Abstract

Supposition, Reference and Nonexistence

--- The Supposition Problem and Its Solutions



I. The supposition Problem

Peter is a real person. Now, imagine that it WERE the case that Peter does not exist. The following inference shows that we seem facing a problem given certain ordinarily acceptable philosophical assumptions.



[1] Peter does not exist. (Supposition)

[2] If P, then “P” is true. (Tarski Truth Schema)

[3]”Peter does not exist” is true. ([1] & [2])

[4] If “P” is true then “P” expresses a proposition. (Traditional Doctrine on Propositions)

[5] “Peter does not exist” expresses a proposition. ([3] & [4])

[6] If a statement containing a name expresses a proposition, then the name refers to something which the proposition is about. (Direct Referential Doctrine of Names)

[7] “Peter” refers to something. ([5] & [6])

[8] “Peter” refers to Peter or someone (thing) else. ([7])

[9] Whatever referred must exist. (Axiom of Existence)

[10] If “Peter” refers to Peter, then Peter exists. ([9])

[11] “Peter” does not refer to Peter ([1] & [10])

[12] “Peter” refers to someone (thing) else. ([8] & [11])



Notes:

-- [2] is one side of T-Schema. Some people disagree on how to understand “true” predicate in T-schema, but few people disagree on the truth of the schema.

-- [4] is an orthodox doctrine on propositions. According to the doctrine, propositions are primary truth value bearers and statements are secondary bearers.

-- [6] is a direct referential doctrine on names. It says that the semantic contribution of a name in a singular statement is its referent, and the semantic content of the singular statement is a singular proposition which is about the name’s referent.

-- [9] is the so called the axiom of existence which can trace back to Plato and taken for granted for long.

--Our discussion presupposes that the ontology containing propositions is reasonable.



The above inference shows that if we take principles[2][4][6][9]as true, as ordinarily taken, then if we suppose that Peter does not exist， “Peter” will refer to some one(thing) other than Peter. This contradicts our intuition. People might think “Peter” does not refer at all. The reason is if “Peter” refers, then it must refer to Peter, but Peter does not exist. People also might think that “Peter” still refers to Peter, because as long as Peter’s namer gives the name “Peter” to Peter, and “Peter” is used to refer to Peter in the chain of the speakers’ community, we should take “Peter” to refer to Peter, even if it is supposed that Peter does not exist. No matter what, we have no reason to think, “Peter” will refer to a person (or thing) which is not Peter, just because it is supposed that Peter does not exist. Let us call the problem “the supposition problem” for convenience.

In the above inference, [1] is the supposition, and [2] [4] [6] [9] are premises. One can choose to deny one of them to avoid the supposition problem. In the second part, I will discuss five possible ways which deny [1] [2] [4] [6] [9] separately. In the third part, I will propose a different solution which is based on the logic of supposition, and try to make justification for it.



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