This one is long overdue, I think. To avoid having to repeat myself, I've attempted to make this entry adequately elaborative and encompassing. Hopefully, I've succeeded.
In order to appreciate just how relevant negative feelings are to sentient organisms, it is perhaps necessary to start by defining how analysis of physical qualia should work, then defining which individual qualities, in the abstract, are worth applying the process of pragmatic selection to. Based on my own observations of physical reality, and on the confirming observations of others (even if I must always observe that a person has observed something myself, making all observation slightly suspect, but that's a separate topic), I've found that the quality of sensation is inherently negative, as it could not exist in the absence of discomfort or perceived deprivation (more on this later). However, this premise warrants further analysis if we are to properly convey that such sensations are, in effect, "bad" according to a well-defined and organized value system; otherwise, we'll wind up with people saying, "So what if things hurt? Your assertion that pain is bad isn't based on anything empirical!"
Most children grasp why such statements are bloated and borderline pretentious on a raw, intuitive level, but rarely are they equipped to actually deal with the slew of contrived counter-arguments in support of the idea of the "subjectivity" of suffering. Let's see if we can help.
Firstly, I cannot honestly claim to still support the dichotomy of empirical/a posteriori knowledge and mathematical/a priori knowledge. Math only appears "unempirical" because it is a raw abstraction, meaning that it is a mental conception of a general principle without any applied context, making it data rather than physical information. However, both data and information are essentially the same thing; it's just that data, again, lacks context, and, in being rather non-specific, cannot be useful until it has been properly interpreted and stored or acted upon as information. Math and empirical phenomena, then, are part of a unified continuum, just as data and information are, because math is essentially data, and empirical information is, well, information.
What role does logic play in this? It can be applied to both empirical information and math; claiming that logic is somehow synonymous with math, while empirical information is in a realm entirely separate from logic is blatantly fallacious. Of course, logic itself could be said to be taken a priori, but given that I always refrain from making truth claims of any kind, this isn't so important to note.
A visualization might look something like this:
Logic=>Contextualization; qualification; processing; interpretation; understanding (what it is)
Logic=>Information; understanding (what it entails, concludes in, etc.)
I apply logic to all three steps; it should be applied not only when converting data to information, but also when gleaning data, or when understanding information after it has been interpreted.
With the above in mind, is it not likely that all "logical" claims are predicated on some kind of empirical observation via the senses? 2+2=4 is data, but two apples being combined with two other apples to form a group of four apples (or one group, depending on abstraction level) is an empirical phenomenon which requires repeated observation and peer review, just like anything with which we physically interact. 2+2=4, therefore, could not exist without the myriad claims similar in content to "Two apples plus two apples equals four apples." The bottom line: It's all empirical; in order for math to exist, we have to be able to first test things which provide empirical evidence of the existence of quantity.
But what kinds of empirical information are there? Are there any divisions that we can make in order to bring coherence to our worldview? Well, the most obvious and fundamental of all empirical divisions appears to be into analytic and synthetic statements, as originally proposed and defined by Immanuel Kant in his Critique of Pure Reason. In this work, Kant quite accurately proposes that there are two kinds of concepts: subjects and predicates. The logic goes that all syntax structures can be fundamentally divided into these two parts, with the latter being necessary in conjunction with the former if a syntax structure is to qualify as complete and independently functional. In essence, subjects define what a sentence is about, while predicates affirm or support the subject in some way with additional information, usually conveyed via verbs. Additionally, subject concepts can subsume predicate concepts, or contain them; in such cases, the subject can be defined by the ensuing predicate, making the statement as a whole an analytic statement. The inverse, of course, is when a predicate concept is not contained in a subject concept, making the statement as a whole a synthetic statement.
If the definition of "circle" requires that things must be round in order to qualify as circles, then roundness is part of the subject concept of "circle." In a sentence, if additional clarification is provided after a verb, and the information presented is inherent in the definition of "circle" ("...are round"), then that second half of the sentence is not only the predicate half, but is also contained in the subject itself. Where a quality is not inherent in the definition of "circle," however, like when stating that a particular circle is eight inches in diameter, the quality can be said to be a supporting predicate concept independent of the subject concept. To put it simply, "All circles are round" contains a subject ("...circles") and a predicate which is inherent in the essence of the subject ("...are round"). "This circle is eight inches in diameter" contains a subject ("...circle") and a predicate which is independent of the concept of a circle, meaning that not ALL circles must, by definition, possess the predicate quality ("...is eight inches in diameter").
Bold though it may be, I am, here and now, claiming that "bad," "needs to be fixed," "should be avoided," "needs to be reduced," etc. are predicate concepts contained in the subject concept of "suffering," making "Suffering is bad and must be reduced or eliminated altogether" not only an empirical statement (due to all logical statements being derivatives of some kind of empirical experience), but an analytic one as well.
Part II will include more on how I view the process of qualitative analysis.