By Uwe Meixner
Axiomatic Formal Ontology is a reasonably entire systematic treatise on normal metaphysics. The axiomatic approach is utilized during the booklet. Its major topic is the development of a basic non-set-theoretical thought of intensional entities. different vital issues mentioned are the metaphysics of modality, the character of exact lifestyles, mereology and the taxonomy of entities.
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Extra info for Axiomatic Formal Ontology
On this basis I frequently use the word "whole" as a noun (without the adjective "complete"), when I refer non-discriminately to entities of the universe of discourse (see for example [*1] above). [*6] The concepts defined in DP8 - DPlO are not used in what follows. The reason is: already in the system AP1-AP4 we can prove the existence of a minimality and a totality, and thus we can also prove: allxallyOV(x,y), allxallyEV(x,y). In other words, the concepts "OV" and "EV" become trivial: they apply to everything in the universe.
Normally, a universal is indeed in some sense part of that meaning; but it is likely enough that there are some meaningful predicates (predicates having a meaning) that do not even have a universal corresponding to them as part of their meaning (such predicates might be assigned a universal by courtesy; but they are of course useless for showing that there are universals). This being so, it seems difficult, if not impossible, to argue from the meaningfulness of a predicate to the existence of a universal as its intension without blatantly assuming from the very beginning that there is such a universal.
Frequently, expressions of the object-language are used (not mentioned) in the meta-language. ) Letters t,t', ... , A,B,C, ... , etc. ; but at times they are also bindable metalinguistic variables for the intended object-language expressions (both these functions may be combined). [*2] There may be doubts about the (extended) logical validity of AP3. To dispel these, consider that "tPt'" means no more than "tis either a proper part oft' or is identical with t' " "Is logically valid," "is logically true" are here used as predicates of sentences and, derivatively, as predicates of schemata of sentences.