The Argument from Degrees of Perfection: Less Than Perfect

Arguments for the existence of god come in many sorts, and they often have lengthy histories. One dating at least as far back as Augustine is the Argument from Degrees of Perfection (hereafter ADP). It is also put forth by Anselm, but its most famous presentation is as Aquinas' Fourth Way of proving god's existence. Two modern exponents of the ADP are Boston College professors Peter Kreeft and Ronald Tacelli, who give the argument, along with 19 others(!), in their Handbook of Christian Apologetics: Hundreds of Answers to Crucial Questions. I will focus primarily on Kreeft and Tacelli's version.

The ADP is easily stated; this is Robert Schihl's formulation:

1. Objects have properties to greater or lesser extents.
2. If an object has a property to a lesser extent, then there exists some other object that has the property to the maximum possible degree.
3. So there is an entity that has all properties to the maximum possible degree.
4. Hence God exists.[1]

As it stands, Schihl's version of the ADP is not valid. Premise 1 is obviously true, but proposition 3 (I hesitate to say premise 3 since [I think] it is supposed to be a consequence of what has come before) does not follow from premises 1 and 2. Indeed, at most what most can be inferred from 1 and 2 is that there exist entities—one for each property—that has its property to the maximum possible degree. If there were one entity that had all properties to the maximum degree, and if god is defined to be that which has all properties to the maximum possible degree, then the conclusion (4) would follow (I am ignoring Schihl's capitalization of 'God' because I don't know for sure if he has a particular god in mind).

It might be that this can be cleaned up some. For the ADP to work, it needn't be the case that if an object has any property to a lesser extent then there exists some other object that has the property to the maximum possible degree. Taking god to be that which personifies perfection to the maximum degree, premise 2 need only involve the property of perfection. This gives the following, revised ADP:

1. * Objects are perfect to greater or lesser extents.
2. * If an object is perfect to a lesser extent, then there exists some other object that is maximally perfect.
3. * So there exists a maximally perfect object.
4. * Hence god exists.

For purposes of argument, I am taking perfection to be a single property. I am also assuming that it is unproblematic to objectively order objects from least perfect to most perfect. This may be objectionable to some, but I am trying to be as fair as possible to the ADP. Now, given this latitude, 1* is true. 3* follows from 1* and 2*, and 4* follows from 3*. Clearly, the soundness of the argument depends squarely upon the truth value of premise 2*.

Let us consider, then, Kreeft and Tacelli's argument in detail. They begin innocently enough:

"We notice around us things that vary in certain ways. A shade of color... can be lighter or darker than another, a freshly baked apple pie is hotter than one taken out of the oven hours before ... [W]e arrange some things in terms of more and less."[2]

This is surely uncontroversial, but Kreeft and Tacelli continue:

And when we do, we naturally think of them on a scale approaching most and least ... [W]e think of the lighter as approaching the brightness of pure white, and the darker as approaching the opacity of pitch black. This means that we think of them at various "distances" from the extremes, and as possessing, in degrees of "more" or "less," what the extremes possess in full measure.[3]

Kreeft and Tacelli may be correct in asserting that we do this naturally, but this does not mean that it is the correct way of proceeding. Their example of color is of the sort where this kind of reasoning is appropriate, but there are examples and there are examples. Consider the sequence of numbers 5, 6, 7. It is easy to arrange them from least to greatest (in fact, I have done so), but this doesn't mean that I think of them on a scale approaching most and least (it is more complicated than this, but more on that presently). Back to Kreeft and Tacelli:

Sometimes it is the literal distance from an extreme that makes all the difference between "more" and "less." For example, things are more or less hot when they are more or less distant from a source of heat. The source communicates to those things the quality of heat they possess in greater or lesser measure. This means that the degree of heat they possess is caused by a source outside of them.[4]

Here again, Kreeft and Tacelli's example is well chosen to support their position, but it is only a single example. It is easy to see why they do not stick with their color example because being lighter in color ("closer" to pure white) is not in any way caused by being "closer" to white in the way that being closer to a source of heat causes an object to be hotter; while there is such a thing as radiant heat, there is no such thing as radiant lightness (in color). Thus, it is important not to go too far with a literal reading of "distance" in this example. Even granting this, not all hot objects are warmed from without (consider the sun). This will prove to be important later when we consider whether the degree of perfection in a less-than-maximally perfect object must come from an outside source.

Now when we think of the goodness of things, part of what we mean relates to what they are simply as beings ... [A] relatively stable and permanent way of being is better than one that is fleeting and precarious. Why?... [B]eing is the source and condition of all value ... being is better than nonbeing ... [S]o we recognize the inherent superiority of all those ways of being that expand possibilities, free us from the constricting confines of matter, and allow us to share in, enrich and be enriched by, the being of other things ...[5]

It may be tempting to wonder what Kreeft and Tacelli are on about with "ways of being." Surely there is only one way to be: either something (a horse, say) is or it isn't (a unicorn). Kreeft and Tacelli have in mind, I think, a Platonic notion of existence, where the truer or better is more real than the less true or less good. They continue:

"[I]f these degrees of perfection pertain to being and being is caused in finite creatures, then there must exist a 'best,' a source and real standard of all the perfections that we recognize belong to us as beings."[6]

This is, of course, the rub. Before I continue, let me allow Kreeft and Tacelli to finish.

"This absolutely perfect being—the 'Being of all beings,' 'the Perfection of all perfections'—is God."[7]

All forms of the ADP contain as a stated or unstated (and in either case crucial) premise that every set of objects that may be ordered in terms of perfection exists on a scale that has a "greatest" and "least" element. Taking Kreeft and Tacelli's color example as an analogy, we may order colors from darkest to lightest. Then pure white is the greatest element and pitch black is the least element. In my numerical example (the set {5, 6, 7}), I said I don't think of them on a scale approaching most and least. Of course, 5 is the least element of the set and 7 is the greatest, but I don't necessarily think of them on a scale that has a greatest or least element. Whether a greatest or least element exists depends on how one thinks of the terms in the sequence. If one takes {5, 6, 7} to be a set of natural numbers, then the scale does have a least member, 1, but not a greatest member. If we take 5, 6, and 7 to be integers or real numbers (R), the scale in which they are embedded has neither a greatest nor least element. If we choose to show off and take them to be elements of a two-point compactification of the reals, (R∪{-∞,∞}), there is both a greatest and a least element (don't think too hard about this—Georg Cantor, who did groundbreaking work on transfinite arithmetic, died in a German insane asylum; you have been warned). The point I am trying to make is this: It is simply not true that all scales containing orderable sequences have a greatest or least element. This, by itself, does not demonstrate the invalidity of the ADP. The ADP, as I see it, is invalid because something stronger than its crucial assumption is necessary. It is not enough that every set of objects that may be ordered in terms of perfection exists on any old scale that has a greatest and least element. Rather, it must be that every set of objects that may be ordered in terms of perfection is most appropriately viewed as existing on a scale that has a greatest or least element, where "most appropriately viewed" involves being reflective of reality (and not the logico-mathematical hijinks of manufactured endpoints). It turns out that it matters what scale we place elements on. If we take 5, 6, and 7 to be elements of R, they are elements of a field; if we take them to be elements of R∪{-∞,∞}, they are not. If we are concerned with fields, adding the endpoints to the scale isn't justified; if we are not, then it is. Any scale can be fitted with endpoints if we are so inclined (assuming it doesn't have them to start with): We just stipulate the endpoints, et voila! Greatest and least elements appear. The question, however, is whether such an addition is warranted. This will vary from case to case.

How these cases are separated will be based on how the world actually is, not on a mathematical trick of endpoint stipulation. There are some scales where maximum and minimum values exist that many find surprising. Most are familiar with absolute zero, the temperature below which matter may not fall, but it is less widely known that, according to our best current theories, there is a maximum temperature that matter may attain. This is the Planck temperature, 1.42×1032) degrees Kelvin, give or take a million trillion trillion or so. It might be that Kreeft and Tacelli's temperature example is more on point than they know. On the other hand, some scales do not appear to have a maximum value realized in the real world. Richard Dawkins, in responding to the ADP, humorously points out that "people vary in smelliness but we can make the comparison only by reference to a perfect maximum of conceivable smelliness. Therefore there must exist a pre-eminently peerless stinker, and we call him God."[8] I do not take Dawkins to have refuted the ADP with his example, but rather include it to show that there are some scales where we are not justified in assuming there is a realized maximum value.

To be fair, it must be noted that the advocate of the ADP needn't show every ordered sequence is most appropriately viewed as existing on a scale with least and greatest elements. However, the advocate must demonstrate that the elements in the not-so-perfect, kinda-perfect, pretty-well-perfect ... sequence are (strictly, only a greatest element--this would be god—must be shown to exist). But that is precisely the problem. There seems to be no justification whatsoever for this rather weighty proposition. To simply assume its truth is question begging of the baldest kind. Unless or until an argument supporting the notion that since objects attain various levels of perfection there must be an extant maximally perfect entity, the ADP goes nowhere in supporting the existence of god.

Kreeft and Tacelli have done nothing (at least nothing effective) to meet this burden, but others have tried. Augustine, Anselm, and Aquinas' arguments appear to be based on Platonic conceptions of forms or a neo-Platonic (specifically Plotinus') notion of Unity or The One. Plotinus' "One" has very little to do with modern monotheistic conceptions of god. The One is a principle that underlies all being, but it is not a being itself. Ultimately simple, all plurality emanates from it. While The One is the source of the universe, the universe is not the creation of The One; indeed, The One does not act at all. Platonic Forms are similarly inert. This makes Kreeft and Tacelli's use of "God" (that is, capitalized) a little puzzling since, even read in the most generous manner, they have not demonstrated the existence of the Christian god. In any case, if one wishes to define god as that which underlies being or inhabits a Platonic realm along with numbers, justice, courage, and the like, it is hard to object, but Kreeft and Tacelli (and Augustine, Anselm, and Aquinas) want much more than this: In the end, of course, they want to prove the existence of the Christian god (though they leave this unstated in the Handbook). Not only is the Christian god not supported by Plotinus' and Plato's arguments, it is directly contradicted. Therefore, even granting everything that, say, Augustine says, all we have for "god" is the principle of the supremely simple that supports existence. I am willing to grant this, but it seems a very watered-down god indeed.

In sum, without a method of showing that the scale within which a sequence of objects ordered in terms of perfection is embedded has more in common with R∪{-∞,∞} than R (or more in common with colors than smelliness), no headway can be made in demonstrating god's existence. Even assuming such a method, if the ADP advocate has a specific god in mind, it still remains to be shown that the god thus proved is anything at all like that conceived by the advocate. For Kreeft and Tacelli, this task has yet to be accomplished.

### Notes

[1] Robert J. Schihl. (2012). "Argument from Degree." http://www.enotes.com/topic/Argument_from_degree

[2] Kreeft, P. and R. Tacelli. (1994). Handbook of Christian Apologetics: Hundreds of Answers to Crucial Questions. Madison, WI: InterVarsity Press, 54.

[3] Kreeft, P. and R. Tacelli. (1994). Handbook of Christian Apologetics: Hundreds of Answers to Crucial Questions. Madison, WI: InterVarsity Press, 54.

[4] Kreeft, P. and R. Tacelli. (1994). Handbook of Christian Apologetics: Hundreds of Answers to Crucial Questions. Madison, WI: InterVarsity Press, 54.

[5] Kreeft, P. and R. Tacelli. (1994). Handbook of Christian Apologetics: Hundreds of Answers to Crucial Questions. Madison, WI: InterVarsity Press, 54.

[6] Kreeft, P. and R. Tacelli. (1994). Handbook of Christian Apologetics: Hundreds of Answers to Crucial Questions. Madison, WI: InterVarsity Press, 55.

[7] Kreeft, P. and R. Tacelli. (1994). Handbook of Christian Apologetics: Hundreds of Answers to Crucial Questions. Madison, WI: InterVarsity Press, 55.

[8] Dawkins, R. The God Delusion. (2008). First Mariner Books: New York, 102.

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