Before I can overcome objections, let me present my argument. I believe, unless I have misinterpreted, that the argument entirely comes from Gottfried Wilhelm Leibniz. My adaptation argues the following:
Let an impossible being mean a being that is self-contradictory.
Let a necessary being mean a being whose opposite is a contradiction; that is a necessary being is one which cannot be conceived not to be, and one whose reason for being is self-sufficient.
Let a contingent being mean a being whose opposite is not a contradiction, that is a contingent being is one which can be conceived of as not existing, and one whose reason is not self-sufficient.
If there are possible beings, they have a reason sufficient to explain them—either as a necessary being, that being self-sufficient or as a contingent being, that needing a reason outside of itself. (principle of sufficient reason).
There cannot be an infinity of contingent beings (law against infinite regress with the definition of a contingent being).
Either all beings are necessary, or there are both contingent and necessary beings (follows from the above premise).
Therefore, if there are possible beings, there are necessary beings (follows from the above premise).
If there were no possible beings, then all beings would be impossible; that is, they would be self-contradictory (by definition).
Impossible beings do not exist. (law of noncontradiction and the definition of an impossible being).
If impossible beings do not exist, neither does an argument claiming that nothing exists (follows from the above premise, and the assumption that there are no possible beings).
This argument would not be an argument. (follows from the above premise).
An argument that is not an argument is absurd. (law of noncontradiction).
Therefore, possible beings exist because they involve no contradiction (law on noncontradiction and the absurdity which follows from the above premise).
Therefore, necessary beings exist (follows from the premise seven above and the above premise).
The next terms we should examine are those of possible, impossible, contingent, and necessary. The most confusing of these is the term possible. Many people take possible to mean the same as "might." If something possibly exists, then it typically means that something might exist or might not exist. This is what is meant by contingent, but I do not necessarily mean "might" when I write of possible existence. A possible being simply is one which is not self-contradictory. Maybe, the possible being in question must exist. This is okay under my definition of possible. Like having only one possible choice after eliminating all other apparent possibilities on a multiple-choice exam, this meaning of possible does not need to infer in any way "might not." The term necessary refers to a possible being which is impossible to deny. God, potentially, is one such being. The term contingent, as stated already, refers to a possible being, which is possible to deny. One example of a contingent being is the chair you now sit. Maybe, it is quite unlikely that you could really not be sitting on a chair, but there are a number of people who think all sorts of things who turn out to be wrong. It is conceivable, within the "realm of possibility" that that chair does not exist. Finally, the term impossible refers to a being which contradicts itself, that is incoherent and not rationally understandable. How can something impossible be? That question shall be addressed in answering the first objection—the first objection is that existence is not a predicate.
You should now spend a moment rereading the argument. The terms, now hopefully clear, should shed light to the substance of the argument.
Before going at the objections, let me make a few comments about the argument. First off, it takes the form of two classical arguments for the existence of God. The first part, designed to show the impossibility of everything being contingent (that is, deniable) is really a cosmological argument. Cosmological arguments begin by observing things which exist, then drawing conclusions based on the observations. The last part of the argument is an ontological argument. Without observing anything, these arguments claim to deduce from definitions something about the nature of reality. The primary substance of this argument rests on the ontological part of the argument. Without it, the observations of existing things might well be nonsense. For example, what good would it do in a discussion of reality for a schizophrenic to deduce the natures of all the people out to attack him? In the end, the people out to attack him remain a part of his mind, and his observations were based on a contingent sketch of reality. On the other hand, if the nature of possibility, impossibility, contingency, and necessity are understood as conditions of observation, then the argument has no doubts as to its relation to reality and the observations from nature have relevancy. I realize that I stir a hornet’s nest by making the claim that knowledge depends upon observation secondary to ontology, but this paper is not meant to answer the empiricist’s objections. Let us just realize at the start that this is an ontological argument, and it is not friendly to a radical empiricism. Addressing such criticisms is for another paper, but they are relevant to keep in mind when looking at this paper. It is relevant because the objections in this paper are used as grounds for the claims of empiricists. Once these grounds disappear, I believe the anti-rationalist empiricist rests on a more slippery slope.
This argument, then, concludes that a necessary being exists. It argues that it exists because there cannot be only contingent beings and because a necessary being is not only impossible to deny but also possible to assert. For example, a common criticism of St. Anselm’s argument for a necessarily existing being is that although he may prove that such a being is impossible to deny, that it might be that a necessary being itself is impossible. For instance, the "necessarily existing square circle" may be impossible to deny, but a square circle itself is impossible. This is why it is important to express the possibility of a necessary being, and not just the impossibility of denying such a being.
The first objection to my argument states that existence is not a predicate. What is meant is that existence is not the quality of an object. For instance, cars may be red, or large, or convertible, but what is added to a car by saying that it "exists?" Immanuel Kant, in arguing that existence is not a "real predicate" says that propositions like "God exists" do not express anything new to the subject. As Kant says, "exists" is really just the copula of a proposition. He means that a proposition typically has the word "is", called the copula, to connect the subject and predicate of a proposition. "Exists" simply translates to "is" and so is not properly a predicate.
So, what is the point of this objection? Is it simply to say that "God exists" is redundant? That clearly is not the point or else it would not be offered as an argument against proving the existence of God. The larger point of this most common of objections against my argument is to demonstrate the absurdity of rationally speaking about the existence of beings. For instance, this potential objector points out:
For every value of x which does not have the predicate of existence, then x (exists).
The above proposition is what I apparently favor when I set up distinctions between impossible and possible beings. I have not only given the so-called predicate of existence to impossible beings; I have contradicted myself by saying that x does not have the predicate of existence. How do I defend my argument against such a charge?
The paradoxical position that I must defend, then, is that there is a sense in which something that does not exist exists. I must defend my notion of "impossible beings" in order to save my claim that possible beings exist because they involve no contradiction and any denial of all possible beings do. Rather, my claim that possible beings exist seems to rest on the dubious premise that I can make a meaningful distinction between possible and impossible beings.
I defend my paradox by noting that the objection rests on an equivocation of the word "existence." The assumption in the objection is that when I define a being as "impossible" or "not existing" that I must mean the same thing as I do when I define a being as "possible" or "existing." This seems, at first glance, to be a reasonable assumption. Logic generally is not equipped to understand the copula of a proposition as anything more than a connector between subject and predicate. Philosophy, however, is.
Let us look at the case of the thing which does not exist, and see if we can make sense of it as a thing which exists in the sense that we can talk about it but not in the sense that such a thing is real. Let us look at the chair on which you sit. Or, perhaps, you do not sit on a chair, but you can imagine a chair which is not there. The chair which does not exist, in this case, is still something, is it not? In this case, the chair is the object of your imagination. Now, look outside. Maybe, there are no chairs there. But, there is still something there, is there not? The "not chair" is perhaps a sidewalk, or some trees, or some grass, or something else. When we speak of chairs which are not, we can and do speak meaningfully of them. Maybe, they do not have our predicate of existence, but they at least exist in the sense that there is a real "something" that is the true object of the "not chair."
An "impossible being" likewise is something we can speak about. Now, I have never had an acquaintance with an "impossible being." Also, I do not really find myself able to imagine one in any way, but the garble that we speak of when we speak of such things at least represents the sentence which constitutes them, the semantics, or the sounds, or the words we cannot make sense. "A bull with horns that has no horns" is an impossible being, but the meaningfulness in speaking about such a being is that the being really is a something, it is at least the words which comprise it, or the opposites we are not able to understand in combination but are able to understand on their own. I know what a bull with horns is, and I know what a bull without horns is, but I do not know what one is in combination with and without horns. This impossible being I understand as a combination of things I do understand whose combination I cannot understand. It is a something, though it expresses in itself nothing which really exists.
So, now, what is so absurd about "existence" as a predicate? Impossible beings do not exist, but as objects of discussion do represent something else which is real. What does not exist refers to something else—"What is outside your window?-not a chair." Surely, that is meaningful. The logician’s objection to my argument is naïve. It treats "is" merely as an "=" in mathematics when "is" clearly refers to something more complex than that. "God" does refer to "God existing" but "Impossible being" does not refer to "Impossible being existing" anymore than the chair you do not sit on means that the object of your imagination is really a chair you can sit on. It is something, the object of your imagination, but it is not ascribing the same sort of existence at all. I think this now is clear.
In that way, then, "God exists" does not merely refer to the copula of a proposition. Since we can and do talk about things not existing in a meaningful way, it is meaningful whether we say of something that it exists or that it does not exists. If it exists, then we may have added nothing to our brand new car at first notice, but take that car’s existence away, and you may have a chair instead. You may now sit on this "not car" while we move to the second objection.
The second objection to my argument states that of everything that exists, it is possible to conceive that it does not exist. That is, this objection states that everything may be contingent. Immanuel Kant argued that although it was necessary, by definition, that triangles have three angles, he saw no reason why one could not deny the existence of triangles, existence and all. Though God may have the property of existence by definition, what forbids one denying the object along with its definition? Might it be possible that every definition is capable of denial? Furthermore, defining God not merely as existing but as "necessarily existing" may not answer the objection because "necessary" may not be a proper way to define a being, especially if it is possible that all beings might not exist. Bertrand Russell thought that arguments like mine failed because they attribute necessity improperly to objects. Russell translates the definition of "necessary being" to mean, "If x is God, then x is God will always be the case." In other words, everything might not exist, and defining it as existing does not make it exist any more just by doing so.
My particular argument is meant to deal specifically with this objector. The cosmological portion of the argument is meant to answer this objection that everything might not exist. However, the objection runs deeper than that. The objector will emphatically deny the truth of two of the axioms. Those axioms are the principle of sufficient reason, and the law against infinite regress. This objector says:
A contingent being was defined as a possible being whose opposite was possible. The opposite of a contingent being is simply whatever that being is not. The opposite of the chair which you sit, by this definition, could potentially mean God, a car, the number 19, or anything else so long as it was not a chair. Now, since there are nothing but contingent beings in this universe, there needs to be an opposite. The definition of a contingent being requires it. Yet, without a reason to make a distinction between opposites, there are no true opposites at all. What I mean is, what if there was nothing to tell chairs apart from what was not a chair? With nothing to tell things apart, there would be nothing to tell apart and the distinction between contingent beings would be false. Contingent beings would not exist. So, it is for that reason that a principle of sufficient reason is supposed. Without sufficient reason to distinguish opposites, there can be no opposites, and this universe of nothing but contingencies would prove false.
So, in a world with nothing but contingent beings, a reason must be sufficient to explain the difference between beings or else there is no difference between beings. Yet, can a sufficient reason involve an infinity of reasons? Clearly, the answer is "no." If the reasons are allowed to go on forever, then no reason is ever established to distinguish contingent beings from each other. Imagine trying to tell your child why the sky was blue without being able to ever stop, without even being able to stop and say for sure that the sky is really something else altogether. Even if we allow that for the sake of practicality that we ourselves could stop the onslaught an infinity of reasons would put upon a universe of absolute contingency, we fail to establish the reality of such a universe without a law against infinite regress.
However, once the two axioms prove necessary to keep a world of nothing but contingent beings rational, we make such a world self-contradictory. My argument need not prove that there are such axioms to prove that one cannot at the same time deny the axioms and also assert that there can be only contingent beings. It is impossible to assert a universe of only contingent beings without the two axioms. Once one realizes that, one can realize that it follows from my argument that it is impossible to assert a universe of only contingent beings at all.
The upshot, then, is that it is not enough to deny a necessarily existing being on the ground that it is simply a definition, and that definitions have yet to be grounded in reality because the assumption that everything might not exist does not hold true.
The final objection to my argument is the most clever because it realizes something very odd about my argument. This objector notes that I assume what I set out to prove. The axioms upon which the argument rest are unproved, and so if I wish to prove that a necessary being exists, I have begged the question with this argument. I have assumed necessity in trying to prove necessity:
The objector is right, but the objection itself is problematic. I do assume the axioms, and I do assume existence. I assume it now in answering the question. Yet, does the objector put a dent in my arguments simply by noting that? Or, does the objector assume the axioms as well.
Let us look at the objection and see if the objection rests on the axioms. Rather than trying to look outside the axioms, let us only see if we can object without them. First of all, what is an "assumption" without any one of the axioms? Without the law of noncontradiction "assumption" could very well be anything and everything. If the intent was for the objection to speak against the necessity of the axioms, then how could the objector even hope to communicate what an "assumption" was without the axiom of the law of noncontradiction to be true? The objection itself depends upon the truth of at least that axiom, and so if it is meant as a possible denial of the axioms, it is a hopeless failure. It is much like if I claimed that I was telling a lie right now. The lie would depend on me telling the truth, as would saying that you cannot prove the axioms by assuming them depend upon the axioms to utter.
The point is that the objection that my argument begs the question cannot be rationally formed. The rational grounds of understanding the question assume what it asserts may be possible to deny. There are no grounds then for the charge that my argument is a vicious circle. There is nothing in the realm of possibility that allows a coherent expression of the question without also assuming existence and the axioms. So, yes, I assume existence, and prove necessity by assuming necessity, but there is nothing wrong with that as I have formed my argument.
This does not mean that it is impossible to beg the question. What it means is that if by accusing a question of being begged your own accusation depends upon the truth of what you try to logically deny, then the denial is without substance. Imagine telling your daughter, "You are my daughter, but how can you be sure that you are a girl?" Since the truth is that she is your daughter, and since all daughters are girls, on what grounds could she possibly answer you. "I know that my making you understand what I mean depends upon the truth of certain axioms, but how can you be sure that such axioms are necessary?" Certainly, the objector never consciously assumes what he tries to deny. Yet, the assumption is tacit. If someone can think of a denial, which does not assume the axioms, then I will reopen this part of the paper. Until then, I will wait.
This paper set out to begin to answer the question, "How do you know God exists?" It set out to begin by answering three objections to an argument, which I gave in favor of a necessarily existing being. I answered the first objection that existence was not a predicate by noting that it was possible to make distinctions between existing and non-existing things and that it was possible to speak meaningfully of both. I answered the second objection that everything which exists might not exist by arguing that it was impossible to accept that everything might be contingent without also accepting the axioms which make such a universe false. Finally, I answered the third objection that I assumed what I set out to prove by noting that although it was true that I had, that the objection itself was incoherent because it depended upon the truth of at least one of the axioms in order to be understood. I hope this begins to answer the question for some of you in rational terms.