Over at Greenbaggins, a discussion has arisen concerning the nature of our knowledge. Lane Keister's post seeks to contribute to the Clark-van Til debate. Lane suggests that God's knowledge forms a coherent whole that forms a context for all facts that He knows. Hence, our knowledge (lacking said context) cannot be identical to His, even in the knowledge of a single fact. Historically, the fact that van Til and Clark disagreed over was "2 + 2 = 4."
This led to a discussion in the combox as to the putative differences between God's knowledge and ours over brute facts, such as
"Jacques" is a longer word than "Jeff."
I have suggested that there are four major differences.
(1) God's knowledge is infallible, or non-contingent. Ours is contingent, hence fallible.
(2) God's knowledge is infinitely precise; ours is not.
(3) God's knowledge has complete context; ours does not (Lane's point).
(4) God's knowledge is immediate, with no need to reason or discover; ours is not.
Three objections have arisen to the notion that our knowledge is imprecise, which is point (2) above. I've justified the point thus: all of our knowledge is approximate because in every area of knowledge, we rely on words and symbols (which have a semantic range of meaning), sense experience (which is imprecise), and reasoning (which is subject to error). Hence, although we may know certain facts to a very high degree of certainty, we cannot claim exact knowledge of any fact. As a simple example, I observed that every single measurement we make is approximate. At one stroke, this makes all of our knowledge approximate in the sense mentioned above.
Here are the objections that have arisen.
O1: "All (human) knowledge is approximate" is self-defeating
The first objection comes from Jacques, who observes that "the claim that our knowledge is an approximation is itself urged as exact knowledge."
In other words, the concern is that "knowledge is approximate" is self-defeating. One thinks here of Plato's destruction of relativism ("'There is no absolute truth' is itself an absolute truth") or the more recent failure of empirical positivism ("Only statements that are empirically verifiable can be considered true" is not itself empirically verifiable).
I've responded that it is acceptable for "knowledge is approximate" to be itself an approximate statement. However, the discussion has not blossomed beyond that point.
O2: Obvious defeaters
The second objection comes from Don and Ron, who observe that a fact such as "Jacques is a longer word than Jeff" can be resolved by simply counting, with no approximation required. This is a self-evident defeater to the claim that all knowledge is approximate. Likewise, Ron urges that although we may not be able to measure 12 inches to infinite precision, we can nevertheless know without approximation that a length is between 11 and 13 inches.
Don wonders further in what way our knowledge of this fact could possibly be different from God's.
O3: Meta-claims about confidence intervals
Ron further objects that if we now speak of confidence intervals (for example, "this tile is 12 inches wide, plus or minus 0.1 inches"), then we have now created a new proposition that is known exactly.
I would like to open this space for discussion of the propositions (1) - (4) and the three objections. I believe they all have entirely adequate responses.
In particular:
Response to O1
Suppose that "All knowledge is approximate" turns out to be true for only 99.9% of human knowledge. Perhaps there is some undeniable proposition (perhaps "I think, therefore I am"; or perhaps "'Jacques' is a longer string than 'Jeff'")) that is known absolutely and precisely. Perhaps there are even a large number of such propositions, comprising as large as 0.1% of human knowledge.
This outcome would not be disastrous for the claim "All knowledge is approximate." For given any particular proposition P, it would still be highly likely that P is approximate. And if non-approximate P's can be identified and distinguished from the approximate, then so much the better.
That's the worst case.
In point of fact, it's not yet clear that any non-approximate P's have certainly been identified, for such a P would have to be
Criterion 1: Known without possibility of error (that is, an infinitesimally thin confidence interval), Criterion 2: Completely determined in unambiguous language, whether mathematical or otherwise (that is, infinitely precise in its boundary)
To my knowledge, no P meeting Criteria 1 and 2 has ever been produced.
In short: It is acceptable to say that "All knowledge is approximate" is itself theoretically approximate; and so far, no counterexamples have been produced.
Response to O2
Here, we need to dip into some statistics. Likely, Don and Ron will agree that counting letters is not itself an infallible process. If we gave out the string "Jacques" to 100,000 English-speaking adults and asked them how many letters are in that string, we are very likely to get at least a couple of responses of "6" or "8". Every process has an error rate, and many of those error rates have been studied by process engineers (eg here or here).
For sake of example, let's suppose that we get back a response of 99,997 people who count 7 letters, two who count 6, and one who counts 8. I suspect this is generous.
Then we can now ask the important question, "How many letters *are* in that string, anyway?" Based on the responses, we can calculate an average (6.99999) and a standard deviation (.00001). This gives us a delightfully narrow confidence interval: We can be 99.9% confident that the true number of letters lies between 6.99995 and 7.00003 letters -- in other words, 7.
BUT
If we are willing to consider extremely outside chances, there is a very, very small chance that our two people who counted 6 were correct, and everyone else was wrong. How small? Absurdly small -- my calculator gives a p value of "0", but it's actually about e^-350.
Well, practically speaking, this is exact for all useful purposes. There is no meaningful risk that the two people who counted 6 are actually correct. "Jacques" has 7 letters, the end.
And that's my larger point. The word "approximation" is not a synonym for "poor estimate." It means simply that there is some kind of error bar, no matter how small.
And in this case, because the error bars are truly and absurdly small, Don and Ron understandably round down and simply say that "Jacques has seven letters, with no approximation."
In reality, the approximation is so good that no one doubts it.
The point is that excellent approximations are sometimes confused for perfect precision, and I believe that O2 stems from that confusion.
Response to O3
Actually, the knowledge of the error bars is itself approximate. Interested readers can start here. There are two sources of uncertainty -- random error, and systematic.
The random error is described in the formula in the link.
The systematic error cannot be mathematically captured, and comes about from the possibility that our process is actually flawed in some way without our knowledge:
- The ruler is inaccurately calibrated
- The user of the ruler is using the wrong procedure (This happens a lot in high school labs)
- The boundaries of the object to be measured are not precisely defined.
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Why does this matter to the theologian? It is certainly interesting philosophy, but the payoff for the theologian is to recognize that our readings of Scripture will always and only give fallible approximations to the original meaning. And it is for this reason that Confessions are needed and yet revisable. If we could perfectly and precisely know the meaning of Scripture, then solo scriptura would suffice, and Confessions would not be needed. If on the other hand, if a council could perfectly and precisely know the meaning of Scripture, then it would not be true that " All synods or councils, since the apostles' times, whether general or particular, may err; and many have erred. Therefore they are not to be made the rule of faith, or practice; but to be used as a help in both."
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But now we must reckon with the fact that Derksen supplies an impressive array of quotations from various Westminster Divines and other Reformed theologians that plausibly show that these divines thought of baptism as a "confirming, not converting ordinance." This part will therefore directly challenge the arguments of BWS.
(1) Derksen's over-relies on the Westminster Divines as the primary window for understanding the Confession.
Citing the Westminster Divines Rutherford, Gillespie, Ussher, and others, together with the Reformed theologians Cunningham, Manton, and Turretin, Derksen claims that these representatives of Reformed thinking taught his two theses:
In this installment we will begin to show that the Westminster Standards’ teaching on baptism is in full accord with the historical Reformed understanding of the sacraments, as was outlined in Part 1. That is, baptism does not intrinsically confer spiritual grace, but rather spiritually benefits only the elect. Or, as it has frequently been stated in historical Reformed language: the sacraments are confirming and strengthening ordinances, and not converting ordinances -- BWS Part 3.
The problem is that the language of the Confession is drawn heavily from the writings of Calvin and from previous Reformed Confessions. Derksen in particular omits any discussion of Calvin in reference to his second thesis. The result is that he ends up pitting statements from Rutherford and Cunningham -- unwittingly -- against the dispositive statements of Calvin that we have already seen.
(2) Derksen improperly conflates his two theses; as a result, he illegitimately takes evidence for the one as if it proved the other.
Take a second look at Derksen's quote above, which explicates his two theses. With the word "Or", he signals his anti-ex opere operato thesis is to be considered as logically equivalent to the claim that baptism is confirming and not converting. And in fact this is precisely how he reads his sources. Statements against ex opere operato are taken as evidence that baptism does not confer, but only confirms salvation.
We note that Derksen's sources are addressing the question of ex opere operato. Their opposing formula of "confirming, not converting" is specifically directed against the view that the act of baptism creates grace or faith of itself. Their opposition is certainly not directed against Calvin's view that in baptism, we are ingrafted into Christ.
For example, Derksen cites: Our divines do not say that the sacraments are exhibitive ordinances, wherein grace is communicated to those who have none of it, to unconverted or unbelieving persons. (Gillespie, Aaron's Rod Blossoming p. 233, cited in BWS part 4)
As an anti-ex-operato statement, this is clear. Baptism does not, via its action, give grace to the unconverted.
But as a denial that baptism exhibits and conveys justification, it is much less clear. Gillespie is certainly not saying that the divines reject the idea that sacraments exhibit and convey grace, since they most certainly believed this! (WCoF 27). Nor could he be denying that sacraments are effectual means of salvation, since the divines affirmed this also (WLC 161).
So some of Derksen's citations are being applied to an issue different from their original context. This criticism applies also to his citations of Gouge, Gataker, Reynolds, Willet, and Turretin. All of these gentlemen affirm that baptism is ineffectual without faith; none of them affirm that the effect of baptism is something other than salvation, or deny that baptism effects our washing of sins.
(Incidentally, many of his citations are taken from treatises on the Lord's Supper, which makes them less obviously relevant to baptism.)
(3) Derksen's reliance on Rutherford creates some difficulties.
Despite the forgoing criticisms, some of Derksen's quotes do substantially show that some Reformed theologians of the Westminster era held to the "confirming, not converting" formula for the sacraments.
Rutherford is his best example:
Baptism is not whereby we are entered into Christ’s mystical and invisible body as such, for it be presupposed we be members of Christ’s body, and our sins pardoned already, before baptism come to be a seal of sins pardoned; but baptism is a seal of our entry into Christ’s visible body, as swearing to the Colors is that which entereth a soldier to be a member of that army, whereas before his oath, he was only a heart-friend to the army and cause.”)
...We teach not that baptism constituteth the Church simply, as the Church, but that it is a seal of a visible membership. -- S. Rutherford, Due Right of Presbyteries, pp. 211, 218, cited in BWS, part 4
But what difficulties has Rutherford involved himself in! For he flatly contradicts Calvin and the 2HC here, that baptism ingrafts us into Christ.
As Rutherford develops his theology, he is forced to say,
Christ by his Seals [sacraments] rightly and in faith used, do not only confirm grace and pardon, but also really exhibit and give grace and pardon in a further degree, and a new measure of assurance to the conscience which there was not before...” -- ibid, 217.
Since Rutherford denies that pardon is the effect of baptism, there is nothing left for baptism to effect except assurance and "pardon in a further degree."
Dear reader, stop and contemplate what the phrase "pardon in a further degree" might mean. Is not our justification "done and done", once-for-all, at the moment of faith?
No doubt Rutherford believes this also, but it is difficult to understand his position on the sacraments as a proper window into the understanding of the Confession.
(4) "Converting" and "confirming" are not strict opposites.
The issue in the ex opere operato debate was whether (as some Anglicans had it) the act of baptism creates faith. Thus, baptism was claimed to be a "converting" ordinance.
The Westminsterian divines clearly rejected this position.
But the opposite of "converting" is not "confirming." There might be other options besides either of these.
And in fact, I have argued here that baptism is "initiating." It is not "converting", except in the very narrow sense of Calvin's "secondary instrument." The action of baptism does not create faith (though its sealing of the spoken promise of the gospel might). But nor is it "confirming", increasing a faith that already exists.
No, the purpose of baptism is "initiatory." It unites us to Christ when (and not after) we believe. This is not merely Calvin's position, but it is expressed in the Reformed Confessions also, as we saw earlier.
"Converting" and "confirming" are false opposites, an unfortunate pairing born out of the ex-opere-operato conflict and pressed into a different service here.
(5) The baptism of infants argues against the view that baptism presupposes faith.
If baptism presupposes faith, then how can we baptize infants? Derksen is aware of this challenge, and he addresses it in BWS part 5. His argument in favor of infant baptism pursues the traditional lines of Reformed reasoning (which I affirm together with him). However, he does not answer the question, except to speculate that covenant children might have seed faith -- or they might not.
This is unsatisfactory. For if baptism of adults presupposes faith, then either baptism of children must be a different rite entirely from baptism of adults, or else the seed faith view must be correct. The first notion, that baptism of children has a different meaning than that of adults, has been tried in Reformed circles and rejected. The second view, that all children of believers contain seed-faith within them, is hotly contested.
But most telling is that Calvin denied that baptism of infants presupposed their faith. Contra Cunningham, he says,
Master. - If these things are requisite to the legitimate use of Baptism, how comes it that we baptize Infants?
Scholar. - It is not necessary that faith and repentance should always precede baptism. They are only required from those whose age makes them capable of both. It will be sufficient, then, if, after infants have grown up, they exhibit the power of their baptism. -- Geneva Catechism.
Far better to acknowledge that baptism means but one thing to all recipients: it is the objective seal of the truth of the Gospel, and the reception of the Gospel is the moment at which baptism takes its effect.
(5) Baptism is outwardly a symbol of initiation; its inward grace should correspond.
Baptism is outwardly a sign of solemn admission into the visible church. As an outward sign, it symbolizes initiation. Why then should we deny (as Rutherford does) that the inward reality is also initiation?
(6) Rebaptism is universally rejected
If baptism were a confirming ordinance, rebaptism would be perfectly legitimate. Just as communion confirms Christ's death for us, yet without re-sacrifice, so also a confirming baptism would confirm our justification -- and that sign could be continued indefinitely.
Instead, it is but once applied because it symbolizes (and therefore sacramentally effects) our once-for-all justification.
(7) Derksen (and those he cites) completely overlook the stated Confessional meaning of the sign.
The Shorter Catechism says this:
Q. 94. What is baptism?
A. Baptism is a sacrament, wherein the washing with water in the name of the Father, and of the Son, and of the Holy Ghost, doth signify and seal our ingrafting into Christ, and partaking of the benefits of the covenant of grace, and our engagement to be the Lord’s
What is signed is the ingrafting into Christ, the initiation into our relationship with Him. Likewise the Larger Catechism:
Question 165: What is Baptism?
Answer: Baptism is a sacrament of the New Testament, wherein Christ has ordained the washing with water in the name of the Father, and of the Son, and of the Holy Ghost, to be a sign and seal of ingrafting into himself, of remission of sins by his blood, and regeneration by his Spirit; of adoption, and resurrection unto everlasting life; and whereby the parties baptized are solemnly admitted into the visible church, and enter into an open and professed engagement to be wholly and only the Lord's.
The things signed are the things conveyed! Derksen, by contrast, has the things signed not conveyed, but merely confirmed. I humbly submit that the language of "confirmation" is not how the Standards describe the efficacy of the sacraments.
Increasing of faith? Yes. Signing, sealing, and applying the benefits of Christ? Yes. But "confirming the thing signified?" No.
To summarize: Derksen's arguments carry some weight, given his copious research into the views of the Westminster Divines. But his sources are concentrated too heavily in the Divines, not heavily enough in the early Reformers (especially Calvin), and they create odd difficulties on the very point he wants to establish. In short, Derksen has over-emphasized the views individual theologians to provide an idiosyncratic read of the Confessions.
In particular, Derksen's adoption of the "confirming, not converting" formula creates a false opposition. Baptism is neither; it is a kingly seal that testifies to God's promise, and it is an initiatory sacrament.
By contrast, the Westminster Confession presents a clear testimony, consistent with Calvin, Ursinus, 2HC, and the Gallic Confession that baptism effects what it signifies: namely, the washing away of sins and our union with Christ, at the moment of faith.
Charles Hodge deserves the last word:
How then is it true that baptism washes away sin, unites us to Christ, and secures salvation? The answer again is, that this is true of baptism in the same sense that it is true of the word. God is pleased to connect the benefits of redemption with the believing reception of the truth. And he is pleased to connect these same benefits with the believing reception of baptism. That is, as the Spirit works with and by the truth, so he works with and by baptism, in communicating the blessings of the covenant of grace. Therefore, as we are said to be saved by the word, with equal propriety we are said to be saved by baptism; though baptism without faith is as of little effect as is the word of God to unbelievers. -- C. Hodge, Comm. Eph. 5.17-33.
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