# Précis of epistemology/What is knowledge?

« He said that true opinion, combined with a reason (logos), was knowledge, but that the opinion which had no reason was out of the sphere of knowledge; and that things of which there is no reason are not knowable -such was the singular expression which he used- and that things which have a reason are knowable.» (Plato, Theaetetus 201d)

## Rational knowledge must be public and proven

For a knowledge to be rational it must be justified. A claim to reason that is not justified is vain and foolish. We justify knowledge by giving proofs. Without proof, there is no rational knowledge.
Rational knowledge must be public. An exclusively private belief, which can not be communicated and proven, is not rational knowledge. Reason is a collective work. It must be shared to exist and we share it by giving proofs.
Rational knowledge is necessarily a talking knowledge. It is developed from a silent knowledge: all the forms of knowledge that can do without speech. Perception, imagination, reflection, memory and emotions are sources of a fundamental knowledge that precedes the one we acquire with speech.
The theory of knowledge given in this chapter is a theory of rational knowledge. "X knows that K" means "X knows that K in a rational way".

## Conclusive justifications

X knows that K if and only if X can give a conclusive justification of K.
A justification of K is either a reasoning that has K for conclusion or the affirmation that K is a fundamental premise. A reasoning is acceptable if it respects logic and if its premises are acceptable. A premise is acceptable if it is an acceptable fundamental premise or if it is already justified from acceptable premises. To precisely define the concept of justification of knowledge, it is sufficient to define precisely the logical rules and the acceptable fundamental premises.
A statement of the form "X rightly observed that O", where O is an observation statement, is an acceptable fundamental premise, at least for the observations that result from the ordinary use of our natural faculties in good conditions. A theoretical truth that can be accepted by definition of its terms is also an acceptable fundamental premise. For example, "If X rightly observed that O then O" is true by definition of the concept of right, or good, observation. An observation can not be right if it is false.
A justification is acceptable if it is a logical reasoning based on acceptable premises or if it is the assertion that an acceptable fundamental premise is fundamental.
A justification is conclusive when it is acceptable and when all the fundamental premises on which it is based, explicitly or implicitly through premises already justified, are true. Since logical rules always lead from truth to truth, the conclusion of a conclusive justification is necessarily true. A reasoning establishes that its conclusion is true provided its premises are true. If one of its premises is false, a reasoning proves nothing.
The rationalist principle, that X knows that K if and only if X can give a conclusive justification of K, can be admitted by definition of the concepts of knowledge and conclusive justification. The same goes for the other principles that determine acceptable and conclusive justifications.
We can legitimately believe that we have made a good observation and have been mistaken, because we are the victim of a ploy, or of an illusion, or for any other reason unknown to us which makes that the conditions of a good observation were not met. A fundamental empirical premise may be false even if it is acceptable. The acceptable empirical justifications are not always conclusive.
The purely theoretical or mathematical knowledge is based only on fundamental theoretical premises true by definition of their terms, because a purely theoretical truth deals with logically possible worlds, and because all the truths about them result from their definition. As long as we reason correctly on logically possible worlds, there is no room for error or doubt. This is why the mathematical proofs, that is to say the purely theoretical acceptable justifications, are always conclusive.
Empirical knowledge is based both on empirical and theoretical premises. The theoretical premises define models of reality. These are the logically possible worlds for which the theoretical principles are true. If one gives to the terms of the theory an empirical interpretation, then the theorems, that is to say, the logical consequences of the principles, are hypotheses on the empirical reality. For the fundamental theoretical premises to enable us to develop real empirical knowledge, it is not enough that they are true of logically possible worlds, they must be true about reality. This is why empirical knowledge must justify its theoretical hypotheses. The fundamental theoretical premises of empirical theories must be justified in advance to be acceptable. This poses a problem of infinite regress or of circularity. The principles of empirical theories are the foundations of the justification of empirical knowledge. From what foundations can we justify them while they themselves are foundations?

## Justification of principles

« You will recognize them by their fruits. » (Matthew, 7:20)
« We shall see such demonstrations, which do not produce as great a certainty as those of geometry, and which even differ greatly from it, since instead the geometers prove their propositions by certain and incontestable principles, here the principles are verified by the conclusions drawn from them; the nature of these things not suffering that it be done otherwise. It is possible, however, to arrive at a degree of verisimilitude, which is often not much less than complete evidence, when things, which have been proved by these supposed principles, are perfectly connected with the phenomena which experience has pointed out, especially when there are many, and even more so when we form and anticipate new phenomena, which must follow from the hypotheses which are employed, and which we find that in this the effect corresponds to our expectation. If all these proofs of plausibility are found in what I have proposed to treat, as they seem to me to be, it must be a great confirmation of the success of my research, and it is hardly possible that things are not nearly as I represent them. » (Christian Huyghens, Treatise on light, p.2)
We recognize good principles by their fruits.
We do not know in advance what are all the good theoretical principles that enable us to develop a good knowledge. The theoretical principles of the empirical sciences are at first only hypotheses. They are expected to prove their value, to bear fruit, to prove truths that explain observed phenomena or predict new phenomena.
That a good principle bears fruit is a truth that can be accepted by definition of the concept of good principle.
Principles are justified with the principle of justification of principles:
If a principle has borne fruit and if it has not been refuted then it is an acceptable fundamental premise.
A deduction consists in justifying a conclusion with a logical reasoning based on principles or hypotheses. In contrast, we speak of abduction when we justify principles from all their consequences. Justification by induction, that is, justification of a law from particular observed cases, is a form of abduction. Abduction is also called inference to the best explanation. Deduction and abduction are complementary. Deduction gives principles their explanatory power. Abduction selects the principles that help us most in understanding reality.
We justify the principles from their consequences. A skeptic could denounce a vicious circle: the principles are justified by the consequences that they must justify.
There is a circle but it is not necessarily vicious. The principles are not the only sources of knowledge. The observations are too. We have two ways of justifying an observation statement, a direct way, by observing what it says, and an indirect way, by showing that it is a logical consequence of theoretical principles and hypotheses particular to the observed case. Our empirical theories are expected to explain and predict our observations. The truths justified by the observations are also justified by the theory. We want the real to be intelligible, that what is known by the senses be also known by reasoning.
The circle of justification of knowledge is an incessant dialogue between theories and their applications. Observations take us out of the circle of the justification of principles by principles.
The justification of the principles by abduction makes the acceptability of a justification dependent on the circumstances. New knowledge may refute previously acceptable principles by showing that they lead to consequences contrary to observation.
"If A then B, now A, therefore B" is a logically correct deduction. On the other hand, "if A then B, now B, therefore A" is a fallacy. When we justify a principle by its consequences, it is not a logically correct deduction. A conclusion of a logically correct reasoning is infallible as soon as the premises are so, but the justification of a principle by abduction is not infallible. It is legitimate because principles are expected to bear fruit. But it can always be questioned.

## Justification of observations

- How do you know it?
- Because I saw it.
- Are you sure that you saw it?
- Yes. I saw it clearly.
- How do you know you saw it clearly?
- Because I saw it clearly.
A statement of the form "X rightly observed that O" is not always an acceptable fundamental premise. If someone declares that he makes good telepathic observations, it seems that his justification is not acceptable.
An observation must often be justified before one can admit that it is a good observation. We must verify that the conditions of a good observation were well met. We can then fear a problem of infinite regress, since we need new good observations to verify that an observation is good.
It is reasonable to assume that our natural powers of observation do not deceive us in ordinary circumstances. Some observations seem good enough that we do not need to justify them from other observations. They are sufficient to give starting points to our reasoning on the empirical reality.
To justify observations, one can accept the principle of the prima facie acceptability of observations:
If an observation looks good then the assertion that it is good is an acceptable fundamental premise as long as it is not disproved.
Like the justification of principles, the justification of observations makes the acceptability of a justification dependent on the circumstances. New information can show that an observation that we thought was good was not really so.
To show that an observation is good, or to challenge it, one can use the principle of reliability:
A good observation is a true observation that results from a reliable process (Goldman 1986) or from faculties that function properly under appropriate conditions (Plantinga 1993).
A good theory of observation helps to justify all good observations, even those that do not need to be justified.

## Foundationalism or coherentism?

A theory of justification is foundationalist when it states that all justifications must be based on fundamental premises. It is coherentist when it states that all statements are justified by the totality of knowledge to which they belong. Foundationalism is opposed to coherentism if it asserts that fundamental premises are self-justifying, that they can be accepted independently of the totality of knowledge to which they belong. Coherentism is opposed to foundationalism if it denies the existence of fundamental premises, if it affirms that a statement is never more fundamental than another.
The present theory is both foundationalist and coherentist. Good observations and good principles are the fundamental premises from which everything must be justified. But good observations and good principles must also be justified by the totality of knowledge to which they belong. Only the principles true by definition and the good observations which result from the ordinary use of our natural faculties in good conditions are fundamental premises that need not be justified by other premises, but they are nevertheless justified by the totality of knowledge to which they belong.

## Knowing without knowing that we know

If we have given a conclusive justification and if we only know that it is acceptable, then we know without knowing that we know, because we must know that we have given a conclusive justification to know that we know. As soon as a justification leaves room for doubt, we can not hope for more than knowing without that knowing we know.
We do not know or not always if our observations are really good observations. We can also doubt the empirical truth of our principles even if they are well verified. As soon as an empirical knowledge leaves room for doubt, which often happens, we do not know that we even know if we know.
Knowing without knowing that we know is contrary to common intuitions. If we have given a justification for a statement p, we feel entitled to affirm not only p but also that we know that p. But if we only know that the justification is acceptable, without knowing that it is conclusive, we should only affirm p without stating that we know it.
If we defined knowledge only from acceptable justifications, without demanding that they be conclusive, then we could keep the principle that we always know that we know when we know. But this would lead to an unacceptable consequence, that a conclusion could be a knowledge even if it is false.
The counterintuitive character of a theory is a legitimate objection against it, but not decisive. Our current intuitions are not always consistent. The present theory of knowledge is often consistent with common sense, but not always. A disagreement with common sense is not necessarily a theoretical weakness, it is sometimes an asset. To know that one often claims to know when one does not really know that one knows, even if one knows, is not a consequence contrary to all our intuitions. We are not the masters in our own house, even in the house of knowledge.
A theory of justification is internalist when it states that an agent can be aware of all the conditions that make a belief justified. For an internalist theory, an agent can always know that a justification is really a justification. A theory of justification is externalist when it is not internalist, when an agent does not always have access to the conditions that make a belief justified. For an externalist theory, an agent can not always know that a justification is really a justification. The present theory of justification is both internalist and externalist. It is internalist for acceptable justifications and externalist for conclusive justifications.

## Fallible justifications and the Gettier problem

Apart from the mathematical proofs, our justifications are rarely infallible. We can not define knowledge simply by saying that it must be justified, because a false statement can be the conclusion of a fallible justification. One can then think of giving a stricter condition: knowledge is true and justified belief. But then we encounter the Gettier problem (Gettier 1963): a true and wrongly justified statement is not knowledge whereas it is still true and justified. Hence we can not define knowledge by saying that it is a true and justified belief. For example, Lamarck explained the gradual evolution of species from the principle of inheritance of acquired characteristics. In its time this principle could be considered justified, because hereditary phenomena are commonly observed and because the difference between the innate and the acquired characteristics is difficult to observe. We now know that this principle is wrong. Lamarck's justification of the gradual evolution of species was therefore wrong. Lamarck had a true and justified belief but not a knowledge.
To solve the Gettier problem, it is enough to require that knowledge be conclusively justified (Dretske 1971, Zagzebski 2017). If there is an error in the justification, if it is not conclusive, then it is not a warrant of knowledge.
A theory of justification is infallibilist when it requires that all justified statements be true. It is fallibilist otherwise.
The infallibilism of justification is sometimes rejected because it is mistakenly believed that it requires our justification methods to be infallible. But it is compatible with the fallibility of our methods. From the point of view of infallibilism, the wrong justifications produced by a fallible method are not justifications at all, but the good justifications produced by a fallible method are nevertheless good justifications.
The present theory of justification is both fallibilist and infallibilist. It is fallibilist for acceptable justifications and infallibilist for conclusive justifications.

## Justification of knowledge about knowledge

Knowledge about knowledge is justified in the same way as other knowledge. By showing how to justify knowledge, knowledge about knowledge shows at the same time how it should itself be justified.
A theory of justification defines an ideal of rational knowledge. As a theory of an ideal, it is purely theoretical and true by definition, like a mathematical theory, provided that it is not contradictory. But we expect an ideal to be more than just a logical possibility, we want it to help us to think, to work, to live.
Just as an ideal of life shows us its truth by making us capable of living well, an ideal of knowledge shows us its truth by making us capable of acquiring good knowledge. We know that our ideal of knowledge enables us to recognize and justify a good knowledge simply because it works very well, because it produces fruits, because with this ideal we give ourselves the means to acquire much good knowledge, while without it we remain at an impasse.
White needs Blue , Blue needs Green and Green needs White, to stand up.
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