4.1 Knowledge and understanding
According to standard theories, knowledge consists in having reasons to believe a fact – also known as ‘descriptive knowledge’ or ‘knowing that’. In more philosophi- cal jargon, to know something is to have a true belief about that something, and to be justified in having such a belief.4Epistemologists, that is, philosophers specialized
in theory of knowledge, lay out three general conditions for knowledge. Follow- ing the standard literature, the following schemata is in order: a subject S knows a proposition p if and only if:
(i) p is true,
(ii) S believes that p,
(iii) S is justified in believing that p
The above schemata is known as ‘Justified True Belief’ – or JTB for short –, where the first premise stands for true, the second for belief, and the third for the justification. Epistemologists take it to be the minimal conditions for a subject to claim knowledge.
Let us now reconstruct JTB in the context of computer simulations. Let us call p the general proposition ‘the results of a computer simulation are correct (or approx- imately correct) of the target system,’ and S the researchers making use of computer simulations. It then follows that S has knowledge of p if:
(i) it is true that the results of a computer simulation are correct (or approximately correct) of the target system,
(ii) the researcher believes that it is true that the results are correct (or approximately correct) of the target system,
(iii) the researcher is justified in believing that it is true that the results are correct (or approximately correct) of the target system
Condition (i), the truth condition, is largely uncontroversial. Most epistemolo- gists agree that what is false cannot be known, and therefore there is little to debate around this condition. For instance, it is false to believe that Jorge L. Borges wrote Principia Mathematica, or that he was born in Germany. This is an example of the sort of thing that nobody would claim – or be in a position to claim – as knowledge. Similarly, no researcher would claim knowledge over results of computer simula- tions that depends upon basic arithmetic operations such as a + b = (b + a) + 1.
Condition (ii), the belief condition, is more controversial than the truth condition, but still largely accepted among epistemologists. It basically states that in order to know p, S is required to believe in p. Although a seemingly obvious claim, it has received several objections from philosophers that consider that knowledge without belief is also possible (Ichikawa and Steup 2012). Consider for instance a quiz where the student is asked to answer several question regarding Argentinean literature. One
4There are many good philosophical works on the notion of knowledge. The specialized literature
such question is “where was Jorge L. Borges born?”. The student does not trust her answer because she takes it to be a mere guess. Still, she manages to answer many of the questions well, including saying “Buenos Aires, Argentina”. Does this student have knowledge about Argentinean literature? According to JTB, she does. This is an example brought up by Colin Radford in (Radford 1966), and counts as a fine piece of philosophical argumentation against JTB.
Now, neither the belief condition as presented by proponents of the JTB nor the criticism against it are issues that interest us here. This is so not only because of the inherent complexity of the subject matter that would take us too far from our main course, but mainly because there are good reasons for thinking that it is very unlikely that researchers get away with mere guesses about the results of computer simulations. First, it would be frankly quite amazing that somebody could guess the results of a computer simulation – in fact, in section 4.3.2 I argue against this possibility. Second, there are dependable methods that reduce the possibilities and need of any epistemic luck about the correctness of the results. I then take it that the belief condition does not really concern us, and move to the real problem for computer simulation, that is, condition (iii), the justification condition.
The importance of condition (iii) is that a belief needs to be properly formed in order to be knowledge. A belief might be true and yet be a mere lucky guess, or even worse, induced. If I flip a coin and believe for no particular reason that it will land on tails, and if by mere chance the coin actually lands on tails, then there is no basis – other than chance – to say that my belief was true. Nobody can claim knowledge on the basis of mere chance. Consider now the case of a lawyer that employs sophistry to induce a jury into a given belief about a defendant. The jury might take that belief to be true, but if the belief is insufficiently well-grounded it does not constitute knowledge and thus lacks grounds for judging a person (Ichikawa and Steup 2012). How could we accomplish justification in computer simulations? There are sev- eral theories of justification found in the specialized literature that come to our aid. In here, I am particularly interested in the so-called reliabilism theory of justifica- tion. Reliabilism, in its simplest form, takes that a belief is justified in the case that it is produced by a reliable process, that is, a process that tends to produce a high proportion of true beliefs relative to false ones. One way to interpret this in the con- text of computer simulations is to say that researchers are justified in believing that the results of their simulations are correct or valid with respect to a target system because there is a reliable process (i.e., the computer simulation) that, most of the time, produces accurate and precise results over inaccurate and imprecise ones.5The
challenge now consists in showing how computer simulations qualify as a reliable process.
Alvin Goldman is the most prominent advocate of reliabilism. He explains it in the following way: “reliability consists in the tendency of a process to produce be- liefs that are true rather than false” (Goldman 1979, 9-10. Emphasis in orginal). His
5Strictly speaking, p should read: ‘the results of their simulations are correct’, and therefore the
researchers are justified in believing that p is true. To simplify matters, I will simply say that researchers are justified in believing that the results of their simulations are correct. This last sen- tence, of course, is taken to be true.
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proposal highlights the place that a belief-forming process has in the steps towards knowledge. Consider, for instance, knowledge acquired by a reasoning process, such as doing basic arithmetic operations. Reasoning processes are, under normal cir- cumstances and within a limited set of operations, highly reliable. There is nothing accidental about the truth of a belief that 2 + 2 = 4, or that the tree in front of my window was there yesterday and, unless something extraordinary happens, it will be in the same place tomorrow.6Thus, according to the reliabilist, a belief produced by
a reasoning process qualifies, most of the time, as an instance of knowledge. The question now turns to what it means for a process to be reliable and, more specific to our interests, what this means for the analysis of computer simulations. Let us illustrate the first answer with an example from Goldman:
If a good cup of espresso is produced by a reliable espresso machine, and this machine remains at one’s disposal, then the probability that one’s next cup of espresso will be good is greater than the probability that the next cup of espresso will be good given that the first good cup was just luckily produced by an unreliable machine. If a reliable coffee machine produces good espresso for you today and remains at your disposal, it can normally produce a good espresso for you tomorrow. The reliable production of one good cup of espresso may or may not stand in the singular-causation relation to any subsequent good cup of espresso. But the reliable production of a good cup of espresso does raise or enhance the probability of a subsequent good cup of espresso. This probability enhancement is a valuable property to have. (28. My emphasis)
The probability here is interpreted objectively, that is, as the tendency of a pro- cess to produce beliefs that are true rather than false. The core idea is that if a given process is reliable in one situation then it is very likely that, all things being equal, the same process will be reliable in a similar situation. Let it be noted that Goldman is very cautious in demanding infallibility or absolute certainty for the reliabilist ac- count. Rather, a long-run frequency or propensity account of probability furnishes the idea of a reliable production of coffee that increases the probability of a subse- quent good cup of espresso.
Borrowing from these ideas, we can now say that we are justified in believing that computer simulations are reliable processes if the following two conditions are met:
(a) The simulation model is a good representation of the empirical target system;7and
(b) The reckoning process does not introduce relevant distortions, miscalculation, or some kind of mathematical artifact.
At the very least both conditions must be met in order to have a reliable computer simulation, that is, a simulation whose results most of the time correctly represents empirical phenomena. Let me illustrate what would happen if one of the conditions above were not met. Suppose first that condition (a) is not met, as is the case of using the Ptolemaic model for representing the planetary movement. In such a case,
6Let us note that these examples show that a reliable process can be purely cognitive, as in a
reasoning process; or external to our mind, as the example of a tree outside my window shows.
7As mentioned in the first footnote, we do not strictly need representation. Computer simulations
could be reliable for cases when they do not represent, such as when the implemented model is well-grounded and it has been correctly implemented. I shall not discuss such cases.
although the simulation could render correct results, they do not represent any real planetary system and therefore the results could not be considered as knowledge of planetary motion. The case is similar if condition (b) is not met. This means that during the calculation stages there has been an artifact of some sort leading the simulation to render incorrect results. In such a case, the results of the simulation are expected to fail to represent the planetary motion. The reason is that miscalculations directly affect and downplay the degree of accuracy of the results.
In section 2.2.1, I described with certain detail the three levels of computer soft- ware; namely, the specification, the algorithm, and the computer process. I also claimed that all three levels make use of techniques of construction, language, and formal methods that make the relations among them trustworthy: there are well- established techniques of construction based on common languages and formal methods that relate the specification with the algorithm, and allow the implemen- tation of the latter on the digital computer. It is the totality of these relations that make the computer simulation a reliable process. In other words, these three lev- els of software are intimately related to the two conditions above: the design of the specification and the algorithm fulfill condition (a), whereas the running computer process fulfills condition (b). It follows that a computer simulation is a reliable pro- cess because its constituents (i.e., the specification, the algorithm, and the computer process) and the process of construing and running a simulation are based, individ- ually and jointly, on trustworthy methods. Finally, from establishing the reliability of a computer simulation it follows that we are justified in believing (i.e., we know) that the results of the simulation correctly represent the target system.
We can now assimilate Goldman’s realibilism into our question about knowledge in computer simulations: researchers are justified in believing that the results of a computer simulation are correct of a target system because there is a reliable pro- cess – the computer simulation – whose probability that the next set of results are correct is greater than the probability that the next set of results are correct given that the first results were just luckily produced by an unreliable process. In other words, results are to be trusted because computer simulations are reliable processes that produce, most of the time, correct (or approximately correct) results. The prob- lem now lies in spelling out how to make computer simulations reliable processes. Let us now stop here and pick this issue back up in section 4.2 where I discuss some of the conditions for reliability of computer simulations. Now it is time to discuss understanding.
At the beginning of this chapter, I mentioned that to know that 2 + 2 is a reli- able operation that leads to 4 does not entail an understanding of arithmetic. Un- derstanding, unlike knowing, seems to involve something deeper and perhaps even more valuable that is comprehending that something is the case.
Why is an analysis on understanding important? The short answer is that scien- tific understanding is essentially an epistemic notion that involves scientific activi- ties such as explaining, predicting, and visualizing our surrounding world. There is, however, general agreement that the notion of understanding is hard to define. We say that we ‘understand’ why the Earth revolves around the Sun, or that the velocity
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of a car could be measured by deriving the position of the body with respect to time. But finding the conditions under which we understand something are surprisingly more difficult than for knowing.
A first characterization takes understanding as the process of populating a coher- ent corpus of scientific true beliefs (or close to the true beliefs) about the real-world. Such beliefs are true (or close to the truth) in the sense that our models, theories, and statements about the world provide reasons to believe that the actual world is not likely to be significantly different (Kitcher 1989, 453).
Naturally, not all scientific beliefs are strictly true. Sometimes we do not even have a perfect understanding of how our scientific theories and models work, let alone a complete grasp of why the world is the way it is. For these reasons the notion of understanding must also allow some falsehoods. The philosopher Catherine Elgin has coined an adequate term for these cases; she calls them ‘felicitous falsehoods’ as a way to exhibit the positive side of a theory of not being strictly true. Such felicitous falsehoods are the idealizations and abstractions that theories and models purport. For instance, scientists are very well aware that no actual gas behaves in the way that the kinetic theory of gases describes them. However, the ideal gas law accounts for the behavior of gases by predicting their movement, and explaining properties and relations. There is no such a gas, but scientists purport to understand the behavior of actual gases by reference to the ideal gas law (i.e., to reference a coherent corpus of scientific beliefs) (Catherine Elgin 2007, 39).
Now, although any scientific corpus of beliefs is riddled with felicitous false- hoods, this does not mean that the totality of our corpus of beliefs is false. A coherent body of predominantly false and unfounded beliefs, such as alchemy or creationism, still does not constitute understanding of chemistry or the origins of beings, and it certainly does not constitute a coherent corpus of scientific beliefs. In this vein, the first demand for having understanding of the world is that our corpus is mostly populated with true (or close to the truth) beliefs.
Taken in this way, it is paramount to account for the mechanisms by which new beliefs are incorporated into the general corpus of true beliefs, that is, how it is pop- ulated. Gerhard Schurz and Karel Lambert assert that “to understand a phenomenon P is to know how P fits into one’s background knowledge” (Schurz and Lambert 1994, 66). Elgin echoes these ideas when she says that “understanding is primar- ily a cognitive relation to a fairly comprehensive, coherent body of information” (Catherine Elgin 2007, 35).
There are several operations that allow scientists to populate our scientific corpus of beliefs. For instance, a mathematical or logical derivation from a set of axioms incorporates new well-founded beliefs into the corpus of arithmetics or logic, mak- ing them more coherent and integrated. There is also a pragmatic dimension that considers that we incorporate new beliefs when we are capable of using our scien- tific corpus of belief for some specific epistemic activity, such as reasoning, working with hypotheses, and the like. Elgin, for instance, calls attention to the fact that un- derstanding geometry entails that one must be able to reason geometrically about new problems, to apply geometrical insight into different areas, to assess the limits of geometrical reasoning for the task at hand, and so forth (C. Elgin 2009, 324).
Here, I am interested in outlining four particular ways of incorporating new be- liefs into the corpus of scientific knowledge. These are, by means of explanation, by means of prediction, by means of exploration of a model, and by means of vi- sualization. To this end, I show how each of these epistemic functions work as a coherence making process capable of incorporating new beliefs into our scientific corpus of beliefs. In some cases, the process of population is rather straightforward. Philosophers working on scientific explanation, for instance, have largely admit- ted that the aim of explanation is precisely to provide understanding of what is being explained. The philosopher Jaegwon Kim says that “the idea of explaining something is inseparable from the idea of making it more intelligible; to seek an explanation of something is to seek to understand it, to render it intelligible” (Kim 1994, 54). Stephen Grimm, another philosopher of explanation, makes the same point with fewer words: “understanding is the goal of explanation” (Grimm 2010). Explanation, then, is an important driving force for scientific understanding. We can understand more about the world because we can explain why it works the way it does, and thus populating our scientific corpus of beliefs. A successful account of explanation for computer simulations, then, must show how to render understanding by simulating a piece of the world. A similar argument is used for the other epis- temic functions of computer simulations. This is, however, the subject for the next chapter.