We have a knowledge of reality. Reality is presented to us by our senses through the medium of percepts and our intellect fashions concepts or ideas which are representations of reality in an abstract and universal manner. But mere percepts and concepts do not as yet constitute knowledge; they are the raw materials from which we make the finished product.

We have knowledge when we affirm or deny something of something and that takes place in an interpretive judgment made by us. A judgment is always a mental pronouncement about reality in some form or other, and this pronouncement represents the actual condition of reality as it is in itself. Judgments, therefore, possess a truth-claim.

The Three Primary Truths
There are three truths which must be accepted at the beginning of any investigation into the problem of knowledge and truth:

The First Fact: The fact of our existence. “I exist.”
The First Principle: The principle of contradiction. “A thing can not be and not-be at the same time in the same respect.”
The First Condition: The essential capability of the mind to know truth. “My intellect can reason and discover truth.”
These primary truths cannot be “proved” by a positive demonstration because they are presupposed and involved in every demonstration. They are so evident that any attempt to doubt or deny them would already mean they have been affirmed and accepted. They are, therefore, fully grounded in reason and no reasonable person can dispute them consistently.

In fact, if anyone questions you as to their truth, simply ask: “What will you accept as proof for the truth of these three primary truths?” Put the challenge to the opponent. No opponent can even tell you what form of proof he would find acceptable without accepting the truth of the three primary truths in the first place!

Different Theories of Truth
Truth and falsehood may be applied to propositions, but never to arguments. The attributes of validity and invalidity can belong only to deductive arguments, never to propositions. It is very important to have a firm grasp of the notions of true, false, valid, and invalid. Many people get the “true” confused with the “valid” and the “false” confused with the “invalid.” Let’s first consider the terms “true” and “false.”

An idea itself cannot be, strictly speaking, true or false. An idea is simply the intellectual representation of a thing. An idea may be clear or fuzzy, useful or useless, represent a real thing or a non-existent thing, but it cannot, strictly speaking, be true or false. An idea just “is.” It may be a good representation of a thing or a bad representation of a thing.

The notion of true and false is applicable only to judgments. Judgments are expressed in propositions. Propositions express the agreement or non-agreement between at least two ideas. Therefore, only propositions may be properly said to be true or false.

Arguments are made up of propositions. Arguments are never “true” or “false.” The propositions making up the argument may be “true” or “false,” but not the argument itself. An argument is either “valid” or “invalid.” More about this in a moment.

The meaning of truth and falsity is very important. What is truth? How do we know that a proposition is true? As far as we know at the present time, there seems to be only three tests of “truth.”

The Correspondence Theory This is probably the most common way in which we check to see whether or not a judgment is true. All we have to do is check our judgment with what really is the case and if our judgment corresponds to what is the case, we say the judgment is true. Basically, truth rests on the conformity or correspondence of our mind with reality.

Let’s suppose one of us says, “It is raining outside.” This is a judgment expressed in a sentence called a proposition. How do we know if it’s true? Well, we can go outside and check to see if our judgment is correct, that is, if it is true. If it is raining outside, the judgment is true. Our judgment has conformed to or is in correspondence with the fact that it is raining outside.

We can check many fact-claims this way. Go look! Go feel! Go hear! Go taste! Go smell! In order to apply the correspondence test, we have to have two things:

The judgment we make about something, and
Real objects or events to which the judgment corresponds.
If it corresponds, the judgment is true; if not, the judgment is false. Keep in mind, however, it is possible to have a judgment we cannot be certain is true or false. We may express a judgment as an opinion, informed or otherwise, because we are not certain whether or not it is true or false.

The Coherence Theory According to this test, a judgment may be accepted as true if it harmonizes or is coherent with other facts which we have already accepted as true. This test becomes very valuable when we don’t have access to a personal observation for ourselves. This test is useful in the discipline of history, for instance, where we don’t have direct observation of past events. We also use it when we cannot personally witness an event.

Let’s suppose someone says to us, “There are sharks in the Mississippi River.” We would reject this judgment and say it is untrue. Why? We already know that sharks cannot live in fresh water. We already know that the Mississippi River consists of fresh water. We can’t make the judgment, “There are sharks in the Mississippi River,” fit coherently with what we already know about sharks and the Mississippi River.

The Pragmatic Theory This is a fairly recent test of truth and is applicable to only certain judgments made in specific situations. This theory says that the truth of a judgment can be determined by its results. Basically, it says that “if a judgment works, it’s true.”

The problem with this theory of truth is that it is extremely limited and can lead to abuses when applied inappropriately. For instance, there are many cases where something “works,” but we would not say it’s true. This test of truth does not work well with statements of “fact,” and one could argue that it really doesn’t test “facts” at all. What it can test is a hypothesis or a judgment made on the basis of trial and error.

If we examine carefully the three theories of truth presented above, we can reasonably draw the following conclusions. The Coherence Theory and the Pragmatic Theory are not primarily tests of truth at all. They are, at best, only secondary tests of truth.

The Coherence Theory demands that an initial judgment or several initial judgments be “true” in the first place. These initial judgments can be determined to be true only by applying the Correspondence Theory of truth. Without the truth of the primary truths determined by the correspondence test, the coherence test is subject to error.

The Pragmatic Theory is also a secondary test. It demands that “facts” be true at the outset, in setting up a hypothesis for instance, and also requires that our judgment regarding the results involving the hypothesis be true in the sense of corresponding to what is actually the case. Without the Correspondence Theory of truth, the Pragmatic Theory is useless.

We may use the coherent test or the pragmatic test at some point in an argument, an investigation, or an experiment, but we need the correspondence test at the beginning and we need it at the end. That is why we can define truth as “the correspondence of our judgment with reality” or “the correspondence of a proposition with what is actually the case.” The Correspondence Theory is, therefore, the primary test of truth. The Coherence Theory and the Pragmatic Theory are only secondary tests and are initially dependent on the Correspondence Theory.

The Meaning of Validity
We have learned that truth and falseness are attributes of a judgment. Only a judgment can be said to be true or false and judgments are expressed in propositions that can, therefore, be said to be true or false. Furthermore, we have learned that arguments, and not propositions, are valid or invalid. Additionally, we have learned that these terms apply only to deductive arguments. What do we mean by valid and invalid?

A deductive argument is valid when its premises, if true, provide conclusive grounds for its conclusion. This means that the premises and conclusion are so related that it is absolutely impossible for the premises to be true unless the conclusion is true also. Every deductive argument is either valid or invalid.

It is possible for the conclusion of a deductive argument to be true but invalid. It is also possible for the conclusion of a deductive argument to be false but perfectly valid. We can see that “truth” and “validity” do not have an essential relationship with one another.

“Truth” means a conforming of judgment (or proposition) with reality. “Validity” mean a consistent and proper relationship between propositions and conclusions according to certain rules of logical thinking.

Again, it is very important to keep in mind that only propositions are true or false, and only deductive arguments are valid or invalid.

Before we leave this matter of valid and invalid arguments, we need to consider that other branch or type of logic called the inductive argument. Are inductive arguments valid or invalid? Strictly speaking, they are neither valid nor invalid. Inductive arguments are evaluated as better or worse, according to the strength of the support provided their conclusions by their premises. Here we enter the world of probability, an exciting world that actually impacts our lives everyday.

The Sources of Certainty
The term “evidence” is used often in everyday discourse and, unfortunately, it is also used loosely, so let’s take a brief look at the types of evidence we may have.

Some truths (very few, of course) are what we call “self-evident.” This is sometimes called “immediate” evidence because it requires no thinking out, no medium of reasoning through which it can be made to appear. It appears at once and directly. We know it immediately without having to work it out. The three primary truths mentioned above are examples of truths based on immediate evidence. Another example is the truth, “A totality is greater than any one of its parts.” If we understand what is meant by “totality” and “part,” we can immediately see the truth of the statement.

Another type of evidence is “mediate” evidence. Most of the time, truth does not appear to us immediately and must be sought by some other method. It must be worked out through the medium of reasoning. We do not know immediately that water boils at 212 degrees F. at sea level. It has to be worked out. Of course, once scientists worked it out, we can accept it based on their authority. But if we doubted the truth of it, we could actually do the necessary experiments ourselves to establish the evidence for the truth of the matter.

Evidence, to be of any value to us, must be objective. It must not be a mere feeling or simply an opinion or a matter or personal taste. In other words, evidence must not be subjective. The ultimate criterion of truth, as we shall see shortly, is, then, objective evidence, and is based on three possible sources:

The evidence of the senses which, rightly used, are infallible.
The evidence of the intellect which, using its ideas to form judgments based on correct reasoning methods, can formulate true propositions which are in accord with reality.
The evidence of authority which is reliable testimony. There are strict rules for evidence from authority and there are tests which can be applied to evaluate the reliability of any authoritative source. Much, if not most, of our knowledge comes from the evidence of authority. We accept the findings of trained historians, for example, as well as the findings of empirical scientists.
However, we must be cautious even accepting the authority of historians and scientists and, for that matter, any person claiming to be an authoritative source. All authority must be willing to be challenged, although normally we would not go around challenging every one all the time. It is the willingness to be challenged that is important. Historians have been wrong in the past about historical data. They have even lied on occasion. Scientists have been wrong about scientific matters. They have also been known to “cook the books.” And judges, lawyers, juries, priests, ministers, physicians, and so forth, have been in error on many occasions.

Truth and Error
It is an unfortunate fact that our judgments are not always true, and we need to establish the criterion to be used to determine truth and error. What constitutes truth and error? How can we discriminate between true and erroneous judgments? What is the proper test of truth?

We have said that an idea is the intellectual representation of a thing. We are, however, incapable of grasping the full reality of an object within the content of a single idea due to the limited power and capacity of our intellect. Because of this limitation, our intellect turns its attention first to this, then to that property or attribute of a thing, and makes a separate concept for each one.

Things in nature are actually undivided and one, although potentially divisible and many. But in our intellect, the ideas of things are actually divided and many, although potentially undivided and one. None of our ideas represents the full reality of things, but each idea represents an aspect, a phase, or a portion of the thing.

The material object of the idea is the total object in all its properties and attributes. The formal object of the idea is the thing in its single property or attribute in so far, of course, as it is represented by the single idea.

In order that the idea be a correct representation of the thing, it must agree with its formal object. The idea, then, is seen to be a piecemeal representation, but it is correct as far as it goes. To be incomplete is not the same as to be incorrect.

Our intellect acquires a more or less complete grasp of a thing by means of a mental division of its reality into a number of concepts. It subsequently makes a mental synthesis of the objects and its attributes in the judgment.

What was divided in the process of abstraction becomes united in the act of making a judgment. Consider these judgments:

That dog is black.
That dog has four legs.
That dog can run fast.
In each case, the attribute, presented as the predicate, is referred back to the thing, presented as the subject. The subject “dog” stands for the thing in a general way, while the predicates, “black,” “four legs,” and “run fast,” stand for the particular attributes which belong to the thing. These attributes are recognized as belonging to the thing in its objective existence.

What the judgment pronounces of its ideas is meant to be pronounced of the reality itself because ideas are partial, yet correct, representations of objective reality.

Every judgment implicitly expresses a correspondence between the thing as it is in itself, and as it exists ideally in the intellect. Explicitly, the judgment merely pronounces an identity between the predicate-idea and the subject-idea. Such is the nature of an affirmative judgment.

Regarding a negative judgment, much the same can be said. Here we take an attribute not found in the thing and deny its presence in the thing. The predicate-idea is excluded from the subject-idea. We assert that the reality designated by the predicate is lacking in the thing designated by the subject. Here again we express a conformity between the reality as it exists in nature and as it exists ideally in our intellect. When we say, “That dog is not black,” we pronounce the non-identity between subject and predicate or thing and non-attribute.

Truth and error, then, reside in the judgment, not in the ideas taken alone by themselves. Truth can now be defined as the conformity of judgment to reality. Error can now be defined as the disconformity of judgment to reality. This is in accord with our common sense, everyday meaning of truth.

The Criterion of Truth
Knowledge is useless if it does not agree with reality.

A criterion of truth is a rule, or norm, or standard, or test by which we distinguish true judgments from those which are false. Since the judgment is a natural mental process, the criterion of truth must be a natural norm or test, well within the reach of every individual. Since the judgment is an intellectual process, the criterion of truth must be discoverable by the intellect.

Certitude is that state of the mind in which the mind gives a firm assent to a judgment without fear of error, due to recognized valid reasons. The valid reasons, according to their convincing strength are:

Moral certitude: based on the customary action of human beings, and exceptions to the law are recognized as physically possible, i.e., “We are sure that parents love their children”;
Physical certitude: rests on the physical laws of the world, and exceptions here are impossible in the ordinary course of nature, i.e., “Iron will sink in water”;
Metaphysical certitude: has its foundation in the metaphysical laws of being, so that an exception is intrinsically impossible, it would involve an internal contradiction, i.e., “The whole is greater than any of its parts.”
Whenever we are certain in such judgments, we are conscious of a motive of certitude.

We can distinguish between subjective and objective certitude. Subjective certitude consists in the mere firmness of our assent, and it does not exclude error in our judgment. It does exclude the fear of error, considered solely as a subjective state of the mind itself.

Objective certitude consists in the reasons contained in the terms of the judgment, in virtue of which the judgment is considered to be a true representation of reality.

The same reasons which determine the truth of the judgment determine also the certitude of the assent. Hence, the criterion of truth and the motive of certitude are objectively identical, although conceptually different.

The criterion of truth is objective evidence.

Nature of Objective Evidence
Objective evidence is that characteristic of reality whereby it becomes objectively manifest to the perceiving faculty. There are various kinds of objective evidence.

Internal evidence: exists when the ground for our judgment is clearly perceived to lie in the reality affirmed by the judgment. It is immediate if this interpreted reality is directly presented to the intellect or the senses. For example, “2+2=4,” and “This paper is white.” It is mediate if this interpreted reality is not directly presented to the intellect or the senses, but is presented in some other way. For example, a process of reasoning, or ballistic evidence used, for instance, by the police.

External evidence: exists when the ground for our judgment lies, not in the reality itself affirmed by the judgment, but in some other reality outside it. For example, from some authority and it rests on the evidence of the motives of credibility, such as a witness to some event or some historical evidence. Or by imprudence of doubt, when it is not sufficient to compel our assent, but is clearly perceived to be sufficient to exclude all unreasonable doubt. For example, a complex mathematical problem performed by a mathematician whose credibility is unquestionable. Or one who claims to be my mother, even if I can’t provide evidence at the moment.

Evidence is the Criterion of Truth.

It is important to realize that a strict demonstration of the fact that evidence is the criterion of truth is impossible. Primary facts cannot be demonstrated, but are shown to be true by an appeal to fundamental experience and reflection. For example, I cannot demonstrate that I can see, the fact of seeing is its own proof. Similarly, I cannot demonstrate that evidence is the criterion of truth because it would require the criterion of truth to prove that it is true, and this is the fallacy of “begging the question.”

Experience and reflection clearly show that as a matter of fact objective evidence is the criterion of truth and our motive of certitude.

We do not arbitrarily apply predicates to subjects and consider such judgments true.

The intellect needs a ground or reason outside itself because judgments are clearly perceived to be interpretations of reality outside our minds.

The clear presentation of reality is the ground for considering judgments to be true and worthy of firm assent, and that is the objective evidence of reality.

The difference between the attitudes of the intellect in certitude, doubt, and opinion is due to the difference of reality in its self-revelation to the mind.

This analysis of truth and certitude shows that objective evidence of reality, or reality itself as clearly manifested to the intellect, is the criterion of truth and the motive of our certitude. Without it, our intellect must remain in doubt or, at the very best, can form only a probable opinion, and then the fear of error will always be present.

The ultimate criterion and ultimate motive must be such as to exclude the possibility of doubt or error. To do this, reality must be self-evident. The external evidence of authority and of the imprudence of doubt does not exclude the possibility of doubt and error, and mediate evidence always rests on immediate evidence.

Experience proves that all knowledge derives its validity from a few fundamental principles which are self-evident, because they are based on the self-evident concepts of being and non-being.

The Causes of Error
Error is not caused by reality because reality reveals itself as it is. Nor is it caused by the mind directly because it tends toward truth.

Error is the result of the influence of the will on the intellect, inducing the intellect to assent to a judgment without sufficient objective evidence on the part of reality.

The factors which move the will in this way include:

The complexity of reality;
Imperfections in the sense organs;
The necessity of action;
Partisanship and prejudice;
Emotional instability.
The desire to shirk protracted labor.
Error, therefore, is not an inherent characteristic either of reality or of the intellect. It is the result of the determining influence of the will.

Error as such is incidental and accidental to judgments. We must pay proper attention to the objective evidence of reality. In this way, we can avoid error. Then our judgments are essentially valid as true interpretations of reality.