The science of artificial intelligence. An a priori or an empirical enterprise?

MARTIN SCHEIDEGGER

In this essay, I will deal with a very fundamental question concerning artificial intelligence (AI). The question I want to discuss is about the methodological status of the science of AI. Basically, it is a question about the sources from which our knowledge in AI research comes from. It can be formulated like this: Is the science of artificial intelligence an a priori or an empirical (i.e. a posteriori) enterprise? This question seems to presume that there are at least two options to answer this question. If one takes the ‘or’ in the question to be exclusive, only one of the options—either a priori or empirical—can be right. However, if the ‘or’ is taken to be inclusive, it could be that both is right. As I will show, we should read the question as using the inclusive sense of ‘or’ and recognize how both methods are important in the inquiries that are made in the science of AI. Therefore, my thesis is that, in a certain sense, a one-dimensional picture of the science of AI, opting for only one of the options the exclusive reading offers, would be inadequate.

In what follows, I will first outline the account of Newell and Simon. Then I shall present Kukla’s critique of it and his own view that is fundamentally opposed to what Newell and Simon thought. Furthermore, I will partly defend the view that Newell and Simon support by a critique of Kukla and the way his approach is seemingly defended in Walmsley (2012). In the end, I will conclude with a kind of synthesis.

The thesis that the science of AI is empirical in its nature has been endorsed by Allen Newell and Herbert A. Simon (1976). (To be precise, Newell and Simon speak of computer science.) The competing thesis that the science of AI is in principle a priori and therefore basically “armchair psychology” (Kukla 1989, 58) has been advocated by André Kukla (1989), who critically discusses the account of Newell and Simon. While, at first glance, both views seem to be reasonable options, we have to look more closely at the arguments that have been put forth by the two parties in order to be able to assess them critically.

Newell and Simon’s argument is based on the practice we often find when we look at how AI researchers test the outcomes of computer programs. Since the code of many programs they are dealing with is too long and complicated in order for us to see or anticipate what their results are purely by using our limited human capacities, we often have no other way than to run the programs and observe what the computers do. Exactly this procedure is what Newell and Simon call ‘empirical’ because it is experimental in its nature. Being an empirical discipline, Newell and Simon compare computer science to other empirical sciences, however, noting the special sense in which it is ‘experimental’:

“Computer science is an empirical discipline. We would have called it an experimental science, but like astronomy, economics, and geology, some of its unique forms of observation and experience do not fit a narrow stereotype of the experimental method. None the less, they are experiments. Each new machine that is built is an experiment. […] Each new program that is built is an experiment.” (Newell & Simon 1976, 114)

We know the machines and programs because we made them. So, when we run them (i.e. make an experiment), we “can relate their structure to their behavior and draw many lessons from a single experiment” (ibid.). In this way, computer science can progress by observation and trial and error. Thus, machines and programs can be optimized.

Kukla argues against Newell and Simon that “AI is not an empirical science” (Kukla 1989, 56) because it is about “constructing programs that perform in a predetermined manner” (ibid.). This means that the relation between the programs and the behavior of the computers is purely deductive. Therefore, the science of AI is a priori like mathematics, according to Kukla. The analogy to mathematics plays an important role in Kukla’s argument. For, mathematics apparently serves as the standard of an a priori science. Kukla, therefore, constantly compares both sciences in order to prove his thesis that they are essentially alike. So, if we accept that mathematics is an a priori science, we would then have to say the same about AI research.

Interestingly, Kukla seems to suggest that most AI researchers (like Newell and Simon), in contrast to philosophers (like him), have a wrong view about what the nature of their discipline is (cf. ibid.). Some could see this, indeed, as a quite presumptuous claim.

Kukla finds an argument in Newell and Simon, according to which AI is an empirical science because it “seeks to establish a contingent proposition” (Kukla 1989, 57), namely that “physical systems are capable of intelligent action” (ibid.). Now, Kukla states that this “conclusion is evidently based on the hidden premiss that the truth of a contingent proposition can only be settled by doing empirical work” (ibid.). Here, the position of “only” in this sentence is important. It does not exclude a priori work, unless an “only” is also inserted after “doing” (making the empirical work sufficient rather than just necessary). It is not clear whether Kukla saw this. Kukla goes on by giving an example of a contingent hypothesis the truth of which “can only be settled by a priori means” (ibid.): “Fermat’s mathematical intuitions were always correct.” In order know that this hypothesis is true, we would also have to prove Fermat’s Last Theorem (as Andrew Wiles did a few years after Kukla’s paper), which would mean doing a priori work. However, at least his example cannot show that we can know this hypothesis only by doing only a priori work, since he himself said in advance: “let us assume that we are already in possession of all empirical facts that could bear on the truth or falsehood” of this hypothesis (ibid.). This is very important, since it does not work without empirical data. This means, it is a problem that cannot be solved purely a priori. Therefore, in this kind of examples that Kukla wants to use against Newell and Simon, at least a plurality of methods seems to be at work.

According to the second argument that Kukla claims to have found in Newell and Simon, they assert that in principle we could “ascertain the success or failure of an AI program by a priori means” (Kukla 1989, 58). (I really cannot reconstruct where exactly he found this thesis. He does not cite any passage or page number in order to support this claim.) The main thesis of Newell and Simon is, now, according to Kukla, that although we could do it in principle, in practice our cognitive limitations often force us to use empirical methods. Therefore, we have to actually run programs in order to test their functionality (cf. ibid.).

Kukla goes on to compare the work of AI researchers and mathematicians by claiming that the use of empirical trial-and-error methods does not make the science of AI any different to what is going on in mathematics. First, I would like to notice that Kukla thereby did not show that AI is an a priori science. He shows only the trivial similarity that sometimes things work out in science as one would like them to do and sometimes they do not. Secondly, there is an important disanalogy he overlooked. In order to show this, I, unfortunately, have to quote the passage in its entirety:

“The first sense is that AI researchers use an empirical trial-and-error approach in discovering the programs they want: they construct provisional programs largely on the basis of empirical rules of thumb, run them to see how they go wrong, and tinker with them until they work. But this modus operandi is identical in every essential respect to the one followed by mathematicians who are hunting in the dark for a proof: they try first one line of approach and then another until they find something that leads them to where they want to go.” (ibid.)

The important contrast is that in the one case, a computer is operating, in the other case, it is a mathematician who is in control of the operations. Therefore, the modus operandi is not at all the same. Kukla’s analogy is too superficial and imprecise.

We find a similar disanalogy in Kukla’s last comparison. He mentions the computer proof of the four-colour map theorem. His argument is, basically, that the use of computers in such cases differs only in degree to the use of other tools like paper and pencils, wherefore one should not count it as an empirical element in research that would forbid calling it ‘a priori’ (cf. Kukla 1989, 59). However, I think that although these might all be instruments (to speed things up), they are still quite different in kind and not only in degree. Paper and pencil do not operate on their own. There is no similar experimental character to them when compared to running a program.

Kukla concluded that if “our criterion for an a priori science does not permit this kind of empirical involvement, then there are no a priori sciences” (ibid.). One could remark that maybe there are really none. Would that be a problem? At least, maybe some sciences are just not “purely” or “merely” a priori. Moreover, at one point, Kukla even seems to contradict his own main thesis:

“Once AI researchers have a program that works the way they want, their belief in the corresponding necessary truth (that such a program exists) is based on the evidence of their senses—i.e., on seeing the program work correctly […]. There is no denying that the foregoing description of AI research is correct.” (ibid.)

In what follows, I will point out some problematic assumptions Kukla seems to make, according to the presentation and apparent defence of his position in Walmsley (2012). First, I would like to note some difficulties surrounding the idiosyncratic interpretation and use of the term ‘a priori’ I observed there. It seems to me as if the term ‘a priori’ (and also ‘empirical’) is applied in the wrong way because it is used there to characterize “issues” (Walmsley 2012, 24). However, not “issues” are a priori or empirical, but judgements are. So, the question we would have to ask is: By which method do we proceed in order to attain our judgements in AI research? (Maybe some parts of the science of AI could be done a priori alone. Would the same be true empirical research?) Yet, this first critical note is only of minor importance, I think, and it could be easily worked around by rephrasing.

I see a more important problem in the alleged asymmetry of the a priori and the empirical (cf. ibid.). It seems to me to be only a result of pure stipulation and can, therefore, not ground the priority claim Kukla makes concerning the a priori in AI research. I could stipulate as well that calling an issue ‘empirical’ does not rule out the possibility of an a priori solution. Remembering my first objection, it should be clear that judgements can only either be a priori or empirical, not both at the same time. However, the solution of certain problems might involve empirical and non-empirical methods. (Another point one could contemplate on is whether analytic truths, as in the example ‘All bachelors are unmarried adult males’ [mentioned in Walmsley 2012, 24], are really the interesting cases we should think about.)

What really bothers me, though, is what weird notion of ‘science’ we would have if we followed Kukla, i.e., if we would define a science by what it in principle could be rather than by what it actually is in practice. Why should the potential have priority over the actual in these matters? That does not make any sense to me. In addition, even if the science of AI could be a priori in principle, this does not make it necessary that it has to be done a priori (however, the same might be true for the empirical work in some sense). Accordingly, it is not clear to me why “the question of whether AI is an empirical or an a priori enterprise just is one such in-principle question” (Walmsley 2012, 25). Walmsley

gives no reasons for this thesis. It does not sound plausible to me. The philosophy of science behind this thesis seems anaemic to me, depriving science of its life. Maybe one could get something out of this approach by interpreting it as an answer to a different and more specific question (e.g. How would doing AI be like if we had no auxiliaries?).

Ultimately, it seems as if Kukla’s notion of AI as a science is just too narrow for it to be descriptively adequate. As Walmsley rightly remarks, AI is about more than just the relations between programs and their behavior; it is also about developing programs—for instance Newell and Simon’s General Problem Solver (cf. ibid.). These developing processes (especially weak AI which is about simulating human cognition) can involve empirical elements (cf. Walmsley 2012, 26). But if some parts of AI research are empirical, the whole should not count as a priori. Instead of labelling the whole of AI research either as a priori or empirical, I would like to take it as what it really is. This means that we should accept the plurality of empirical and non-empirical methods that are deployed in AI research and come see it as a hybrid enterprise.

References

KUKLA, André. 1989. “Is AI an Empirical Science?”. In: Analysis 49 (2), 56-60.

NEWELL, Allen & SIMON, Herbert A. 1976. “Computer Science as Empirical Inquiry: Symbols and Search”. In: Communications of the Association for Computing Machinery 19, 113-126.

WALMSLEY, Joel. 2012. Mind and Machine. Palgrave Macmillan.