The Mistery of Belicena Villca verified mainly by formulating a " law of nature ", which explains the behavior of a phenomenon establishing causal relationships between aspects of it . I ' ll give a simple example : you want to " measure " the side of a regular polyhedron . Here the phenomenon is a body shaped like a regular polyhedron , that is to say , a “ phenomenal entity ”. The " graduated ruler " is used for this , that is , a flat surface on which the units of length are engraved and of which we are sure that one of its sides is perfectly straight . The zero of the ruler is made coincide with the " beginning " of the side to be measured . It is now observed that the " end " of the side coincides with the number five of the ruler and it is stated without further ado that " in the polyhedron , the side measures five centimeters ". It has been carried out , as will be seen , a series of subjective operations whose conclusions , however , can be confirmed by other observers ; this possibility of verification is what gives weight of " law of nature " to the fact mentioned .
But it happens that in the ruler , which is believed to be numbered , there are actually engraved signs representing numbers , not numbers themselves . The numbers are mathematical principles of the cultural structure , that is , subjective elements , which intervene in the act of “ recognizing that the side limit coincides with the sign 5 ”. If it says " it measures five centimeters ", the assertion of an empirical quality : “ there is a proportion ( that is , a mathematical relationship ) between the length of the side of the polyhedron and the length of the terrestrial meridian ”. This proportion is fixed or constant (= 5cm .) and constitutes a " relationship between aspects of a phenomenon ", that is , a " law of nature ".
The centimeter is equal to one hundredth of a meter and this to one tenmillionth of a quarter of terrestrial meridian .
The phenomenal entity appeared complete , integral in its manifestation . However , it is not possible to apprehend it in its entirety ; as soon as you observe it a part of it becomes eminent , standing out over other aspects . The unity of the phenomenon has been broken in favor of the plurality of qualities that one is able to attribute to it . Two square faces are distinguished , and on each face , four edges and four angles , etc . Then its practiced the measurement of an edge or side and established a " law of nature ”: “ the length of the side is proportional to the length of the terrestrial meridian and its ratio is 5 cm ".
In this operation that has just been described , the “ mathematical principles ” ( when two faces , four edges , etc . are distinguished ) and the " Preeminent cultural premises " ( when the face , side , or any other quality turned eminent ). The two sources concur in the rational act of " relating " ( measure ) aspects of the phenomenon and postulate a " law of nature " ( measures 5 cm .) that can be universally proven .
I hope I have made it clear that the mathematical principles ( the one , the two , the square , etc .), as they are intrinsic properties of the mental structure , intervene a priori in the formulation of a law of nature . As to the " numbers " of the world , those that appear engraved on the graduated ruler , they are only cultural signs of representation that are distinguished thanks to the conventional learning . There were ancient peoples that represented the numbers with knots or ideograms ; it is presumable that an instrument of measurement composed of a stick on which hieroglyphs have been engraved , would not mean , in principle , nothing for us if we cannot " read " the signs , that is , make the numerical representations .
The epistemological analysis of the way in which man establishes a law of nature must lead fatally to the conclusion that it would be impossible that the principle of the enclosure was located in the world as the property of the entities and could be formulated in a sociocultural language . On the contrary , what can happen , in any case , is that the principle of the enclosure is projected , consciously or unconsciously , about a phenomenon and is later discovered in it as an eminent relationship between qualities ; naturally , it will depend on the type of phenomenon represented by the complexity with which the principle of the enclosure is empirically recognized and introjected into the psychic structure .
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