Being, first principles, Metaphysics

Mere Metaphysics: Part Five. The Principle of Excluded Middle

by Dave Seng
Photo courtesy of Nathan Perkins

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.

Being, first principles, Metaphysics

Mere Metaphysics Part Two: Being Is

by Dave Seng

We may have three main objects in the study of truth: first, to find it when we are seeking it; second, to demonstrate it after we have found it; third, to distinguish it from error by examining it. — Blaise Pascal

The introduction to this series can be found here.

Part one of this series can be found here.

In my recent post on first principles, we learned that a foundational metaphysical principle is that from which everything else in its order follows, a self-evident axiom of thought or being that is actually undeniable. We briefly looked at the principle of noncontradiction and the principle of existence as axioms which correspond to this definition. Regarding the principle of noncontradiction and the importance of first principles, Aristotle reminds us,

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.1

Now we will examine the first premise in the cosmological argument from Being, or reality itself. The argument follows this line of reasoning:

1. Something exists (e.g., I do)

2. Nothing cannot produce something.

3. Therefore, something exists eternally and necessarily.

A. It exists eternally because if ever there was absolutely nothing, then there would always be absolutely nothing because nothing cannot produce something.

B. It exists necessarily because everything cannot be a contingent being because all contingent beings need a cause of their existence.

4. I am not a necessary and eternal being (since I change).

5. Therefore, both God (a Necessary Being) and I (a contingent being) exist. (= theism)

We will explore all of the principles for this demonstration as we move through this series. For now, we will look more carefully into premise one: Something exists (or, more technically, being is). This premise is simply the principle of existence. The principle of existence is a statement of reality. Reality exists. Something does in fact exist. This principle cannot be denied because one must exist in order to deny existence. This is not the same point that Descartes was making with his circular statement, “I think, therefore, I am” (his famous Cogito dictum). Descartes had to be, or to exist, in order to think, doubt, or do anything else. He had to exist first. The principle of existence is primary.

The principle of existence is so clear, fundamental, and directly knowable in itself that it requires no proof or further demonstration. It is self-evident and simply foolish to deny.

The principle of existence is an affirmation of being – the totality of the universe and reality.

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

Being, first principles, Metaphysics

Mere Metaphysics Part One: What is a First Principle?

by Dave Seng

In all our knowledge of general principles, what actually happens is that first of all we realize some particular application of the principle, and then we realize that the particularity is irrelevant, and that there is a generality which may equally truly be affirmed. – Bertrand Russell

We are continuing our series called Mere Metaphysics and this post will focus on what a principle is and some of the defining characteristics of what philosophers call “first principles.” I think, however, that before we get to the first principles of metaphysics, it is important to step back and get a general understanding and broad panoramic picture of what we mean by the term “principle”. This will be helpful, because the concept of principle really is not that different in metaphysics than in other fields of study, contexts, and applications. This approach will also help us understand why it is that no one who wishes to think correctly about reality, science, and human behavior can do so without an understanding of basic first principles.

A principle may be one among many temporally (as in a series of phenomena), or logically (as in the axioms of mathematics). Since, in many cases, there could be a hierarchy of principles, we are primarily interested in what philosophers call “first principles,” the most basic and foundational principles which underlie all human knowledge and action.

What is a principle? A principle is that from which something else follows. According to its Latin derivation and the equivalent root in Greek, “principle” means a beginning or foundation.1 In other words, a principle is the basic source of origin or the foundation from which something proceeds. The Dictionary of Scholastic Philosophy gives another helpful definition—“that from which something in some way proceeds; the starting point of being, or change, or knowledge, or discussion.”2 This definition is important because it illustrates that every field of study and human action has basic foundational principles.

In economics, for example, the principle of scarcity is one of the foundational concepts upon which the entire study of production, distribution, and consumption of goods and services depends. Both goods and money are considered scarce because they are not infinite and therefore economists study consumer exchange and behavior in light of such scarcity. Mathematics, also, has basic first principles. The entire reason Euclid, in his Elements, provides his definitions, postulates, and axioms (his mathematical principles) is that they are logically prior to all his theorems and demonstrations which he comes to by means of them.

In the realm of ethics, a principle is the rule or ground for determining the rightness or wrongness of a person’s action. If I respond unkindly to someone, I am forgetting the principle that kindness as such is always a virtue. The statement that it “is wrong to torture babies for fun” is based on the prior principle that it is wrong to harm another human being. A principle in human conduct can also serve as a guide for correct behavior or policy. In the area of public administration, someone might say that a particular government is acting “without principles” or in an unprincipled manner. That statement is not about the rightness or wrongness of the government’s action (that is a separate concern), but points to the claim that the government may not be acting with a uniform policy in place that will serve as a foundation for its actions. Regarding human conduct, principles are the most basic and foundational rules that guide correct action in the realm of ethical behavior and public policy. Principles are that from which all policy follows.

Science itself is based upon first principles. In order for science to be successful, it not only must assume the foundational laws of logic—noncontradiction, excluded middle, and identity, but also necessarily accept the following principles: The principle of existence (something is in fact the case, it exists), the principle of causality (every event has a cause and in identical situations the same cause always produces the same effect), the principle of predictive uniformity (a group of events will show the same degree of interconnection or relationship in the future as they showed in the past or show in the future), the principle of objectivity (requires the scientist to be impartial with regard to the data and treat it, carefully, openly, and honestly. The facts must be such that they can be experienced in exactly the same way by all normal people, the ethic of reproducibility, and an essential principle to the scientific method itself), the principle of empiricism (scientific knowledge is the result of observation, experience, as opposed to authority, intuition, or reason alone.)3 Although there are other first principles of science that should be mentioned, the above are enough to demonstrate that science itself relies on first principles. Every field has basic foundational concepts in place before anything else can be determined, discussed, or understood.

We can now see how the concept of principle works in many other contexts. This also explains why it is impossible to reject or deny the existence of primary foundational truths from which all correct thinking, scientific inquiry, and ethics derives. It is an interesting quality of first principles that they are not provable in the scientific or strict empirical sense and yet they can not be denied, unless one wants to fall into absurdity and chaos. Aristotle, Pascal, and John Stuart Mill (among others) believed it was neither possible nor necessary to prove basic foundational principles. Mill, for example, states, “to be incapable of proof by reasoning is common to all first principles; to the first premises of our Knowledge, as well as to those of our conduct.”4 The reason, as we shall see below, is that it is ultimately foolish to deny self-evident truths.

Aristotle was among the first of the great metaphysicians to point this out. Not only did Aristotle express the basic need for first principles, he believed they should be clear, simple, self-evident, and univocal. Aristotle, and many other thinkers after him, believe that one cannot prove a first principle positively because it is so self-evident that it would be ludicrous to deny. Take for example, the principle of existence, that something exists. One has to exist in order to deny that something exists. To deny existence is absurd. Or take another example, the principle of noncontradiction—nothing can both be and not be at the same time and in the same respect. To say that the principle of noncontradiction is false assumes that the opposite is true. Since opposites cannot both be true it is irrational to reject the principle of noncontradiction. As C. S. Lewis once put it, you cannot have a proof that no proofs matter. An attempt to do so is self-contradictory. It is possible to reject these basic principles but the result is chaos and conceptual incoherence.

In his Metaphysics, Aristotle provides two other reasons why first principles are needed for clear communication and correct reasoning. The first is that not every principle or starting point needs to be argued for or there would never be an end to argument and demonstration. Regarding the principle of noncontradiction, Aristotle puts it this way,

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 than the present one.5

It is genuinely hard to conceive of what principle can be more self-evident than the principle of noncontradiction.

The second reason Aristotle gives in defense of first principles is that correct reasoning comes from fixed principles and their definitions. At the most foundational level of existence, definitions are reduced to their principle. If the principles are equivocal, ambiguous, or have several definitions, no communication or reasoning can take place. Aristotle, taking on the poststructuralists of his day explains,

If, however, … one were to say that the word has an infinite number of meanings, obviously reasoning would be impossible; for not to have one meaning is to have no meaning, and if words have no meaning our reasoning with one another, and indeed with ourselves, has been annihilated.6

And Aristotle further explains,

Those, then, who are to join in argument with one another must to some extent understand one another; for if this does not happen how are they to join in argument with one another?7

Why are metaphysical principles important? Metaphysical first principles are the basis of all clear and correct reasoning. Argument about axioms and principles cannot go on forever or no real progress will be made. Without first principles, no communication or genuine argumentation can be accomplished. In addition, metaphysical first principles provide certainty. Without basic principles in place, we run the risk of conceptual incoherence on one hand and mere opinion on the other. If we have no axioms or principles to start from, all postulates become a matter of opinion, probability, and uncertainty. We will never achieve genuine knowledge. As Dr. Mortimer Adler once said, “axioms express the very essence of knowledge.”8

In our next post, we will examine the mere metaphysical principle of existence and seek to understand its role in the argument from being.

1 Mortimer Adler, ed., The Syntopicon: An Index to The Great Ideas, vol. 2, Great Books of The Western World (Chicago: Encyclopedia Britannica, Inc., 1996), s.v. Principle.

2 Bernard Wuellner S.J., Dictionary of Scholastic Philosophy (1956; repr., Fitzwilliam, NH: Loreto Publications, 2012), s.v. Principle.

3Herold Titus, Marilyn Smith, and Richard Nolan, Living Issues in Philosophy, 9th ed. (Belmont, California: Wadsworth Publishing Company, 1995), 218–19.

4 J.S. Mill, Utilitarianism, ed. Mortimer Adler, vol. 40, Great Books of The Western World (Chicago: Encyclopedia Britannica, 1993), 461.

5 Aristotle, Metaphysics, trans. W. D. Ross, vol. 7, Great Books of the Western World (Chicago: Encyclopedia Britannica, Inc., 1996), 525.

6 Ibid., 525.

7 Ibid., 590.

8 Mortimer Adler, ed., The Syntopicon: An Index to The Great Ideas, vol. 2, Great Books of The Western World (Chicago: Encyclopedia Britannica, Inc., 1996), s.v. principle.