Literature on self-referring is  mainly within Logic  (for example The Liar paradox, Keit Eric Georg Simmons; Diagonalization and Self-Reference, Raymond Smullyan;  Autologic, Neil Tennant).  For what I  know there are  only two empirical science studying self-refence: Neurology and Quantum physics. The current physical theories of fields include the physical property-reference. Through it the unified field can "perceive itself". In neurology there are current researches on mirror neuron. I don't know if we can really consider neurology as an empirical science, for sure self-reference is the characteristic aspect of consciousness and of  sentient beings. Most of  sciences of consciousness are considered subjective and non-empirical. There is a gap between objective and subjective science, you  inevitably encounters if you interested in putting together empirical and self-reference.

 Lukas – 'Testing testing' can be unpacked as testing whether your testing gives the correct result. Another way to frame the general question then is about testing the notion of 'one right answer' to a question. This is the same as testing 'objectivity'. This is the same as the idea of testing the Scientific Hypothesis (SH). SH is that reality is governed by One universal (objective ) order. Quantum theory (and relativity) served to undermine the notion that there is only one right way to observe (test) and understand reality. This doesn't mean that all conceivable ways are valid. But what is important is that the valid alternatives are 'opposites' (complementary). Consider the difference between republican social science and democratic social science. When you observe a soccer game are you observing competition or cooperation, the conceptual opposite?

My background is philosophy of science and I have just published a book that centers on this and related questions, titled: Give Space My Love: An Intellectual Odyssey with Dr. Stephen Hawking. It is based on an actual four-city lecture tour I organized for Hawking the 1990s. This is just available on Amazon. The eBook will be released April 1, and the audible version soon after.

There is another somewhat deeper interpretation of your question. Is testing (measuring and observation) an appropriate 'tool' in the solution to some problem or in the advancement of some value-agenda. In other words, can you reasonably draw any valid or useful considerations from the results of testing (testing the now) that will be applicable to, for instance, a rapidly developing situation. (Look at the literature in economics concerning the ceteris paribus presupposition (all things being equal).

Also I had a friend in college who always wanted to test his girlfriends to see if they really loved him. Very supportive and attentive in the beginning of the relation, he would then initiate little 'tests' like being late for a date, or not calling. You can imagine. As his attachment grew his need to 'test' escalated. Needless to say heard his relationships were disasters. – All this leads to the questions of trust and honesty is social science testing. (Why do you want to know that about me?) And this seem to reveal the importance of trust and honesty in a society and relationships. 

One real world example of the testing of testing can be found in the work of Hahnemann and Tversky (see Thinking Fast and Slow). Much (most) of testing in psychology was done on college sophomores in highly abstracted environments. Kahnemann reasoned that these 'tests' were not representation of how people think, learn and reason. For instance whether someone would take a bet or respond in a particular way ACTUALLY depends on their history both recent and earlier. Economic reasoning of those who went through the Great Depression think and respond to economic situations differently. This is the basis of what is now being called Behavior Economics (but shouldn't be taken as the correct or best understanding of K/Tv). This line of questioning relates to question of whether you test, or sample, is representative of a larger whole. Testing testing can also be understood as testing the validity of the inductive inference (generalization); uniformity presupposition.

There is also the general about observer interference. This is a major question in quantum theory although just leading mostly to confusion. There is a huge literature in psychology on observer interference/influence: do the actions of the observer influence the response of the subject. The observer is supposed to be 'detached' as if behind a two-way mirror observing reality. The most obvious examples are perhaps in anthropology - can you study a South Seas culture with interfering? Does your questioning tend to alter the 'mind-set' of the population? Does the scientific approach tend (presuppose) that all the members of the culture have the same beliefs (viz. official religion)?

Another area involves the effects of using testing to gain information that you then use to 'manipulate' a population or members of a population. This is central to modern political testing. First if you review the polling during the Vietnam War you see how seemingly minor variations in how a question is asked result in widely differing results. More generally modern society has 'learned' (key concept) that testers are using the results to manipulate them. So there has developed a resistance to providing 'the right answer' or 'response'. (Why do you want to know that?) Arguably modern societies are moving to a post-testable cultural attitude/wisdom. Again the question of embodied trust in a society is important. Does 'testing' (at least potentially) undermine the general trust essential to the operation of civil society? 

Napoleon Ono Imaah: First, are you referring to external validity in the sense of Effects Application or Theory Application? I thereby refer to a paper written by Calder, Phillips, and Tybout (1981). Second, I understand your idea as the problem that from a theory, an infinite number of other theories can be derived from by applying it to itself. Now, they all depend on the truth of the original theory they have been derived from. Obviously, it is "risky" to develop a theoretical framework that depends on a single theory, but isn't this common in a way that weakens the criticism? The theory that is applied to itself would not be the only one which determines the truth of many resulting theories. I'm thinking of "logical laws" like the principium contradictionis. However, these are not dependend on observations.

Paola Cattabriga: Thank you for your suggestions! Can you specify how quantum physics is self-referential or suggest literature with a respective explanation? I find your thoughts on self-reference being linked to logic very interesting, although I don't see a reason yet to banish self-reference from empiricism.

Terry Bristol: Is there a way to evaluate empirical methods empirically? The only ways I have encountered such evaluations use rather philosophical argumentation. I believe I already encountered what you call the Scientific Hypothesis, does it refer or does it resemble the Duhem-Quine-Thesis? I agree in using such a depiction of theories against self-application.

Of course I don't mean to banish self-reference from empricism, on the contrary I think it should be investigated, possibly without falling into incoherence, but it seems that the institutional distinction between empirical sciences and science of consciousness traces historically a schism. 

I do not have references. They are border investigations between quantum physics and disciplines such as transcendental meditation, according to which consciousness can be understood as a unified field. They are just not accepted in academic field since not objective, or not empirical.

Some of the literature on the Sociology of Scientific Knowledge (SSK)

https://en.wikipedia.org/wiki/Sociology_of_scientific_knowledge

and on the Strong Program in Sociology of Knowledge

https://en.wikipedia.org/wiki/Strong_programme

addresses the issues of self-reference (aka reflexivity). Many of the criticisms of relativism also apply to the strong program:

http://www.degruyter.com/dg/viewbooktoc.chapterlist.resultlinks.fullcontentlink:pdfeventlink/$002fbooks$002f9783110325904$002f9783110325904.41$002f9783110325904.41.pdf?t:ac=product/208994

There is a vast literature in these areas so you should be able to find articles etc. very specific to your concerns by googling key words or phrases that the above webpages might suggest to you.

Based on the simple understanding, there are two main factors that differentiate, namely:

Empirical theory requires scientific evidence that meets the conditions so that the truth can be formulated. Meanwhile, scientific theory is formulation requiring the sufficient facts to prove the truth.

On the other hand, the both theories have the same goals that it can be applied to anticipate and/or to prevent a condition that have the same from an indication or symptoms based on scientific evidence or sufficient facts that will be able to provide results in efficient and effective for the achievement with the limited deviation or small risk or if there may not be at all.

Karl –

Thank you. Good material. There is also considerable literature in psychology – the psychology of science.

Karl Pfeifer: Thank you for the recommendations! I find the assumption of reflexivity highly interesting. Has there been a corresponding attempt to develop a philosophy of science including reflexivity?

Following Teguh Yuniarto: Maybe the problem is that "empirical theories" are seen as observations? A prohibition of levelling theories up (or down?) to observations could be thought of (e.g. depicting empirical theories as imperfect models, or temporary attempts at explanation). Would self-applicable theories have to be banished otherwise?

Lukas:

You should read "Metafísica y Lenguaje" of Alejandro Llano. I think there is a translation to English. He deals with self-reference in Language and Knolewedge. I might state that the answer to your question lies in metaphysical assumptions. If concepts refers to other concepts and so on, the infinite regress is unavoidable. Empircal knowledge could not grasp no more than regularities of causes and effects. The grounds for to evaluate those regularities presuposses an answer to what a concept is. To put in another way, the concept of "concept", as Putnam might have said it. 

Regards,

Luciano 

If 'empirical science' refers to any science about actual occurrences then historiography is an empirical science, and descriptive psychology can have empirical sub-disciplines. Every scientific activity is a new historical fact, and that fact is open to historical investigation, which will generate new historical fact, which will be open to historical investigation... There is nothing vicious about such a regress. Those who point out that issues about what sorts of occurrences actually happen are metaphysical are quite correct. There is nothing wrong or otherwise horrible in that. Issues about self-referring propositions are primarily issues in logic, and they suggest strongly a need to abandon the principle of bivalence in logic. 

I address precisely this question for the epistemology/psychology pair in the following (Researchgate posted) paper: http://tinyurl.com/zs7p8ep

Dear Lukas, perhaps the work below may be related to your inquiry:

QUANTUM THEORY AS A SELF-REFERENTIAL THEORY OF INFERENCE

https://quantumasselfreference.com

http://arxiv.org/abs/1705.04307