Précis of epistemology/The search for reason

"- ... I'm willing to join you in examining virtue and inquiring into what it could be.

''- But how will you inquire into this, Socrates, when you don't at all know what it is? For what sort of thing, from among those you don't know, will you put forward as the thing you're inquiring into? And even if you really encounter it, how will you know that this is the thing you didn't know?''

''- I understand the sort of thing you want to say, Meno. Do you see what an eristic argument you're introducing, that its not possible for someone to inquire either into that which he knows or into that which he doesn't know? For he wouldn't inquire into that which he knows (for he knows it, and there is no need for such a person to inquire); nor into that which he doesn't know (for he doesn't even know what he'll inquire into)." (Platon, Meno'' 80de, Fine 2014)

The two premises of Meno's argument are false.

We can know what we search for before we find it. It is obvious. This is what we do whenever the problems we are trying to solve are well-defined.

We can search without knowing what we search for. It is less obvious. This is what we do when we search without knowing in advance where we are going or what precisely we want, with an open mind, being ready to welcome what will come.

Knowing what to search for before finding it
As soon as we have a perception or detection system, we are able to search knowing what we search for, before finding it. We search by trying to detect what the system is capable of detecting. We know what we search for if we know what we are able to perceive. We find what we search for when we perceive it.

To pose a problem is to give oneself an end, a goal, an objective. We have solved the problem when we have reached the end or when we know how to reach it. We know an end when we know how to perceive or detect it if it has been reached.

Meno's argument confuses the knowledge of a problem with the knowledge of its solution. We can know an end, so we know what we search for, before having reached it, so we have not yet found it.

We develop our intelligence by developing our ability to solve problems. We discover this ability through experience. If we do not pose problems to ourselves, we do not try to solve them, and we cannot learn whether or not we are able to find solutions.

Any goal-oriented activity is problem solving (or at least an attempt). The problem is to achieve the goal. But we can also find solutions without doing anything, just by using our imagination. When we have to imagine what we are going to do before acting, we replace one problem with another: to imagine an action or program of actions that solves the initial problem. One can then explore by imagination the space of the possibilities of solution. We can solve many problems without leaving our chair. Of course, one needs to know how to anticipate in order to determine by imagination whether a sequence of actions is feasible and whether it achieves the goal. When the knowledge acquired beforehand is sufficient, imagination alone, without action, makes it possible to find solutions. Thanks to our imagination, the knowledge already acquired is a springboard to acquire more knowledge.

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 has 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.

Mute imagination, without speech, is enough to solve many problems. The possibilities of solution are explored by the imagination. The talking imagination, that is to say the thought, the capacity to make theories, is also a very powerful means to solve very many problems. We solve theoretical problems by using reasoning to increase our knowledge. A 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 not well identified, 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.

In order for a theoretical problem to be well-defined, it is necessary to make explicit all the conditions of the problem, including the principles with which we will reason to solve it.

When we know the principles of a theory, we are able to recognize the proofs founded on these principles. We thus have a system for detecting proofs and theorems. One can thus know what one is looking for, a proof of a theorem, before having found it.

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.

When we solve a problem by imagination or reasoning, we find in ourselves solutions that we did not already know. How is it possible ? How can I find knowledge within myself that I do not already have?

When we know principles or laws, we know at the same time all the beings to which they can be applied. But this knowledge remains implicit. The statement of the principle or the law is explicitly known, but not its application to all particular cases.

When we know principles, we know their logical consequences implicitly, because they are determined by the principles, but we do not know them explicitly until we have reasoned. One must reason in order to learn what principles implicitly determine.

Everything I learn by imagination and reasoning I find in myself because I already know inferences, principles and laws, but I do not already know it, because I am mot aware of all their logical consequences. I can find knowledge in myself that I do not already have because I can learn by reasoning what good principles teach.

Searching without knowing what to search for
To search for the answer to a question, one must understand the question. How to search for the answer to the question "what is virtue?" if we do not know what virtue is?

We know what we search for when we are able to detect it if we have found it. But we do not have in advance detectors of virtue, reason or wisdom. To be able to recognize wisdom, we must already be wise. How can we seek wisdom if we cannot recognize it? Even if we hit upon it by chance, we would not even know we met it.

We have to be expert to recognize expert knowledge. A beginner must become an expert, and therefore acquire knowledge that he is unable to recognize. How does he do it ?

A problem is well defined when the statement of the problem is sufficient to completely determine the set of its solutions. We know what we search for when we search for solutions to a well-defined problem, provided we know its statement. The knowledge of the statement of the problem is enough to make us capable of recognizing its solutions.

When we search for solutions to a problem that is not well defined, we do not know very well what we search for, if at all. For example, I want to find something interesting, good principles, good theorems or good applications. I have in advance some assumptions on what is interesting, on what is a good principle, a good theory or a good application. But the statement of the problem, "to find something interesting", even if it is accompanied by all my assumptions, is not enough to determine all its solutions. I cannot know what a good theory is in advance, I have to learn it, I can change my mind along the way. At the beginning, I do not have the means to detect all the solutions of my problem, I search without knowing what I search for.

We can move forward without knowing where we are going, simply by going straight ahead. We try to go further, but we do not know what we search for, because the statement of the problem, "to go further", says very little about its solutions.

A beginner is able to solve beginner problems, to recognize the knowledge and mistakes of a beginner. This is enough to start. The ability to recognize knowledge progresses with the acquisition of knowledge. This enables us to learn to solve increasingly difficult problems. This is how one becomes an expert. It is enough to want to move forward, take one step at a time, and always be willing to learn what comes along the way.

To learn by exercise, through trial, error and success, it is not necessary to know where we are going, we just have to want to progress.

We do not need to know in advance what we search for, we can learn it along the way.

We can learn to perceive. We do not know in advance what we will be able to perceive. We do not know in advance what we will be able to find because we are not yet able to perceive it.

We do not know what we are capable of. The list of problems that we can solve is not known in advance.

We do not know ourselves. We do not know in advance what we can become. We search without knowing what we search for because we search for ourselves.

We can be carried and guided by ideas without knowing where they lead us.

For a theoretical problem to be well-defined, it is necessary to make explicit all the conditions and all the principles which determine its solutions. In general, the statement of a problem is not sufficiently explicit to be a well-defined theoretical problem. We must find ourselves the principles with which we will reason (Aristotle, Topics).

How to find the good principles? - We recognize good principles by their fruits. - How do we recognize fruit? - Reason bears fruit when it helps us to think well and live well. But we do not have the detectors of good thinking and good living in advance. We must already be wise to recognize the fruits of reason. It is not always easier to recognize the fruits than to recognize the good principles. And good principles are themselves among the fruits.

Reason bears fruit when it helps us to think well, to act well, to live well. But we are easily deluded. We can very easily believe that we think or act well for very bad reasons. Reason does not always provide definite answers because the difference between real fruits and illusions, between good wheat and tares, is not always neat and clearly marked.

When we search for good principles, good knowledge, reason, virtue or wisdom, we search without knowing what we are searching for, because we do not have sufficient knowledge in advance to recognize all the good principles, all the good knowledge or all the fruits of reason. But we are ready to welcome whatever reason can teach us.

The great theoretical problems (what is reason? Virtue? Wisdom? ...) are necessarily indefinite problems. For them to be well-defined problems, we would have to know in advance all the conditions and all the principles which determine all forms of reason, virtue and wisdom. We would hardly have anything more to learn. It would only remain to verify in each particular case a knowledge known in advance. But for us reason is not to know everything in advance, it is rather the opposite. We know very little in advance. We must always have an open mind and welcome what comes along if we want to find the fruits of reason.

The touchstones of reason
A touchstone is a hard and rough stone on which a sample of precious metal is rubbed to test its purity. The assayer identifies the metal from the trace it leaves on the stone. We are both touchstones and assayers for reason. We experience reason on ourselves and assess it from its traces on our spirits.

A beginner is not always able to recognize the fruits of reason and the good principles, because he is not yet a very good assayer of reason, he must learn it, but he is nevertheless a beginner assayer, able to recognize the fruits and the good principles accessible to the beginner. He becomes aware of good principles when they make him progress, when they make him more competent. Good principles must make people competent. If they do not make them competent, they are not good principles. Reason must be good for everyone, otherwise she would not be reason.

I am the source, the middle and the end of reason, the source because reason is born from my thoughts, the middle because she develops in me when I seek her, the end because she is accomplishing herself when I am accomplishing myself.

I am for myself a fundamental criterion of recognition of good knowledge, since I recognize it by recognizing my competence.

Reality, life and thoughts continually try thoughts. Thought cannot develop without criticizing itself, because it has to adapt to reality, including the reality that it is itself. A spirit does not know in advance what is good for herself. She learns it through experience and criticism.

Each spirit is for herself as for all the others a criterion of recognition of reason, because reason is necessarily what is good for all spirits.

True knowledge can always be shared. It makes me competent because it can make all spirits competent. If I acquire knowledge without knowing how to explain it, and how to give proof acceptable to all spirits, it is because I did not understand it well. To master knowledge, one must be able to teach it clearly to all those who want to acquire it.

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 spirits develop good knowledge.

Lonely thinking is naturally self-critical, as long as it does not deny reality. But the development of reason is above all a collective work (Leibniz 1688-1690, Goldman 1999), in which each human being can participate as soon as he wants, that he knows that he is capable of it and that he voluntarily submist to its discipline: justification and critical evaluation.

In order to evaluate our proofs we must voluntarily submit them to the criticism of all human being. Objections and attempts at refutation may lead us to modify our reasoning, and sometimes even to abandon it, 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 to think well and live well. 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). But we seek without knowing what we are looking for, because we do not always know in advance how to recognize reason.

What can we hope?
Reason makes us capable, but of what? What can we achieve with the skills we develop rationally? What can we hope?

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.

If the list of problems that we can solve rationally was known in advance, we would know what to hope. But precisely, it is not known in advance. We do not know the range of skills that reason can give us.

Since we do not know what reason makes us capable of, we can place our hopes very high, that the ephemeral present be the splendor of eternal truth, or very low, reason will never be more than a poor consolation in a valley of tears.

The development of reason is the story of a perpetually renewed astonishment. The sciences have exceeded our expectations. Nature has revealed many more secrets than we could dream.

To know what reason makes us capable of, the best way, and the only way, is to try. If we do not try we have no chance to see what works.

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