Priest (P7) One, ‘Noneism’, summary

 

by Corry Shores
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[The following is summary. All boldface, underlying and bracketed commentary are my own.]

 

Summary of

Graham Priest

One:
Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness

Preface

P.7 Noneism

Brief Summary:

We often speak coherently about things that do not actually exist. What is important is that when we use quantification, we do not imply that such a non-existent thing exists.

 

Summary

 

We may speak coherently sensibly about things which do not exist. Priest gives these examples:

Some objects do not exist: fictional characters, such as Sherlock Holmes; failed objects of scientific postulation, such as the mooted planet Vulcan; God (any one | that you do not believe in).  (Priest xxi-xxii)

Yet even though they do not exist,

we can think of them, fear them, admire them, just as we can existent objects. Indeed, we may not know whether an object to which we have an intentional relation of this kind exists or not. We may even be mistaken about its existential status. (Priest xxii)

Thus within the domain of all objects there are both existent and non-existent objects.

Regarding the notion of existence, Priest takes it to be “to have the potential to enter into causal relations.” (xxii)

[In logic there is the issue of quantification. We might be speaking of all, some, or none of a set of things.] In order to avoid the idea of existence in quantification, Priest substitutes the symbol G for ∃. This way we would read Gx as “some x” and not “there is an x”.

We can also quantify over the objects in the domain, whether or not they exist. Thus, if I admire Sherlock Holmes I admire something; and I might want to buy something, only to discover that it does not exist. I will write the particular and universal quantifiers as G and U, respectively. Normally one would write them as ∃ and ∀, but given modern logical pedagogy the temptation to read ∃ as ‘there exists’ is just too strong. Better to change the symbol for the particular quantifier (and let the universal quantifier go along for the ride). Thus, one should read GxPx as ‘some x is such that Px’ (and UxPx as ‘all x are such that Px’). It is not to be read as ‘there exists an x such that Px’—nor even as ‘there is an x such that Px’, being (in this sense) and existence coming to the same thing. (To put it in Meinongian terms, some objects have Nichtsein—non-being.) If one wants to say that there exists something that is P, one needs to use the existence predicate explicitly, thus: Gx(Ex∧Px). Quantifiers, note, work in the absolutely standard fashion: GxPx is true iff something in the domain of quantification satisfies Px; and UxPx is true iff everything in the domain of quantification satisfies Px.
(xxii)

[Note, the G and U (G and U) above should look like:

  ]

 

Priest, Graham. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University, 2014.