On Existence

This is a short note on whether anything exists. Bishop Berkeley (1710, 1713) had some ideas on this on his discussions on reality. Let me go further. Let us assume that EXIST is a semantic prime. It is the ultimate semantic prime (Wierzbicka (1996). EXIST takes one argument:

(1) EXIST (x)

Here, the argument x can be anything: an object or a predicate. The claim is then that at least one thing exists. ‘x’ can be a set of smaller sets or elements.

This claim becomes more interesting if we introduce another semantic prime TRUE. TRUE cannot be defined in terms of EXIST:

(2) TRUE (x)

(2) is binary. If EXIST is an argument of [+TRUE], then EXIST is true, if it is an argument of [-TRUE], then it is false. TRUE takes one argument. However, TRUE and FALSE are equivalent to ‘+’ and ‘-‘. [-EXIST] means that ‘x’ does not exist, which is equivalent to saying that EXIST (x) is false. The negative operator in English is also equivalent.

Suppose we make the following claim:

(3) [-EXIST (x) or NOT (EXIST (x)).

This means that ‘+’ and ‘-‘ are binary operators. Which notation is should be used seems to be optional.

If (3) is posited, then nothing exists: neither a predicate nor an object can exist. However, (3) is a paradox: if nothing exists, then the predicate EXIST cannot exist. This means the semantic prime EXIST does not exist. EXIST would be some kind of concept, but concepts cannot exist. To avoid this paradox, then we must posit (1). At least something exists. Given (1), then it not unreasonable to assume that more than one thing exists. The negative operator confirms this.

Bibliography

Berkeley, George. (1710). Treatise Concerning the Principles of Human Knowledge. LaSalle, Illinois: Open Court Publishing Company (reprinted 1950))

Berkeley, George. (1713). Colin M. Turbayne ed. Three Dialogues between Hylas and Philonous. Indianapolis: Bobbs-. Menill Educational Publishing, (reprinted 1954)

Wierzbicka, Anna. (1996). Semantics: Primes and Universals. Oxford: Oxford University Press.