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Original URL: http://peterpike.us/philosophy/philosophy0002.aspx

Rescue Date: June 20, 2009

Original author: Peter Pike

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Logic Presupposes the Existence of God

by Peter Pike

Such a simple statement carries a wealth of content. Naturally, in philosophical endeavors our first task must be to define our terms. In this particular case, we must look at two terms with greater care than others (i.e. “logic” and “God”), but we must also look at the other two terms as well.

First let us examine what is meant by the word “existence.” When something “exists” it is. Note that this does not mean that we are dealing with physical or material existence. Indeed, immaterial existence also exists. (For evidence of this, imagine a red ball. The red ball you have imagined does not have any physical existence; it exists immaterially. Granted, one can argue that the immaterial existence is based on a material brain, but the ball that is imagined is not material. It does not exist physically anywhere.)

Contrary to Ayn Rand, it is not true that “existence exists” however. Existence is an attribute that describes some other thing. That is, whether material or immaterial, objects that exist have the attribute of existence. Existence itself cannot exist, for it is not an object but an attribute of objects. Existence, therefore, presupposes objects.

And that brings us to the second term: presupposes. Presuppositions are concepts that must be true if something else is true. It might be easiest to think of in terms of cause and effect chains, but this is not the only way in which presuppositions come about. However, for a simple example, the statement “Adam died today” presupposes that before today Adam was alive. This is a necessary truth, for only living beings can die. If Adam dies, then we are required to believe that Adam first lived. The presupposition here is a necessary requirement due to structure of the word “died” as well as the time frame (“today”) given.

This will be the primary usage of the term “presupposes” in the statement: “Logic presupposes the existence of God.” In other words, just as the term “died” in “Adam died today” presupposes Adam’s former life, so “Logic” presupposes the existence of “God.” That is, if we accept the validity of logic we must necessarily accept the truth that God exists.

Now we must look at the more difficult terms, starting with “God.” What is meant by God? While it is true that I primarily hold the Christian theistic view in mind when I use this term, the argument I will present does not necessitate the existence of the Christian God at all. Other forms of theism may, indeed, fit the argument as well, provided the “God” in view holds to these attributes:

By “God” we mean an eternal, self-existent, necessary, immaterial being who is transcendent, omnipotent, and immutable. Other attributes may, perhaps, fit in as well, but I think it sufficient for the task to limit ourselves to these attributes.

Finally, what is meant by logic? Here I shall limit myself to two simple laws of logic: the Law of Identity (A is A) and the Law of Non-Contradiction (A is not ~A).

The logical law of identity is perhaps best represented by the Greek philosopher Parmenides’ statement: “Whatever is, is.” This statement can be symbolically represented in the logical format:

A is A.

In such a case, whatever A is, is (by definition) A. Because we are dealing with abstract levels of thought here, it does not concern us to actually flesh out what A is. We are concerned with seeing the relationships that go on between all objects, and therefore A can stand for any object—it could be an apple or it could be the entire universe (viewed as one lump sum), or it could be an immaterial thought (e.g. “love”); but whatever A is, that is what A is.

This is what is known as an analytically true statement (that is, it’s true by definition). Other examples of analytically true statements include: “A bachelor is an unmarried man” and “A square has four sides.” Analytically false statements, on the other hand, are statements that are false by definition: “A bachelor is a married man” would be analytically false, as would “A square has seven sides.” (Note that “A square has three sides” is still a true statement, since if an object has four sides it is also true that it has three sides; but a square cannot have more than four sides by definition.)

Parmenides’ statement, “Whatever is, is” was challenged by Heraclitus who stated, “Whatever is, is changing.” Heraclitus has given us some clichés that survive to this day based on this concept, such as: “You cannot step into the same river twice.” Because the river is moving, it is altered through time. The difference between Parmenides and Heraclitus boils down to the difference between “being” and “becoming”, which is often restated as the difference between “actuality” and “potentiality.” However, we note that even Heraclitus’ statement can be reduced to “A is A.” If “whatever is, is changing” is valid, then we cannot define A without including the property of change. Thus, A is A remains valid because A includes within the definition of “A” the property of “becoming” if, in fact, A is becoming.

If we do not wish to include the changing aspect of A in the definition, there is another way to get around it. Since “becoming” carries with it a temporal aspect (that is, change can only happen through time) then we can also intentionally view A non-temporally to avoid that aspect. Thus, we can say “A is A” is a truth about A frozen in a specific time. Either way, the Law of Identity as expressed by “A is A” is analytically true.

Regarding the Law of Non-Contradiction, it is most simply put in the form:

A cannot be both A and ~A at the same time and in the same relationship.

To clarify, the tilde (~) represents the word “non”, and the “non” refers to the contrary of A. If A is “a horse” then ~A would be that which is not “a horse.” The Law of Non-Contradiction follows easily enough because if we know that A is A, then we know that A is not whatever A is not. A is not ~A immediately follows from A is A, because in defining A we are distinguishing A from everything else (~A). Whatever is not A, is not A.

I’ve always found the above definition of the Law of Non-Contradiction to be a bit misleading though. To demonstrate, let us define A as “A man” and restate the sentence: “A man cannot be both a man and not a man at the same time and in the same relationship.” This statement is still valid, to a point, but it can be simplified to: “A man cannot be not a man.” The rest of the sentence is ultimately superfluous because there will never be a case when a man might be not a man without violating the definition of the terms involved with ambiguity. Instead, I believe it is more precise to define the Law of Non-Contradiction as:

A cannot be (or “A cannot have the property of”) both B and ~B at the same time and in the same relationship.

Now if we substitute “A man” for A, we do not immediately run into definitional gibberish. We need to establish what B is, so let us define it as “a father.” Thus we can say: “A man (A) cannot be both a father (B) and not a father (~B) at the same time and in the same relationship.” This sentence now makes sense, because while there will never be a time when a man will be a non-man, there are times when a man may be a non-father, just as there are times a man may be a father.

In both definitions of the Law of Non-Contradiction (the classic definition and my tweaking of it), we see the temporal aspect come into play (“at the same time”), and there is also a relational aspect that we deal with (“in the same relationship”). To be sure, a man can be both a father and not a father at the same time, as long as it is not in the same relationship (indeed, this is the definition of every father: every father is the father to his own sons and daughters, but is not the father to anyone else’s children). Thus, the Law of Non-Contradiction automatically deals with the existence of multiple objects and temporal relationships—we do not need to create another law of logic when we expand out from single objects frozen in time.

These two laws of logic are the most important Laws of Logic, and from them we derive several other rules for rationality (for example, we say that circular reasoning is invalid because both sides of a contradiction can be “proven” with circular reasoning, thus resulting in a violation of the law of non-contradiction). However, we shall look at those rules of reason only as we need to in the following argument, in order to save on time.

With the framework in place, let us again examine the proposition: “Logic presupposes the existence of God.” Let us look first at the issue of time as it regards logic and existence.

Time has fascinated me greatly for years, and it is quite possible for me to go on a lengthy bunny trail on this subject. However, I will resist that and instead limit our discussion for the moment to only those specific aspects of time that we can logically link to the concept of existence. First of all, we must ask: what is meant by time?

This is a difficult question to answer, much as defining “existence” is difficult. We could take Einstein’s view that “Time is that which clocks measure.” Or we can take the other physicist’s common idea: “Time is what keeps everything from happening all at once.” Neither of these is very satisfactory.

We are not helped much by the advent of Special and General Relativity. Instead of simplifying the problems for us, conceptually it increased the difficulty. There is no such thing as a universal time anymore. The rate of time depends upon the rate of movement through space, such that the faster you move through space the slower you move through time. In fact, one way of illustrating this is by imagining that you have an engine that can move through four dimensions (three space and one time), but that the combined rate of movement must equal exactly the speed of light. As such, since light moves through space at the speed of light, it moves through time at a speed of 0. On the other hand, we move through space at a much slower rate, and the leftover bits get transferred to how fast we move through time. Thus, the faster we move through space, the slower we move through time.

While this brings up immediate bunny trails (for instance, how would one determine my “age” when, for instance, no time has elapsed for a proton that escaped the sun at the exact moment I was born—although this is weakened by the fact that according to relativity, there is no such thing as simultaneous events anyway), again we need only speak of a few points here.

The first is this: no matter how we look at time, we are always reduced to a question of existence. If time is that which clocks measure, then clocks must exist before there can be knowledge of time. Note that this does not mean your bedroom alarm clock must exist before time exists! A clock is simply a device that has repetition built in. The Earth rotating once on its axis is a clock—1 rotation = 1 day. The Earth rotating around the Sun is also a clock—1 rotation = 1 year. Furthermore, most of our watches today are built by counting the frequency of quartz crystals that vibrate at a specific rate when electricity passes through them—32.768 kHz = 1 second.

Naturally, while clocks measure time clocks are not time themselves. Indeed, we can imagine that if all physical processes stopped, time could still move on. However, time’s “moving on” is only meaningful if things later change back to movement. Then, the period between the stop and the start of physical process would be a unit of time. Time is meaningless if all physical processes ceased and never picked up again.

This leads us to a related point: the perception of time. We are primarily convinced of the existence of time because we are able to perceive change. We know things today that we didn’t know yesterday, and we can remember learning these things. We can put a piece of bread on the counter and watch as it first becomes stale and then eventually grows moldy. We perceive these changes.

Again, this does not mean our perceptions are valid. Just as we cannot prove other objects exist via our perception of those objects, we cannot prove that those objects change via our perceptions. But we can prove we have the perception of change, for we have memories of the change.

In this case, however, our perception is not able to do for time what it could do for existence. That is, while our perception means we know something exists by direct knowledge, our perception of the passage of time could be an illusion. Our memories could be false memories. We could possibly exist as beings outside of time with false memories of the passage of time, including thoughts of our remembering certain things occurred “more recently” than other things. But while this might be possible, it is hardly probable. Indeed, it is difficult to see how it would be possible for a timeless existence to have beings that exist with the memories of time, especially as elaborate as these memories are.

So let us assume the existence of time. It is not only most likely to be right, but if it is a false assumption it doesn’t matter. After all, if this is a false assumption then I can never change my mind on the issue as I will be forever frozen with this idea that time is real. No one can “convince” me otherwise, as that would require change and change can only be expressed through time. Thus, there remains absolutely no reason to doubt the existence of time.

Let us now couple this notion of time with our ideas of existence. Since I know for a fact that something most certainly exists due to my direct knowledge of my own perceptions (and due to the fact that even if my perceptions are imaginary, I must exist in order to be deceived by them) and since there is no reason to doubt the validity of time, what does this mean for us?

First (and most paradoxically) it means that there must be some form of existence that is outside the realm of time! In other words, existence within time presupposes existence outside of time too. How does this work? To answer that question, we must first ask another: where did my own existence come from, or did it come from anything?

There only seem to be a grand total of three possible options here:

1. I am self-created.

2. I am self-existent.

3. I am created by something else that is self-existent.

(Another option that philosophers have used is “4. My existence is an illusion” but since the being I call “myself” does indeed perceive, even if all that is perceived is illusion something must exist in order to have those illusions; therefore, I know that 4 is wrong due to the direct knowledge of my own perceptions—not that this helps you know that I exist, of course.)

So what would it mean if I were self-created? Basically put, it would mean that at one point there was nothing, and out of that nothing I created myself. But this explanation already seems absurd (and it is), for if there is “nothing” then not even I existed then. But if I didn’t exist then, then I would not be able to create myself. Self-creation, therefore, results in a logical contradiction: I exist and yet I non-exist at the same time and in the same relationship, if I am self-created.

So self-creation is illogical. Logic dictates instead that there must be some form of self-existence. What is self-existence then?

Self-existence means simply that the self-existent object has the “power” of existence with itself. If I am self-existent, then I contain as one of my attributes the attribute of existence. This, in turn, would make me a necessary being—for if I hold the power to existence within myself then it is impossible for me to cease to exist without ceasing to be me.

But my perceptions are not that I am myself a self-existent being. Instead, I perceive that I have parents. Let us suppose this perception is right (and I have no reason to deny it). The question moves back one step. Where did my parents come from? Either they are self-existent, or they too were created by something else.

My parents claim to have parents. The chain moves back up another link and we repeat the question again. Soon, we have travelled quite some distance. In fact, some might be tempted to ask “Why isn’t it possible that there are an infinite number of links in this chain? If the chain is infinitely long, then we never need to stipulate that there was some being that was self-existent.”

The problem with the infinite chain idea is the infinite time involved. See, if my existence comes from something else, and that something else’s existence comes from another something else, and this continues forever, then we have continual change. Change, as we talked about earlier, is the essence of time. An infinite chain of change would take an infinite amount of time to form. But if it took an infinite amount of time to form, then we could not presently be in our current time—we would still be an infinite time in the past from this point!

In other words, an infinite chain involves us with what is called an infinite redux. The same position must be taken back one step an infinite number of times, and therefore nothing is ever gained. The only way to stop this is if, at some point, we break out of the chain and stipulate there must be something to start the chain, and that chain-starter must be self-existent.

For the same reasons as the infinite redux, this self-existent being must be able to transcend time itself. In other words, the self-existent being must be eternal (by eternal we do not mean infinite, as that would bring us back to the infinite chain problem; we mean only that an eternal existence is not bound by time). It exists apart from time (which, being linked to space, means that the self-existent chain-starter must have non-physical existence too, that is it must be immaterial).

Thus we have established that logic demands that there be some form of immaterial self-existence. I might be that self-existent being, of course, assuming I exist immaterially. But whatever the case may be, logic requires that whatever or whoever the self-existent being is must be the cause of my own being. If I am not the self-existent being and were not created by that self-existent being, my being would never existed (for we would be back to the infinite regress).

So, the fact that I exit proves the necessity of some object with self-existence that caused my existence. This object could not have been created by anything else (for the same reasons of the infinite regress). The “first” object to ever exist in the chain that ends with my own existence must be self-existent.

If an object is self-existent, it is a necessary object. It holds the power of its own existence, and therefore nothing can keep it from existing. If nothing can keep it from existing, then it must logically always exist.

Other attributes can be logically deduced from this same being. For instance, omnipresence (all existence derived from this self-existent source must come from this self-existent source, so the source must be omnipresent–there is no existence outside of the existence of this self-existent object); omnipotence (all power is derived from existence, so all power flows from the self-existent source—without that source, there is no power); and immutability (since logic is immutable, the source of logic must be unchanging as well).

All of these attributes are necessary requirements of logic. All of them fit the definition of “God” provided above. Therefore: “Logic presupposes the existence of God.”

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