Does the Bible adjudicate the debate between empiricism and rationalism? It's possible that Scripture attests a position that's less specific than either alternative. It's possible that Scripture doesn't divvy up knowledge in the way these two alternatives do.
i) Although empiricism is committed to sense-knowledge, commitment to sense-knowledge doesn't entail commitment to empiricism. Strict empiricism considers sensory experience to be the only source of our concepts and knowledge. But, in principle, you can espouse sense-knowledge without regarding the senses as the exclusive source of what we know.
Conversely, rationalism regards some or all of our knowledge as innate or intuitive and inferential. However, to say our knowledge is not acquired through the senses does not entail that our knowledge is innate. A third possibility is that our knowledge is acquired by extrasensory means. It could still be derivative.
ii) Sense-knowledge is fairly easy to prooftext from Scripture. God designed our senses (Exod 4:11; Ps 94:9). Scripture places great stock in the value of eyewitness testimony, in the broader sense of audio, visual, and tactile sources of information (e.g. Lk 1:2; Acts 1:3; Heb 2:4; 1 Jn 1:1-2).
This is sufficient to disprove rationalism, if rationalism is taken to mean that none of our knowledge is sense-knowledge.
iii) On the other hand, Scripture also affirms extrasensory knowledge. For instance, visionary revelation bypasses the physical senses to communicate information directly to the mind of the seer. A kind of telepathy. It simulates sensory stimuli. The seer hears and sees things in his mind or imagination. But there's no external stimulus producing or corresponding to that impression. It's not innate or empirical, yet it's still derivative.
Put another way, the seer acquires knowledge through experience, but it's not empirical experience. A posteriori rather than a priori.
At the same time, visionary revelation mimics sensory experience. To that extent, the intelligibility of visionary revelation depends on prior experience with the sensible world. That supplies an interpretive frame of reference. If a seer had no prior experience of the external world, the simulated imagery would be incomprehensible. For instance, to someone born blind or deaf, if his sight or hearing is restored, that will be very disorienting at first. It will take him time to adjust. To lean how to decode his newly-found sensory experience.
iv) Rationalism is often associated with logical, mathematical, and/or moral intuition. Scripture doesn't have a theory of logic. But Scripture does take informal logic for granted. Here's a classic discussion:
Of course, that, by itself, doesn't select for rationalism. Empiricists use logic too. And they attempt to ground and justify logic through empirical resources. We can debate how successful they are, but that's an essentially philosophical debate which goes well beyond the witness of Scripture.
v) It's difficult to prooftext rationalism from Scripture. 1 Jn 2:20,27 may be the closest. That suggests a kind of spiritual illumination which detects heresy. But it's not properly innate or a priori. It's the result of regeneration. And it operates in tandem with external revelation (e.g. apostolic teaching). In addition, it has a narrow scope.
One might also appeal to Jer 31:33-34 The question is how to unpack that metaphor. It is literally referring to internalized knowledge, or spiritual renewal? The latter interpretation is more likely.
At best, rationalism is underdetermined by Scripture. And we need to avoid a false dichotomy. You can be a rationalist about math, but an empiricist about astronomy or biology.
As I recall, Gordon Clark once defended rationalism by contending that Adam and Eve had innate knowledge. But there are two problems with that appeal:
a) Clark rejects inductive logic. If you see 50 black ravens in a row, the 51st raven may be albino. Clark can't extrapolate from Adam and Eve to humans generally. That would commit the "fallacy of induction." He can't derive a universal or even general conclusion that goes beyond the sample. Not to mention that a single breeding pair is a barely minimal sample to begin with.
b) In addition, Adam and Eve are hardly representative. Of necessity, they had innate knowledge because they were created as adults. That's not analogous to normal human cognitive development, which tracks maturation.
Moreover, even Adam and Eve subsequently acquired additional knowledge through their senses. Their empirical knowledge of the garden. Hearing God tell them things.