Consolation, Book III prose X:
For everything is said to be imperfect is held to be so by some loss of its perfection. Which is why, if something is seen as imperfect in any genus, there it is necessary that there be some perfect thing in it. For if you take away the perfection, it cannot even be imagined (fingi) how something might be held to be imperfect. For reality (natura rerum) does not take its origin from what is lower or unmade, but, proceeding from things whole and absolute, it falls down into these last, worn down things.
omne enim quod imperfectum esse dicitur id imminutione perfecti imperfectum esse perhibetur. Quo fit ut, si in quolibet genere imperfectum quid esse uideatur, in eo perfectum quoque aliquid esse necesse sit; etenim perfectione sublata unde illud quod imperfectum perhibetur exstiterit ne fingi quidem potest. Neque enim ab deminutis inconsummatisque natura rerum cepit exordium, sed ab integris absolutisque procedens in haec extrema atque effeta dilabitur.
Gerrigou- Lagrange argues that all the proofs for the existence of God are contained virtually in the principle that Boethius articulates here. I think he is right, but there is an ominous corollary to the point since, mutatis mutandis, all such proofs are virtually refuted or made impossible for one who thinks this principle is false or impossible. And since the whole edifice of Scholastic theology rests on the initial view we get of God from the arguments about his existence, one who considers Boethius’s axiom might see all scholastic theology as standing in the balance.
We can, I think, get a view of Boethius’ claim that makes it axiomatic. Imperfection is to fall short of something, and nothing can fall short of what doesn’t exist. We can’t play the game “you’re getting warmer- you’re getting colder” without some real object that we can be closer or further from.The axiomatic character of the claim is manifested in the words – imperfect = non-perfect, which presupposes that the perfect is already known and given before the imperfect is even thought of.
On the other hand, we can understand why someone would take exception with Boethius. It is not clear how this axiom is about nature – in fact, does it even make sense to speak of coming to be from the perfect? “Perfect” means done – it is not a term applied to initial conditions. The scholastics were aware of this, of course, and so they placed “the perfect” which is present at the beginning in the order of intention. But isn’t this to simply add an entire idealized order on top of the nature that we actually observe?
But a more radical objection to Boethius sees the very idea of perfect or imperfect as, at best, concepts of only limited application to nature. It might make some sense to speak of living things as maturing and thus as moving to a definite perfection, but most of the universe is neither alive nor presently involved with its generation or benefit. Is there any sense to speaking of weather patterns, planetary orbits, radioactive decay, tidal forces, the voyage of a photon from Rigel to Jupiter, etc. as perfect? So far as the Medievals knew about any of these things, they really did strive to relate them to some perfection – in general, they saw the cyclical motions of nature as essentially subordinate to the generation of life.
But the fundamental problem we have with seeing nature as Boethius sees it comes from being trained to see that the real view of nature is the one where the qualities of things recede into a background of mere lines and equations. Reality for us is the fact – shown by evidence, that is, the object appearing to us in a domain under our control. Whatever one wants to say about such a domain, there is no perfect or imperfect realities in it. The first sense we have of what is perfect or imperfect is from our ideas of good and evil (which might be why the first definition that Aristotle gives of “quality” is that in virtue of which a man is such-and-such), and good an evil are not under realities we control but realities that, fundamentally, we must accept. Thus in our very first idea of the perfect we divide it from fact (which gives rise to our strange, mythical oppositions of experience into facts and values, the objective and the subjective, the practical and the ideal, the quantifiable and qualia, etc.)
JJ said,
May 10, 2012 at 9:42 pm
Gerrigou- Lagrange argues that all the proofs for the existence of God are contained virtually in the principle that Boethius articulates here.
Is this similar to Kant’s contention that all arguments for the existence of God are some form of the ontological argument?
Alan Aversa said,
May 11, 2012 at 12:14 am
The principle is basically “Nemo dat quod non habet” or “No one can give what he has not.” (cf. Summa I q. 2 a. 3). Proving this principle a priori is not possible because the objects in the intellect are not mobile beings (ens mobile); it is possible to prove this principle by noticing, via our senses, that change is evident in the world, that there is such things as ens mobile.
JJ said,
May 11, 2012 at 1:55 am
Yes, but bracketing the question of whether the objects are in the intellect prior to sense experience (Plato) or after (Aristotle), is the basic argument of Gerrigou- Lagrange and Kant the same? Do they both claim that arguments for God’s existence are arguments from the imperfections of reality to a necessary perfection (i.e. God)? Is Kant right to then claim that every instance of this argument (i.e. from imperfection to perfection) relies upon the Ontological argument? Or is it better to understand the Ontological argument as merely an instance of the argument from imperfection to perfection?
JJ said,
May 11, 2012 at 3:14 am
By the by, Mr. (Professor?) Aversa, I enjoy reading your blog in addition to Mr. (Professor?) Chastek’s.
Brandon Watson said,
May 11, 2012 at 5:54 am
I think Kant’s claim is a very different kind of point than Garrigou-Lagrange’s. Kant’s claim is not that rationalist (cosmological) and empiricist (physical or teleological) causal arguments for God’s existence are virtually contained in the ontological argument but that to make them arguments for God’s existence requires adding the ontological argument to them in some form. When considering this particular issue, he assumes for the sake of argument that you can make the causal argument; he thinks, however, that you have to add the ontological argument to the causal argument to get from its conclusion to God.
I take it that Garrigou-Lagrange, on the other hand, argues that Boethius’s principle implicitly contains every claim that is required to have the right kind of causal reasoning for the Five Ways. So some principle at least derivable from Boethius’s is necessary for getting such causal arguments off the ground in the first place. Thus the two claims are actually concerned with different parts of the argument — Kant’s with how the conclusion about the cause can be a claim about the existence of necessary being and Garrigou-Lagrange’s with how the conclusion about the cause is reached at all. And Garrigou-Lagrange’s claim is also weaker; Kant is claiming that the other arguments really and truly require an actual use of the ontological argument, while Garrigou-Lagrange is simply claiming that you can get a key premise of each of the Five Ways from Boethius’s principle. (Unlike James, I’m not actually convinced that this latter is true. But it’s a weaker claim than saying that all of the Five Ways use Boethius’s principle.)
RP said,
May 11, 2012 at 8:37 am
Isn’t genus a mental thing? or is Plato right? Anyway, we don’t know the imperfect from the perfect – we don’t know the perfect at all. We know better from not so good (from some aspect or another). What would be a perfect plant?
Is Perfection a genus?
Is there a genus of all genera?
Is the set of all sets a member of itself?
No matter the answer to these questions: the jabberwocky words of “virtually contained” and “participation” can calm all seas and allow smooth sailing past any contradiction.
Brandon Watson said,
May 11, 2012 at 10:21 am
There is no mystery about ‘virtually contained’; conclusions are always virtually contained in their premises — that’s just what it is to be premise and conclusion in a deductive argument. But ‘virtual containment’ here is creating a problem, not calming the seas; if there is no virtual containment, the problem James is discussing in the post doesn’t really exist, since very little would be affected by whether Boethius’s principle is right or wrong.
RP said,
May 12, 2012 at 8:50 am
Thirty years ago or so I wrote an assembler language program as a floating-point emulator for a mainframe without floating-point hardware. I patched it into the operating system so that a FORTRAN program with REAL variables would have a normalized floating point number returned to it rather than crash with an invalid operation exception. In my code I followed the logic of the firmware manuals that were given to the hardware maintenance guys so the code consisted of ANDs and NOTs and shifts, etc. I find it very hard to see then that there is any sense in saying 4.2 is virtually contained in 1.5 + 2.7 knowing as I do (or did then) each step in obtaining the result. So I think virtually contained means: I think it’s true but don’t know how to show it. It’s a euphemism for ignorance. In fact, no one has the slightest notion of what the process of the intellect is in taking two premises and drawing the conclusion in spite of the fact we are able to symbolically say that when following given rules if the major premise has a certain structure and the minor premise has a certain structure the conclusion will have a certain structure. At best, to say the conclusion is virtually contained in the premises simply means no one yet has done the work of drawing the conclusion.
But suppose I’m simply wrong (inordinately dense). How does one know what is virtually contained in something?
Brandon Watson said,
May 12, 2012 at 12:26 pm
So I think virtually contained means: I think it’s true but don’t know how to show it. It’s a euphemism for ignorance.
(1) This is manifestly not what James is using it to mean. The most you can really be saying is that you think it is evidence of ignorance. I think this requires actual support rather than mere speculation.
(2) However, even the ‘containment’ part of virtual containment can be rigorously represented in topological representations of logical derivation — you can have topological models of logical structures in which that which is represented by derivation in symbolic logical systems is represented by literal spatial containment in topological systems.
Yes, it’s a metaphor, a translation from another domain, but it’s a metaphor that is supported by close formal analogies. One shows virtual containment in the same way one shows logical derivation, because they are two metaphorical ways of talking about exactly the same thing — the first using a spatial metaphor, the second using a process metaphor. It is as legitimate a symbolism as your talk about rules and structures, which are also metaphors in origin; and which one prefers to use is simply a matter of taste and convenience. In this case Boethius’s principle virtually contains the other causal principles if you can get from it to them using only definitions and restrictions of domain.
It is true that this is not always going to be simple; derivations are often not simple. And it is also true that it is metaphorical in origin — but all our terms in logic are metaphorical in origin; unless you are arguing that there is no such thing as logic and that we don’t actually know anything about what logically implies what — in which case your issues really have nothing to do with virtual containment as such — this really doesn’t have any relevance. But as this post wasn’t using virtual containment as an answer to anything, but simply used G-L’s claim about Boethius’s principle virtually containing the other causal principles used in the Five Ways as an occasion for talking about Boethius’s principle, I’m not really sure why you jumped on it the way you did.
James Chastek said,
May 11, 2012 at 1:56 pm
There’s a lot here to respond to, but I have a free afternoon.
JJ,
I’m not sure I get why Kant makes his claim that the cosmological argument depends on the ontological one, and so I can’t compare it to Gerrigou. My working hypothesis is that Kant is starting from Leibniz’s idea that one can argue both a priori and a posteriori for God by the principle of sufficient reason. If this is true, the cosmological and ontological arguments are more like two sides of one and the same argument, since one can either start with the concept of God and prove his reality by the PSR, or with contingent creatures prove their sufficient reason – namely, a being whose necessary existence gives a sufficient reason for all contingent existence. So if Kant really has a single argument against a “being characterized by necessary existence” or “a being whose existence is a sufficient reason”, he can nullify both arguments at a stroke, and he famously believes he’s found such an argument.
Alan,
You’re right that one can argue from the causal axiom Nemo dat to Boethius’s principle, but it’s better to say that actuality is prior to causality. Causality begins to exist only with creation. So it would be better to argue to Nemo dat from Boethius’s principle than vice versa.
RP,
I share the exasperation. Nothing is more hateful than a scholasticism that appears to only defend itself by making claims so vague and qualified that it is hard to see how they could ever be false, or by positing distinctions that seem merely ad hoc. At any rate, I would not present Boethius’s axiom as he does: it seems to me better to present it as a dilemma:
We have good reasons for accepting both – and so an idea like “virtual containment” or participation arises not because we are trying to defend a dogmatic scholastic claim at all costs, but because we are trying to make a synthesis of diverse truths. It won’t do to just throw out one truth for the sake of the other. There is an aporia that invites us to uncover a new truth that makes the synthesis possible – but far too many scholastics want to just jump over the aporia an right to the truth. But this amounts to thinking that great truths are dispensed on the cheap. No answer is more hateful and cheap than one given to a problem no one has struggled with.
RP said,
May 12, 2012 at 8:25 pm
Brandon:
Chastek has already explained why I “jumped on” virtual containment: “I share the exasperation.”
I think what I said (virtual containment means ignorance) is a paraphrase of this: Thus it is evident that for the self-same reason our intellect understands by discursion, and by composing and dividing, namely, that in the first apprehension of anything newly apprehended it does not at once grasp all that is virtually contained in it. And this comes from the weakness of the intellectual light within us, as has been said (Article 3). (ST I, 58, 4)
But then this: And such are whatever are virtually contained in the first self-evident principles, that is, whatever truths man is naturally able to know. (ST I, 94, 3)
And all the world’s physicists will be glad to know they can learn all the laws of physics by drawing “topological diagrams” since: To prove this, we must observe that the consideration of a speculative science does not extend beyond the scope of the principles of that science: since the entire science is virtually contained in its principles. (ST I-II, 3, 5)
One more: Since, however, some who know the principles are unable to consider all that is virtually contained therein, it is necessary, for their sake, that scientific conclusions should be traced to their principles. (ST II-II, 44, 2)
Ed L said,
May 13, 2012 at 8:23 pm
When I say that the conclusion of a syllogism is contained “virtually” in its premises, isn’t the first thing this means that some rational creature could put together the premises and derive the conclusion? Then, if the premises are true, prior, etc. (As Aristotle specifies in the Posterior Analytics) virtual containment would mean that the truth of the conclusion depends on the truth of the premises. Finally, if Aristotle and St. Thomas are right in thinking that to know is to be another in some way, and if the argument is from the cause, it would seem that the thing signified in the conclusion is an effect of the things signified in the premises. In this last case, virtual containment would indicate that some cause is able to produce X as an effect. (i.e. an artist contains the painting “virtually” because his power is such that he can produce such a thing).
RP said,
May 14, 2012 at 5:06 am
Godel showed, at least for Arithmetic, that what everyone thought was “virtually contained” in the “principles” (axioms), namely, all theorems, were not. In fact, if some theorems could be proven then Arithmetic was contradictory and as we know, false in one, false in all.
It’s probable his results apply to scholastic claims that all the conclusions are virtually contained in some set of first principles – whether of this or that science, or the set of self-evident principles which virtually contain all that is naturally knowable. If so, that would mean there would be an infinity of conclusions not deducible from any set of first principles.
By the way – can anyone list all these self-evident first principles? I haven’t found anyone who has listed more than 3 or 4.
Alan Aversa said,
May 14, 2012 at 11:44 am
@RP: Check this out: A Scholastic List of Philosophical Axioms
Brandon Watson said,
May 14, 2012 at 7:07 pm
No one can list all self-evident principles; Aristotelian accounts of demonstration imply that there are infinitely many. And whether something is a first principle depends on what you are talking about.
Since Godel’s results do not in fact apply even to every kind of mathematical system, I am very skeptical of claims to generalize them. But it is true that people can be wrong about what axioms imply.
Brandon Watson said,
May 14, 2012 at 7:16 pm
I find your entire response baffling. We’re not talking physics, we’re talking logical implication. We aren’t talking all principles, but a very, very small selection of them — Boethius’s principle and the principles of the Five Way. And ‘virtual containment means ignorance’ is an absurd paraphrase of ST 1.58.4, since Aquinas’s point there is simply that it takes discursive work to see what is virtually contained in first apprehensions, which is obviously true but also obviously not accurately summarized with ‘virtual containment means ignorance’. In fact, this whole problem seems more and more to be some shadow in your head. James seems to me to have been pretty clearly expressing sympathy at exasperation at uncritical appeals to participation, since that’s a complaint he’s made in other contexts. But what you’ve done with ‘virtual containment’ is pick on a phrase that is (1) expendable, since we could just rephrase the original claim as “Boethius’s principle is a more general principle that is logically presupposed by the causal principles of arguments for the existence of God” without talking about ‘virtual containment’ at all, if you’re really that allergic to the claim; and (2) not especially important in context.
RP said,
May 15, 2012 at 5:47 am
Brandon:
The shadow is not in my head but on the wall of the cave you are in.
In ST I, 58, 4 you missed the “weakness of intellect” phrase.
My point is that words such as virtual containment and participation are weasel words thrown in wherever needed to disguise the fact the particular philosopher or theologian has no idea what he is talking about. I’ve never read anywhere Aquinas saying, “I don’t know”. Have you?
But as for virtual containment my point in particular is simply that no one can possibly know what is virtually contained in anything else until it has been derived in some way from it first. After the fact, it can be said to have been contained in it, whether virtually or in some other way. And it is silly, lacking this derivation (or at least an argument for it), to claim that something is virtually contained in anything.
My guess is that Godel applies whenever self-reference or recursion occurs. But I’ve been away from mathematical concerns for a long time so I’ll accept your opinion.
By the way Watson, why do you so often defend Chastek by telling us what he means? Are you and he the same person? If not, I’m sure he can defend himself if he is so inclined against any foolishness or nonsense I write.
Alan Aversa: Thanks. I have that list but it’s not what I’m looking for. Many, many philosophical works will mention self-evident first principles and list non-contradiction, whole greater than part, and infrequently, one or two others. I was hoping that after a thousand years a more complete and settled consensus had somewhere been listed. In all my reading I have not come across anyone who has derived “all natural knowledge virtually contained” in these 2or 3 or 4 self-evident first principles. But I guess that shows my ignorance and not the philosopher making the claim.
Edward Langley said,
May 17, 2012 at 11:14 am
As Brandon pointed out “Aristotelian accounts of demonstration imply that there are infinitely many.” For, when any nature is known, certain things are known about it immediately: knowing place, for example, it is self-evident that no incorporeal substance is in place. So, any attempt to enumerate the principles would require a complete enumeration of the kinds of existing things.
Brandon Watson said,
May 18, 2012 at 5:23 pm
My point is that words such as virtual containment and participation are weasel words thrown in wherever needed to disguise the fact the particular philosopher or theologian has no idea what he is talking about. I’ve never read anywhere Aquinas saying, “I don’t know”. Have you?
(1) You have done nothing whatsoever to prove that there is any sort of weaseling going on; and merely assuming that there is nothing to understand is the first step to failing to understand.
(2) Your question is, again, baffling. When Aquinas doesn’t know, he gives the suggested solutions without deciding between them, at most ranking them according to apparent advantages. It’s not at all difficult to find him doing this. And the aporetic method shared by scholastics generally recognizes that intellectual humility and intellectual timidity are distinct: the humble approach to truth is to propose boldly, not timidly, but let the proposal be hammered into proper shape by truth itself through reason and evidence. You may disagree with this; but merely dismissing it is misguided.
My guess is that Godel applies whenever self-reference or recursion occurs.
Presburger Arithmetic allows for self-reference and recursion, but not of a kind to which Godel’s results apply. The particular kind of self-reference on which Godel’s results rely depend on prime factorization, or something formally equivalent to it (like general and unified conceptions of multiplication and division); any system, like Presburger, that lacks those kinds of general conceptions is not touched by Godel’s results. Godel’s arguments, in other works, make assumptions; they are assumptions precisely tailored to certain important kinds of arithmetic, and thus very powerful; but they are not assumptions universal even in mathematics.
By the way Watson, why do you so often defend Chastek by telling us what he means?
I don’t really see myself as defending James very often, rather than simply rejecting arguments I think are weak. As it happens, I disagree with James a lot, especially about details — as I explicitly did above, in fact. I just don’t usually find the disagreements all that important, and so more interested in seeing where it all goes. But the answer is pretty obvious: the criticisms themselves are usually telling us what the post meant, as you quite clearly were with your insistent claims about the real meanings of virtual containment and participation. And the first test of someone telling us of the problems due to what an argument really means is to see whether it survives simple paraphrase or contextual analysis. James usually seems to have reasons for the vocabulary he uses, but criticisms that can’t survive a vocabulary change aren’t worth the time spent typing them.
RP said,
May 20, 2012 at 7:24 am
There are none so blind than those who think they see.
And you perchance will fling that back at me.
Yet I counter barren logic with richest intuitions.
In my comments, now of several renditions,
The Truth most firmly maintained -
In which they’re virtually contained
Alan Aversa said,
June 21, 2012 at 5:57 am
Brandon Watson: No one can list all self-evident principles; Aristotelian accounts of demonstration imply that there are infinitely many.
Yes, 88b4 ff. of Aristotle’s Posterior Analytics:
St. Thomas commentates: