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.8 Characterization
Brief Summary:
When we characterize something, we mean that were it a real thing it would have its ascribed properties. But if it does not exist in the actual world, it can be misleading to say that its characterization is true, even though technically it is, because it might imply the fictional thing is true as well. One solution is to think in terms of impossible and possible worlds, with the actual world as one of the possibles. We would say that a thing with a certain characterization may not exist on our world but does on some other. That way we eliminate the problem of implying the fictional thing truly exists in the actual world, while still affirming the truth of its characterization.
Summary
When we characterize a non-existent entity, we are saying that the characterization holds even though the thing bearing it may not exist.
Consider the first woman to land on the Moon in the twentieth century. Was this a woman; did they land on the Moon? A natural answer is yes: an object, characterized in a certain way, has those properties it is characterized as having (the Characterization Principle). That way, however, lies triviality, since one can characterize an object in any way one likes. In particular, we can characterize an object, x, by the condition that x = x∧A, where A is arbitrary. Given the Characterization Principle, A follows.
(xxii)
To add clarity to this issue in our discussion of dialetheism, Priest will construe the matter using the concepts of possible and impossible worlds. Some worlds are possible, others impossible. The actual world, @, is one of the possible worlds.
In dialetheism, certain contradictions in the actual world are true. But if contradiction does not indicate the impossibility of a world, then what does? Priest says that an impossible world is one with different logical laws than our own, and truth is relativized for each world [on some impossible world, what is true there depends on its particular logical system.]
One might wonder, therefore, what makes a world impossible. Answer: an impossible world is one where the laws of logic are different from those of the actual world (in the way that a physically impossible world is a world where the laws of physics are different from those of the actual world). Given the plurality of worlds, truth, truth conditions, and so on, must be relativized to each of these. That is a relatively routine matter.
(xxiii)
Priest then explains how characterization can be described in this context of worlds. [My interpretation is imperfect, so I invite better ones to the passage that I quote below. It seems he is saying something like the following. Recall from the previous section how instead of the existential quantifier, Priest proposed the particular quantifier G as in GxPx meaning ‘some x is such that Px’. This was so that we do not imply the existence of x, which may be a non-existent entity. It seems now we are thinking of objects not in terms of existence or non-existence but rather as existence on one or another world, perhaps on an impossible one. Priests also says that by using paraconsistent logic well, we can say that each thing with its designating characterization is possible on some world. So we can speak of things as if they do exist, but the question is, ‘where?’ So instead of G Priest uses ε as in εxPx, meaning ‘an x such that Px’. It seems to be then implying its existence but being indefinite about which world it exists on. Priest writes: “Hence, we know that if GxPx is true at @, so is P(εxPx); but if not, P(εxPx) is true at at least some world.” I cannot with certainty interpret what this means, but it seems to be saying that if it is true that there is some object with property P in the actual world, then it is also true that indeed a thing with property P has that property P (the ‘indeed’ is my best interpretation of the first P in the formulation, as if the redundancy is an affirmation of its existence). Please interpret this paragraph for yourself:]
If we characterise an object in a certain way, it does indeed have the properties it is characterized as having; not necessarily at the actual world, but at some world (maybe impossible). Specifically, suppose we characterize an object as one satisfying a certain condition, Px. We can write this using an indefinite description operator, ε, so that εxPx is ‘an x such that Px’. Given that we play our paraconsistent cards right, for any condition, Px, this is going to be satisfied at some worlds. If @ is one such, the description denotes an object that satisfies the condition there. If not, just take some other world where it is satisfied, and some object that satisfies it there.The description denotes that. Hence, we know that if GxPx is true at @, so is P(εxPx); but if not, P(εxPx) is true at at least some world. Thus, consider the description εx(x is the first woman to land on the Moon in the twentieth century). Let us use ‘Selene’ as a shorthand for this. Then we can think about Selene, realize that Selene is non-existent, and so on. Moreover, Selene does indeed have the properties of being female and of landing on the Moon—but not at the actual world. (No existent woman was on the Moon in the twentieth century; and no non-existent woman either: to be on the Moon is to have a spatial location, and therefore to exist.) Selene has those properties at a (presumably possible) world where NASA decided to put a woman on one of its Moon flights.
(xxiii)
[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.
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