematical or grammatical rules of logic).

 

Now, even if we make any effort, any terrific enormous effort to try to identify the correspondence of human laws with scientific theories, we can see only a few, very few civil or common laws eligible as theory. In all other cases they are just a power imposition.

 

 

 

Conclusion

 

Nomology is the study of human lawmaking (theorisation) that controls and verifies the correspondence of human laws to a correct theory, i.e. to the respect of the statement of true premises, and of a valid argument.) If so, then any conclusion is true, any theory is true, any law must be true.

With such a conclusion we do not want to side neither with Natural Law, nor Positive Law, nor with the polyvalent Logic of Karl Popper. We just want to assume that any human law can intervene if, and only if, it is sure to produce a benefit or en improvement to the natural order; in any contrary case no law (control brought about by enforcing rules) is needed, or can be admitted.

In this work we have tried to investigate the process of codification referred to the major aspects of society, nature, science, and other acts or facts token into consideration by a body of law.

 

Enrico Furia

School of World Business Law

John Ayto, Dictionary of Word Origins, Arcade Publishing New York, 1990.

Douglas Downing, Dictionary of Mathematics Terms, Second Edition Barron’s, New York, 1990

 

Giacomo Devoto, Dizionario Etimologico, Le Monnier, Firenze 1968.


 

 

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