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. — Aristotle, Metaphysics

So far, we have been exploring two of the most essential properties of Being, or existence—the principle of noncontradiction and the principle of identity. Now we will examine the third principle of metaphysics and epistemology, the principle of excluded middle. The principle of excluded middle states that either something exists and shares some important properties of being, or it does not. In logic this is known as an “either/or” statement. Computers and logic gates in integrated circuits are built on this principle (either certain conditions are met such as a voltage or a “1,” or not). Results depend on the input.

What we are learning is that there are important logical applications to metaphysics. This should not be surprising, after all, because the principles of logic are properties of being (which is the object of study for the metaphysician). Further, because of the principles of logic are properties of being, they have important epistemological and metaphysical implications. They tell us how we can think correctly (logic), how we know something (epistemology), and what the ultimate foundations of reality are (metaphysics).

It is important to remember that these principles of metaphysics are not products of our thinking or our minds. That is, they are not created by our minds or thoughts. They are properties of reality. They inform how we think about reality but are not created by our thinking. This is part of what it means to be a realist—the laws of logic are real properties of actually existing things (being). Idealists, such as Kant, Berkeley, and others believed that reality is a product of ideas or one’s mind. Idealism is a magnificent error of modern philosophy.¹ Reality is the determinant of order—not our thoughts, feelings, or desires.

But what can the principle of excluded middle tell us about cosmological arguments for the existence of God?

At the most basic level, something either is or it is not. I can have a good day in one sense and a bad day in another sense but there is no denying that I experience the day itself (unless I slept through it, but the day occurred nonetheless). Ontologically (the nature of existing things), my cat, my son, or my computer either exist or do not. Being either is or it is not. As Aristotle reminds us, one of the starting points of all demonstration and thought is that everything at its most basic level must be either affirmed or denied. In this case, being can not be denied.

Philosopher Peter Kreeft puts it this way (calling it the law of excluded middle), assuming no ambiguity of terms:²

A thing is either x or not x. A predicate must be either affirmed or denied of a subject; there is no third possibility. A proposition is either true or false, there is no third possibility. This is the law of excluded middle.³

This helps us to apply the principle of excluded middle to the first premise of our cosmological argument—something exists, being is. Reality cannot be denied. (Click here for the particular cosmological argument being explicated.)

The laws of identity, noncontradiction, and excluded middle are not only necessary for thinking correctly about something, and knowing the truth of something, but they are laws, principles, and properties of being, or reality. They tell us how all being has to be and everything that makes up being (that which has being) must be. Kreeft helpfully puts it this way,

The universe and everything in it, and also the self, (1) can’t ever be what it isn’t (the Law of Non-contradiction), (2) always must be what it is (the Law of Identity), and (3) always either is or isn’t (the Law of Excluded Middle). Also, (4) all that comes into being—i.e. all changing being—has a cause (the Principle of Causality), and (5) everything that is has a sufficient reason why it is and is what it is (the Principle of Sufficient Reason).⁴

All being and becoming (changing being) rests on these metaphysical, epistemological, and logical principles. We will examine the Principle of Causality and the Principle of Sufficient Reason in future posts. For now, it is enough to know that anything that participates in reality either is, or it is not. Being itself either is or it is not.

Works cited

Adler, Mortimer J., Adler’s Philosophical Dictionary: 125 Key Terms for the Philosopher’s Lexicon New York: Scribner, 1995.

Kreeft, Peter, and Trent Dougherty. Socratic Logic. 3rd ed. South Bend, Ind: ST Augustines Press, 2008.

Sources for digging deeper:

H. W. B. Joseph, An Introduction to Logic (1916; repr., Cresskill, NJ: The Paper Tiger, 2000).

Norman Geisler, God: A Philosophical Argument from Being (Matthews, NC: Basion Books, 2015).

Notes:

1 Mortimer Adler, for example calls idealism “the greatest of all modern philosophical mistakes” in his book entitled Adler’s Philosophical Dictionary, S.V. Idea.

2 At this point, we don’t need to distinguish between the terms “principle” and “law”. For this series we will use the terms synonymously. The concept is the same. At the most elemental ontological level of reality, a third option of being is eliminated or ruled out.

3 Kreeft, Peter, and Trent Dougherty. Socratic Logic. 3rd ed. South Bend, Ind: ST Augustines Press, 2008, 188.

4 Kreeft, Peter, and Trent Dougherty. Socratic Logic. 3rd ed. South Bend, Ind: ST Augustines Press, 2008, 359.