Being, Epistemology, Logic, Ontology

On the Law of Noncontradiction

by Dave Seng

The law of noncontradiction states that nothing can both be and not be at the same time and in the same relationship. Put more formally, “A” can not be “B” at the same time and in the same relationship. The first part of the law is pretty straight forward. A fish can not be a cat or a frog can not be a table, at least at the same time. Being can not be nonbeing at the same time. Opposites can not be true at the same time and in the same relationship. It is contradictory to say that nonbeing is being at the same time. Contradictories can not both be true. One must be false, while the other is true.

Sometimes, however, the relationship part of the law is not understood. For example, I can be both a father and a son at the same time but not in the same relationship. I am my father’s son, and my son’s father but those are different relationships. Further, I can be my son’s biological father but not my son’s legal father if he were to be legally adopted. That, too, is a different relationship.

A basic feature of reality is that opposites can not exist in the same way and same relationship.

Because the law of noncontradiction is a basic property of being (reality), we learn that it is foundational to a proper understanding of metaphysics, ontology, and epistemology (theory of knowledge). Truth is clarified when the law on noncontradiction is properly understood.

The law of noncontradiction is a metaphysical first principle because it speaks to basic nature of reality. It helps us understand what is or is not so.

The law of noncontradiction is an ontological first principle because it points to the act or type of being a thing is–what can or can not be.

The law of noncontradiction is an empistemological first principle because it tells us what can or can not be known.

Finally, the law of noncontradiction helps us determine what is true and false, because opposites can not both be true. At the most fundamental level one statement or act of being can not be both true and false at the same time and same relationship.

Logic, Ontology, Uncategorized

Mortimer Adler on The Correspondence Theory of Truth

by Dave Seng

I do not remember when I first learned learned that the laws of logic are properties of being but they are, nonetheless, intuitively and metaphysically correct. Mortimer Adler provides a clue for why this is the case as he connects the law of noncontradiction with the correspondence theory of truth (truth is that which corresponds to reality):

The correspondence theory asserts (1) that there is a reality independent of the mind, and (2) that truth (or, what is the same thing, knowledge) exists in the mind when the mind agrees with, conforms or corresponds to, that independent reality. When what I assert agrees with the way things really are, my assertions are true; otherwise they are false. . . . The principle of noncontradiction is both an ontological principle (the principle that contradictories cannot coexist in reality) as well as a logical rule (the rule that thinking cannot be correct if it is self-contradictory).

Mortimer J. Adler, Intellect: Mind over Matter (New York: Macmillan, 1990), 98 – 99.

The law of noncontradiction is both a property of being (ontology) and logic (correct reasoning) which is perhaps one reason why it is true (corresponds to reality).

Intellectual History, Metaphysics, Philosophy

Aristotle and Augustine on Being, Truth, and Logic: Part Three

by Dave Seng

Part one can be found here.

Part two can be found here.

The law of noncontradiction holds primacy in another way as well. Aristotle believes that the law of noncontradiction is self-evident and it must be assumed before any other study, or science can get started:

For a principle which every one must know who knows anything that is, is not a hypothesis; and that which every one must know who who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect. (524)

The law of noncontradiction and the resulting axioms of logic are self-evident, just as being is the first thing one experiences when waking up in the morning, and the first thing a baby experiences when he or she is born. Being is undeniable, and so are the laws of logic. (Even Descartes, with his systematic doubt, ultimately concludes that being can be known.) Aristotle believes that the law of noncontradiction “is the most certain” principle one can know and, in fact, is prior and foundational to all other knowledge and learning. It is important to note, however, that the basic law of noncontradiction cannot itself be proven. Because it is self-evident, one must have to assume the law of noncontradiction in order to deny it. In other words, one must rely on the law of noncontradiction if one were to try to disprove it, which is ultimately circular and self-refuting. The basic principles of logic are among the transcendent first principles of reality. Being cannot both be, and not be at the same time and same way. Further, Aristotle claims that there must be some basic first principles of reality in order to prevent an endless regression of explanations that ultimately lead nowhere. He believes it was the mark of an uneducated person to not understand this point:

But we have now posited that it is impossible for anything at the same time to be and not to be, and by this means have shown that this is the most indisputable of all principles. Some indeed demand that even this shall be demonstrated, but this they do through want of education, for not to know of what things one should demand demonstration, and of what one should not, argues want of education. For it is impossible that there should be demonstration of absolutely everything (there would be an infinite regress, so that there would still be no demonstration); but if there are things of which one should not demand demonstration, these persons could not say what principle they maintain to be more self-evident that the present one. (525)

The laws of logic are important when one gives reasons why something is true or not, or demonstrating why something is, or is not the case. They simply provide the rational grounds for avoiding definitional equivocation1. These laws are foundational when trying to understand being because they indicate what can or cannot be, (they also help us understand what we can or cannot know). They are transcendent in nature because they are part of being. They indicate truths which all things participate in if they exist at all. Nothing whatsoever can both be, and not be in the same way and same relationship. In a very real way, the laws of logic are part of being and help one to know and understand truth, because they are fundamental properties of reality. Aristotle refers to the laws of logic in many places, primarily in his works of logic, called the Organon (Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics, and On Sophistical Refutations), and in his Metaphysics. Regarding the laws of logic themselves, he says that, “these truths hold good for everything that is, and not for some special genus apart from others” (524). In other words, the truths of logic reflect the order of being as a whole and hold for everyone regardless of time, place, or perspective.

Not surprisingly, Augustine takes a more theological position regarding the laws of logic and applies the laws of logic to science, ethics, and the existence of God2. Although Augustine rarely explicates the laws of logic directly, he does believe that logical reasoning deals with the question of how truth may be discovered (319). He thinks that the Greek philosophers who first discovered the laws of logic are essentially correct because they “made efforts to discover the hidden laws of nature and the right and wrong in ethics, and in dialectic what was consequent according to the rules of logic and what was inconsequent and erroneous” (191). He also believes that philosophy has three branches or areas of investigation and that logic is one of these fields of study: “…philosophers have aimed at a threefold division of science, or rather, were enabled to see that there was a threefold division (for they did not invent, but only discovered it), of which one part is physical, another logical, the third ethical” (389). The natural (physical), rational (logical), and moral elements of philosophy have being in focus in some way, just as the field of ethics has to do with the discovery of right or wrong actions, the possibility of natural law, and the being of moral life—questions about whether or not humans are moral beings, rests upon metaphysical assumptions of freedom, the will, and what it means to be human and to flourish in this world. (Although it is beyond the scope of this essay, both Aristotle and Augustine believe that there are metaphysical foundations to the science of ethics.) For Augustine, however, the ultimate ground of all reason, logic, and ethics is found in the existence of God and is in agreement with the ancient Jewish understanding of God as the “ground of being3.” Augustine explains this position when he says, “And yet the validity of logical sequences is not a thing devised by men, but is observed and noted by them that they may be able to learn and teach it; for it exists eternally in the reason of things, and has its origin with God” (734). Augustine believes that logic is a natural part of reality.

Interestingly, Augustine applies the law of noncontradiction when it comes to the nature and existence of the universe. He believes that the universe did not create itself:

Earth and the heavens also proclaim that they did not create themselves. “We exist,” they tell us, “because we were made. And this is proof that we did not make ourselves. For to make ourselves, we should have had to exist before existence began.” And the fact that they plainly do exist is the voice which proclaims this truth. (114)

Augustine is simply making the point that something cannot exist before it exists. If something did exist before it existed, it would have to be, and not be at the same time and same way, which is impossible according to the law of noncontradiction. In order for the universe to create itself, it must be before it is. Augustine thinks that self-creation violates the law of noncontradiction. But in a larger perspective, Augustine agrees with Aristotle, that the principles of logic are properties of being because they exist eternally in the “reason of things” (734). For each thinker, at least one way being corresponds to reality is through the laws of logic, the first metaphysical principles of existence.

Why does one find so much overlap and commonality between Augustine and Aristotle? It is important to note that Augustine does not always follow Plato exactly. (I have written more about how Augustine modifies his Platonism, here.) As with Plotinus, he makes changes to his Platonism to better take account of reality. Augustine modifies his Platonism by placing forms or essences in the particular things—at least when it comes to describing change in physical reality4. Augustine believes that the form must be in the material object itself in order to account for change. “There can be no change where there is no form” (129), according to Augustine. This parallels exactly what Aristotle holds about nature and reality in general. Augustine realizes that without the potentiality of form, something can not change. If the acorn does not have the form and potency of the oak tree, it will not grow into a majestic oak tree. Augustine, then, has a higher respect for physical reality than Plato. That is why he can conclude that logic and truth are properties of being which reside in the nature of things. Aristotle, of course, agrees with this line of thought. Plato, however, would disagree due to his strict emphasis on the Forms and his “divided line” of reality5.

Questions of being, truth, and correct reasoning underlie humanity’s most important concerns and conversations about the meaning of reality and one’s place within it. Without the ability to reason correctly, investigations and discussions of perennial questions would lapse into conceptual incoherence, and it would be impossible to discuss anything in a meaningful way. In different ways, both Aristotle and Augustine help one to realize that truth is essential when it comes to understanding reality, and logic is a helpful tool that allows one to discover these most basic and ultimate concerns.

Works Cited

Aristotle. The Works of Aristotle: 1. Great Books of the Western World. Vol. 7. Encyclopedia Britannica, Inc., 1999.

Augustine. The Confessions, The City of God, On Christian Doctrine. Great Books of the Western World. Vol. 16. Encyclopedia Britannica, Inc., 1999.

1 Although there are places when much common ground is possible in different positions, the laws of logic simply point out that only one thing or concept can be what it is at a time. If equivocation occurs the argument or discussion looses conceptual coherence and language becomes meaningless.

2Aristotle, however, believes that theology is a branch of metaphyics, see his Metaphysics, book I.3 and book VI.1.

3God’s self-disclosure to Moses in Exodus 3:14, “I am who I am” is generally understood to mean that God is the ground of all being. Another valid translation of the verse is “I am who causes to be.”

4While it is true that Augustine, as a Platonist, places the ultimate forms in the mind of God, in several places he has to modify his Platonism to account for physical change, which Plato is unable to do. For the brevity of this essay, I can only provide one example from Augustine here.

5Plato’s “divided line” is in book six of the Republic, Vol. 6, pages 386 – 387.

Logic, Metaphysics, Philosophy

Logic: The Art of Reason

by Dave Seng

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