I Don’t Understand the Fourth Way

The fourth way of demonstrating the existence of God, says St. Thomas,

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…

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. (ST, I, 2, 3)

Note that there are two claims here: (a) that the greatest or perfect or infinite thing exists and (b) that it is the cause of all imperfect and finite things.

Objecting to this, Richard Dawkins writes,

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 preeminently peerless stinker, and we call him God. Or substitute any dimension of comparison you like and derive an equivalently fatuous conclusion.

1. The number line has lesser and greater integers, but there is no highest integer, nor is ∞ the cause of any number. Perhaps we need to restrict our inquiry to “perfections.”

2. How about sharpness of a knife? A knife may be more or less sharp, but there is no perfect sharpness (an edge one atom in width? I doubt such a blade could work), and even if there were, the perfect sharpness would not cause the sharpness of my own kitchen knives. Now sharpness is a perfection of a means to an end (of cutting things); so perhaps we need to consider only perfections of living things that are ends in themselves.

(I.e., whose final cause of their own happiness is within them.)

3. Dawkins’ smelliness example suggests that there must exist a perfectly noxious skunk. The ability to spray stinky fluid is useful to the skunk but hardly defines it. Very well, let’s focus on intrinsic or essential perfections of 2nd-grade things.

4. Swiftness is an essential perfection of a horse. A slow or lame horse is unlikely to survive and reproduce in the wild. Yet there is no self-subsisting swiftness; nor can any horse run at the speed of light; nor does the speed of light cause horses to run fast. I guess we must deal only with the most general essential perfections of life.

We are left with things like power, understanding, love, happiness, relation to time, unity, and so on. But at this point, the fourth way collapses, because all the analogies with (1)-(4), including “fire,” have been eliminated.

Searching James Chastek’s blog suggests that the principle “whenever something is more or less great by being more perfect, there is something most perfect” may be an “axiom.” But I do not find it self-evident. So, I don’t know how to salvage the Fourth Way.

I mean, it is conceivable that there is something most perfect, but conceivability does not entail possibility, and possibility does not entail actuality. The Fourth Way thus gives us only an idea of God as a perfect being without even spelling out the meaning of perfection, not a proof that this God exists or that He is even possible.

Perhaps if we assumed (b), that creaturely perfections are caused, then (a) would follow straightforwardly. Just as we deduced that God is pure act by considering creatures that are mixtures of act of potency, so we can argue that there is a perfect being by extrapolating from creatures’ falling short of perfection though not completely.

It may be a non sequitur, though, since proving that God is an Unmoved Mover on the physical level is much easier than proving that He is a Happy / Perfect Attractor on the spiritual level.

Effects of Sin

Guilt means “a feeling of culpability for offenses” and is the opposite of righteousness.

Shame is “a condition of humiliating disgrace or disrepute” and is the opposite of glory.

And pain, of course, is the opposite to health, whether bodily or spiritual, and of pleasure.

Now we can associate St. Thomas’ effects of sin with these:

1. Guilt corresponds to debt of punishment and the evil of fault.
2. Shame, to stain on the soul and the evil of self-hatred.
3. Pain, to corruption of nature and the evil of punishment.

A Proof of God’s Infinity

One of St. Thomas’ proofs of the infinity of God is this:

Again, an effect cannot transcend its cause. But our intellect can only be from God, Who is the first cause of all things. Our intellect cannot think of anything greater than God. If, then, it can think of something greater than every finite being, it remains that God is not finite.” (SCG, I, 43, [11])

The sense of infinitude he is promoting here is “spiritual greatness,” meaning either completeness of nature and ad intra happiness or ad extra omnipotence.

This is very similar to Descartes’ arguments in Meditations on First Philosophy, e.g.,

It is true that I have the idea of substance in me in virtue of the fact that I am a substance;

but this would not account for my having the idea of an infinite substance, when I am finite, unless this idea proceeded from some substance which really was infinite.

It might seem that the difference is that Descartes wants to prove God’s existence (the idea of God is “the mark of the craftsman stamped on his work”), while St. Thomas is only concerned with His infinity.

But since proving God’s existence is identical to demonstrating which attributes are co-instantiated in the same being, both philosophers are doing essentially the same thing.

Quine Confuses Modalities

Quine writes:

Perhaps I can evoke the appropriate sense of bewilderment as follows.

Mathematicians may conceivably be said to be necessarily rational and not necessarily two-legged; and cyclists necessarily two-legged and not necessarily rational.

But what of an individual who counts among his eccentricities both mathematics and cycling? Is this concrete individual necessarily rational and contingently two-legged or vice versa? (Plantinga, Nature of Necessity, Ch. 1, 2)

This is a case of confusion of necessity of the consequent with necessity of the consequence. In order to conclude that

(30) Zwier is necessarily bipedal,

we need

(31) Cyclists are necessarily bipedal


(32) Zwier is a cyclist.

But (31) can be read de dicto as □(x is a cyclist → x is bipedal), in which case it’s true, yet (30) does not follow;

or de re as (x is a cyclist → □(x is bipedal)), from which (30) would follow but which is unfortunately false.

In other words, we have the following 4 true statements:

(1) □(x is a mathematician → x is rational)
(2) ~□(x is a mathematician → x is bipedal)
(3) □(x is a cyclist → x is bipedal)
(4) ~□(x is a cyclist → x is rational).

Suppose in the actual world x is both a mathematician and a cyclist. Then he is both rational and bipedial. Suppose in some world W our x is a cyclist and is irrational. Then in that world he is not a mathematician. And so on. Whence the bewilderment?

Contingent Identity + Leibniz’s “Law”

Allan Gibbard tries to understand when a lump of clay and a statue made from this lump are identical. There are situations in which they are not, if the clay and the statue are generated or corrupt at different times. But:

I make a clay statue of the infant Goliath in two pieces, one part above the waist and the other part below the waste.

Once I finish the two halves, I stick them together, thereby bringing into existence simultaneously a new piece of clay and a new statue. A day later I smash the statue, thereby bringing to an end both statue and piece of clay.

The statue and piece of clay persisted during exactly the same period of time. (“Contingent Identity,” Journal of Philosophical Logic 4 (1975), 187-221)

Gibbard in this part of the paper thinks of the statue (Goliath) as form-in-matter: “By a statue here, I do not mean a shape of which there could be more than one token, but a concrete particular thing… A clay statue consists of a piece of clay in a specific shape.”

And he thinks of the clay (Lumpl) as matter-under-particular-form: “They began at the same time, and on any usual account, they had the same shape, location, color, and so forth at each instant in their history; everything that happened to the one happened to the other…”

Obviously, the two are one and the same thing, even if different aspects of them are emphasized in their definitions.

But later on Gibbard suggests otherwise: “Take a possible world in which I squeeze Lumpl into a ball, and suppose all the molecules involved are clearly identified. There are still two distinct things in that world, the statue Goliath which I destroy by squeezing, and the piece of clay Lumpl which survives the squeezing.”

If Lumpl survives the squeezing, then its particular shape cannot be its essential but must inevitably be an accidental property. But the statue’s exact shape is essential to it. If it were remade into a statue of David, then the old statue would cease to exist and a new statue would come into being. What our author calls “persistence criteria” for the two things differ. Goliath’s persistence criteria are more stringent that Lumpl’s.

In short, Lumpl has the power to endure even if squeezed into a ball; Goliath does not have this power. Consequently, their essences differ, and they are discernible.

We can conclude that if Goliath and Lumpl are identical, then only contingently, in the actual world; but not necessarily, as in the possible world in which the statue is squeezed into a ball, Goliath corrupts, and Lumpl persists.

Therefore, the Leibniz’s law of indiscernibility of identicals is false; but a weaker relation, “necessarily identical → indiscernible” probably holds.

De Re vs. De Dicto

Kenneth Konyndyk defines these two as follows:

Modality de re is modality thought of as applying to a thing (res), more precisely, as a way a thing possesses a property.

For example, one thing might be said to possess a property necessarily, or something can be said to possibly have some given property, as in the claims that Socrates is necessarily rational or Socrates is possibly a sailor.

Modality de dicto is the modality applied to a statement (dictum). It refers to the manner or mode of a statement’s being true.

For example, it is necessarily true that all bachelors are unmarried. Here it is the statement (the dictum) that is said to be necessary. More exactly, it is the statement’s being true that is necessary. (Introductory Modal Logic, 78-9)

Sometimes it is useful to interpret a proposition either de re or de dicto.

“The number of planets in the Solar system is 9,” when interpreted de re, means “It is true of the number which is equal to the number of planets in the Solar system that that number is 9.” Since the number of planets in the Solar system is, indeed, 9, the de re reading is a trivial “9 = 9.” In order to carry information, our proposition must be read de dicto.

“Agatha believes that the tallest spy is a spy,” when considered de dicto, is analytic and self-evidently true. Of course, the tallest spy is a spy! He must be, necessarily. The de re reading, on the contrary, looks like this: “There is an object in the actual world, x, of which Agatha believes something, namely that he is a spy; in addition, perhaps unbeknownst to her, x also happens to be the tallest spy out there.” This is much more meaningful.

Consider the statement, “George IV wondered whether the author of Waverley was such-and-such.” The de re reading is inappropriate, because it means: “George IV wondered of x which had the properties (1) of existing; (2) of being unique; (3) of having written Waverley, whether x was such-and-such.” He may not have realized that x had these properties, though if he did, the de re reading would be equivalent to the de dicto reading.

In the statement “Socrates is necessarily rational” the modal modifier “necessarily” is applied de re, and the statement is true (it is the essence of men to be rational);

in the statement “It is necessary that Socrates is rational” the same modifier is applied de dicto, and the statement is false, because Socrates does not exist in all possible worlds.

On the other hand, “Necessarily, what is seen sitting is sitting” is de dicto and true; “What is seen sitting is sitting necessarily” is de re and false.

Whether Actual Grace Is Irresistible?

Actually bestowed grace would as a rule seem to be irresistible, unless it is a part of a series of soul-designing events, such that even if some grace in that series is resisted, nevertheless, the entire series accomplishes God’s end which moreover could not be achieved with less unpleasantness or greater efficiency than by allowing that grace to be resisted.

Another possibility is that God may supply a grace that would be poorly received for the sake of some greatest good for the greatest number.

The only other reason to bestow a grace that is resisted is in order to have a better “legal” reason to condemn a person, which is nuts. God is a maker of gods not devils.

As the Catholic Encyclopedia relates, Jansen

did not shrink from reviling sufficient grace, understood in the Catholic sense, as a monstrous conception and a means of filling hell with reprobates, while later Jansenists discovered in it such a pernicious character as to infer the appropriateness of the prayer: … “From sufficient grace, O Lord deliver us.”

I agree with the Catholic opinion, even though they do distinguish sufficient and efficacious grace.

Further, to think that grace can fail to do what the omnipotent and omniscient God wants it to do seems absurd, as well: grace

may be considered, secondly, as it is from God the Mover, and thus it has a necessity — not indeed of coercion, but of infallibility — as regards what it is ordained to by God, since God’s intention cannot fail…

Hence if God intends, while moving, that the one whose heart He moves should attain to grace, he will infallibly attain to it… (ST, II-I, 112, 3)

Natural virtue is a necessary condition for being eligible for grace, and it is also a quasi-sufficient condition — for God is so good that He won’t miss any opportunity for uplifting a person into deiformity. The Catholic Encyclopedia agrees:

God, out of mere liberality, does not withhold His grace from the one who accomplishes what he can with his natural moral strength, i.e. from the one who, by deliberate abstention from offenses, seeks to dispose God favorably towards him and thus prepares himself negatively for grace.

Some theologians… declared even this most mitigated and mildest interpretation to be Semipelagian. Most modern theological authorities, however,… see in it nothing else but the expression of the truth:

To the one who prepares himself negatively and places no obstacle to the ever-ready influence of grace, God in general is more inclined to offer his grace than to another who wallows in the mire of sin and thus neglects to accomplish what lies in his power.

In this manner the cause of the distribution of grace is located not in the dignity of nature, but, conformably to orthodoxy, in the universal will of God to save mankind.

It may be objected to this reasoning that “Those who are well do not need a physician, but the sick do. I did not come to call the righteous but sinners.” (Mk 2:17) Very well, grace for the sake of the individual receiving it can be divided into common (which heals nature) and sanctifying (which uplifts nature), e.g.,

For one [love] is common, whereby He loves “all things that are”…, and thereby gives things their natural being.

But the second is a special love, whereby He draws the rational creature above the condition of its nature to a participation of the Divine good; and according to this love He is said to love anyone simply, since it is by this love that God simply wishes the eternal good, which is Himself, for the creature. (110, 1)

I expect that most graces bestowed by God are in fact not resisted, since in the event that God foresees that a grace would be rejected, He would refrain from giving it in the first place.

A Modal Ontological Argument

The argument looks like this:

  1. A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
  2. A being has maximal greatness if it has maximal excellence in every possible world.
  3. It is possible that there is a being that has maximal greatness. (Premise)
  4. Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
  5. Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
  6. Therefore, an omniscient, omnipotent and perfectly good being exists.

(NB: if X is possibly necessary, then it is necessary in some possible world. Or, in some possible world W’ it is true that it exists in all possible worlds.

So, X “expands” into all the possible worlds from W’, as opposed to from the actual world. But it makes no difference. Hence X exists in all possible worlds or is necessary. You need the right system of modal logic to make this conclusion. S5 works.)

However, why must we assume that (3) is correct? If maximal greatness is impossible, then it is impossible that any being has maximal excellence in every possible world: ~◊□(God exists) = □~□(God exists) = □◊(God does not exist) = there is a possible world in which God does not exist = (since God’s existence is possible) God is contingent.

Thus, the modal ontological argument starts by attempting to prove that God is necessary and from that concludes that God exists in the actual world. Doesn’t this seem like an overkill? Denying the crucial premise (3) does not lead to any absurdity but to a seemingly modest conclusion that God is a contingent being. And why can’t God be contingent? If He is contingent, then it is unclear whether or not He exists in the actual world, because the actual world may happen to be a possible world in which God exists, or it may happen to be a possible world in which God does not exist. So Plantinga’s argument does not work. What’s more, I don’t see how the modal ontological argument is at all equivalent to the Anselm’s original version of the argument.

We might be tempted to say that (3) is contingent. But simple modal transformations show that that’s not possible: either (3) is necessarily true, or it is necessarily false. At best we can say that it’s conceivable that God is necessary, and it’s conceivable that God is contingent. But we can’t say: God is possibly necessary and is possibly contingent.

Argument for God from “Nothingness”

Mises writes:

Negation, the notion of the absence or nonexistence of something or of the denial of a proposition, is conceivable to the human mind.

But the notion of an absolute negation of everything, the representation of an absolute nothing, is beyond man’s comprehension.

The Lord, teaches the Bible, created the world out of nothing; but God himself was there from eternity and will be there in eternity, without a beginning and without an end. …

It follows that scientific research will never succeed in providing a full answer to what is called the riddles of the universe.

It can never show how out of an inconceivable nothing emerged all that is and how one day all that exists may again disappear and the “nothing” alone will remain. (Ultimate Foundation of Economic Science, 52-3)

Thus, nothingness is “inconceivable.” And it should be obvious that it is meaningless to talk about “complete nothingness.” Language itself falters. There “is” or “was” nothing? But when we use the verb “to be” we talk about existence. We cannot even say that “nothingness ‘is not’,” because is-not-ness, too, presupposes a non-existent essence, which still must have an ideal existence in somebody’s mind. A unicorn does not exist really, but it can exist ideally as, say, a phantasm, when we imagine it.

Nothingness is obviously a term of some kind, but it does not refer. The absence of both ideal and actual existence is therefore literally inconceivable, because one cannot conceive of something which cannot by definition be not only “out there” but in the mind, as well.

It may be objected that nothingness is indeed inconceivable, but it may still be possible. Start from “∀x” and delete from existence one object after another. At the end you will end up with nothing.

However, ∀x… iterates over actual things. Even if all such things were eliminated, there would still be ideal things, in particular necessary truths and possible worlds.

For example, under nothingness, it would still be true that 2 + 2 = 4; or that possibly, there exists a world just like the (formerly) actual world.

But the natural and proper place of ideal abstract objects is in a mind, being known by it. Now the human minds as real entities are contingent; and in fact we have one by one disappeared them, as per the procedure above. In addition, a human mind does not, by virtue of its mere potential infinity, know all possible worlds.

There must then be an actually infinite mind, call it G-mind, which exists necessarily and which knows and can contemplate all the necessary truths and all possibilities. Thus, such a mind cannot all of a sudden decide to disappear, because then we’d end up with “nothingness” which as we have seen is not at all meaningful.

The G-mind, too, is real, as distinct from its thoughts and propositions expressed by them. But we have banished all the reals. How does the G-mind escape destruction? Only if the subject-mind is numerically identical both to the object-understood (as all truths) and to the thought grasping these truths. In the G-mind, the ideal and the real coalesce. As we must retain all the ideals, the real G-mind is saved from certain doom, as it stays in existence by clinging perfectly tightly to the ideals against our attempts to produce nothingness.

And now, of course, we recognize that being as God.

Detecting Design Depends on Specified Complexity

Michael Behe's book Darwin's Black BoxOn infidels.org there appeared to me this random quote:

Mr. Behe has of course compared, like it or not, the extraordinary complexity of the human cell to the mousetrap. He said if we look at that mousetrap, it was created by a human.

In fact, Mr. Miller improved on it, as you saw earlier tonight. Therefore, if that’s complicated, then indeed the cell must also have been designed by an intelligence.

And as I thought about it tonight, it’s a little bit — we were all talking about nature analogies — it’s a little bit like looking at a mole build a molehill. You say, That’s very interesting. Then we walk out in the woods the next day and we notice a big mountain off in the distance. And we say, Good grief, that’s enormously large. A really big mole must have built that.

The truth of the matter is, it’s not logical. We should be looking for different forces that result in different things.

Your mousetrap was built by human hands because its components are inanimate objects. Cellular life is living, vibrant, breathing, changing matter.

You’re not just comparing apples to oranges, you are comparing plastic apples to organic oranges, and I think therefore this analogy fails. (Ken Miller in “Resolved: That evolutionists should acknowledge creation,” Firing Line, 4 December 1997, 50)

But wait a minute, the big mountain lacks specified complexity; it is not a machine; it performs no function; it does not move or do any work. There is no room for a design inference here.

Miller’s error is that he thinks that our abduction in the case of irreducibly complex biological systems is based on an analogy with man-made machines.

In fact, a mousetrap is an illustration of a principle according to which design can be reliably inferred in anything. That principle, (contingent) specified complexity, governs our speculations of the origins of both mousetraps and, say, bacterial cilia with equal authority.

However, if there is an argument from analogy here, it has in the following form:

(1) Everything that exhibits specified complexity and is such that we can find out independently whether or not it was the product of intelligent design, in fact was the product of intelligent design.

(2) Many biological systems exhibit specified complexity.

(3) Therefore, these systems are most likely the products of intelligent design.

Secondly, it is true that “cellular life is living, vibrant, breathing, changing matter.” That property — life, the soul, teleological causation, the vital principle that animates every living creature and makes it different from inanimate objects — is surely fascinating.

But life is something in addition to the molecular nanotechnology within a cell. Now ID focuses on these sophisticated robots only because they are scientifically tractable, as “life force” is not. And it is sufficient, ID proponents claim, given also the failure of evolutionists to offer anything interesting in response, to infer design.

Life, consciousness are far beyond the design-theoretic research program which is preoccupied with material objects carrying high information content. However, if anything, they make the case for design much stronger than it has so far been made, insofar as life cannot be reduced to matter, or consciousness to computation, and assuming that the origins of both cannot have been purely natural.

Perhaps Miller’s point is simply that life can change, unlike a mousetrap. But that’s where Behe’s irreducible complexity comes in. Even though life can change through random mutations, natural selection cannot build the systems Behe examines in his Darwin’s Black Box.