Human beings have several different ways of coming to believe what we believe. While the idea that our senses and even our own introspection may be fallible is surprising to many, it is a relatively common topic considered for philosophical musing that many have considered. Stranger yet is the idea of reason itself, the very rules of common sense that govern our assessment of this data, may too be flawed. But what is really involved in the process of reasoning? Can we trust reason? Can we really know anything by using our ability to reason? Are there some things that can be known without resorting to reason? Philosophers who advocate the classical view of reason have given answers to these questions, and careful examination of the truths of reason reveals that much of what we take for granted in our everyday reasoning may not be as simple as we so often suppose.
Some propositions, upon reflection, seem true simply by definition. Take, for example, the sentence, “All bachelors are unmarried”. Once we understand the terms being discussed, can anyone reasonably doubt the truth of this proposition? It is simply a tautology, substantiated. This sort of proposition is a self-evident proposition. Self-evident truths have two distinct properties. First, they can be known independently of sensory experience. For example, you can conclude all dogs have hair or fur if you adequately understand that all dogs are mammals and that all mammals have either hair or fur. Secondly, self-evident truths are necessary. This is to say that it is not possible for the proposition to be false; it is true on pain of contradiction. For example, to say that you know a married bachelor is contradictory, and shows a lack of adequate understanding of the term bachelor.
The reason we can know these self-evident truths apart from any deeper analysis, according to the classicist, is because we can analyze the conceptual containment relationships within the terms. For the statement, all bachelors are unmarried, when one refers to a “bachelor”, they are using a term that (when properly understood) automatically entails unmarried as necessarily contained within the term. Thus, one can be justified in believing that all bachelors are unmarried by mere reflection of the containment relationships between concepts. If one adequately understands it, then he knows it and cannot deny it. Analytic truths are immediate and intuitive, and do not require any additional logical inferences to be accepted. As Immanuel Kant established, truths known by an adequate understanding of the containment relationships of concepts are known as analytic truths.
Kant also established a distinction between two different types of self-evident truths: analytic truths and synthetic truths. As opposed to analytic propositions, propositions can also be known synthetically, via a proper synthesis of concepts. Synthetic statements are propositions that seem to be self-evident truths of reason, but whose predicate concept is not contained in the subject. To illustrate with an example, consider the statement “all bachelors are bald.” There is nothing in the definition of the term bachelor that necessitates baldness. It is perfectly possible that one could be a bachelor and have hair. But it is also possible for bachelors to be bald as well. The term bachelor does not contain any necessary concepts concerning hair style.
The analytic/synthetic distinction should not be confused with another important propositional distinction within the classicists’ view of the truths of reason: the a priori/a posteriori distinction. A priori reasoning requires no appeal to experience, but can be justified through appeals to reason alone. Therefore, all a priori statements (like all analytic statements) are necessarily true on pain of contradiction. Within the category of a priori truths, there are three categories: strict sense a priori, broad sense a priori and ultimately a priori. Strict sense a priori truths are the types of truths that are known only by reason, directed towards them and their concepts. Broad sense a priori truths are the product of a logical train of thought. They are not known immediately (in the way that strict sense a priori truths are), but are known because they follow logically from a series of self-evident propositions. Mathematical theorems are often thought of as being a priori, but they require considerably more self-evident steps than broad sense a priori truths. These can be rigorously proved, and are known as ultimately a priori.
When a truth is not a priori, but based on some sort of experience, they are known as a posteriori truths. A posteriori reasoning is therefore logically contingent, since its truths can be falsified by observation. A posteriori propositions are knowable based on perception or introspection.
A little more detail is required in order to fully explain the concepts of necessarily true statements, necessarily false statements and contingent propositions. A necessarily true statement, as explained earlier, is a statement that is true upon pain of contradiction. There is no possible world in which a necessarily true statement can be false. The statement “truth exists” is necessarily true, because it is impossible to affirm it’s negation, “truth does not exist”. Similarly, necessarily false statements are always false, and there is no possible world in which a necessarily false statement could be true. Any statement that violates this principle of non-contradiction would be a necessarily false statement. For example, “Elijiah is human and Elijiah is not human” would necessarily be false, because it is logically impossible for Elijiah to be both human and not human at the same time, in the same way. Contingent truths are non-necessary truths, or truths that depend on reality. Unlike necessarily true statements, contingent propositions are not necessary. Take, for example, the statement, “There are eight planets in the solar system.” This is a true statement, but not necessarily true. The concept of the solar system does not “contain” the concept of eight planets; presumably solar systems can have any number of planets. However, our solar system currently contains eight planets (and a handful of dwarf planets) and this can be verified by references to astronomy.
When the four concepts (analytic/synthetic and a priori/a posteriori) are combined together, you have four possible options: analytic a priori, analytic a posteriori, synthetic a priori and synthetic a posteriori.
Analytic a priori propositions are statements that are known by logic alone because of a containment relationship between concepts.
Ex: All bachelors are unmarried.
Why? Because we do not need to interview every bachelor in order to verify this claim.
Analytic a posteriori propositions are generally accepted to be impossible, because one cannot accept something based on an adequate understanding of containment relationships and from empirical evidence. Kant thought that the idea of an analytic a posteriori was self-contradictory. How could the subject of an analytic proposition not be contained within the predicate?
Synthetic a priori propositions are statements based on an adequate understanding of the synthesis of concepts, based on logic and reason alone.
Ex: Cars can be red.
Why? Because the concept of a car does not exclude the possibility of it being the color red.
Synthetic a posteriori propositions are statements reached based on evidence gained from the world.
Ex: All swans are white.
Why? Because the concept of a swan does not depend on it being white and this statement’s verification depends on whether or not non-white swans actually exist in the real world.
The complex issues involved in the process of reasoning are often taken for granted by people in everyday life. When we properly understand how to reason (and why reasoning works in the first place), we can trust our own reasoning abilities to give us reliable conclusions. There are debates among philosophers concerning virtually all of the topics discussed here, but the classicists seem to have done a decent job providing an explanatory framework in which we can begin to properly understand the role of reason in epistemology.
This post was originally submitted during my epistemology class (phi309: knowledge and justification) as an overview of classical reason. The research was done as a group (with two others) and I wrote the final copy. The resources used were “An Introduction to the Theory of Knowledge” by Noah Lemos, “Epistemology” by Robert Audi and class notes.