In his book "The Problems of Philosophy", Bertrand Russell draws attention to the fact that the ancien philosophers centered the notion of universal ( for example: Man and Rose are universals) in substantives and adjectives and despised the verbs and prepositions as universals. Russell wrote:
«Consider such a proposition as "Edinburgh is north of London". Here we have a relation between two places, and it seems plain that the relation subsists independently of our knowledge of it. (...) We may therefore now assume that it to be true that nothing mental is pressuposed in the fact that Edimburg is north of London. But this fact involves the relation "north of", which is a universal; and it would be impossible for the whole fact to involve nothing mental if the relation "north of", which is a constituent part of the fact, did involve anything mental. Hence, we must admit that the relation , like the terms it relates, is not dependent upon thought. but belongs to the independent world which thought apprehends but does not create.»
«This conclusion, however, is met by the difficulty that the relation "north of" does not seem to exist in the same sense in which Edinburgh and London exist. If we ask «Where and when does this relation exist?» the answer must be: "Nowhere and nowhen". There is no place or time where we can find the relation "north of". It does not exist in Edinburgh any more than in London, for it relates the two and is neutral as between them. Nor can we say that exists at any particular time. Now everything that can be apprehended by the senses or by instrospection exists at some particular time. Hence, the relation "north of" is radically different from such things. It is neither in space nor in time, neither material nor mental; yet it is something» (Bertrand Russell, «The problems of philosophy», page 55-56, Oxford University Press; the bold is put by me).
Certainly, I agree with Russell when he says that the relation "north of" is an universal, although he sidesteps the fact that "north" means the position of the polar star of the constellation Ursa Minor- so "north" means an object in the space and the relation "north of" means being spatially closer to the pole star than something else (located further south).
Hence, Russell makes a mistake when he says that «There is no place or time where we can find the relation "north of"». This thesis is refutable: this relation exists objectively in space and time, and in thought, so universals do not exist out of material world or of mental world. Where could they be? In a supersensible world as the one of the archetypes of Plato. Hence, "north of" should be an archetype.
© (Direitos de autor para Francisco Limpo de Faria Queiroz)