In Mathematics, one counter-example proves that something is not true.
If there is a large number of examples that validate an hypothesis, a few
allowed processes of generalisation may be used to make it become a theorem, that is, a rule or
a way to generate valid mathematical assertions.
It may be possible to build a similar system in Language.
It is possible that the computer systems currently used to translate/interpret texts in place of human beings contain theorems in them.
How do systems analysts design systems: what reasoning makes them build a system that actually finds a perfect match - amongst so many that are possible - for a certain word, from the original text, in the English language?
Maybe they make use of theorems that deal with each, and every, one of the pieces of any given sigmatoid individually.
After thinking about the couple (English; Portuguese) for a time, we came up with quite a few
possible theorems.
Proving that some of them are not true is a really hard task, so that it is difficult finding even one counter-example, but proving that some of them are one hundred per cent true is almost impossible.
Consider, as possible theorem, the following:
whatever ends in ão in Portuguese will have an English language equivalent ending in ion.
Examples that support the hypothesis: (constellation; constelação), (prohibition; proibição), (castration; castração), (constipation; constipação), (lotion; loção); (notion; noção), (portion; porção), (condition; condição), (preparation; preparação), (continuation; continuação), (manipulation; manipulação), (prostration; prostração), and etc.
Counter-examples: (no; não); (pike; sapatão); (heart; coração), (solitude; solidão), (ledger; razão), (meal; refeição); (coat of arms; brasão), (pagan; pagão), (transport; condução), (pressure; pressão), (printing; impressão), (captain; capitão), (saint; são), (card; cartão), (sex drive; tesão), (reason; razão), and etc.
Now this:
whatever ends in ia in Portuguese will have an English equivalent ending in y?
The initial list: (lethargy; letargia), (metallurgy; metalurgia), (iridology; iridologia), (geology; geologia), (geography; geografia), (musicology; musicologia), (theosophy; teosofia), (philosophy; filosofia), (anthroposophy ; antroposofia), (allergy ; alergia), (mastectomy; mastectomia), (sexology; sexologia), (ontology; ontologia), (allegory; alegoria), and etc.
Counter-examples: (apologia; apologia), (claustrophobia; claustrofobia), (haemorrhage; hemorragia), (merchandise; mercadoria), (aunt; tia), (stationery shop; papelaria), (bookshop; livraria), (rectorship; reitoria), (directorship; diretoria), (bitch/slut; vadia), (neighbourhood; periferia), (mania; mania), and etc.
This text proves that creating linguistic hypotheses, and testing them is good entertainment, and may someday lead to useful findings or actual theorems, which will meaningfully add to our
Inner Reality rules, and that will help us reject wrong reasoning at an early stage, and therefore is something that help us save resources.
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