Obviously 'paradox' is a concept, we name certain things to be so. We share the knowledge of those things through the use of language. But those things, "in themselves", those particular "instances of paradox", are they concepts? They seem neither fact nor fiction, inconcrete yet clearly existent.

And speaking of instantion, is every paradox an instance of the same form? What could be the form of Paradox? If not concepts, individually or grouped, what are they

Question: What is the ontological status of paradoxes? Is every paradox in an ontology unto its own?

This, then, is the ultimate paradox of thought: to want to discover something that thought itself cannot think. - Søren Kierkegaard

  • You mean is something like round square or the set of all sets a concept? Sure, there is no requirement on concepts to be coherent. As for ontology, one can use Meinongian subsistence (kind of existence), or Russell's paraphrase (linguistic device for eliminating them), it is a matter of taste, see SEP Nonexistent Objects. – Conifold May 19 '19 at 10:37
  • @Conifold Deep down you think paradoxes are basically a problem of 'definition'? Also see comments to Geoffrey. – christo183 May 19 '19 at 12:19
  • Gap of information is, in a way, the opposite of paradox, which is its excess, too much to hold together. But I agree that resolution of a problem often goes through a paradox. Ideally, it sharpens the view by circumscribing ingredients that are responsible for the problem. It remains to cut out the excess by making more subtle distinctions. But perhaps what you have in mind is what can only be shown and not said, as Wittgenstein put it. Cogito would be an example, attempts to verbalize it result in a fallacy (Curry's is not, it is just Russell' paradox in disguise, and resolved similarly). – Conifold May 20 '19 at 4:37

Nice question.

Your textbox opens with what was going to be the first line of my answer!

Take Russell's barber paradox about the town in which the barber is the "one who shaves all those, and those only, who do not shave themselves". The question is, does the barber shave himself?

Plainly this is a proposition followed by an interrogative. It is not a concept. Of course, it contains concepts and cannot be stated without them: 'barber', 'all', 'self-shaver' and 'non-self-shaver'.

Each paradox is unique in the sense that it can be individuated from all other paradoxes. But there's a sense in which this doesn't make it 'an ontology unto itself' because every paradox fits into a typology of paradoxes. The barber paradox belongs to the class of self-referential paradoxes; and this is not a class of 1.

As a self-referential paradox it also belongs to the class of logical or formal paradoxes as distinct from that of material or (merely) linguistic paradoxes. Class membership denies the barber or any other paradox ontological uniqueness in the sense in which (I think) you are interested.

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    I used to think there was no such thing, it was all wordplay with poorly defined concepts. I still think that paradoxes exist in a sort of gap in information, things not said or thought of yet. This is why I suspected that a paradox proper is a non-concept. Typifying them adds information that often gives the clues to the problem, e.g. self-reference, that help us handle them. Now I'm starting to think that in some instances the information is not forthcoming, that filling the "gap" may require something not even characterizable as information at all. – christo183 May 19 '19 at 12:06
  • The sense I thought they had ontological uniqueness is akin to how all "null" values in a SQL database is treated as having a unique data type. So their ontology would need be described with all the information needed to comprehend the paradox. This seems kind of backwards from the normal hierarchical nature of creating ontologies... – christo183 May 19 '19 at 12:15
  • Something usually at least, if not always, skids on 'poorly defined concepts' in the case of a paradox. Russell, for instance, a fertile source of paradoxes, punctured his paradoxes by specifying something at fault in a paradox's logical structure; his theory of types tries to nail this fault and to deactivate at least a range of paradoxes as spurious on a proper analysis. – Geoffrey Thomas May 19 '19 at 12:36
  • Was looking into Russell here: philosophy.stackexchange.com/q/54384/33787 - Adding categories or types... It may be that all paradox will eventually be dissolved, but something like Curry's paradox seem to be resistant to any logical treatment. Whether or not there ultimately is such a thing as paradox, well this will tell if the human mind is susceptible to the halting problem, or thoroughly vindicate absurdism. – christo183 May 19 '19 at 13:25

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