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Markus Gabriel’s Argument Against the World

Markus Gabriel is an interesting character. He’s enough in the ‘Continental’ tradition to have co-authored a book with Slavoj Zizek. But he also engages with analytical philosophy, and not just in a superficial way. Most interestingly to me, he has a fair amount to say about mathematical logic.

He’s also done a bit to popularise philosophy. Here he is giving a Tedx Talk:

The talk is on the topic of his bestseller, Why the World Does Not Exist (review here), which must be one of the most surprising bestsellers of recent history.

There is a lot to like about Gabriel’s work, for me at least. He does old-fashioned ontology in a generally rationalist mode. He moves in the direction of Spinoza or Hegel and very much against the flow of most contemporary philosophy, either ‘Continental’ or ‘analytical’. That’s always a good direction to be moving in, I think.

On the other hand, his main metaphysical position seems to me to be inconsistent.

He advances two big metaphysical theses. The first is a theory of existence: what it means for x to exist is that there is a “field of sense” or “domain” in which x appears. He never (to my knowledge) adequately defines a field of sense/domain, but his examples suggest that any intelligible description defines a field of sense (“things on my desk”, “nineteenth-century Spanish paintings”). To be is to be under a description [note on this below].

His second big thesis is that there is no such thing as the world — that is, the totality of existing things. Thus “existing thing” cannot count as a field of sense.

My problem is with his argument for this second thesis.

He identifies the world with “the domain of all domains”. I guess the reasoning is as follows: things exist by occurring in fields of sense, so the world — the totality of existing things — will be the field of sense in which all things occur. The inference seems to me not quite valid, but it doesn’t matter; it does at least follow from Gabriel’s definition of existence that if there is a world, meaning a totality of existing things, then there must be a field of sense in which that totality occurs. And if we like we can call this the ‘domain of all domains’.

With the notion of a ‘domain of all domains’ in place, Gabriel argues as follows (Transcendental Ontology, xxvii):

Now we can raise the question of whether the domain of all domains, the DD, in fact exists. If it existed, there would have to be a higher-order domain DD* that contained both the DD and all other domains. In this case, DD* would be what we were looking for, when we tried to grasp the idea of a domain of all domains. Therefore, DD* would be the “true” instance of a DD. If we ask the question whether DD* exists, we will have to form the notion of a DD** and so on ad infinitum. Therefore, there is no ultimate, all-encompassing object domain, no field of sense that would be capable of encompassing all fields of sense.

It seems to me that we could arrest Gabriel’s regress at the first step. If a domain can contain itself, then DD and DD* can be identical, and likewise for DD**, etc. And the one domain identical with all these would be a “field of sense … capable of encompassing all fields of sense”, including itself.

However, Gabriel’s words “higher-order” suggest that this is somehow impermissible. If a field of sense can only occur in a higher-order field of sense then a field of sense can’t occur in itself. I must note that if a field of sense is equivalent to a description, it is hard to see how we could avoid having some fields of sense contain themselves, e.g. “things discussed in this blog post”. But, for the sake of argument, suppose we grant Gabriel the premise that no field of sense can contain itself.

The problem is that Gabriel often needs to refer to all fields of sense. What he calls the Second Main Principle of Positive Ontology is: “every field of sense is an object” (Why the World, 79) — meaning every field of sense, like any object, exists insofar as it appears in a(nother) field of sense. But in which field of sense does every field of sense exist? The totality of fields of sense cannot exist in any field of sense, unless a field of sense can exist in itself. And we had to rule this out to make Gabriel’s argument work. But if “every field of sense” does not refer to an existing collection, then how can Gabriel make true statements about it?

We could simply deny that he can. Perhaps we should reject universal quantification over fields of sense in the same way that some philosophers reject unrestricted quantification. But if we reject it, we cannot say, for instance, that “every field of sense exists by appearing in another field of sense”. And so again we lose a crucial premise in Gabriel’s argument. We can’t deny that some fields of sense might appear in themselves, because we can’t say that every field of sense must appear in a distinct field of sense. His conclusion thus seems inconsistent with his argument.

Note: Gabriel seems to think that his first big metaphysical thesis is a modification of Frege’s view, but I don’t see why it isn’t just Frege’s view. For Frege, existence is analysed in terms of an “unsaturated expression” — a predicate — being such that the function that is its reference yields the value truth for at least some arguments that are referents of proper names. But for Frege every expression has sense as well as reference. So you could just as well construe him as analysing existence in terms of the sense of an unsaturated expression being such as to yield the sense of a true proposition when completed by the sense of a proper name. And that, I think, is Gabriel’s account.

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