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J. L. Shaw
excludes certain possibilities. The proposition "all tigers exist' sometimes means that all of thein are alive or did not escape. This use of 'exists' is applicable to both general and singular existential proposions. Moreover, general existential proposition of this type can always be expanded into a finite conjuction of singular propositions. “All tigers exist will be equivalent to 'x exists and y exists', if there are only two tigers. Since we have to examine eaoh tiger our list cannot end with 'etcetera'.
There is another use of the term 'exists' which may be called exiguous use. If 'exists' is used exiguously in the proposition 'tigers exist', it says something about tigers, but not about each and every tiger. This use of 'exists' is symbolized in classical symbolic logic in terms of the existential quantifier. The expansion of the proposition 'tigers exist' i.e. (Ex) (Tx) would be 'a is a tiger or b is a tiger', if there are only two objects in our domain. If the domain contains infinite number of objects, this expansion is bound to end with 'etcetera'.
Moreover, in the case of non-exiguous use the expansion of a general proposition is resolved into a set of singular exisential propositions such that 'exists' is used non-exigously. For example, 'some tigers exist will be expanded into *x exists or y exists' if there are only two tigers. In the case of exiguous use the expansion of 'some tigers exist will be 'x is a tiger or y is a tiger' if there are only two objects in our domain. In this expansion 'x' and 'y' are logically proper names. Since the acceptance of logically proper names creates certain other problems, we modify this expansion in order to avoid those problems. Instead of 'x' is a tiger or y is a tiger' we should say "x is a tiger and 'x' is non-empty, or'y is a tiger and 'y' is non-empty".
Now the question is whether the proposition " 'x' is non-empty" means the same as 'x exists' and whether this use of 'exists' je exiguous or nonexigous (i.e. excluder). If 'x' is treated as a logically proper name, then the proposition 'x exists' is meaningless.10 If 'x exists' is translated as (y) (y=x), then it will be an analytic proposition. Since “ 'x' is nonempty" is not an analytic proposition, it cannot mean the same as (ay) (y=x). If this use of 'exists' is treated as an excluder use, then we cannot make the distinction between the proposition " 'x' is non-empty" and *x did not die or did not escape or was not destroyed etc.' Since we do make a distinction between these two propositions, we require a third use of exists' to give an account of 'x-exists' in the sense of " 'x' is nonempty". By making a distinction between attribute and property, we can explain this third use of 'exists'. The expressions 'red', 'hard', etc. are to be treated as property--referring terms and 'exists' in this sense is to be
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