My Theodicy: Explaining the Possibility of an Omnipotent, Omniscient, Omnibenevolent Being

One of the premises of the ontological argument is that the concept of the omnipotent is logically consistent, but is the concept of the omnipotent, omniscient, omnibenevolent also logically consistent? Or, is it impossible and we are left with only an omnipotent being? According to the Argument from Evil, it is not.

The Argument from Evil is relatively simple. To make things easier, let's just call the omnipotent, omniscient, omnibenevolent being God. If God is omnibenevolent, God would stop all evil that God is capable of stopping and knows about from happening. Since God is omniscient, God knows when something evil is going to happen and since God is omnipotent, God is capable of stopping it. So, why is there evil in the world? The atheist's response is that, at least, God doesn't exist, or, at most, the concept of the omnipotent, omniscient, omnibenevolent being is logically incoherent; that is, God is impossible. So, what's my answer?

Evil exists because, in order to create an ethically relevant world, which God is obligated to do because God is omnibenevolent, God must create a world in which free will is possible (thus allowing for intentional evils); also, the best of all possible worlds, one in which all free willed beings freely choose to do good, must be possible. In order to do this, God is obligated to make it so that causation is probablistic, that is, that, given any particular present, there is more than one possible future (in a deterministic cosmos, there is one and only one possible future given any particular present); this allows for so-called natural evils such as hurricanes, earthquakes, etc.. Furthermore, because God is omnipotent, God is obligated to not directly interfere with the world unless free will becomes impossible; this is because the active will of an omnipotent being determines one and only one possible outcome, thus negating free will.

So, in short, I'm a deist.

The Leap of Faith: Omniscience and Omnibenevolence

Is the omnipotent also omniscient? That is, does omnipotence imply omniscience? An omnipotent being can do all possible things; knowing something is a possibility, thus, an omnipotent can know things. This means that an omnipotent being must have a mind, otherwise it could not know anything. So, omnipotence is at least consistent with omniscience. However, since the omnipotent has a mind, it can have desires and if it desires to know something, because it is omnipotent, it knows it ... but this presupposes specific desires above and beyond omnipotence and therefore doesn't allow the derivation of omniscience from omnipotence. What does this all mean? It means, I believe, that a leap of faith is required to get from omnipotence to omniscience.

If something is omniscient, is it omnibenevolent? If the Platonic principle of Ignorance, which states that evil is only done unintentionally (when a being acts contrary to what is good they still believe they are acting in the interest of what is at least good for themselves), is true then a being which knew all truths would necessarily only be capable of doing good.

Omnipotence

In "Anselm and Actuality", David Lewis presents an interpretation of the ontological argument. He argues that while it is a valid argument, it isn't sound; according to Lewis, one of the premises is false because the actual world is not unique. What he means by this is that all possible worlds are equally concrete, just like the world around us; that is, they are dynamic spatiotemporal expanses of energy and mass. To my mind, the actual world is unique; even if there were spatiotemporally distinct cosmoses from ours, that doesn't mean they are entire actual worlds individually. It's just that the actual world would consist of two or more spatiotemporally distinct dynamic expanses of energy and mass.

So, with that in mind, let's continue on to the argument itself. The argument consists of three premises: the Consistency Premise, the Possibility Premise, and the Actuality Premise. It's the Actuality Premise which Lewis argues is false. Some philosophers may argue that the Possibility Premise is (also) false because they think that there are metaphysical principles in addition to the minimal constraint of logical consistency; I can't think of any way of verifying supposed metaphysical principles beyond seeing if they are logically necessary or at least consistent. Also, some philosophers may argue that the Consistency Premise is false, based on "rock heavier than an omnipotent being can move" objections; my counterobjection to this is that the concept of something heavier than can be moved by an omnipotent being is inconsistent, that is, such a thing is literally impossible, which means that an omnipotent being doesn't have to be able to do it. That is, an omnipotent being only needs to be able to do all possibilities; this is so-called logical omnipotence.

1. Consistency: The concept of the omnipotent is logically consistent.
2. Possibility: Logical consistency implies metaphysical possibility.
3. Actuality: Something actual is more powerful than something merely possible.
Conclusion: The omnipotent is actual.

Another presupposition of this argument is that the concept of omnipotence is comprehensible. Perhaps omnipotence is so far beyond our finite capacities that even our best understanding of it fails woefully short of truly grasping the nature of omnipotence. I would counter that we have developed finitely long sentences which intuitively express the nature of infinity and the transfinite hierarchy. In a meta-predicate logic, there are propositions which intuitively express simple infinity, such as that of the natural numbers (0, 1, 2 ...). Beyond that, you can prove that there are infinities which are bigger than simple infinity; for instance, the real numbers (such as pi, e, etc.) are more numerous than the natural numbers. You can also prove that for each infinity, there's at least one other one which is strictly larger than it. So, the question becomes, how many possible powers are there?

A power is an ability to bring about some possible state-of-affairs. So, how many possible states-of-affairs are there? Even if the physical is all there is and is necessarily finite, there's no logical limit on how big it can be; that is, it is finite, but arbitrarily large. There may be limits on how much energy you can stuff into a particular volume of spacetime (the amount that would cause a black hole to form in that volume), but there seemingly is no logical limit on how big spacetime can itself get (the rate of cosmic expansion is accelerating currently, in fact). That means, there are at least a simple infinity of possible states-of-affairs that are consistent with the laws of nature; but there's seemingly no logical necessity to the laws of nature. Given that there can be spatiotemporally distinct regions of the actual world, there could be other universes out there that operate under different laws of nature; each set of laws would generate at least a simple infinity of possible states-of-affairs. So, the physical cannot be all there is, since it is necessarily finite, but something infinite, namely, possibility itself exists given that the physical exists (which it apparently does). So, the number of possible states-of-affairs is at least simply infinite, which means there are at least a simple infinity of powers. So, given that the omnipotent exists and has all powers, it is not a finite being; if the physical is necessarily finite, then the omnipotent is non-physical.

Beyond Meta-Predicate Logic: Set Theory

Set theory is a powerful tool in the logic of mathematics and other abstract areas of philosophical study. In set theory, there are two types of entities: elements and sets. In pure set theory, there are only sets; this is possible because sets can be elements of other sets and there is a such thing as the empty set. We will discuss pure set theory first. There is one relation in set theory or set theoretic operator which is that of membership. You can construct another set theoretic operator which expresses the concept of subsethood. A set, S, is a subset of another set, T, if and only if every member of S is a member of T (this also means that the empty set is a subset of every set). Two sets are identical just in case each is a subset of the other. Another set theoretic operator you can construct is called the powerset relation. A set, S, is the powerset of another set, T, if and only if S is the set of all subsets of T. Interestingly, the powerset of a set is always strictly larger than the set itself. For instance, the powerset of the empty set, {}, is the set which contains only the empty set {{}}; the powerset of the set which contains only the empty set is the set which contains only the empty set and the set which contains only the empty set {{},{{}}}. Etc. You can continue the powerset relation ad infinitum, constructing (or discovering) an infinite hierarchy of infinities.

Another Paradox of Standard Logic

Prelinearity isn't the only counterintuitive consequence of propositional logic. Another is called explosiveness or ex falso quodlibet, which is Latin for "from the false, anything follows". That is, from a contradiction, you can deduce any proposition; (P & ~P) implies Q or, in another form, (P implies (~P implies Q)). These statements are logically true because of the principle of non-contradiction (which states that there are no true contradictions) combined with the formal semantics of implication; the formal semantics of implication guarantees that if the antecedent of an implication is false, the implication is true. (The antecedent of an implication is the proposition that comes before "implies"; the proposition after "implies" is called the consequent.) My intuitions regarding this are that, if you presuppose a true contradiction (in order to exploit explosiveness), then you are undermining the very principle which licenses concluding anything from a contradiction; consequently, when confronted with a contradiction, one ought not to conclude anything they like, but instead consider that at least one of their premises must be false.

A Consequence of Classical Negation

In standard propositional logic, there is a theorem which follows from no premises that can cause some controversy. So-called prelinearity states that, given any three arbitrary propositions, either the first implies the second or the second implies the third, i.e., (P implies Q) or (Q implies R). For example, either "I'm sitting at my computer" implies "the Moon is made of green cheese" or "the Moon is made of green cheese" implies "the Sun rises in the west". I'm sure you, the reader, can come up with many other absurd examples of prelinearity. However, the absurdity of it follows from a seemingly innocuous principle of standard propositional logic: classical negation.

There are four different forms that classical rules of negation take: the excluded middle, double negation elimination, dilemma, and classical reductio. The excluded middle states that there are only two truth-values for any proposition, true or false; that is, (P or ~P). Double negation elimination states that if it is false that some propositions is false then that proposition is true; that is, (~~P implies P). Dilemma states that if a proposition follows from both some other proposition and the second proposition's negation, the original proposition in question is true; that is, (((P implies Q) and (~P implies Q)) implies Q). Classical reductio states that if you can prove a contradiction from the negation of a proposition, that proposition is true; that is, (~P implies an absurdity) implies P. These rules of classical negation follow from the truth-table conception of the meanings of logical operators. An alternative approach, introduction-rule semantics (where the meanings of logical operators are determined by their associated introduction-rule), does not license the classical rules of negation.

Metaphilosophy 2: A Brief Introduction to Logic

Logic is the fundamental tool of philosophy. While philosophers puzzle over inductive logic, deductive arguments form the vast bulk of philosophical argumentation. Consequently, I will be discussing deduction at this point in time.

There are three broad types of basic logic: propositional, predicate, and meta-predicate. Propositional logic deals with what are expressed by whole sentences, namely, propositions. It studies the effects of the operations of the so-called logical operators on the truth-values of various propositions. The logical operators are: "... and ...", "... or ...", "if ... then ...", and "not ...". Each operator has an introduction and elimination rule associated with it that is designed to capture the standard English meaning of the operator; also, a good number of philosophers associate each operator with a truth-table, which governs how it affects truth-values in complex propositions.

An important type of logical argument in philosophy is called reductio ad absurdum or reductio for short. The name is Latin for "reduction to absurdity" and signifies a general type of argument where you suppose some proposition, prove a contradiction (an absurdity) from it, and subsequently conclude that the proposition is false. Because of the nature of truth-tables, if you suppose for reductio some proposition that begins "not ...", you end up concluding "not not ..." and can conclude "..." from there. That is, if you suppose not-P, you may be able to prove, via reductio, P.

Predicate logic breaks propositions down into a predicate-subject format; usually, this is signified by something of the form "Ps" (read "s is P"). Predicate logic allows generalization over subjects, but not predicates, by introducing two new logical operators "for all ..." and "there exists ..." (a subject goes in the "..."); these operators are called the universal and existential respectively. Introduction and elimination rules exist for these operators as well; truth-table advocates utilize so-called truth-trees to establish the effects of these new operators on the truth-values of propositions.

Finally, meta-predicate logic doesn't introduce any new operators, but allows the universal and existential operators to generalize over predicates as well as subjects. Meta-predicate logic is important because certain important things, like "finite, but arbitrarily large", cannot be expressed in any merely predicate logic.

Metaphilosophy

+Traci Auerbach talked me into starting this. So, what's this blog going to be about? Philosophy in general, by which I mean, my continuing ratiocination about what I believe to be various fundamental, necessary features of reality. Where to begin?

I'll begin with the question, "What is philosophy?" In a nutshell, philosophy is the use of intellectual intuition to discover necessary truths about reality. Let's break that sentence down: reality is all of existence; a truth is a proposition which accurately encodes information about reality; necessity means that something cannot be other than it is; discovery is the process of exploring different aspects of a thing in search of truths about it; intellectual intuition is the ability of sapient beings to analyze experience and synthesize coherent worldviews.

The next question is, "What is the method of philosophy?" The primary method of philosophy is logical analysis. Logic is the art and science of argumentation; there are two broad types of logic: deductive and inductive. A deductive argument is valid if and only if, if all of its premises are true then its conclusion must be true; it is sound if and only if it is valid and all of its premises are true. An inductive argument is cogent if and only if the conclusion is more likely to be true if its premises are true. While doing philosophy, one attempts to construct valid and cogent arguments in order to uncover truths about reality.

Next, "To what purpose does one do philosophy?" My purpose is to discover what my intuitive worldview is, analyze it for hidden contradictions, and synthesize a more accurate and coherent worldview. Why is this good? In my opinion, if ones worldview is incoherent, then one will find themselves in situations where they cannot, in principle, know what to do; also, the more accurate ones worldview is, the better one is able to navigate reality.