Sunday, November 10, 2013

A Simplicity Objection to the Moral Argument from Ontological Simplicity

Brief Recap

In part 1 of the moral argument I noted that morality appeared to exist as part of the nonphysical realm to at least some degree (e.g. moral wrongness is a nonphysical property), that morality is metaphysically necessary (e.g. kindness is a good thing in all possible worlds), and I argued that if we posited just one nonphysical thing as the foundation for objective morality and tried to find the simplest explanation for that entity grounding objective moral values and obligations, we end up with an eternal, transcendent, metaphysically necessary entity that imposes moral duties upon us with supreme and universally binding authority. This observation (and the claim that it rationally supports theism to at least some degree) is what I’ve called the argument from ontological simplicity.

The Challenge

One could challenge whether the ontological explanation I proposed (a single metaphysically necessary entity) really is the simplest explanation. But since, in an attempt to coincide with Ockham’s razor, I posited only one entity in my explanation and ascribed it only with those properties needed to simply explain the explananda, what could be simpler?

Part of simplicity, or at least Swinburnian simplicity, is positing fewer types of entities. In the explanation that I gave for the argument from ontological simplicity, I posited a metaphysically necessary entity, i.e. one that exists in all possible worlds. Yet contingent entities (those that exist in some possible worlds but not all) are what we are really familiar with. So instead of having an ontology where just contingent entities exist, my explanation adds a new type of entity: a metaphysically necessary one. So, a simpler explanation would be to just have multiple contingent entities spread about in different possible worlds grounding morality because this explanation would be positing fewer types of entities.

The Rebuttal

There are a number of problems with this objection. First, it should be noted that the argument from ontological simplicity only posits one entity—and thus only one type of entity—in explaining morality’s metaphysical necessity. The explanation contains only one type of entity: a necessary one. It doesn’t posit a mixture of contingent and necessary entities.

Still, I think that problem can be overcome to at least some degree. One of the factors in assessing the quality of an explanation is how well it fits with background knowledge, and as I pointed out before simplicity plays a role in how well a theory fits with background knowledge. Ceteris paribus we are to prefer theories that fit our background knowledge more simply in a way that provides for a simpler overall worldview. For example, when discovering a new chemical compound, it is possible that instead of electrons surrounding the atomic nuclei, those surrounding particles are different particles that behave in an empirically identical way to electrons, and then get transformed into electrons if they ever leave the compound. This would involve positing a new type of particle however, and it’s simpler to posit that the negatively charged particles surrounding the atomic nuclei are electrons, since that would yield a worldview with fewer types of entities. Similarly, our background knowledge consists of contingent entities but no metaphysically necessary entities, and so it would be simpler to posit contingent entities instead of metaphysically necessary ones.

Even this amended objection has problems. First, whether there are metaphysically necessary entities in one’s background beliefs will depend on the person. Second, how does one weigh the simplicity of having just one morality-grounding metaphysically necessary entity in explaining morality’s metaphysical necessity over multiple contingent entities explaining it? Which one is simpler might be a bit unclear. Third and I think most problematically, the multiple contingent entity hypothesis is explanatorily inadequate and ultimately less simple than single-metaphysically-necessary-entity explanation of morality’s metaphysical necessity.

Why is that true? For one thing, any contingent entity can fail to exist, so the fact (if it is so) that there is some morality-grounding contingent entity in every possible world grounding morality cries out for explanation if we’re to satisfactorily account for morality’s metaphysical necessity. So how to explain why there is some contingent entity grounding morality in every possible world? Three options present themselves:
  1. In every possible world there is some contingent entity X ensuring that some morality-grounding entity G exists. But this simply pushes the problem back a step; what ensures that there is such a contingent entity X in every possible world?
  2. There is no explanation; it just happens to be the case that there is a contingent entity G in every possible world grounding morality. But since the number of possible worlds is quite literally infinite, it seems extraordinarily improbable that there just happens to be a contingent entity G in every possible world.
  3. There is something metaphysically necessary that ensures there is a contingent entity grounding morality.
So three options are (1) explanation via some other contingent thing; (2) no explanation; (3) explanation by reference to something metaphysically necessary.

Option (1) pushes the question back a step and so is explanatorily inadequate in ultimately explaining why a contingent morality-grounding entity is present in every possible world. If there is some contingent entity X to ensure there is a morality-grounding entity G, then to really explain why morality exists in every possible world we’d need an explanation for why there is some X in every possible world. If we are to avoid a vicious infinite regress we need to stop sticking with option (1) somewhere down the line. So even if option (1) were viable in explaining morality’s metaphysical necessity, to avoid an infinite regress we’d need something like option (2) or option (3) for contingent entity X (or at least to end any series of contingent entities responsible for entity X). Yet option (2) and (3) each have trouble.

Option (2) at least gives us a stopping point, saying that ultimately there is no explanation, but given the infinite multitude of possible worlds, the likelihood of this explanation seems infinitesimally small. Moreover, there is “the argument from subtraction” that suggests there are possible worlds with no contingent entities. There are surely possible worlds with fewer contingent entities than those that exist right now. And upon reflection it seems there is a possible world where only a thousand contingent things exist, and it seems there is a possible world where only fifty contingent things exist etc. all the way down to zero contingent things existing (at least if there is nothing non-contingent to ensure that some contingent thing exist). But if there are possible worlds with zero contingent things existing, then no set of contingent things can provide an ontological explanation for morality’s metaphysical necessity.

Option (3) is the best one, positing something non-contingent to ensure there is some contingent morality-grounding thing. But Ockham’s razor suggests we prefer fewer explanatory entities ceteris paribus, and so it’s better to posit just one metaphysically necessary entity to ground morality rather than a combination of contingent and metaphysically necessary entities.


At least when amended, I think the objection raises a substantive point. Arguably, metaphysically necessary entities are so unfamiliar with what we experience that it’s simpler to posit multiple contingent entities than a single metaphysically necessary entity when the multiple contingent hypothesis is adequate.

But ultimately I do not think the multiple contingent entity hypothesis is explanatorily adequate (particularly in regards to explaining morality’s metaphysical necessity) or simpler. It’s explanatorily inadequate in part because (1) it seems like there is a possible world with no contingent entities, in which case it would be false that in every possible world there is a morality-grounding contingent entity; (2) even ignoring (1), we’d need some explanation for why there happen to be morality-grounding contingent entities in every possible world, and appeals to “there is no explanation” and “the explanation is another contingent entity” don’t quite work. The multiple contingent entity hypothesis is less simple because to ultimately make it work—if we were to ignore problem (1)—we’d need an appeal to a metaphysically necessary entity, and it’s simpler to cut out the contingent entity middlemen and just posit the metaphysically necessary grounding entity.

Part of the explananda in an ontological explanation for objective morality is morality’s metaphysical necessity, and the best explanation for this seems to be a metaphysically necessary entity grounding morality.

Friday, November 8, 2013

What is Simplicity?

It is commonly accepted that ceteris paribus the simplest explanation is the most likely one. But what is simplicity? In this blog entry I’ll borrow heavily from Richard Swinburne’s excellent Simplicity as Evidence of Truth. I’ve talked a bit about this before but in this post I’ll go into more detail. Because I’m talking about the sort of simplicity that Richard Swinburne has in mind, I’ll refer to this sort of simplicity as “Swinburnian simplicity.”

Other Explanatory Virtues

In explaining what simplicity is it is helpful to contrast it with what simplicity isn’t. Below are some explanatory virtues (things that help make an explanation good) apart from simplicity. Richard Swinburne notes two a posteriori factors (1 and 2) and one a priori one (3):
  1. Yielding the data. This category covers both explanatory scope (how much data the theory explains) and explanatory power (the probability of expecting the data if the explanation were true).
  2. Fitting in with background knowledge. For example, “The hypothesis that John stole the money is rendered more probable if we know [due to our background knowledge] that John has stolen on other occasions and comes from a social group among whom stealing is widespread.”[1] The likelihood of such background beliefs being true plays a role in our judgments. As I explained and wrote about earlier, part of how well a theory fits background knowledge depends on simplicity.
  3. Content. The greater the content of the hypothesis, the less likely it is to be true. In this context, “content” refers to how much a theory “claims.” For example, the claim “at least one swan is white” has less content then “most swans are white.” The claim “at least swan is white” makes no claim as to whether or not most swans are white, whereas “most swans are white” contains the claim that at least one swan is white and that this whiteness holds for the majority of swans. As Swinburne explains, “The more claims you make, the greater the probability that your claims will contain some falsity, and so be as a whole false.”[2]
The next a priori factor is simplicity.

Factors of Simplicity

Swinburne also says that “One theory is simpler than another if and only if the simplest formulation of the former is simpler than the simplest formulation of the latter.” He also delineates several facets of simplicity. Here are some of them (note that since the topic of his book is largely philosophy of science, some of these factors have to do with physical laws):
  1. Number of entities. The theory that postulate fewer entities is simple than if it postulated more entities. As Swinburne notes, “The application of this facet in choosing theories is simply the use of Ockham’ razor.”[3]
  2. Number of kinds of things. A theory that postulates fewer different kinds of entities is simpler than if it postulated many different kinds of entities, e.g. a theory that postulates fewer different kinds of quark is simpler than a theory that postulates more of them.
  3. Fewer separate laws is simpler than many separate laws. All else held constant, a theory is simpler than another if it contains fewer laws.
  4. A theory in which individual laws have fewer variables is simpler than a theory where the laws have more variables ceteris paribus. For example, suppose we have two theories that have physical laws yielding the data equally well; one set of laws uses three variables to yield the data and the other uses seven. All else held constant, the theory which uses only three variables is simpler.
The above three are more quantitatively ontological in nature, i.e. having more to do with quantity with respect the nature of reality: fewer laws, fewer variables in how laws work, fewer entities, and fewer kinds of entities. The next ones are more conceptual.
  1. A theory that uses a term T1 that can be grasped only by people who grasp some other term T2 (whereas T2 can be understood without grasping T1) is less simple than if the theory otherwise just used T1. For example, if someone defined “grue” in terms of green, blue, and time (say, something is grue if and only if it was green before 2000 CE but blue after 2000 CE) is less simple than the predicate “green.” Swinburne notes that the “general force of this requirement is of course, other things being equal, to lead us to prefer predicate designating the more readily observable properties rather than ones a long way distant from observations.[emphasis mine]” Swinburne also says this “facet of simplicity says: do not postulate underlying theoretical properties, unless you cannot get a theory which yields the data equally well without them.”[4]
  2. A theory with a mathematically simpler formulation is simpler than it would otherwise be. Two facets of mathematical simplicity:
    1. Fewer terms. For example, y = x is simpler than y = x + 2x2.
    2. Simpler mathematical entities or relations to one another. Let S (for simple) and C (for complex) be placeholders for mathematical entities/relations. A mathematical entity/relation S is simpler than another one C if S can be understood by someone who does not understand C but C cannot be understood who does not understand S. For example, 0 and 1 (S) are simpler than 2 (C), 2 is simpler than 3, and so forth; you cannot understand the notion of 2 rocks (C) without first understanding the notion of 1 rock (S).So 1 of something is simpler than 2 of something. For this reason, y=z+x is simpler than y=z+2x.
      1. Consequently, multiplication is simpler than addition (you need to understand addition to understand multiplication); power is less simple than multiplication (you need to understand multiplication to understand power) e.g. y=x is simpler than y=5x2, vector addition is less simple than scalar addition.
      2. Swinburne says that an infinitely large quantity is graspable by someone who hasn’t grasped a very large number. “One does not need to know what a trillion is in order to understand what is the infinitely long or lasting or fast. It is because infinity is simple in this way that scientists postulate infinite degrees of quantities rather than very large degrees of quantities, when both are equally consistent with the data. The medieval postulated an infinite velocity of light, and Newton postulated an infinite velocity for the gravitational force, when in each case large finite velocities would have been equally compatible with the data then available measured to the degree of accuracy then obtainable.”
And there you have it, six factors illustrating what simplicity is—or at least Swinburnian simplicity (the sort of simplicity that Swinburne has in mind). Not all philosophers have the same precise conception of simplicity when they use the term. For example, one could have an idea of simplicity that unlike Swinburnian simplicity includes content, where a theory that contains fewer assumptions is considered simpler.


To give an example of math simplicity, suppose we had these two equations (physics nerds will recognize these as equations for gravity) that are empirically identical to each other as far as our precision was able to determine:

F = G

F = G
r2.000...(100 zeroes)...0001

A person needs to understand whole numbers (1, 2, 3...) before he understands decimals, and so by criterion 6 if nothing else we should prefer the first equation all else held constant. In my Simplicity and Theism article, I explain how the principle of simplicity can be used in the service of theism.

[1] Swinburne, Richard. Simplicity as Evidence of Truth (Milwaukee, Wisconsin: Marquette University Press, 1996), p. 18.

[2] Swinburne, Richard. Simplicity as Evidence of Truth (Milwaukee, Wisconsin: Marquette University Press, 1996), p. 18.

[3] Swinburne, Richard. Simplicity as Evidence of Truth (Milwaukee, Wisconsin: Marquette University Press, 1996), p. 29.

[4] Swinburne, Richard. Simplicity as Evidence of Truth (Milwaukee, Wisconsin: Marquette University Press, 1996), p. 31.