By Paolo Valore

This booklet provides the normal ontological dedication process, including a safety of the thesis of ontological relativity. It presents, while, a wide-ranging review of the floor conceptual instruments of ontology. Their attainable purposes are defined via a wide array of examples and open difficulties, and crucial references to the classics of philosophy.

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Let us recall the case of winged horses. “∀x P(x) → Q(x) ” says that any existing winged horse will be bay; “∀x P(x) → ¬Q(x) ” says that any existing winged horse will not be bay. It is immediately clear that in quantified logic traditional contrariety no longer holds: A and E can both be true. If it is the case that there is nothing which is P, then “∀x P(x) → Q(x) ” will be true, because its antecedent is false; and the same holds for “∀x P(x) → ¬Q(x) ”, which shares the same antecedent. But then, in cases of non-existence, contrariety needs to be dropped.

Brought to you by | Universität Osnabrück Authenticated Download Date | 2/6/16 4:48 PM 6 Categorial Realism The first (more or less¹) exhaustive list of categories was conceived by Aristotle, in his Categories²: 1 2 3 4 5 6 7 8 9 10 substance quantity quality relation place time position state action affection as in as in as in as in as in as in as in as in as in as in Aristotle is a man Aristotle is 182cm tall Aristotle is pale Aristotle is Plato’s teacher Aristotle is at the University Aristotle is here today Aristotle is sitting Aristotle is wearing a tie Aristotle is reading a book on ontology The book is read by Aristotle In this table, categories replicate predication schemes: the class of substantives, which only serve as subjects, is the class of substances and can stand in relation to other substantives (of greater generality), to adjectives (quantity and quality), or in a complex relation, such as with “double”, with comparative adjectives, or with spatial and temporal determinations (place and time).

Körner (1970), p. 48. 4 All references to Plato and Aristotle, in this chapter, will be very loose, principally aimed at the possibility of reinterpreting some of their theoretical arguments in the light of contemporary interests. From an historical point of view, it is doubtful that there is any explicit ontology in Plato. 2 The Diairetic Procedure | 51 None of these forms overlaps with the others, so they respect the disjointness condition. Moreover, such a structure shows the two-fold nature, typical of categories, of being both a formal classification based on logical and linguistic analyses and an ontological characterization.

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