Posts Tagged ‘logic’

Owen’s Fallacious Argument

October 21, 2016 Leave a comment
9jygm-2i_bigger DPatrickRamsey
If God denies baptism to children of believers then it must be because he denies them the grace signified by baptism- John Owen
10/18/16, 5:29 PM

God having appointed baptism as the sign of regeneration, unto whom he denies it, he denies the grace signified by it. Why is it the will of God that unbelievers and impenitent sinners should not be baptized? It is because, not granting them the grace, he will not grant them the sign. If, therefore, God denies the sign unto the infant seed of believers, it must be because he denies them the grace of it; and then all the children of believing parents dying in their infancy must, without hope, be eternally damned. I do not say that all must be so who are not baptized, but all must be so whom God would have not baptized.

-John Owen, Of Infant Baptism

Some think this is a good argument. Others recognize there is something off – but it’s not easy to pinpoint precisely what. In such instances, translating an argument into syllogistic form often helps to reveal the error in logic.

  • P1: If God denies someone the grace of regeneration, he denies them the sign of regeneration.
  • P2: God denies someone the sign of regeneration.
  • C: Therefore he denies them the grace of regeneration.

That’s a logical fallacy called affirming the consequent. Thus Owen’s argument is invalid. (Which is probably why he never published that tract 😉 ).

Paul’s Enthymemes on the Law

September 30, 2015 2 comments

One of the questions that comes up for those studying 1689 Federalism is whether or not the Mosaic Covenant (which was a covenant of works) offered eternal life as a reward for obedience to the law. Historically, some have said yes, while others no. I (following Coxe, Owen, Renihans, Barcellos, etc) say no, the Mosaic Covenant only offered temporal life and blessings. However, two passages in particular seems to suggest I am mistaken and that the Mosaic Covenant did in fact offer eternal life and that Christ in fact earned our righteousness through the Mosaic Covenant.

For all who rely on works of the law are under a curse; for it is written, “Cursed be everyone who does not abide by all things written in the Book of the Law, and do them.” Now it is evident that no one is justified before God by the law, for “The righteous shall live by faith.” But the law is not of faith, rather “The one who does them shall live by them.” Christ redeemed us from the curse of the law by becoming a curse for us—for it is written, “Cursed is everyone who is hanged on a tree”—so that in Christ Jesus the blessing of Abraham might come to the Gentiles, so that we might receive the promised Spirit through faith. (Galatians 3:10-14 ESV)

But when the fullness of time had come, God sent forth his Son, born of woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons. (Galatians 4:4-5 ESV)

What are we to make of these passages which seem to teach that our blessings were earned by Christ as a reward for obedience to the Mosaic Covenant (“the law”)? Well, we need to understand Paul’s rhetoric as an enthymeme. An enthymeme is “a syllogism in which one of the premises is implicit.” Britannica explains:

in syllogistic, or traditional, logic, name of a syllogistic argument that is incompletely stated. In the argument “All insects have six legs; therefore, all wasps have six legs,” the minor premise, “All wasps are insects,” is suppressed. Any one of the propositions may be omitted—even the conclusion; but in general it is the one that comes most naturally to the mind. Often in rhetorical language the deliberate omission of one of the propositions has a dramatic effect.

Wikipedia refers to it as an “informal syllogism”

Here is an example of an informal syllogism, an enthymeme:

  • Socrates is mortal because he’s human.”
The complete formal syllogism would be the classic:
All humans are mortal. (major premise – assumed)
Socrates is human. (minor premise – stated)
Therefore, Socrates is mortal. (conclusion – stated)

While syllogisms lay out all of their premises and conclusion explicitly, enthymemes keep at least one of the premises or conclusion unsaid. The assertions left unsaid are intended to be so obvious as to not need stating.

I highly recommend that everyone take some time to listen to John Robbins’ mp3 course on logic (Course 11). Education in logic used to be a prerequisite to any formal study of a subject (such as theology). The Westminster Assembly produced The Directory for Publick Worship which includes the following rule for examination of a pastor:

He shall be examined touching his skill in the original tongues and his trial to be made by reading the Hebrew and Greek testaments and rendering some portion of them into Latin. And if he be defective in them, inquiry shall be made more strictly after his other learning and whether he hath skill in logick and philosophy.

page 72

I never received any formal logic instruction, so I’m doing my best to play catch-up. We all need to play catch-up. Logic is not common sense. It’s not something everyone knows and understands. Logic is “the rules of proper thought” or “the science of necessary inference.” It is a study of the proper way to think, and it’s something a lot of us are ignorant of (and we correct this by studying how God thinks by studying Scripture and thereby developing proper rules of thought – not by looking to “natural theology”). But back to enthymeme (from Robbins’ second lecture “Definition of Terms”):

It means an argument in which one of the premises is omitted, or understood. And he [Clark] gives the illustration of a youngster convincing his parents to let him to buy some gloves. And he doesn’t express the full argument. Most of our ordinary conversations in life are enthymemes. Some of the premises are not stated, they’re understood. It would be very burdensome, very tedious, if every time we wanted to talk to someone to repeat all the premises and ask them to agree to the conclusion. So we operate on the premise that some things are understood. It’s an ellipses, as it were, in the argument.

Some people have charged the bible with committing logical fallacies, and what they normally have in mind are enthymemes. Perhaps they’ve run across an argument in Paul’s letters where he leaves out a premise as being understood. And they say, “Look, the bible can’t be the Word of God, there’s a logical fallacy.” And all Paul has done is written down an enthymeme. The bible is written in ordinary language. It’s not written as a logic textbook or a botany textbook or a geology textbook. It’s written in ordinary language and in ordinary language, ordinary conversation, usually the complete argument is not stated. Sometimes it is.

In one of the lectures I’ll talk about Paul’s use of logic. Particularly in Romans and 1 Corinthians he states the full argument, on several occasions; no enthymemes. But you need to be aware of the existence of enthymemes when people say the bible has logical blunders in it. Then you can say, ‘Well, perhaps its just an enthymeme that perhaps you’ve overlooked.’ That will drive them to their dictionary.

Bryan Estelle shows an example of this in Galatians 3:10-12

Paul has two arguments in these verses. His first argument is in verse 10 in the form of an abbreviated syllogism. Stated most simply, the argument of Galatians 3:10 assumes the following form:

PREMISE: Cursed is everyone who does not observe and obey all the things written in the book of the law.

CONCLUSION: All who rely on the works of the law are under a curse.

The implied reconstructed minor premise would then possibly look like this:

All who rely on the works of the law do not observe and obey all the things written in the book of the law.

Paul then goes on to make another argument in verses 11 and 12, which stated most simply assumes the following form:

MAJOR PREMISE: The one who is righteous by faith shall live (v. 11b).

MINOR PREMISE: The law is not of faith (v. 12a, reinforced by v. 12b).

CONCLUSION: No one is justified (= receives life) by law (v. 11a).

Let the reader understand the apostle’s line of reasoning here. After stating the cursed condition of every person in his first argument (v. 10), the apostle states the conclusion of his second argument first (v. 11a – “no one is justified, i.e., receives entitlement to heaven, by law”) and then asserts justification is by faith (v. 11b), and furthermore, law and faith are antithetical (read = incompatible, 3:12). The logic is lucid and insuperable: Habakkuk 2:4 and Leviticus 18:5 are “two mutually exclusive soteriological statements.”

Leviticus 18:5 and Deuteronomy 30:1-14 in Biblical Theological Development (133-4)

Much of exegesis involves reconstructing the logic implicit in Scripture, making it explicit and therefore easier to understand.

Returning to Galatians 3:10-14 that we started with, the question we are addressing is how Paul can use “the law” as a reference to the Adamic Covenant in distinction from the Old Covenant. For the sake of argument, assume that I am correct in stating that only the Adamic Covenant of Works offered eternal life upon the condition of obedience to the law, and the Mosaic Covenant blessings were limited to temporal life and blessing in Canaan upon the condition of obedience to the law. (For more on this, see here)


Paul is then appealing to the written law of the Old Covenant as representative of the law of the Covenant of Works (which was unwritten and therefore could not be quoted). In doing so, he is not claiming the Old Covenant offered eternal life. He is using the principle of works established in the Old Covenant to make a point about the obedience required from those seeking to earn by their works. A reconstruction of Paul’s enthymeme might look like:

P1 Though the rewards differ (and thus the covenants are distinct), the law was given in both the Adamic and the Old Covenants as a covenant of works (meaning they operate upon the same principle of works).

P2 I cannot quote from the Adamic Covenant because it was not written down for us.

C1 I can quote statements about the conditions of the law in the Old Covenant in order to explain the conditions of the law in the Adamic Covenant (while keeping the two covenants distinct).

P3 I can quote statements about the conditions of the law in the Old Covenant in order to explain the conditions of the law in the Adamic Covenant (while keeping the two covenants distinct).

P4 “The law” can be used as shorthand reference for the Old Covenant law principle.

C2 “The law” can be used as shorthand reference for the Adamic Covenant law principle (while keeping the two covenants distinct).

We can then unpack the logic of the verses in question to demonstrate they are not teaching that Christ earned eternal life for us through the Old Covenant.

P5 “The law” can be used as shorthand reference for Adamic Covenant law principle (while keeping the two covenants distinct).

P6 Christ redeemed us from the curse of the law by becoming a curse for us.

C3 Christ redeemed us from the curse of the Adamic Covenant (in distinction from the Old Covenant).

P7 Christ was born under the law, to redeem those who were under the law

P8 “the law” can be used as shorthand reference for the law principle found in the Adamic Covenant.

C4 Christ was born under the law principle found in the Adamic Covenant.

P9 Christ was born under the law principle found in the Adamic Covenant.

P10 The law principle itself (do this and live) can be distinguished from a specific covenant.

C5 Christ was born under the principle of “Do this and live” although he was not born under the Adamic Covenant.

Long story short, understanding Scripture requires unpacking the logic implicit in the explicit statements. The simple fact that the law often has reference to the Old Covenant does not therefore mean that Christ earned our reward via the Old Covenant. Contextual clues help us know which covenant/law Paul is referring to, such as the fact that Gentiles were never under the curse of the Old Covenant, and thus could not be redeemed from it. And of course all of this assumes a distinction between the moral law itself and the moral law as a covenant of works.

See also:

A. W. Pink the “Rationalist”

May 12, 2015 3 comments

The following quote from A.W. Pink is representative of Christianity down through the ages. Sadly, many today (even reformed) reject this view as “rationalism.”

HT: Reformedontheweb

The exposition made of any verse in Holy Writ must be in entire agreement with the Analogy of Faith, or that system of truth which God has made known unto His people. That, of course, calls for a comprehensive knowledge of the contents of the Bible—sure proof that no novice qualified to preach to or attempt to teach others. Such comprehensive knowledge can be obtained only by a systematic and constant reading of the Word itself—and only then is any man fitted to weigh the writings of others! Since all Scripture is given by inspiration of God, there are no contradictions therein; thus it obviously follows that any explanation given of a passage which clashes with the plain teaching of other verses is manifestly erroneous. In order for any interpretation to be valid, it must be in perfect keeping with the scheme of Divine Truth. One part of the Truth is mutually related to and dependent upon others, and therefore there is full accord between them. As Bengel said of the books of Scripture, “They indicate together one beautiful, harmonious and gloriously connected system of Truth.”

Arthur W. Pink-Interpretation of the Scriptures

Compare with Robert Reymond’s section on “Paradox as a Hermeneutical Category”

Let no one conclude from this rejection of paradox (as Marston has defined it) as a legitimate hermeneutical category that I am urging a Cartesian rationalism that presupposes the autonomy of human reason and freedom from divine revelation, a rationalism which asserts that it must begin with itself in the build-up of knowledge. But make no mistake: I am calling for a Christian rationalism that forthrightly affirms that the divine revelation which it gladly owns and makes the bedrock of all its intellectual efforts is internally self-consistent, that is, noncontradictory. Christians believe that their God is rational, that is, that he is logical. This means that he thinks and speaks in a way that indicates that the laws of logic—the law of identity (A is A), the law of noncontradiction (A is not non-A), and the law of excluded middle (A is either A or non-A)—are laws of thought original with and intrinsic to himself. This means that his knowledge is self-consistent. And because he is a God of truth he will not, indeed, he cannot lie (see Tit. 1:2; Heb. 6:18). Accordingly, just because God is rational, self-consistent, and always and necessarily truthful, we should assume that his inscripturated propositional revelation to us—the Holy Scripture—is of necessity also rational, self-consistent, and true. That this view of Holy Scripture is a common Christian conviction is borne out, I would suggest, in the consentient willingness by Christians everywhere to affirm that there are no contradictions in Scripture. The church worldwide has properly seen that the rational character of the one living and true God would of necessity have to be reflected in any propositional self-revelation which he determined to give to human beings, and accordingly has confessed the entire truthfulness (inerrancy) and noncontradictory character of the Word of God. Not to set the goal of quarrying from Scripture a harmonious theology devoid of paradoxes is to sound the death knell not only to systematic theology but also to all theology that would commend itself to men as the truth of the one living and rational God.

Reymond, Robert L. (1998-08-09). A New Systematic Theology of the Christian Faith: 2nd Edition – Revised and Updated (Kindle Locations 2338-2353). Thomas Nelson. Kindle Edition.

Categories: theology Tags: , ,