The Semantic-Galois Connection of Fine-Grainedness
Notes on Franz Berto’s first talk of the 2023 Cátedra Gaos
Just as to be an intentionalist (like Kripke, but unlike Quine) is to take extentionality to be too coarse as tool for philosophically analyzing some phenomena, to be a hyperintentionalist (like Dunn and Restall, Berto, Chalmers, Yablo, Fine, etc. but unlike Lewis (sometimes), Stalker (sometimes), Montague, etc.) is to take intensionality (traditional modality) to be too coarse as tool for philosophically analyzing some phenomena.
Intentionality is to material equivalence as hyper-intentionality is to necessary equivalence, but this can be extended ad infinitum, at least in principle, thus:
Let R be an equivalence relation on a representational domain D, then H is a hyper-R operator iff not-R(H(p), H(q)) in spite of R(p, q).
In this schema, intentionality is hyper-extensionality, and hyper-intentionality is, well, hyper-intentionality. Thus, there can be hyper-hyper-intentionality and hyper-hyper-hyper-intentionality and so on.
The series can keep going up and up until it reaches total concreteness, i.e., until H is just the identity relation.
Notice that we can define a new equivalence relation ER, H such that ER, H(p, q) iff R(H(p), H(q)). In cases like these, it is said that ER, H is more fine-grained that R. Another example dualist strategy is to appeal to R for ideal situations and E for the fully detailed account, as Echeverri suggests).
But, of course, defining these notions is the easy part; what we need is a manifestation that these notions correspond to a genuine logical phenomenon, i.e., we need a real application. For example, framing, explanation, essence, information / content, seems to be a manifestation of the reality of hyper-intentionality.
A good heuristic to go looking for hyper phenomena is to look at vacuous cases. Notice that every equivalence relation H has a diamond structure, i.e., it makes some good distinctions in the middle, but collapses a lot of different cases at the top and bottom. So look for phenomena where collapsed cases seem to be actually different.
I am worried about using "seems" here, because it signals that intuitions are lurking behind these counter-examples. Thus, what we have here is a case of intuitions pulling in one direction (more fine-grained) and theory pulling in the other (less fine-grained). Thus, if I am right in (2021), it is not surprising that dualist solutions are so commonly offered (content contains two components one for E and another for R).
In the inverse direction, there are usually four strategies against the postulation of more fine-grained distinctions: the Gricean (switch from p to p’), the Stalnakerian (go meta, i.e. switch from p to “p”), the Lewisian (1982) (fragmentation), and the Williamsonian (R is an abstraction of E) strategies.
Also, notice that the schema can be satisfied by many H operators for the same R equivalence relation. And these many H operators do not have a simple structure. For instance, there is no total ordering of hyperintensional notions, for example, and presumably there is not either for any other hyper- notion.
**Hyper-Hyperintensional Reflections**
ResponderBorrar**Case Analysis:**
Let's consider a hyperintensional operator *H* that operates on propositions related to the property *P*: "being a work of art." The equivalence relation *R* could represent traditional intensionality related to Category *C*: "being a painting."
**Definitions:**
1. **Hyperintensionality *H*:
- Let *p* be the proposition: "The Mona Lisa is a work of art."
- Let *q* be the proposition: "An abstract painting is a work of art."
- Under *R*, both propositions are equivalent because both are paintings.
- However, under *H*, *H(p)* and *H(q)* could be distinct, capturing finer nuances of "being a work of art," considering styles, historical context, etc.
2. **Hyper-Hyperintensionality *H'*:
- Now, consider a hyper-hyperintensional operator *H'* that goes beyond *H*.
- Let *r* be the proposition: "A cubist painting created by Picasso is a masterpiece."
- Under *H*, *H'(p)* and *H'(q)* could be equivalent, as they share the category of "being a masterpiece."
- However, under *H'*, *H'(p)* and *H'(r)* could be distinct, capturing even subtler nuances of "being a masterpiece" in *r*, such as historical significance and the artist's influence.
These examples illustrate how hyperintensional and hyper-hyperintensional operators allow us to distinguish between propositions that might be considered equivalent under more traditional intensionality. Hyperintensionality focuses on finer distinctions at the same level, while hyper-hyperintensionality takes these distinctions to even deeper levels.
*In summary, hyperintensionality and hyper-hyperintensionality unveil layers of nuance within the realm of propositions, transcending traditional intensionality and offering a profound understanding of distinctions, even at the most subtle levels of meaning.*
**Hyper-Hyperintensionality**
ResponderBorrar**Case Analysis**
*Feeling Mountains of Gold by Hume and Seeing Flying Men in the Air by Hume*
"It is vain to pretend that any object becomes present to the mind which is not perceived by it. Whoever pretends to feel a mountain of gold, for instance, or to see men flying in the air, must either be out of his wits or have the most extraordinary faculty of dreaming."
Hume, D. (1739). A Treatise of Human Nature. Oxford: Clarendon Press. Page 181.
Hume's quote on the "mountain of gold" can be analyzed in terms of hyperintensionality and hyper-hyperintensionality:
1. **Hyperintensionality:**
- Let *p* be the proposition "Feeling a mountain of gold is possible."
- Under a standard intensional perspective *R*, *p* could be considered equivalent to another proposition *q* like "Feeling a mountain of silver is possible" because both imply the possibility of feeling a nonexistent object.
- However, under hyperintensionality *H*, we could have *H(p)* and *H(q)* as non-equivalent, as there might be subtle nuances in the nature of the experience, such as texture, symbolic value, etc.
2. **Hyper-Hyperintensionality:**
- Now, let's imagine an even more subtle level of analysis with a hyper-hyperintensional operator *H'*.
- Let *r* be the proposition "Feeling a mountain of gold in a vivid dream is possible."
- Under hyperintensionality *H*, *H'(p)* and *H'(q)* could be considered equivalent, as both imply the possibility of feeling unreal objects in vivid dream experiences.
- However, under hyper-hyperintensionality *H'*, we could have *H'(p)* and *H'(r)* as non-equivalent, capturing even more subtle distinctions related to the specific nature of the dream experience.
In conclusion, Hume's quote on the "mountain of gold" can be analyzed from hyperintensional and hyper-hyperintensional perspectives to highlight potential differences in the philosophical and conceptual interpretation of the experience of feeling an unreal object.