# Definitions

## Conventional use of the term

In most of the existing literature, the following definition of explanatory gap is used:[1] Let ${\displaystyle {\mathcal {P}}}$ denote the description of a phenomenon ${\displaystyle P}$.

Definition 1
${\displaystyle P}$ exhibits an explanatory gap iff ${\displaystyle {\mathcal {P}}}$ cannot be deduced (i.e. derived logically) from physical facts or physical theories.

Here, ${\displaystyle P}$ usually denotes a type of phenomenal consciousness or a conception of qualia, and "physical facts" or "physical theories" refer to the physical broadly construed.

The problem with the above definition is that deductive forms of explanations are not the only forms of explanation in science. While deductive forms were first thought to be prevalent[2], there are in fact many other notions of explanation in use in science.

This point has been made particularly clear by[3]. She argues that explanatory gaps need to be studied relative to the different connotations of explanations that arguably are in use in science. Alternatively, it might be tempting to define an explanatory gap as in the next section.

## Updated definition

As a result of the above, one might be tempted to define an explanatory gap as follows. Let again ${\displaystyle {\mathcal {P}}}$ denote the description of a phenomenon ${\displaystyle P}$.

Definition 2
There is an explanatory gap between a phenomenon ${\displaystyle P}$ and natural science iff ${\displaystyle {\mathcal {P}}}$ violates a necessary condition of all notions of explanation that are considered valid in science.

# Existence

It does not seem unreasonable that Definition 2 can actually be satisfied. In virtue of being scientific explanations, the various modes of explanation might make common assumptions. E.g., one such assumption could be that the phenomenon is intersubjectively accessible, which might not be the case for certain aspects of conscious experience. Cf. [4] for one way of conceptualising this. Since Definition 2 implies Definition 1, the same holds mutatis mutandis w.r.t. the latter.

## References

1. For the emphasis of deductive notions of explanation, cf. Taylor, Elanor. "Explanation and the explanatory gap." Acta Analytica 31.1 (2016): 77-88.
2. Hempel, Deductive Nomological Model of Explanation
3. Taylor, Elanor. "Explanation and the explanatory gap." Acta Analytica 31.1 (2016): 77-88.
4. Kleiner, Johannes. "Mathematical Models of Consciousness." Entropy 22.6 (2020): 609.