The Greek empeiria translates generally to the Latin experientia which then relates to our word experience. The question arises that, if our epistemology is ostensibly "empiricist", just what sort of experience are we talking about? Are we talking about any experience at all, or is there is a difference between different kinds of experiences, and perhaps crucially, are there experiences which we must bracket out, which cannot count as grounds for empirical knowledge.
Without articulating the idea in so many words, past forms of empiricism have the tendency to leave out large terrains of experience in favour of experiences which - paradoxically - are more easily rationalizable. The pretended opposition of empiricism and rationalism collapses together in the face of what could simply be termed experiences that are too intense for both their tendencies.
Laboratory observation and having sex are both experiences, the latter can be said to be more intense. However in the former, if we have a hypothesis that say a given copepod will swim quicker with increased heat, the observation then is similarly easy to articulate as the experiment-informing hypothesis was - further, the logical trail for subsequent reflection will be likewise as rational as the abstractive process that led up to it. For sex, however, we could say that what led up to it was - relatively speaking - not as expressable in the terms of our laboratory hypothesis, that it was less amenable to linguistic rationalization, and more towards an experience that - while more intense and complex in its moment's sense-data - defies a literal representation in words. Empiricists of the past are more often than not talking about something more like the former experience (in the laboratory) than an experience like sex when they are talking about experience and sense-data as a source for empirically-grounded knowledge. They are preferring the more rational experience which is more agreeable to say the academic and decorum-abiding essay form in which they wrote (which - generally speaking - wasn't commonly used for elaborate erotic digressions). In this way, the classical European divide between rationalism and empiricism can also be comparatively seen on a larger scale as a common European rationalistic and abstractive tendency.
Although an experience like sex is inimicable to certain types of, let us say, "rationalistic" language, it is not at all entirely impossible to express (as the word itself attests), although it shifts the linguistic scope to reveal the contingency of more logical forms of language. Language is forced to more diverse and metaphorical forms to the point that the inarticulate and asemantic (say, sounds made during the sex act) sounds and "words" are needed to effectively approximate the experience itself*. Moreover, sex is an experience (to deny this would be - however blatantly ignored in the past - an absolute absurdity), and so the question becomes how - as one interested in using the label empiricist - can we describe an empiricism that includes such experience.
One thing to do would be to simply use the label empiricist and let the descriptive territory fill out the use of that term (or alternatively and more absurdly, use any term at all and allow descriptions to fill out the general meaning of the word). Insofar as no label actually refers to anything the absurdist move would be justified, however in the interest of differentiating from past accepted forms of empiricism and also in more fully exploring them (and indeed, insofar as the term is taken up, agreeing with their positions, however much they are felt to not be entirely complete), I've thought of other labels, fundamental empiricism, grotesque empiricism, basic empiricism, or - as written in the title - base empiricism.
Sex has been my contrastive example of a more intense, less rationalistic experience that a human may have. The idea of "baseness" can explain it as something that is ridden with taboo - it is low, crude, uncultured and representative of a lack of decorum (say, whether discussing porn in a public speech or being known to be an actor in it) - and it is also a basic, fundamental aspect of human existence. There are certain experiences that are relatively inevitable in a human life - experiences that are fated - experiences that are here referred to as basic. These same experiences are the most taboo and - from a cultural perspective - tendentially "grotesque", and to simply mention them - as in a ramble such as this - is seemingly provocative, transgressive, antagonistic or whatever other socially disruptive term. If one were to take the experiences one has, there are large amounts of people that have existed who have never had the laboratory experience mentioned above. Conversely, no one save the rare apotheotic hero like Heracles or Utnapishtim can say the same of the experience of death. Likewise, there are comparably inevitable instances of experience such as sex, excretion and eating (the devouring/killing of one form by another) that are both fundamental experiences in a generalized human existence and are further acts that are riddled with arbitrary custom and taboo, that are - socially speaking - either unspeakable or cloaked in ritualized forms of language which work to formalize their messiness and uncontainability. Thus these basic experiences are both relatively unavoidable (if we were to find any one instance of what we mean by "experience", these would consistently be our best candidates) and also contain a lowly, socially denigrated and ritualized status, that makes the simple fact of their existence disgusting and transgressive (this same idea is very concisely applied to other inevitable givens of biological existence, such as sexual orientation, health, race, that similarly are fundamentally fated and in given societal contexts denigrated or outcast)
Thus basic empiricism attempts to both affirm and alternately expand upon the idea of empiricism. It can be said to hold that empiricism is methodologically correct yet too narrow, or alternatively that it is misinformed insofar as it is too rationalistic. It can also be seen as an attempt to reaffirm a kind of epistemological naturalism in the face of what some might call a postmodernist turn in philosophy and generalized thought, or what I might call an unprecedented form of rationalism, both in the conventional divide of analytic and continental camps. A new, more severely abstracted form of rationalism, requires a more sensually undermining form of empiricism to disrupt its abstracted idealizations - as comparably you might argue that Locke and Newton's empirical tendencies were for someone like Voltaire, a fitting antidote to the then-prevalent forms of Cartesian rationalism that held sway. The vulgarized postmodernist ideas of total relativity, the magical disappearance of the subject, and the total unfalsifiability of an a priori media-coded existence are here described as a kind of super-rationalism - a rationalism whose proliferation of abstracted terms (think of the Deleuzian set of quasi-abstractions) far dwarfs the few terms such as God or thought or a monad which English empiricists were arguably the refutation for. Empiricism is, in this way, both untimely and perhaps all-too-timely a need in this, an age where the sense experiences of an individual are discarded along with other enlightenment projects that have rightly been critiqued for the overruling and unquestioned role they have come to take. In opposition however to the idea that it is the empirical process itself which is flawed, that it is too reductive and lacks spirit and feeling and so on, the contention here is that classical empiricism's abstractive quality have largely been rationalized and taken the form of an a priori prescriptive methodology rather than the open, fallible process that is arguably empiricism's ideal; in other words, it is not a surfeit of the empirical overlords diminishing the unscientific spirits of our lives, but a general lack of the empirical attitude and an insufficient rigour in that empirical attitude itself. The so-called "enlightenment project" is not problematic in its positivistic approach to epistemology so much as parts of it have evolved into the doldrum dogmatic tale of the human march from being more or less dumb primal morons to the now very intelligent evolved creatures that we are - in other words, totally nonsensical and unfalsifiable ideas that can't be proven or disproven but are just chosen and which ultimately form a relative rationalism. In other words, it is the loss of positivism that forms what might be called the enlightenment problematic, not its overwhelming empirical and analytical heritage. The result of such a misinterpretation is that the antidote to an overly empirical outlook would clearly be a healthy dose of rationalism - the odd result being what could be called the postmodern condition - in contrast with Lyotard's definition, it is not the collapse of metanarratives, but rather the unprecedented proliferation of abstract metanarratives and idealistic terms, creating a rationalism entrenched to an unprecedented level. If then, the enlightenment problematic has been thus misinterpreted, and the postmodernist solution has ironically buried us in an even more formidable version of its problems**, the proposed solution or opposition is a return to a kind of empiricism that both takes past empiricism into its position and works to expand that definition into a more rigorous and fundamental formulation.
*that is, if you were to re-represent as best you could the experience of the event for a random listener, you would tend to these types of language - alternatively, you could describe the act in terms of known biological pathways (sperm to egg and so on), though this experientially would come closer to that of a third, relatively detached viewer, or something like the observation of another species mating (though again, this becomes dangerous as the experience here may be more of disgust or overwhelmed fixation, the rationalized explanation not "being enough"))
** It could also be argued, quite simply, that postmodernism means nothing and/or if it does, it is merely as a reflective description of an empirically-alienated time - this would however be replied to in the same way.