# Types of Truths

## Arithmetical, Geometrical, Logical (Analytic), Synthetic, and Ethical Truths

When someone refers to a "truth" or claims that some statement is "true," just what kind of truth are they referring to? This may seem like an odd question at first because we so rarely think about the possibility that there may be more than one type of truth out there, but there are indeed different categories of truth which need to be kept in mind.

## Arithmetical Truths

Among the simplest and most obvious are arithmetical truths — those statements which accurately express mathematical relationships. When we say that 7 + 2 = 9, we are making a claim about an arithmetical truth. This truth can also be expressed in ordinary language: seven things added to two things gives us nine things.

Arithmetical truths are often expressed in the abstract, as with the equation above, but there is normally a background of reality, as with the statement in ordinary language. Although these may be seen as simple truths, they are among the most certain truths we have — we can be more certain of these than we can of just about anything else.

## Geometrical Truths

Very closely related to arithmetical truths are geometrical truths. Often expressed in numerical form, geometrical truths are statements about spatial relationships. Geometry is, after all, the study of the physical space around us — either directly or through idealized representations.

As with arithmetical truths, these can also be expressed as abstractions (for example the Pythagorean Theorem) or in ordinary language (the sum of the inside angles of a square is 360 degrees). And, as with arithmetical truths, geometrical truths are also among the most certain truths we can have.

## Logical Truths (Analytic Truths)

Also sometimes referred to as analytic truths, logical truths are statements that are true simply by definition of the terms that are used. The label "analytic truth" is derived from the idea that we can tell that the statement is true just by analyzing the words being used — if we understand the statement, then we must also know that it is true. An example of this would be "no bachelors are married" — if we know what "bachelor" and "married" mean, then we know for a fact that the statement is accurate.

At least, that is the case when logical truths are expressed in ordinary language. Such statements can also be expressed more abstractly as with symbolic logic — in those cases, the determination of whether a statement is true or not will be very similar to making such a determination of an arithmetic equation. For example: A=B, B=C, therefore A=C.

## Synthetic Truths

Much more common and interesting are synthetic truths: these are statements which we cannot know as true simply by virtue of doing some mathematical calculations or an analysis of the meanings of words. When we read a synthetic statement, the predicate is offered as adding new information not already contained in the subject.

Thus, for example, "men are tall" is a synthetic statement because the concept "tall" is not already a part of "men." It is possible for the statement to be either true or false — if true, then it's a synthetic truth. Such truths are more interesting because they teach us something new about the world around us — something we didn't know before. The risk, however, is that we might be wrong.

## Ethical Truths

The case of ethical truths is somewhat unusual because it isn't at all clear that such a thing even exists. It is certainly the case that many people believe in the existence of ethical truths, but that is a hotly disputed subject in moral philosophy. At the very least, even if ethical truths exist, it isn't at all clear how we can come to know them with any degree of certainty.

Unlike other statements of truth, ethical statements are expressed in a normative manner. We say that 7 + 2 = 9, not 7 + 2 should equal 9. We say that "bachelors are not married" rather than "it is immoral for bachelors to be married." Another feature of ethical statements is that they tend to express something about the way the world could be, not the way the world currently is. Thus, even if ethical statements could qualify as truths, they are very unusual truths indeed.