Some Logical Basics and Omnipotence

Here are a number of concepts, principles, and distinctions that are important background for the philosophy of religion discussions we will be having.

The Principle of Sufficient Reason is the claim that for every truth or thing that exists, there is a sufficient reason or explanation for its being true or existing, rather than otherwise. The principle is often connected to the notion that nothing can come from nothing. Truths have an explanation, existing things have a reason for their being. Events do not occur, things do not come to exist, and truths do not come to be ex nihilo or from nothing; there is always an explanation behind them. The PSR is the foundation beneath our "why" questions. Why do gold prices rise in a recession? Why are there ocean tides? Why do people get heart disease? Why does a drop in barometric pressure correlate with rain? Suppose the PSR didn't apply and we did not expect or could not assume that there were reasons for facts, then asking "why does ice cream consumption go up during summer months?" wouldn't make any sense. If the PSR didn't apply, then there's be no reasons or explanations. There would be no ground for facts. The PSR figures heavily in Cosmological or First Cause arguments for God's existence. Roughly, the arguments point to the universe itself, or to the Big Bang, and with the help of the PSR, they assert that there must be some divine explanation.

The Law of Non Contradiction is the fundamental logical principle. Roughly, it is not possible for a thing to both possess and not possess a property at the same time in the same way. An assertion cannot be both true and not true at the same time. Aristotle, the ancient Greek philosopher, said: "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect." And, "an affirmation is a statement affirming something of something, a negation is a statement denying something of something…It is clear that for every affirmation there is an opposite negation, and for every negation there is an opposite affirmation…Let us call an affirmation and a negation which are opposite a contradiction." The affirmation and the negation cannot both be true of an object. To make an assertion of the form X is P, like "the ball is blue," is to claim that the ball has the property of blue and that it is false that the ball is non-blue. If we abandon the law of non-contradiction, then there is no meaningful difference between an assertion and its opposite. That is, our assertions cease to have meaning altogether. My claim that, "Today is Tuesday," doesn't say anything unless it denies some other state of affairs like, "Today is Wednesday." The law of non-contradiction is axiomatic to reason; that is, it is one of the most fundamental principles upon which reasoning and rationality are based. It cannot be argued for (it is the principle that makes arguments possible) nor can in be plausibly denied (to deny it is to already assume it.)

~(P + ~P)

Logical Possibility is built upon the law of non-contradiction. Any proposition whose opposite does not imply a contradiction is logically possible. Any description of a state of affairs that does not contain and implicit or explicit logical contradiction is logically possible. That is, if the sentence does not include a contradiction like, "Mike is a married bachelor." then the state of affairs that the sentence describes is logically possible. So it is logically possible that Mike is a bachelor. And it is logically possible that he is married. And it is logically possible that Mike (an unaided human) could fly. But it is not logically possible that 2 + 2 = 5, or that circles have sides, or that the Pythagorean Theorem is wrong, etc. Philosophers sometimes talk about logical possibilities in terms of possible worlds; there is a possible world where Arnold Schwarzenegger is the president of the United States. There is a possible world where you have super powers and can run faster than the speed of light. There are no colorless red balls, however, and no presidents who hold no political office, and no four sided triangles.

Natural Possibility The laws of nature confine the behavior of matter in our world to a subset of the logically possible worlds. The laws of nature such as the universal law of gravitation, F = MA, and e=mc2 determine the range of what states of affairs are naturally possible. So it is not naturally possible for an unaided human body to fly—the musculature, bone structure, and other physiological traits prevent it. But it is naturally possible (we think) to cure cancer. The laws of nature, which are different from the laws of logic, could have been different without logical contradiction. All natural possibilities are a subset of logical possibilities. That is, anything that is naturally possible is also logically possible, but not everything that is logically possible is naturally possible. Being able to move objects with your thoughts alone through telekinesis is ruled out by physics and not naturally possible, but there is no logical contradiction in the scenario.

The periodic table could have been different, gravity could attract at a different rate, or force could be equal to something different than mass times acceleration. If one of those different sets of natural laws were in place, then the range of what events that is naturally possible would be different. The super powers of comic book heroes, for example, such as teleporting, flying, telekinesis, super speed, super strength, and so on would probably be violations of the laws of nature, but they are not logically impossible. Miracles such as walking on water or bringing the dead back to life are violations of the laws of nature, but they are not logically impossible. The distinction between logical and natural possibility becomes important when we try to figure out what is means for God to have omnipotence, or all-power. Can an omnipotent being perform logically impossible acts or naturally impossible acts?

We should contrast events that are naturally impossible, or ruled out by natural law, with events that are statistically improbable. If we dropped a million dice onto a parking lot and all of them came up with a 1 on top, it would be statistically improbable, but it is not ruled out by the laws of physics. The odds of winning the lottery are millions to one, and if your friend said he had the winning ticket, you might say, "That's impossible!" But it violates no logical or natural laws. It's merely statistically improbable. We might also think about it this way: the laws of natural, such as the ones governing the periodic table of elements, constrain the regular behavior of matter. They also make some events improbable. Snow is Sacramento is rare because of the typical weather conditions in the winter. But the natural conditions can happen. On Feb. 5, 1976, two inches of snow accumulated in Sacramento. Such an event is clearly logically possible, and it is naturally possible. But it naturally improbable. Having it snow in Sacramento on 10 consecutive days this winter is exceedingly unlikely. We might even say that it is impossible because it is so improbable. But on the definitions we are using of natural and logically impossibility, this would be a misnomer.

All of these distinctions concerning possibilities are relevant to our figuring out what sort of power God might have. The widespread view for centuries among believers is that God's power is vast. God is the almighty creator of the universe, the originator of reality, and is capable of altering any state of affairs to suit his desires. But it has turned out to be difficult to spell out the details of just what this maximal amount of power is. The temptation for those who have not reflected carefully on the implications is to simply conclude that God has the power to do anything.

Let's call this Omnipotence_A. This power, if a being had it, wouldinclude the capacity to do anything that is logically possible: create or destroy material objects, raise someone from the dead, create the universe from nothing, and so on. But if we take the notion of "anything" seriously, then this question arises: What about acts that are contradictory, paradoxical, or self-limiting? Could an omnipotent God create a square circle, or a married bachelor, or make it so that 2 + 2 = 5? Could such a being avoid unavoidable occurrences, or do things that cannot be done?

The general consensus among philosophers and theologians is that Omnipotence_A .generates paradoxes and it is an incoherent way to define God's power. The particular problem that renders Omnipotence_A nonsensical has come to be known as The Stone Paradox.

Consider this act: creating a stone that one cannot lift. Alternately, we could consider the class of actions where you generate a problem that you cannot address. I can load up a large wheel barrow with sand so that I cannot move the wheel barrow. I can build a garage that I cannot lift. I can dump out a bucket of sand and then not be able to put all of the grains of sand back into the bucket in exactly the arrangement that they were in before. That is, for finite beings, there are a number of actions we can perform that produce an act that we cannot perform. Can God create a stone that he cannot lift?

The answer must either be that God can create a stone that he cannot lift, or God cannot. There are no other alternatives. Let us consider the first case. Suppose a God who is capable of doing anything creates a stone that he cannot lift. Now there is something that God cannot do, namely, lift that stone. So there is something that a being who can do anything cannot do--which is a paradoxical, logically incoherent result.

Consider the other alternative. Suppose that a being that can do anything cannot create a stone that he cannot lift. Now, once again, there is a logically contradictory situation. Being able to do anything does not include being able to do anything. Again, the result is incoherent. That is, what does "anything" even mean, if it doesn't mean what we take anything to mean?

It appears that there are always acts that God cannot do, so it doesn't appear that it is possible to have the property of Omnipotence_A.

It might be tempting to respond to the paradox of the stone this way: "Look God can do anything. He can create a stone that he cannot lift. And then he can lift it." This response is mistaken because if God then lifts that stone, he failed to perform the task that was described. God failed to create a stone that he cannot lift. He created a stone that he can lift. If he lifts it, then there remains something he cannot do--create a stone that he cannot lift.

There are some other considerations that undermine omnipotence defined as "the power to do anything." Call this problem "The Enhanced Problem of Evil." When confronted with the Problem of Evil: "if God is all knowing, all powerful, and all good, then why is there so much pointless suffering in the world?" many people will offer responses such as, "some suffering is unavoidable in order to build moral virtue," or "some evil is necessary in order to contrast with goodness," or "perhaps there are some greater goods that God could not achieve without allowing some lesser evils," or "God can make us free, or he can make us do good acts, but he cannot make us freely do good acts," and so on. Now notice that in each of those answers, there is language outlining some things that not even God can do: "unavoidable suffering," "necessary evils," "could not achieve," or "cannot make us freely. . . " and so on. That is, all of these answers to the problem of evil are predicated on the notion that there are some things that even God is capable of doing. God does not have the power to avoid unavoidable suffering, eliminate necessary evils, or make us freely perform some act. The problem for the theist is that she cannot both attribute the power to do anything to God and impose this list of "cannots," and "could nots," on God in response to the Problem of Evil. If God can do anything, including avoid the unavoidable, then he is not limited and should not have to tolerate suffering in any of the ways typically described by attempts to reconcile God and evil. Another way to put it is that if we attribute Omnipotence_A to God, then there can be no justification or explanation of evil.

In response to these problems and others, philosophers and theologians frequently introduce another account of omnipotence. Omnipotence_LP is the power to do anything that is logically possible. This power, if a being had it, would include the capacity to do any act that does not generate a logically contradictory state of affairs. So this being could create a world that has free rational beings in it, but it could not create a world that both has free, rational beings in it and that is a void world with nothing in it. Understanding omnipotence as LP resolves several problems. Now, the Stone Paradox can be dismissed--creating such a stone is an unintelligible, logically incoherent act. And the wide range of popular answers given to the problem of evil now make some sense again. Responses to the Problem of Evil such as, some kinds of suffering are necessary to achieve a greater good, evil must exist to present a contrast to good, the evil committed by free moral agents is not evil that God can prevent, and God accepts evil as a cost for a greater good, all presume that God has omnipotence_LP. The common preliminary conclusion that many people draw is this: God, if he exists, can at most be omnipotent_LP

Some similar arguments have led philosophers to puzzle over omniscience, or knowing everything. We can introduce a parallel distinction between having all knowledge, and having all knowledge that is logically possible to have: omniscience_A and omniscience_LP In recent years, a number of philosophers have argued that there are serious problems with omnipotence_LP as well. It turns out that even this account gets mired in logical problems. There are a number of challenges when we take an ordinary property like "power" or "knowledge" that is sensible at our finite level and expand it to a God-worthy scale. We will not pursue the complicated details of these arguments here, but for some more information, read the entries on omnipotence, as well as the entry on atheism (written by Prof. McCormick) at the Internet Encyclopedia of Philosophy.

A necessary truth is one whose opposite implies a contradiction. It is a proposition that must be true without exception. Sometimes, it's a proposition that is true in virtue of the meanings of the concepts involved. A = A is a necessary truth, as is "Bachelors are unmarried," and "Triangles have three sides." A necessary being is one whose non-existence is impossible. That is, a necessary being must exist; it cannot fail to exist. God is the only being typically characterized as a necessary being.

A contingent truth is one that can be true or it can be false without logical contradiction. "The Washington monument is 555 feet tall," is true, but it could have been false if the stone mason carving the pinnacle block had opted to make it a foot taller. Contingent truths are assertions whose opposite would not have violated the law of non-contradiction. "The Washington Monument is not 555 tall," is not contradictory. "This triangle does not have three sides," is contradictory. A contingent being is one that could have existed or could have not existed without logical contradiction. We humans are all contingent. The non-existence of Matt McCormick does not imply a contradiction. It has often been alleged that the non-existence of God, however, given his nature, is a contradictory state of affairs.

A priori truths are truths that can be known without an appeal to experience. They are true by definition or in virtue of the meanings of the words involved. "A square is a four sided figure," is an a priori truth. We do not need to count the sides of objects that are squares in the world to know that it is correct. "Mammals have warm blood," is another a priori truth.

A posteriori truths are truths that we discover and know on the basis of experience. "McCormick is 6' 1" tall," is a fact that can only be discovered by experience. It cannot be known by conceptual analysis the way "bachelors are unmarried" can. "Interest rates were at a 40 year low in July" is another example of an a posteriori truth.

Belief To believe a claim is to assent to it or to have an attitude towards it such that you think it is true. It may or may not be true, but to believe it is to think that it is. So many people believed that the earth is flat. Some may still believe it. Belief is subjective because it is dependent upon an individual to possess it. Belief is mind dependent. Smith, for example, believes, "Americans never went to the moon." Smith also believes, "There are 12 months on a yearly calendar." Smith's first belief is false, although she takes it to be true. And Smith's second belief is true. Beliefs can align, or diverge from the objective state of affairs in the world. Beliefs aren't true simply in virtue of being believed. The widespread conviction that the Sun orbits the Earth before Copernicus did not make that claim true. The Earth was orbiting the Sun while lots of people on Earth had an erroneous description of reality in their heads. So claims like, "the truth is whatever everyone believes," or "it was true then that the Sun orbited the Earth" are incoherent.

Truth The truth is what is the case or what the actual state of affairs in the world is. We form beliefs about it on the basis of our information. The truth is objective—it does not depend upon people. Truth is mind-independent. It remains what it is whether we form beliefs about it or not. When people believed that the earth was flat, in fact, it was not. The truth was that the earth was (and is) spherical. The Earth orbits the Sun. Evil demon possession does not cause bubonic plague. There are truths that are not believed by anyone. And there are many beliefs that are not true. Claims like, "the truth is relative," or "there is no objective truth, only belief" are incoherent. Consider the latter. Suppose Smith says, "there are no objective truths, there are only subjective beliefs." Paradoxically, his assertion presumes that what he is saying is false. He is asserting that his claim is actually, objectively true; it is objectively true that there are no objective truths. The real state of affairs in the world is that there are no real or true states of affairs. Relativism about truth is self-contradictory and incoherent.

Natural Theology is the project of attempting to give a successful argument (see below) for the existence of God. Natural theologians, such as William Paley, Aquinas, Anselm, and Craig, believe that reasons can be given that are adequate to make the conclusion that God exists reasonable or justified. Natural theologians are usually not opposed to faith, but they believe that reasonable belief in God can be secured without necessarily appealing to it. In its stronger form, natural theologians have the view that in order for a belief in God to be reasonable or epistemically inculpable, a person must be in possession of a successful argument that is sufficient to justify it.

A Successful Argument for a conclusion (call it C) will be a set of premises or reasons (different than C) that are true and that when taken jointly would imply the conclusion C to a reasonable person who does not already believe C. A prosecuting attorney in a murder trial will attempt to give a successful argument that will convince the jury (who has assumed the defendant's innocence) that the defendant is guilty. So a reasonable person should accept the conclusion of a successful argument. Of course, people rarely hear a convincing argument and then abruptly change their minds. But reasonable people should be prepared to. If you hear an argument with premises that you beleive are true, and you understand that the premises validly imply the conclusion, then you are rationally committed to accept the conclusion. Otherwise, you are being irrational. Disagreements about whether or not an argument is successful will be disagreements about whether or not all of the premises are true or whether or not the premises, if true, would imply the truth of the conclusion. This argument may not succeed in convincing you, but here is an example of an argument that someone who accepts the natural theological approach might find compelling:

1. If there were no God, then the world would not be so well suited to our existence, our sustenance, and our survival.

2. But the world is well suited to our existence, our sustenance, and our survival.

3. Therefore, there is a God.

Whether or not an argument succeeds in convincing a particular person often depends upon her background information, the other beliefs she has, the extent to which she has critically scrutinized the premises of the argument and her underlying assumptions, and many other factors. So success varies from person to person. Determining when a person is being reasonable or unreasonable in accepting an argument or its premises can be a complicated and technical matter.

Faith is a description of a way that people sometimes acquire beliefs. For S to believe p by faith means that S believes p despite the fact that as S sees it, there is contrary evidence or inadequate evidence overall to make p justified. When someone says, "I have faith that my team will win the playoffs even though they are 3 games behind," he is saying that there are significant reasons to doubt the truth of the claim, but he believes it nevertheless. (See belief above.) Consider a parent who is worrying about her child who is dying from leukemia. She might say, "Why would God allow such a thing to happen to someone who is so innocent?" The hospital chaplain might reply, "We must have faith that God has a plan for such events." We can think of a person who has faith that p as someone who believes p despite her not being in possession of a sufficiently successful argument in favor of p. The reasonableness of faith, or the extent to which it is epistemically culpable, is a matter of complicated debate.

Epistemic culpability When a person can be blamed or faulted rationally for believing or disbelieving some claim, we can say he is epistemically culpable. The notion of culpability is borrowed from ethics. When your friend knowingly lies to you, we would fault her. We would say that she has done something wrong. She ought not to have done it. We use prescriptive language--"should" and "ought"--instead of merely descriptive terms about the facts. She is morally culpable for not telling you the truth. Someone is epistemically culpable when she has violated some duty or responsibility to be reasonable, rational, or thoughtful. There is a presumption that people ought to be reasonable or rational, so when they fail and they could have acknowledged the justified, reasonable conclusion, then we find fault in them. If someone has thought about the topic extensively, gathered evidence carefully, and correctly applied logical inferences, then we typically find him to be epistemically inculpable, or without blame, about the resulting belief.