Socrates famously said that the unexamined life is not worth living. It could equally be said that the unexamined idea is not worth having. How can one know, however, whether or not an idea is worth having or if one should accept it as true? Logic is the tool philosophers (and everyone, really) use to discern good ideas from bad ones and true statements from false ones.
It is often said that logic is the primary tool of the philosopher. But why has it been given such a status? Why has logic been called the “key” to philosophizing? In our last post, we discovered that one way philosophy is different from other fields is its development and utilization of logic, or more simply, the art of correct reasoning. This essay will not go into all the ways reasoning can go wrong, such as formal and informal fallacies. I’ll post some good texts that will help one out with those below. Instead, we will examine why one might want to reason correctly to begin with.
Philosophy sets itself apart from other fields because it starts with the basic assumptions of correct reasoning. Everyone uses these basic laws of thought without even realizing it or having special training in philosophy. There are three basic laws of correct reasoning and self-evident features of all reality. They are:
1. The Law of Noncontradiction: Nothing can both be and not be at the same time and in the same respect.
2. The Law of Excluded Middle: Something either is or is not.
3. The Law of Identity: Something is what it is.
It is important to realize that these laws are absolutely necessary for any coherent thought or communication of any kind. Without these laws, communication would collapse into incoherence and chaos. Furthermore, notice that these laws have both metaphysical and epistemological ramifications. They are metaphysical in nature because they indicate what can or can not be. They lay out the basic foundation (what Aristotle calls “first-principles”) or starting points for understanding anything that is. As for epistemology (how we know what we know), these laws show us what can or can not be true. A statement can not be both true and false at the same time and in the same respect. A cat is what it is (the Law of Identity). When reasoning correctly, it is always important to keep in mind that truth is what corresponds to reality. It is impossible to reject one of these laws and write a coherent sentence. Note that the qualifying phrase for the Law of Noncontradiction, “at the same time and in the same respect” is significant. A chair could be red or yellow at different times but it can not both be and not be (anything) at the same time and in the same respect—it can not be four-legged and not four-legged at the same time.
It is important to realize that these laws demand no other foundation or principles in order to be true because they are the first and most basic laws of reason. No further proof is needed for their acceptance. Not everything needs to be proved to be true. Aristotle called these the “first principles” of all reality and logic. In fact, it was the Law of Noncontradiction that Aristotle was speaking of when he said that it was the mark of an uneducated person not to realize that some things cannot be proved, otherwise nothing could be proved. According to Aristotle,
“Some, indeed, demand to have the law proved, but this is because they lack education; for it shows lack of education not to know of what we should require proof, and of what we should not. For it is quite impossible that everything should have a proof; the process would go on to infinity, so that there would be no proof” (Aristotle, Metaphysics, 1006a).
These three laws are simply “anchors” or foundational “first principles” for all human communication and reasoning. Without them, we would simply fall into intellectual confusion and disarray. It really should not worry anyone that these principles are not provable. The principles and axioms of geometry are not demonstrable but it would be impossible to write a geometric proof without them. In the final analysis, all our basic rules of thought and logic have a metaphysical cast to them.
There are two aspects to correct reasoning. Existence (Being) itself is the touchstone for human thought and experience. We learn crucial things about the world through our senses. After all, our senses allow us to experience external reality. Through the repeated data our senses provide to the mind, we learn the essential character of things. Take, for example, the conductivity of gold. By empirical observation, we find that gold is an excellent metal for conducting electricity. We can correctly conclude that one of the essential properties (what Aristotle would call potencies) of gold is to be an electrical conductor. The process of exploring reality and drawing conclusions from sense experience is called induction. Induction is reasoning which attempts to reach a conclusion concerning all the members of a class after inspection of only some of them. If we notice that all the crows we have come across are black, it is valid to conclude that the next one we see will be black. If we plant an acorn, and nothing prohibits it from growing, it is reasonable to think an oak tree will grow. Induction is an empirical process. Induction, however, does not mean we can know and understand things with absolute certainty. It is simply a process that allows for predicting things to a very high degree of probability and provides the basis for the common sense understanding that barring impurities, gold will conduct electricity and if properly cared for, an oak tree will grow from an acorn.
Induction helps us to know the essence of things and speaks to the fact that we do not have to examine every single member of a class in order to come to a valid conclusion. We know that when we discover something it has an essential nature. We do not have to examine every single human to find out that humans are mortal. Similarly, we understand that humans have rational cognitive abilities, an essential feature of being human, but it is not necessary to interview every human in order to discover this feature of humanity. This process is called abstraction. Through empirical observation, humans discover features and properties of the particular class of the thing being examined and detect the essential nature of that thing. The essence of a thing is simply that which makes something the kind of thing it is. In the case of humans, we learn that mortality and rationality (among others) are essential universal features of what it means to be human.
Induction is a fascinating two-way street. In order to test our inductions, we have to refer back to empirical facts and observation. This reverse engineering process where we return from the level of abstraction and universal essence to the level of the senses is an impart part of induction. This is because being and essence are always combined.
The second way we know things is called deduction. This form of reasoning is also based on the three laws of thought discussed above. Deductive reasoning is based on the self-evident principles of all reality (Being) such as the Law of Noncontradiction. Deduction can start from more complex judgments whose truth has been proved and moves to develop further conclusions from these previously known truths or, at other times, simply resolves complex judgments into more basic principles. With this form of thinking, the conclusion of an argument follows by logical necessity from the premises. In other words, when it comes to deductive reasoning, if the premises are true, the conclusion must be true also. With deductive reasoning, we start with a universal principle (true for everyone everywhere) and reach a particular conclusion (what is true for a particular thing or individual). The famous example is:
All humans are mortal (universal proposition)
Socrates is a human
Therefore, Socrates is mortal (particular proposition, conclusion)
This kind of deductive reasoning is also called syllogistic reasoning meaning to consider certain propositions together. The conclusion of the deductive argument must follow by necessity due to the logical entailment or implication of the propositions.
The art of reasoning is really about the human desire and ability to discover truth. Logic is simply the laws of thought which help us to learn whether or not we have correctly formulated inductions or if we have moved from one syllogistic set of propositions to another accurately. It is, of course, possible to reason from the wrong starting point or be mistaken about the truth of our basic premises. Formal logic is concerned with right reasoning but not always with the truthfulness of our reasoning. It is more important to discover how our reasoning corresponds to reality and is, therefore, true.
Further reading:
John Burbidge. Within Reason: A Guide to Non-Deductive Reasoning. Kenmore, N.Y.: Broadview press, 1990.
Irving M. Copi. Introduction to Logic. Fourteenth ed. Routledge, 2010.
Patrick Hurley. A Concise Introduction to Logic. Twelfth ed. Cengage Learning, 2014
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