Being, Ontology, Philosophical Theology

Mere Metaphysics Part Four: The Principle of Noncontradiction

by Dave Seng

Scholasticism … is only popular philosophy made systematic—William James.

The principle of existence relies on the three foundational principles of logic, epistemology, and metaphysics: the principle of identity, the principle of noncontradiction, and the principle of excluded middle. These principles are the most basic properties of reality and form the foundation of what we can know about the world and how to correctly think about it. Many of us use these principles day in and day out without ever really thinking about them. These principles, like the principle of existence, are undeniable because one must use these principles in any attempt to deny them.

Everyone uses the principle of noncontradiction one way or another. Whenever we change the oil in our automobiles, drive to work, or simply try to write or speak a conceptually coherent sentence, we are using the principle of noncontradiction.

In our last post, we explored the principle of existence and why it is such an important principle in cosmological reasoning. This time we will discover how the principle of noncontradiction relates to our cosmological argument from being.

The principle of noncontradiction is this: nothing can both be and not be at the same time and same relationship. Another way of putting the principle is this: A cannot be both B and non-B at the same time and in the same relationship. We understand this principle intuitively. I cannot both exist and not exist at the same time (this is a statement of being, or existence). Further, I can be both a father and son at the same time but not in the same relationship (this is a statement of the being, or existence, of relationships).

Aristotle was among the first to articulate the principle of noncontradiction. He reminds us,

There is a principle in things about which we cannot be deceived, but must always, on the contrary recognize the truth,—viz. that the same thing cannot at one and the same time be and not be, or admit any other similar pair of opposites.1

And,

By the starting-points of demonstration I mean the common beliefs, on which all men base their proofs; e.g. that everything must be either affirmed or denied, and that a thing cannot at the same time be and not be, and all other such premises.2

Why is the principle of noncontradiction important in cosmological reasoning for the existence of God? So far we have seen that the principles of existence and identity cannot be legitimately doubted. The same is true for the principle of noncontradiction. One must assume the principle when trying to deny it. As we shall see, the three main principles of epistemology, metaphysics, and logic are all based on the properties of being. Being is undeniable. Being itself provides the foundation of rational thought and discussion about it. In grounding our theistic argument in being, therefore, we are simply explaining why it is impossible to deny reality. We are faced with only two propositions: either being or non-being (nothing). In the realm of being, we will come to understand the realm of becoming or change—but the argument is based on being, not becoming.

I will explicate this a little more in our next post about the principle of excluded middle. For now, it is important to see how the argument itself reflects the metaphysical principles of reality or being. As Thomas Aquinas would remind us, being is the proper effect of God.

Here is the introduction to this series

Here is the first part.

Here is the second part.

Here is the third part.

1 Aristotle, Metaphysics, trans. W. D. Ross, vol. 7, Great Books of the Western World (Chicago: Encyclopedia Britannica, Inc., 1996), 590.

2 Aristotle, Metaphysics, trans. W. D. Ross, vol. 7, Great Books of the Western World (Chicago: Encyclopedia Britannica, Inc., 1996), 515.

Being, Ontology, Philosophy

Mere Metaphysics Part Three: The Principle of Identity

by Dave Seng

For the introduction to this series click here.

For the first part of this series, click here.

For the second part of this series, click here.

Man is the only metaphysical animal.–William James, Principles of Psychology

One of the premises of this blog is that the laws of thought and logic are properties of being, or reality. Not all logicians hold to this view but it is the position, I think, which corresponds most closely to reality. This post is related to our previous post on the principle of existence (the undeniable principle that being is). As we have seen, a principle is that which something else in its order follows. For example, in order to perform calculations correctly, one must first understand the underlying principles and axioms of mathematics. Principles are the foundation of any science and every other human activity.

The principle we come to now, in our explication of the argument from being (click here if you want a condensed form of it), is the principle of identity.

The principle of identity is simply that being is identical to being, or a thing is identical to itself. A thing is what it is. In a syllogism, the middle term must always have the same meaning and not be equivocal (undergo a change of meaning) in order to be valid. When it comes to reality, the law of identity applies when we are talking about dogs with the understanding that we are discussing animals which belong to the class of canines and not fish, hamsters, or monkeys. My cat cannot be a cephalopod. By virtue of it being a cat, and having all the properties a cat has, it cannot be another species or something else. Anything that exists at all is identical to itself and not to another. A thing can be similar to another (analogically or perhaps metaphorically) but it cannot be univocally the same. The law of identity states that A is A. As we will discover later, the law of identity is related to the law of noncontradiction (A cannot be non-A in the same sense and same relationship.) At the very basic and fundamental level of reality, we all know that there is a difference between A and non-A. A must be A, a thing is what it is.

What might the principle of identity have to do with cosmological reasoning? The answer is that it is a basic property of reality. The principle of identity is true of the cosmos (it does exist, it is what it is) and of every thing within it. It is one of the principles and axioms of reality.

Furthermore, it is an undeniable principle of reality. To say that A is not identical to A assumes that each A is identical. It is self-refuting to deny the principle of identity.

The principle of existence and the principle of identity are important aspects of reality. The truth is, we use these concepts everyday. Being is the most fundamental and basic idea to our existence. Dr. Mortimer Adler, explains it this way,

… You and I and everybody else uses the word ‘exists’ or ‘is’—there’s no commoner word in any language than the ontological predicate ‘is’ or ‘is not’—you and I day in and day out say that is or that does not exist, and when we say something does not exist we are thinking of nothing in its place sometimes. So I think the concept of being and not being or existence and nothingness are, shall I say, part of the very heart of human thinking. (36)

Indeed, the principles of existence and identity are essential to human thinking about reality. It is absolutely impossible to deny that being is. This establishes our first premise in our cosmological argument.

In our next post we will apply the law of noncontradiction to cosmological reasoning.

Works cited

Dzugan, Ken, editor. How to Prove There Is a God: Mortimer J. Adler’s Writings and Thoughts about God. Open Court, 2012

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).