MichaelStJules comments on MichaelStJules’s Quick takes

[MichaelStJules]

Here’s an illustration with math. Let’s consider two kinds of hedonic experiences, $A$ and $B$, with at least three different (signed) intensities each, $a_1<a_2<a_3$ and $b_1<b_2<b_3$, respectively, with $I_A=\{a_1,a_2,a_3\},I_B=\{b_1,b_2,b_3\}$. These intensities are at least ordered, but not necessarily cardinal like real numbers or integers and we can’t necessarily compare $A$ and $B$. For example, $A$ and $B$ might be pleasure and suffering generally (with suffering negatively signed), or more specific experiences of these.

Then, what X does is map these intensities to numbers through some function,

$$f:I_A\cup I_B\to R$$

satisfying $f\left(a_1\right)<f\left(a_2\right)<f\left(a_3\right)$ and $f\left(b_1\right)<f\left(b_2\right)<f\left(b_3\right)$. We might even let $I_A$ and $I_B$ be some ordered continuous intervals, isomorphic to a real-valued interval, and have $f$ be continuous and increasing on each of $I_A$ and $I_B$, but again, it’s $f$ that’s introducing the cardinalization and commensurability (or a different cardinalization and commensurability from the real one, if any); these aren’t inherent to $A$ and $B$.