Handbook of epistemology/Research and discovery

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The will to know[edit]

The acquisition of knowledge is at first natural and involuntary. The development of instincts (Tinbergen 1951, Lorenz 1981), learning and memory (Hebb 1949, Kandel & Squire 1999, Damasio 1989, 2009) enable an animal to acquire knowledge throughout its life. The agent simply learns by living, even if it does not try to learn. But the acquisition of knowledge can also be the goal of a voluntary effort: the agent gives itself as an end the production of a knowledge and endeavors to act, even if only internally, in order to reach it. In other words, it wants to solve a problem it has posed.

How to look for what we do not know? If we do not know what we are looking for, we can not look for it. If we know what we are looking for, there is nothing to look for, since we already know it. So we can never look for anything. Where is the error in this sophistry of Meno, reported by Plato? It confuses the knowledge of a problem with the knowledge of its solution. We can know the conditions of a problem, so we know what we are looking for, without knowing its solution, so we do not know in advance what we hope to find.

A general problem-solving method is to identify all possible solutions (all possible actions and sequences of actions, for example) and to try them until one is found which achieves the desired goal. This method is very effective as long as the number of possibilities to try is not too great. But even the most powerful supercomputers can not solve certain problems in this way because the space of possibilities they have to try is far too great.

A heuristic is a problem-solving method that explores the space of solution possibilities by selecting some which look promising (Newell & Simon 1972, Russell & Norvig 2010). Learning through exercise can be seen as a resolution of a problem based on a simple heuristic. The problem is defined by the objectives which the desired know-how must attain and by their initial conditions. The possibilities of solution are the ways of acting that one can try. We start by selecting a possibility, not too bad if possible, then we experiment with variations and evaluate their results. We modify in successive stages the initial know-how while retaining the variations which seem to bring us closer to the desired know-how. In this way we explore the space of possibilities in small steps, moving from one way of doing things to another that seems to improve it. It is a form of learning through trial, error and success.

Because imagination and abstraction are creative, they enable us to define and explore immense spaces of possibility and thus invite us to solve many cognitive problems.

Theoretical problems[edit]

Solving theoretical problems consists in using reasoning to increase our knowledge. A cognitive problem is theoretical when one is seeking by reasoning to answer a question. If we need to observe or experiment to find an answer, then the question is not a theoretical problem. The prior knowledge, the statement of the question and our faculties of reasoning must suffice to find the solution of a theoretical problem. If there is no reasoning to answer the question, it is because the theoretical problem is badly posed, or that its (meta)solution is to have no solution.

For a closed question, there are only two possible solutions, yes or no. For an open question, the solution must name or describe one or more beings which meet the conditions set out in the question. The beings thus named or described are then the solutions of the problem. For a theoretical problem to be solved, one must state its solutions and justify them, giving a reasoning which proves that they are truly solutions to the problem.

A theoretical problem can be empirical, abstract or ethical depending on the empirical, abstract or ethical nature of the knowledge sought. For an empirical or ethical problem to be a well-founded theoretical problem, it is necessary to make explicit all the conditions of the problem, including the principles which will serve us to reason to solve it. Hence the problem becomes equivalent to an abstract problem, because it is not necessary to take empirical meanings into account in order to reason correctly.

In general, the statement of an empirical or ethical problem is not sufficiently explicit to be a well-defined theoretical problem. We must find or choose ourselves the principles which will serve us to reason (Aristotle, Topics). For this we must of course take account of the empirical meaning of the terms used in the statement of the problem.

The acquisition of knowledge by the solution of theoretical problems requires a prior knowledge already acquired, from which we reason. Thanks to reasoning, the theoretical knowledge already acquired is a stepping stone for acquiring more knowledge.

Solving theoretical problems is a way of approaching the ideal of intelligibility. The more we know how to reason to answer the questions we ask about reality, the more intelligible it is.

Why do reasonings enable us to acquire knowledge?[edit]

When a reasoning is logical, the conclusion can not provide more information than those already given by the premises. Otherwise the reasoning is not logical, because the conclusion could be false when the premises are true. Logical conclusions are always reformulations of what is already said in the premises. In fact many arguments tell us nothing because the conclusion is only a repetition of the premises, in a slightly different form. We then say that they are tautological. They are variations on the theme "it's like that because it's like that."

In the precise sense defined by logicians, tautologies are logical laws, the laws which are always true regardless of the interpretation given to their words (logical operators excepted). When a reasoning is logical, the statement 'if the premises then the conclusion' is always a tautology, as defined by logicians.

Conclusions are only repeating what was already said in the premises. Reasonings must be tautological to be logical. But then why do we reason? It seems that reasonings have nothing to teach us.

The power of a reasoning comes from the general principles on which it is based. If we reduce logic to elementary propositional calculus, a logic in which statements are never general laws, then yes, the tautological character of our reasonings is usually pretty obvious. When it is not, it is only because our logical intuitions are limited. The propositional calculus serves us especially to rephrase our assertions. This can be very useful, because understanding depends on formulation, but this does not explain why reasonings enable us to know what we do not already know.

A statement is a general law when it can be applied to many particular cases. It can always be formulated in the following way:

All x in D is such that A(x)

D is the scope of the law. A(x) is a statement about x.

All statements of the form A(a), where a is the name of an element of D and A(a) is the statement obtained from A(x) by substituting everywhere a to x, are obvious logical consequences of the general law. A(a) is a statement which concerns a special case of the general law.

When we learn a general law, we know at the beginning only one or a few special cases. We can not think at all special cases because they are too numerous. Whenever we apply a known law to a special case which we have not thought of before, we learn something.

A general law is like a condensed information. In one sentence it determines a wealth of information on all the special cases to which it can be applied. When we reason with laws, what we discover is not said in the premises, it is only involved implicitly. Reasonings enable us to discover all that laws can teach us.

Criticism is a heuristic[edit]

When knowledge is abstract, in mathematics in particular, it is possible to give infallible proofs. If one is skeptical, just check the logical correction of the proof to remove any possibility of doubt. In the empirical sciences, it is sometimes possible to approach this ideal of infallibility when we have excellent theories whose principles are well verified by well-controlled experiments. But very generally our proofs and our knowledge are not infallible. If we demanded to knowledge that it be infallible to be honored as knowledge, we should deprive us of most of our knowledge. And we could not even develop any knowledge. A mature science, which has attained or has approached the ideal of infallibility, has not always been so. In its beginnings it was mingled with many errors or uncertainties.

Reason is naturally and necessarily fallible because it is in perpetual development. In order that the truth of a statement may be decided infallibly, the empirical or abstract meaning of the terms employed must be determined and fixed with precision. But that is not how we usually use speech. And that is not desirable. Most often our words are given to be interpreted. We invent new interpretations, new meanings and new expressions every day. Even principles are not immutable, because from the same principle we can invent innumerable variations. The multitude of possibilities of interpretation is vital to the acquisition of knowledge and to the development of reason, but it makes them very fallible, because the truth of a statement depends on its interpretation.

A behavior or an action program is fault-tolerant when error does not prevent it from working properly. If errors occur, they are simply repaired or corrected, and the system continues to function. This is often the case, not always, for the acquisition and use of knowledge. Fortunately. Otherwise we could not develop reason.

If reason were generally infallible, criticism would be reduced to the examination of the evidence. Once their infallibility is verified there would be no room for doubt or discussion. But generally reason is not infallible.

One can doubt a proof by suspecting its logical correction. Most often our reasoning is not completely explicit. We leave in the dark a part of the premises necessary to infer our conclusions, because they seem rather obvious. Explicating everything would be tedious. But this use of the implicit sometimes hides errors of logic. To detect them, the implicit must be made explicit.

Even when its logical correction is not suspect, one can doubt a proof by doubting its premises. We justify our knowledge by proofs based on principles. But the principles must themselves be justified. They have to prove themselves by helping us develop good knowledge. Everyone can use his own experience to put principles to the test and learn to recognize their value. But one must not limit oneself to one's own experience. When one takes a principle as the basis of a reasoning, one implicitly asserts that it has a universal value, that it can serve all those who want to reason. A principle must therefore be put to the test of all the experiences of all human beings. A principle proves itself by helping all human beings develop good knowledge.

In order to evaluate our proofs we must voluntarily submit them to the criticism of all human beings. Objections and attempts at refutation may lead us to modify our reasonings, and sometimes even to abandon them, if refutation is decisive. We develop knowledge by preserving the principles and the proofs which resist the critical tests and renouncing the others.

All the development of knowledge can be conceived as the resolution of a single and vast problem. The objective is a knowledge which satisfies our desire for intelligibility. We explore the space of possibilities whenever we examine knowledge in order to evaluate it. Critical tests are designed to select promising opportunities. Criticism is therefore a heuristic that helps us to solve the problem of the development of reason (Goodman 1955, Rawls 1971, Depaul 2006).

The discovery of reason[edit]

As one can simulate by imagination a critical dialogue, imagine that he must defend what he pretends to know in front of a skeptic who wants to refute him, he can obtain the benefits of criticism simply by exercising his thought alone. But the development of reason is above all a collective work (Leibniz 1688-1690, Goldman 1999), to which every human being can participate as soon as he wants, as he knows that he is capable of it and as he voluntarily submits to its discipline: justification, evaluation and criticism.

We do not know in advance the scope of our ability to solve problems. We discover it through exercise. By solving problems, we become more aware of our abilities. The better we know them, the more we can extend their field of application. We thus discover ourselves as rational beings, that is, capable of developing reason. All the developments of reason are discoveries, because we do not know what reason will reveal to us before we get to work. We discover that we are able to invent or reveal reason.

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