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"No one can prove an unrestricted negative" is the reply usually given to those who claim that science can prove that God does not exist. An unrestricted negative is a claim to the effect that something doesn't exist anywhere. Since no one can exhaustively examine every place in the universe, the reply goes, no one can conclusively establish the non-existence of anything.
The principle that no one can prove an unrestricted negative, however, is itself an unrestricted negative. It says, in effect, that there are no proofs of unrestricted negatives. But, if there are no proofs of unrestricted negatives, then no one can prove that no one can prove an unrestricted negative. And if no one can prove that no one can prove an unrestricted negative, then it must be logically possible to prove an unrestricted negative. So the claim that no one can prove a universal negative is self-refuting-if it's true, it's false. What I intend to show here is not only that unrestricted negatives can be proven, but that a number of them have been proven.
Parmenides realized over 2,500 years ago that anything that involves a logical contradiction cannot exist. We know that there are no married bachelors, no square circles, and no largest number because these notions are self-contradictory. They violate the most fundamental law of logic-the law of noncontradiction-which says that nothing can both have a property and lack it at the same time. So one way to prove a universal negative is to show that the notion of a thing is inconsistent.
To prove that God does not exist, then, one only has to demonstrate that the concept of God is inconsistent. Traditional theism defines God as a supreme being-a being than which none greater can be conceived, as St. Anselm would have it. We know, however, that there is no supreme number because such a notion involves a logical contradiction. Every number is such that the number 1 can be added to it. If there were a supreme number, it would be such that the number 1 can and cannot be added to it, and that's impossible. Many believe that the notion of a supreme being is just as incoherent as the notion of a supreme number.
Consider, for example, the claim that god is all-good and thus both perfectly merciful and perfectly just. If he is perfectly just, he makes sure that everyone gets exactly what's coming to them. If he is perfectly merciful, he let's everyone off. But he can't do both. So the notion of a supreme being may be internally inconsistent.
This is just one of many inconsistencies that have been found in the traditional concept of God. For a more complete review of them, see Theodore Drange, "Incompatible-Properties Arguments: A Survey" in Philo (Fall/Winter 1998). Theists, of course, will claim that, properly understood, there is no contradiction. What if they're right? What if it's logically possible for the God of traditional theism to exist? Does that mean that one cannot prove that he does not exist? No, for in order to prove that something does not exist, one need not show that it is logically impossible. One need only show is that it is epistemically unnecessary-that it is not required to explain anything. Science has proven the non-existence of many things in this way, such as phlogiston, the luminiferous ether, and the planet Vulcan. Scientific proofs, unlike logical proofs, do not establish their conclusions beyond any possibility of doubt. But they are proofs nonetheless, for they establish their conclusions beyond a reasonable doubt and that is all that is needed to justify them.
Phlogiston, the luminiferous ether, and the planet Vulcan are theoretical entities that were postulated in order to explain various phenomena. Phlogiston was postulated to explain heat, the luminiferous ether was postulated to explain the propagation of light waves through empty space, and Vulcan was postulated to explain the perturbations in the orbit of Mercury. Science has shown, however, that these phenomena can be explained without invoking these entities. By demonstrating that these entities are not needed to explain anything, science has proven that they do not exist.
God is a theoretical entity that is postulated by theists to explain various phenomena, such as the origin of the universe, the design of the universe, and the origin of living things. Modern science, however, can explain all of these phenomena without postulating the existence of God.1 In the words of Laplace, science has no need of that hypothesis.2 By demonstrating that God is not needed to explain anything, science has proven that there is no more reason to believe in the existence of God than to believe in the existence of phlogiston, the luminiferous ether, or Vulcan. This may explain why more than 90% of the world's top scientists disbelieve or doubt the existence of God.3
Scientists prefer natural explanations to supernatural ones, not because of any metaphysical bias on their part, but because natural explanations produce more understanding than supernatural ones. As Plato realized, to say that God did it is not to explain anything, but simply to offer an excuse for not having an explanation.4
The goodness of an explanation is determined by how much understanding it produces, and the amount of understanding produced by an explanation is determined by how well it systematizes and unifies our knowledge. The extent to which an explanation systematizes and unifies our knowledge can be measured by various criteria of adequacy such as simplicity (the number of assumptions made), scope (the types of phenomena explained), conservatism (fit with existing theory), and fruitfulness (ability to make successful novel predictions).
Supernatural explanations are inherently inferior to natural ones because they do not meet the criteria of adequacy as well. For example, they are usually less simple because they assume the existence of at least one additional type of entity. They usually have less scope because they don't explain how the phenomena in question are produced and thus they raise more questions than they answer. They are usually less conservative because they imply that certain natural laws have been violated. And they are usually less fruitful because they don't make any novel predictions. That is why scientists avoid them.
The realization that the traditional God of theism is not needed to explain anything-that there is nothing for him to do-has led a number of theologians to call for the rejection of this notion of god. In Why Believe in God? Michael Donald Goulder argues that the only intellectually respectable position on the god question is atheism.5 In Why Christianity Must Change or Die, Reverend Spong, former Episcopal Bishop of New Jersey, argues that the traditional theistic conception of God must be replaced by one grounded in human relationships and concerns.6 Both agree with Stephen J. Gould that religion should not be in the business of trying to explain the world.7
What if there was no plausible natural explanation for some phenomena? Would that justify the claim that god caused it? No, for our inability to provide a natural explanation may simply be due to our ignorance of the operative natural forces. Many phenomena that were once attributed to supernatural beings such as earthquakes, volcanoes, and disease can now be explained in purely natural terms. As St. Augustine realized, apparent miracles are not contrary to nature but contrary to our knowledge of nature.8
Given the inherent inferiority of supernatural explanations and the incompleteness of our knowledge, theists would be justified in offering a supernatural explanation for a phenomenon only if they could prove that it is in principle impossible to provide a natural explanation of it. In other words, to undermine the scientific proof for the non-existence of god, theists have to prove an unrestricted negative, namely, that no natural explanation of a phenomenon will be found. And that, I believe, is an unrestricted negative that no theist will ever be able to prove.
The principle that no one can prove an unrestricted negative, however, is itself an unrestricted negative. It says, in effect, that there are no proofs of unrestricted negatives. But, if there are no proofs of unrestricted negatives, then no one can prove that no one can prove an unrestricted negative. And if no one can prove that no one can prove an unrestricted negative, then it must be logically possible to prove an unrestricted negative. So the claim that no one can prove a universal negative is self-refuting-if it's true, it's false. What I intend to show here is not only that unrestricted negatives can be proven, but that a number of them have been proven.
Parmenides realized over 2,500 years ago that anything that involves a logical contradiction cannot exist. We know that there are no married bachelors, no square circles, and no largest number because these notions are self-contradictory. They violate the most fundamental law of logic-the law of noncontradiction-which says that nothing can both have a property and lack it at the same time. So one way to prove a universal negative is to show that the notion of a thing is inconsistent.
To prove that God does not exist, then, one only has to demonstrate that the concept of God is inconsistent. Traditional theism defines God as a supreme being-a being than which none greater can be conceived, as St. Anselm would have it. We know, however, that there is no supreme number because such a notion involves a logical contradiction. Every number is such that the number 1 can be added to it. If there were a supreme number, it would be such that the number 1 can and cannot be added to it, and that's impossible. Many believe that the notion of a supreme being is just as incoherent as the notion of a supreme number.
Consider, for example, the claim that god is all-good and thus both perfectly merciful and perfectly just. If he is perfectly just, he makes sure that everyone gets exactly what's coming to them. If he is perfectly merciful, he let's everyone off. But he can't do both. So the notion of a supreme being may be internally inconsistent.
This is just one of many inconsistencies that have been found in the traditional concept of God. For a more complete review of them, see Theodore Drange, "Incompatible-Properties Arguments: A Survey" in Philo (Fall/Winter 1998). Theists, of course, will claim that, properly understood, there is no contradiction. What if they're right? What if it's logically possible for the God of traditional theism to exist? Does that mean that one cannot prove that he does not exist? No, for in order to prove that something does not exist, one need not show that it is logically impossible. One need only show is that it is epistemically unnecessary-that it is not required to explain anything. Science has proven the non-existence of many things in this way, such as phlogiston, the luminiferous ether, and the planet Vulcan. Scientific proofs, unlike logical proofs, do not establish their conclusions beyond any possibility of doubt. But they are proofs nonetheless, for they establish their conclusions beyond a reasonable doubt and that is all that is needed to justify them.
Phlogiston, the luminiferous ether, and the planet Vulcan are theoretical entities that were postulated in order to explain various phenomena. Phlogiston was postulated to explain heat, the luminiferous ether was postulated to explain the propagation of light waves through empty space, and Vulcan was postulated to explain the perturbations in the orbit of Mercury. Science has shown, however, that these phenomena can be explained without invoking these entities. By demonstrating that these entities are not needed to explain anything, science has proven that they do not exist.
God is a theoretical entity that is postulated by theists to explain various phenomena, such as the origin of the universe, the design of the universe, and the origin of living things. Modern science, however, can explain all of these phenomena without postulating the existence of God.1 In the words of Laplace, science has no need of that hypothesis.2 By demonstrating that God is not needed to explain anything, science has proven that there is no more reason to believe in the existence of God than to believe in the existence of phlogiston, the luminiferous ether, or Vulcan. This may explain why more than 90% of the world's top scientists disbelieve or doubt the existence of God.3
Scientists prefer natural explanations to supernatural ones, not because of any metaphysical bias on their part, but because natural explanations produce more understanding than supernatural ones. As Plato realized, to say that God did it is not to explain anything, but simply to offer an excuse for not having an explanation.4
The goodness of an explanation is determined by how much understanding it produces, and the amount of understanding produced by an explanation is determined by how well it systematizes and unifies our knowledge. The extent to which an explanation systematizes and unifies our knowledge can be measured by various criteria of adequacy such as simplicity (the number of assumptions made), scope (the types of phenomena explained), conservatism (fit with existing theory), and fruitfulness (ability to make successful novel predictions).
Supernatural explanations are inherently inferior to natural ones because they do not meet the criteria of adequacy as well. For example, they are usually less simple because they assume the existence of at least one additional type of entity. They usually have less scope because they don't explain how the phenomena in question are produced and thus they raise more questions than they answer. They are usually less conservative because they imply that certain natural laws have been violated. And they are usually less fruitful because they don't make any novel predictions. That is why scientists avoid them.
The realization that the traditional God of theism is not needed to explain anything-that there is nothing for him to do-has led a number of theologians to call for the rejection of this notion of god. In Why Believe in God? Michael Donald Goulder argues that the only intellectually respectable position on the god question is atheism.5 In Why Christianity Must Change or Die, Reverend Spong, former Episcopal Bishop of New Jersey, argues that the traditional theistic conception of God must be replaced by one grounded in human relationships and concerns.6 Both agree with Stephen J. Gould that religion should not be in the business of trying to explain the world.7
What if there was no plausible natural explanation for some phenomena? Would that justify the claim that god caused it? No, for our inability to provide a natural explanation may simply be due to our ignorance of the operative natural forces. Many phenomena that were once attributed to supernatural beings such as earthquakes, volcanoes, and disease can now be explained in purely natural terms. As St. Augustine realized, apparent miracles are not contrary to nature but contrary to our knowledge of nature.8
Given the inherent inferiority of supernatural explanations and the incompleteness of our knowledge, theists would be justified in offering a supernatural explanation for a phenomenon only if they could prove that it is in principle impossible to provide a natural explanation of it. In other words, to undermine the scientific proof for the non-existence of god, theists have to prove an unrestricted negative, namely, that no natural explanation of a phenomenon will be found. And that, I believe, is an unrestricted negative that no theist will ever be able to prove.
