[Metadata: crossposted from https://tsvibt.blogspot.com/2023/03/provisionality.html. First completed March 7, 2023.]

A mental element has to be open to revision, and so it has to be treated as though it might be revised.

Thanks to Sam Eisenstat for relevant conversations and for the basic notion of provisionality.

Terms

Provisionality

A mental element E is provisional when it is suitable to treat E as open to revision, i.e. as though it might be suitable to revise E in the future. Provisionality is the state of being provisional.

Many elements are provisional: they have yet to be fully grasped, made explicit, connected to what they should be connected to, had all their components implemented, carved at the joints, made available for use, indexed, suitably redescribed in other terms.

An element is essentially provisional when it is, in its essence, provisional. That is, an essentially provisional element is, by its nature and by its role in the mind, provisional: in all (or a great range of) possible worlds the element is always provisional, even after more explicitizing and correcting has happened.

Provisionality is normative

Provisionality isn't how a mind actually treats the element. A mind might treat an element as-if-provisionally even though really the element is not provisional (i.e., really it ought to be treated as finalized), and a mind might treat an element not as-if-provisionally even though the element really is provisional.

Provisionality is also not whether the element will actually be revised.

So, provisionality is normative (it describes "right" behavior, and so is an imperative for an agent behaving "rightly"), while as-if-provisionality is descriptive (describes actual behavior). Revision of an element is a kind of witness to its prior provisionality, since probably if the element actually gets revised, it should have been treated as though it will be revised.

Openness

An element E is open when it is suitable to treat E as non-closed, non-circumscribed, open to novel relations; that is, as though it might in the future be suitable to relate E to more elements than it currently relates to. Openness is the state of being open. Openness could also be called noncontainedness.

As with provisionality, openness is normative.

Openness is a subclass of provisionality. If an element E is open then E is also provisional in that way, because a novel relation with E is a kind of revision of E. Updating a probability distribution can be a substantial revision that's not (much of) a novel relation, witnessing provisionality but not openness. (On the other hand, to deduce consequences of a hypothesis witnesses openness, because it brings more kinds of evidence to bear on the hypothesis.)

Essentiality

Essentiality is when a property holds of a thing by the nature of that thing: in all (or a great range of) possible worlds, the property holds of the thing.

An example is essentially undecidable logical theories: theories which can't be consistently extended to a decidable theory.

A class of examples comes from logical implication, i.e. analyticity, as in "Pediatricians are essentially doctors.". (The concept of analytic is problematic because it relies somewhat circularly on notions of logical rules and implication, see Quine's "Two Dogmas of Empiricism", but relative analyticity (or enthymemic analyticity, understood to always be relative to unstated premises) seems less problematic.)

In terms of a thing as an inductive nexus of reference, essentiality means centrality or eventual permanence. A thing is essentially P if, following the reference of the thing however deep into its nexus, whatever structure is there will satisfy property P.

Quoting from "Rootedness" about essential provisionality and essential openness:

The novelty can't be geometrically bounded: imagine two copies of $R^3$ minus the open unit ball, glued together along the unit spheres, and imagine enclosing the origin: it is a topological separation, but what's contained in the enclosure is an entire world just as large. Even a topological separation isn't possible: a closed border drawn around a nexus, locally seeming to encompass it, doesn't separate the nexus from the cosmos; the depths of the nexus as it will be expressed in the fullness of all the contexts the mind has yet to have dealings in, will meet up again with the other things via a route that doesn't pass through the closed border. One has to picture the cosmos as infinitely many copies of $R^3$ minus infinitely many open balls from each, which are glued together along their spherical borders, infinitely many spherical boundaries, there being no compact borders to isolate out most of some $R^3$.

Etymon

Pro-vision = fore-sight. Provisional = demanding foresight.

As-if-provisionality

What are suitable ways for a mind to treat an element that's provisional?

• Don't rely on it too much. Don't rely on it to not change, expand, or be translated. Don't rely on it to do X and only X.
• Especially expect breakage when given further diasystemic novelty.
• Given further novelty, check if the new structure calls for the element to change.
• Check if new structure gives new opportunities for the element to change.
• Plan around the element getting more effective (more skillful, more accurate, less costly, more explicit, more widely applicable).
• Explore and investigate the structure and uses of the element.
• Expect other minds to have a different version of the element.
• Expect new contexts to call for the element to change.
• Look for ways to suitably revise the element.
  • Look for ways to make the element more explicit and coherent (that is, possessed).
  • Look for contexts where the element would be suitable if only it were somehow different.
  • Look for conceptual Doppelgängers that can be unified.
  • Look for ways to make crosshatch Doppelgängers of the element, i.e. to refactor the element, to reconstitute the element's uses using other elements.

Examples and sources of provisionality

Uncertainty

To the extent that an element is uncertain, it's provisional, because the uncertainty might shift. For example, a weighting of beliefs might change from evidence and reason, or a decision might change.

Encounters

External things are first encountered as phenomena (things showing themselves) and as surface-level dealings. These encounters induce provisional elements.

• A phenomenon leads by reference into a nexus of reference, starting from somewhere on the border of the nexus. "The shape of the table, the joins between the wood of the leg and the wood of the top, the motions of the carpenter's tools in making the table, all reference each other." The phenomenon is provisional: it should be treated as pointing at things in the world.
• Scientific names are often not True Names, but rather First Names.
• If you're manipulating some strange objects that you've so far only identified as [those floppy things sticking out of my shoe], it's natural to later add the understanding [pulling outward on one floppy thing pulls inward on the other floppy thing]. Surface-level dealings are forced to be deeper dealings when problems are encountered.
• Beyond just being uncertain between ideas of what sort of thing something is, a mind might lack the idea itself. This calls not just for induction (changing weights between possessed ideas), but for abduction (coming to possess new ideas). The mind has a pointer to the thing but can't yet understand the thing, so the mind's pointer to the thing is a provisional representation of the thing.
  • For example, the concept of a mathematical function was continually revised (expanded, abstracted), often in ways deriving from the force of straightforward intuitions about functions, but always in a way that kept a lot of the character of previous ideas of functions (e.g., composability). (See "The concept of function up to the middle of the 19th century", by A. P. Youschkevitch; sci-hub.ru pdf.)

Inexplicitness

An inexplicit element fails to be available for relations with other elements that would be suitable. So an inexplicit element is provisional: the element should be treated as though it might be suitable for the element to become available for those relations.

Elements involved in counting-down incoherence are also provisional, since it might be suitable for the incoherence to be repaired. E.g., two contradictory beliefs have to be treated as though at least one of them will be revised. E.g., if an agent is being money-pumped, it should look to revise the elements that are determining that behavior.

New contexts

• In new contexts, new demands are made of elements. To the extent that an element might be used in a new context that it isn't yet fully suitable for, the element is provisional.
• Expanding the domain of discourse calls for finer distinctions and refactoring.
• Polymorphism tries to deal with potential new contexts ahead of time.
• Since there are always new possible contexts, it may be that every element is at least a little essentially provisional.

Noncartesianness

A fixed external thing can be understood more and more fully, suggesting an asymptote, where the mind is completely informed about the thing. An asymptote of complete information is not possible in cases where the thing grows in complexity along with the growth in the mind's understanding of the thing.

If the thing, by its nature, has to grow in complexity along with the mind, then the mind's understanding of the thing is essentially provisional.

If the thing is bound up with the mind, it might by its nature have to grow in complexity with the mind. Such a thing is essentially noncartesian. See embedded agency. If some thing is essentially noncartesian, then it's essentially provisional: since the mind as a whole is provisional, the thing might also be suitable to revise in the future.

Example: the liar sentence and the notion of truth. Example: Gödelian incompleteness. Another example: the notion of set. See Penelope Maddy's "Believing the Axioms":

The second powerful rule of thumb sometimes cited in support of Inaccessibles is reflection: the universe of sets is so complex that it cannot be completely described; therefore, anything true of the entire universe must already be true of some initial segment of the universe.

Anything that the mind has grasped is stipulated to be an incomplete description of the full reality. A notion of set that conforms to this rule is essentially noncartesian and essentially provisional.

S.E. points out (something like):

• A mind's reflective understanding of itself is essentially noncartesian and therefore essentially provisional.
• In general, elements of a mind relate to each other, and so relate to the mind as a whole.
• Since the mind as a whole is provisional, each element is made somewhat provisional. Since elements are given their meaning by their context, all elements are to some extent essentially provisional.
• That is: every element will be reinterpreted (reincorporated, reintegrated) by the mind as the mind grows and changes, including through diasystemic novelty and large-scale conceptual revisions. So the element will take on new implications, and will sit in the mind in a new way, which amounts to a kind of revision of the element.

Corrigibility

To be corrigible is a fortiori to be provisional.

Examples of nonprovisionality

There may not be such a thing as total nonprovisionality.

• True names, if such exist.
• Untyped lambda terms.
• Generally, scientific progress decreases provisionality of some things. The background conditions under which ideas accurately describe the world are made broader and broader, so that there's less room to step out from under those conditions.
• Reflective stability in general might furnish examples of nonprovisionality.
  • For example, preferences might be nonprovisional: they are kept fixed by the mind, and so it's suitable to treat them as though they are kept fixed. (However, preferences may be pressured to be provisional.)