Here is how I would define axiological hedonism:
- Suffering, i.e. any negatively valenced experience, has intrinsic disvalue.
- Pleasure, i.e. any positively valenced experience, has intrinsic value.
- Nothing else has intrinsic value or disvalue.
The core of my take on axiology is that something has intrinsic (dis)value if and only if it literally is valuable. Intuitions are not evidence for intrinsic value.
I am convinced that suffering (and pleasure) fit this criterion. The disvalue of suffering is self-evident from introspection, i.e. from observing how suffering feels. The disvalue is inherent in the experience; it is not a matter of an evaluation done by me, or a desire for the suffering to stop felt by me (even though there is a strong correlation), or me having a certain attitude towards suffering.
That being said, I think a subjective judgment cannot be avoided when it comes to comparison of (different kinds of) suffering and pleasure. In the words of John Stuart Mill:
Neither pains nor pleasures are homogeneous, and pain is always heterogeneous with pleasure. What is there to decide whether a particular pleasure is worth purchasing at the cost of a particular pain, except the feelings and judgment of the experienced? (What Utilitarianism Is)
An experience does not inherently carry information about its commensurability with other experiences, but it does carry the basic information that its value is positive or negative. The basic variant of axiological hedonism is only concerned with the latter.
We are mostly in agreement, though I don't quite understand what you meant by:
If suffering and pleasure are incommensurable, in what way are such outcomes bad?
I would also be interested in your response to the argument that suffering is inherently urgent, while pleasure does not have this quality. Imagine you are incapable of suffering, and you are currently experiencing pleasure. One could say that you would be indifferent to the pleasure being taken away from you (or being increased to a higher level). Now imagine that you are instead incapable of experiencing pleasure, and you are currently suffering. In this case it would arguably be very clear to you that reducing suffering is important.