The Theory of Items: Items, Nonexistence, and Contexts - Liem, Stephen (My University, 1987)
This thesis is divided into two parts: the Theory of Items, and the Theory of Contexts. The latter is a further elaboration of the former.
In the first chapter I argue against the classical doctrine of ontological-referential theory. This classical position may be represented by Russell's and by Quine's position on nonexistent objects.
The first position that I propose to reject is the view that in order to say anything true about an object its name or description must have an actual reference. This view is represented by Russell's proposition *14.21: t-:Ψ (rx)(øx) .->. E!(rX)(øx) on which Russell writes: "This proposition shows that if any true statement can be made about (1x)(øx), then (1x)(øx) must exist". (Principia Mathematica)
The Theory of Items rejects this view and states that whether a statement about a certain object is true or is false does not depend on the ontic status of that object. Thus, consequently, a true statement about nonexistent objects can be made (without making a distinction between a secondary and a primary occurrence as Russell did).
The second position that is to be rejected is the view that nonexistent objects are mere nothings. This is represented by one of Quine's theorems that nonexistent objects are simply empty sets. *197 t- r -(Eβ) (α) (α=β. ≡ ø) ->. (1α)ø = 9¬
(Mathematical Logic). For the Theory of Items, nonexistent objects are not nothings, they are somethings for they can be said to have any property whatsoever. Thus if we may have a set that contains existent objects, then we may also have a set that contains nonexistent objects. Nonexistent objects are just as much 'items' as existent ones; this is the reason why I call the theory being proposed here the 'Theory of Items' and not the Theory of Objects. The word 'item' is used instead of 'objects' to indicate the ontic neutrality of the matter that we are talking about.
In the second chapter I will present various examples of the classical view and I will try reply to their arguments in the light of the Theory of Items explained previously.
In the third chapter I will discuss the Theory of Contexts. I will argue that semantical features (truth and falsity) should be assigned to various statements about various items (existent or nonexistent). I maintain that the assignment of a truth value is very much context-dependent. The characteristics of contexts and various rules that iv. govern them will be discussed. More attention will be given to the fictional items and fictional contexts for no doubt they present some peculiar problems. For example if a fictional item x in a story C1 has a feature that-p, and the same item in a different story C2 has a feature that--~p, then can we validly conclude that the fictional item x is both p and ~p? My argument is based on the analysis of contexts. Only by presenting a satisfactory theory of contexts can that problem (and many other paradoxes) be solved.
This thesis is far from being complete. There are some important topics that I do not discuss (due to page and time limitation). For example the problems of: significance and nonsignificance; whether we should take a three value logic (by incorporating significance as the third value) instead of the classical two value system; consistencies; and a possible formal theory for the Theory of Contexts. The last two of these problems are stated very briefly in the Appendix.
Keywords: items; contexts; Russell; Quine; mathematical logic; Philosophy; Philosophy