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Monday, November 26, 2012

Fourth Way Corrigan

The well-known science popularizer, Richard Dawkins, once rebutted Aquinas' Fourth Way in an article in the Times (UK).  He first paraphrased Aquinas' argument thusly:
We notice that things in the world differ. There are degrees of, say, goodness or perfection. But we judge these degrees only by comparison with a maximum. Humans can be both good and bad, so the maximum goodness cannot rest in us. Therefore there must be some other maximum to set the standard for perfection, and we call that maximum God.

and then he comments
That's an argument? You might as well say, 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. Or substitute any dimension of comparison you like and derive an equivalently fatuous conclusion.
whereupon Western philosophy crumbles.  What a knockdown!  Astonishingly, no one in history, not even Voltaire, ever noticed this before.  Instead, they sought to rebut at least one of the premises (usually the minor premise).  

Now the Fourth was never TOF's favorite argument, it being rather subtle, and TOF cannot say he follows it.  But let us see what can be made of it. 

The Statement of the Argument

The first question is whether Dawkins has engaged St. Thomas' actual argument, so here it is in the digest form of the Summa:
The fourth way is taken from the gradation to be found in things. Among beings there are some more and some less good, true, noble and the like. But "more" and "less" are predicated of different things, according as they resemble in their different ways something which is the maximum, as a thing is said to be hotter according as it more nearly resembles that which is hottest; so that there is something which is truest, something best, something noblest and, consequently, something which is uttermost being; for those things that are greatest in truth are greatest in being, as it is written in Metaph. ii. Now the maximum in any genus is the cause of all in that genus; as fire, which is the maximum heat, is the cause of all hot things. Therefore there must also be something which is to all beings the cause of their being, goodness, and every other perfection; and this we call God.  
 Quarta via sumitur ex gradibus qui in rebus inveniuntur. Invenitur enim in rebus aliquid magis et minus bonum, et verum, et nobile, et sic de aliis huiusmodi. Sed magis et minus dicuntur de diversis secundum quod appropinquant diversimode ad aliquid quod maxime est, sicut magis calidum est, quod magis appropinquat maxime calido. Est igitur aliquid quod est verissimum, et optimum, et nobilissimum, et per consequens maxime ens, nam quae sunt maxime vera, sunt maxime entia, ut dicitur II Metaphys. Quod autem dicitur maxime tale in aliquo genere, est causa omnium quae sunt illius generis, sicut ignis, qui est maxime calidus, est causa omnium calidorum, ut in eodem libro dicitur. Ergo est aliquid quod omnibus entibus est causa esse, et bonitatis, et cuiuslibet perfectionis, et hoc dicimus Deum.

We note a key phrase in bold.  What did Thomas mean by "and the like"  (et sic de aliis huiusmodi)?  Like what?  (A better translation of huiusmodi, imho, is "of this nature/sort/kind.")  He doesn't say that everything is graduated toward a maximum, or that the maximum of any category is necessarily God; only things of a certain kind -- truth, goodness, nobility, et al., the so-called "transcendentals."  Dawkins' smelliness is not "of the nature of" goodness, nobility, et al."

Something is Rotten in Denmark

The estimable James Chastek has lately reconsidered Dawkins' smelliness and considered how it is a rather neat establishment precisely of Aquinas' minor premise, which is the part of the argument most often questioned:
But "more" and "less" are predicated of different things, according as they resemble in their different ways something which is the maximum
Sed magis et minus dicuntur de diversis secundum quod appropinquant diversimode ad aliquid quod maxime est
 Consider that there are research facilities dedicated to the study of smelliness: fragrance laboratories, for example.  Their products enter aerosols, perfumes, food, marker pens, and countless other things.  Suppose you were to ask such a researcher "What is the stinkiest thing of them all?” And the answer was: “Oh, there’s nothing that I’d call the stinkiest of all.”

What would this mean, Chastek argues, but that "for whatever reason various smells aren’t comparable. Perhaps stinks are irreducibly distinct and [each] stinky in its own way. Perhaps some things smell worse on different days or in different circumstances, etc."  In sum:
If there is no maximal, then it’s because the various things are not comparable in terms of greater and less.
But then, by modus tollens:
If various things are comparable in terms of greater and less, then there is some maximal. 

And this is the minor premise of Thomas' proof.   So stinkiness is not a refutation of the principle. 

Ready, Aim, Fire

A paper on a hot topic
But neither is Fire, which Thomas offers by way of illustration of the principle.  Take a sheet of paper at ordinary room temperature.  Insofar as its heat content, it is imperfected.  That is, it is not as hot as it could be.  To become perfectly hot, the paper must have heat added to it by something else which is actually hot.  Perhaps a match.  But let's stretch things out and say we have placed it on a hotplate.  The paper becomes quantitatively hotter, which we measure by temperature.  At 451°F the paper will ignite.  It will not get any hotter than its ignition point.  This is why the medievals (and ancients) regarded fire as the principle of heat.  (Principle, from principia, "first part, origin, source") 

Notice that this does not mean that fire is the very hottest possible thing -- The sun is hotter than burning paper -- only the hottest that a particular thing can be.  The argument states: ex gradibus qui in rebus inveniuntur... (from the gradations found in things...)  It is well while noodling on "gradation" to pay attention to the "things" in which the attribute is graduated.  After all, when we say one man is more eloquent than another, we don't suppose eloquence is a thing like a man, but rather a form which a man may possess "more or less."  

There is in each thing with the potential for ignition some principle, which we may call 'the ignition point" instead of 'fire.'  The Latin word is ignis in any case.  

Water bursting into wet flames
But TOF (I hear you say) what about water?  You can make it hotter and hotter it will not burst into flame at any point! 

But it will max out at 100 °C (212 °F) at standard pressure.  This is not "fire" in the sense we understand fire; but it is the maximum heat for that substance.  And recall that Aquinas said "Among beings," that is "among actual things."  Like water or paper.  

Now we may be content with replacing "fire" with "molecular motion" or some such thing; or we might note that Aquinas also said  "resemble in their different ways something which is the maximum." So that vaporization and ignition resemble "fire" in their different ways.

Explanations of Continuous Qualities  

Chastek writes that the inquiry the Fourth Way makes into natural science is "what would count as an explanation of things that admit of degrees?" 

Let's call the thing-that-admits-of-degrees a "continuum."  Something that can be more-or-less rather than either-or.  This was developed in the middle ages as "the intention and remission of forms" and led eventually to the notion of applying arithmetic to physics problems.  If one thing was hotter than another, then that thing had the form of heat more intensely than the other, and supposed that forms of heat could be added together.  This led to the notions of a unit of heat and a scale of heat, and so on to temperature and modern science.  But the key thing is that the principle (explanation) had to be something in the nature of the more-or-less "hot" body itself; not something external to it.  The Fourth Way is not the Second Way.  Chastek writes:
Things on earth might be more or less stable, but one can’t explain the stability by invoking turtles for the earth to rest on. But what about sharpness or aerodynamic form? Knives and cars have these things of themselves, and so it is not a matter of looking for some other thing by which a knife is sharp or the car is aerodynamic – but in both cases there is an intelligible reality, which simply waits to be known, which provides a measure that illuminates exactly why each of these things can admit of more and less. This does not mean that there is, say, one and only one perfectly aerodynamic shape,  but rather that one can find a single equation for the drag that we seek to overcome by various shapes. One misses the point if he critiques St. Thomas’s axiom by saying “just because things are more or less aerodynamic doesn’t mean that there exists something perfectly aerodynamic.”  What is “most such” here is the drag equation
And so also for Dawkins' 'most smelly.'  

The Principle of the Transcendentals

Chastek warns:
The proof is based on gradations found in things. ...  The proof therefore starts with a discussion of composites of a form in a subject, or generally of composites of act and potency. If you don’t understand this sort of composition, stop reading the proof immediately, or at least don’t claim to understand what follows. 
Hence, Dawkins also misses the part where Thomas writes "there is something which is truest, something best, something noblest and, consequently, something which is uttermost being."


Thomas references an argument in Aristotle's Metaphysics, Book ii, regarding the convertibility of the transcendentals.  The principle [lit. first cause] of the transcendentals are said to equate to God; not because they are maximal, but because they are convertible to uttermost being.  Neither fire (the analogy Thomas offers) nor smelliness (the example Dawkins gives) maximize to uttermost being.

So immediately, Dawkins' riposte is suspicious.  He doesn't get what Thomas is saying.  He thinks it is a scientific hypothesis in olfactory theory, or something.  Smelly is no more transcendental than heat, which itself is offered only as a homey analogy to the argument on the transcendentals.  Thomas does not conclude that the hottest thing (Fire) is what all men call God.  He only says that the principle of goodness, truth, etc. is like the principle of heat (which is Fire).  It's an analogy. 

One, Two, Three, Infinity

Aside: It is sometimes said that although numbers are comparable more or less, there is no maximal number.  This is not a refutation.  The quantity being discussed by Thomas is not the quantity of magnitude or extent, but of power.  That is, it's not more-and-more-of-the-same-thing, but that which is more actual, more perfected,  more fully what-it-is. Fire is the principle of heat not because it has a higher quantitative extension (temperature) but because it is the explanation of more-or-lessness of heat.  In modern terms: molecular motion. 

Recommended Reading

  1. Disputed question on the key premise in the fourth way
  2. The fourth way as relating to exemplar causes in natural science
  3. The Fourth Way, Part I
  4. The Order of the Five Ways. 
  5. The Thomism of Richard Dawkins


As always in matters of this sort, someone brings up the old chestnut which they earnestly believe is an absolute defeater of the Cosmological arguments that was somehow overlooked by Voltaire and others of the Age of Self-described Enlightenment.  One of Dawkins' fanboys writes in the commbox:
If the answer is "God" then the next question is "who created God?" and "who created the creator of god?" and "who created the creator of the creator of god?". Infinite regress without termination (well.. duh.. or it wouldn't be infinite would it :P).

Even a passing familiarity with the Cosmological Arguments reveals that is God is not simply a stopgap shoved in to prevent an infinite regress.  The infinite regress is shown to be impossible for per se chains, necessitating a First Uncaused Cause, and only then this Uncaused Cause is said to be "what all men call God."  Since one of the consequences of an Unchanged Changer is that it is a Being of Pure Act, this entity is Existence Itself.  So the question "who created God?" translates as "who brought Existence Itself into existence?"  But like most atheists, the writer probably envisioned God as a supreme being among other beings and supposed that creation is just like transformation only magical. 

He also wrote:

My favourite creationist arguement (which is beautifully self defeating) is that nothing can come from nothing. Therefore the world came from god. BUT if nothing can come from nothing, where did god come from?
He evidently is unaware that the principle of ex nihilo, nihil fit goes back to the ancient Greek pagans and is a basic philosophical principle.  I suppose "creationists" may make an argument as silly as the one parodied -- there is very little difference in the mental furniture between them and atheists -- but again, the problem translates as "where did Existence come from?" which sounds even sillier than the original cutely-lower-cased question.  "Come from" can only apply to beings that come into existence.  But an Ungenerated Generator, a being whose essence just is to Exist, does not "come from" anything.  It just is


  1. Dick the Dawk is a symptom, and an efficient cause, of the senility of the West.

  2. This reminds me of all that's wrong with Dawkins' awful "Ultimate 747" argument. His argument goes, in essence, that if every cause must be more complex than its effect, then God must be more complex than the entire universe. From there he argues that, as per information theory, the more complex something is, the more unlikely it is to exist, and he concludes that therefore, God is the least likely thing to exist of all.

    Of course, in classical theism, God is ultimately simple, not ultimately complex. The idea that a cause must be more complex than its effect applies to artifacts designed to produce other artifacts. For instance, if I design a machine that is supposed to produce cars, the machine will need to be more complex than the cars it produces, since the information necessary to specify a car will need to be encoded into the machine in some form or other, in addition to the complexity involved in the construction of the machine itself. There's no reason to suppose this to be the case when you're talking about something being intentionally designed in the intellect of a rational agent, much less the Intellect of The Almighty.

    But that's only the minor problem with the argument. The bigger problem is how he uses information theory. When we say that a complex object is improbable, what we mean is that the event of that particular thing coming into existence by chance is improbable. For a Boeing 747, for instance, the probability of it coming into existence by chance consists of the product of the probabilities of each of its components coming into existence by chance multiplied by each other, multiplied by the probability of them happening to come together in just the right manner, etc. The more components and subcomponents, and the more complex and precise their arrangement, the lower that probability will be.

    But, of course, nobody is trying to claim that God came into existence at all, much less that He came into existence by chance, so Dawkins' entire stupid argument is just irrelevant.

    1. Folks don't really understand probability. For one thing, it does not apply to things that actually are. The probability that there is a blue plastic cup on my desk is 1 for the excellent reason that there actually IS a blue plastic cup on my desk. cf. Leonard Savage, The Foundations of Statistics.

  3. The phrase "Existence exists" comes to mind...


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