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Scripture and Logic - Galatians Print E-mail
Written by Oshea Davis   
Wednesday, 03 August 2016

 

Scripture and Logic: Galatians

Oshea Davis. 2016

 

 

(1.)  Eph. 6:11-13

A.A.A categorical

A note for how to find syllogisms.

Here in Ephesians when we look for a word indicator for a conclusion we see the word “therefore.” However, Paul makes this even easier in that he states the conclusion in verse 11 and then again, slightly differently in verse 13—this time with the “therefore.” Now, as with a syllogism when we have the conclusion we already have the subject of the minor premise (i.e. the second sentence) and the predicate of the major premise (first sentence). One helpful aspect to remember, is that in a logical premise for a syllogism the “literary’ subject and predicate are often flipped to how the “logical” form does it. The reason for this is that with the logical/categorical form we want the subject and predicate to reflect the logical connection of what properly belongs in a “category.” For example, I can say, My favorite two legged creatures are birds.  However, birds belong in the larger logical category of, “two legged creatures.” For this reason, in the logical form, Birds, would be the subject and, two legged animals, would be the predicate. Image a large circle with the label, “two legged creatures,” and then image a smaller circle completely within this one labeled as, “birds.” This is what we mean by categories. However, Paul already has the conclusion in the logical order and so we leave it be. Now, let us look for the middle term. This time, the middle term comes sandwiched between the repeated conclusion in verse 12. 

Ephesians 6:11-13.

(Subject) Put on the whole armor of God, that you may be able to (Predicate) stand against the wiles of the devil.

(middle) For we do not wrestle against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this age, against spiritual hosts of wickedness in the heavenly places.

 Therefore; (S) take up the whole armor of God, that you may be able to (P) withstand in the evil day, and having done all, to stand.

 

This is an (A,A,A) (All S is P) syllogism. The Major Premise, is Middle Term, then the Predicate; the Minor Premise, is Subject then Middle term. And of course, the Conclusion is the Subject of the Minor p. and the Predicate of the Major p.

Major P. (Those who fight/wrestle against rulers of darkness) are (Those that are able to stand against the attacks of Darkness.)

Minor P. (Christians who put on the whole armor of God) are (those who fight/wrestle against the rulers of Darkness.)

Therefore, (Christians who put on the whole armor of God) are (Those that are able to stand against the attacks of Darkness.)

 (2.)  Gal. 1:10

 Denying the Consequent  &  affirming the Antecedent.

Galatians 1:10 (NKJV). Do I seek to please men? For if I still pleased men,[then] I would not be a bondservant of Christ….

& 4:17, “they zealously court you …that you may be zealous for them.”-- i.e. men pleasers. They seek to please men so that in return men will seek them and fill their egos and bellies.

 

This is a logical enthymeme that is not really an enthymeme. What I mean is [1]that this Denying the Consequent is missing the last half. However, the actual “denying the consequent” as it relates to “Paul,” which is missing in the immediate context, is already given to us in the first verse of Galatians. (1:1(LEB)), “Paul, an apostle not from men nor by men but through Jesus Christ.” We learn Paul is a servant of God, whom God sent out to preach to the gentiles. Thus, we know the “hypothetical aspect” for Paul, “I would not be a slave of Christ,” is not true for Paul by the authority of Scripture, for he is. Why does Paul write this way? When Paul askes, “Do I seek to please men?” It is asked in a literally way of writing an obvious declarative sentence in the form of a question. The hypothetical syllogism is asked, “if ….then,” about himself in a similar way, and it is done to make a nifty way to contrast himself to the false teachers. It is false for himself, but affirmative for the false teachers. By this knowledge now have a complete hypothetical syllogism.

In logic we need to define our terms. How does Paul define what a “servant” is? Paul is connecting “pleasing” to how a servant serves: they serve their masters by seeking to please them. False teachers seek to please men, but Paul seeks to please God his Father.

Also, the context of Paul's point “that men pleasers do not serve God,” is already an established truth given by his own letter to the Galatians and also by systematic theology from Scripture. By this the conclusion is sound. This makes syllogisms a little different for Christians, for in Scripture we have an endless supply of true propositions. For example, sometimes a scientist might try to put his “effect to cause” logic—which is affirming the consequent (invalid)—into an affirming the antecedent syllogism (valid) to mask the illogical effect to cause reasoning. However, if Scripture gives us an effect to cause declaration then it is truth; we know there is real effect to cause correlation, not because of experimentation, but because of revelation. “A tree is known by its fruits…out of the abundance of the heart the mouth speaks.”  At any rate, the gospel Paul preached is one commanded to him to preach by God; Paul seeks to please God and so he preaches this gospel. The contrast is that men pleasers, because they serve men/themselves, will preach a different gospel than the one Paul has preached, and they are accursed (Gala.1:8-9).

(P) If I were still trying to please people, (~Q) then I would not be a servant of Christ.
~(~Q) I am a servant of Christ, ~(P) therefore, I am not trying to please people.

The implication is that you are either with Christ or against Him. You cannot serve two masters. Romans 16:18, “For those who are such do not serve our Lord Jesus Christ, but their own belly.” They serve they bellies by seeking to please men, so that men will enrich them. You can be double agent; but you cannot serve two masters as both your final authority.

In context of Galatians, Paul is contrasting himself with the false teachers he is addressing. In fact, this same hypothetical syllogism may now be wittily used as “affirming” the hypothetical syllogism as against the false teachers. The missing enthymeme comes in chapter 4, “they zealously court you …that you may be zealous for them.” They are men pleasers, and thus, with this information we “affirm” this hypothetical syllogism (affirming the antecedent ).

(P)If they are trying to please men, (~Q) then they are not servants of Christ.

(P) (4:16) They are trying to please men, therefore, (~Q) they are not servants of Christ."

As for Paul, he gives proof of his servant-hood of Christ: by the Scriptures infallible testimony about Paul. And so, for him this then turns into denying the consequent.


 

(3.) Gal. 3:6-9

Compound A.A.A. Categorical Syllogisms.

Galatians 3:6-9, NJKV

Just as Abraham "believed God, and it was accounted to him for righteousness."

Therefore know that only those who are of faith are sons of Abraham.

  And the Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel to Abraham beforehand, saying, "In you all the nations shall be blessed."

  So then those who are of faith are blessed with believing Abraham.

Here we have a simple categorical syllogism. In fact, we have two of them. Paul in a nifty way lines up the conclusion of the first syllogism, for the first premise of the second syllogism. This would be a compound syllogism. Literal translations like the NJKV already have both conclusions in categorical (these are those) form;  however, the order of the subject and predicate need to be flipped to insure correct categorical form. This is made more obvious in the NJKV when it says in verse 7 that “only,” those. In categorical form this is a giveaway. For example, to say “only squares are four-sided figures,” means categorically that: “All four-sided figures are squares.” (Therefore, all those are in this category. All S is the category of P.)

When we are given a conclusion we already have the subject of the minor premise and the predicate of the major. The middle term for the first premise is simply a direct quote from the Old Testament. With this we have a complete syllogism. Paul makes this easy by giving us the middle term for second syllogism in the subject of the conclusion of the of the first syllogism. The 8th verse is a quote from the O.T. to give evidence or justification for the predicate of the conclusion in the 9th verse.  Paul will often do this. He will give warrant for why this proposition or use of a term is true with a quote from the Old Testament. He might put both the middle term and a justification for it together in a long sentence. Both syllogisms are an enthymeme where the middle term is given first and then the conclusion follows.  They are a compound syllogism in that the conclusion of the first, is the first premise of the second. The obviousness of this comes in the evidence once the flip the subject and predicate of the second conclusion the predicate of the conclusion fits perfectly in to the order of the first premise given by the conclusion of the first. 

It seems Paul design was to lead his Galatian audience to consider what it means to, or how will they have the same “blessing” that Abraham partook. Paul agrees with the Galatians that there is a real inheritance, prosperity and glory to reach for and acquire for oneself.  He proceeds to inform them that this is found in Abraham’s blessing. However, to lay hold of this inheritance one needs the righteousness of God. Now the question is, how does one become the righteousness of God? This righteousness is found by faith in God through his victorious Son Jesus Christ.  The two following syllogisms were then constructed, it seems from a purpose perspective, to show the Galatians how to receive and drink in that same blessing. 

 

First. (.7)

Major P: (Those who are like Abraham—being made righteous by God in faith and not by works) are (those who are of faith).

Minor P: (Sons of Abraham) are (those who are like Abraham—being made righteous by God in faith and not by works).

Therefore: (Sons of Abraham) are (those who are of faith).

 

Second. (v.9)

Major P: (Sons of Abraham) are (those who are of faith).

Minor P: (Those blessed together with Abraham--who believed) are (Sons of Abraham).

Therefore: (Those blessed together with Abraham--who believed) are (those who are of faith)

 

 

(4.) Gal. 3:18

Denying the Consequent

Galatians 3:18, “For if the inheritance is of the law, [then] it is no longer of promise; but God gave it to Abraham by promise.”

Paul actually does a complete hypothetical syllogism in this verse. The only missing part is the actual conclusion which is automatically given when the consequent it denied in the verse. In context of the verse either the antecedent(which would be invalid) or the consequent could possibly be denied. Paul, this time does not give us an enthymeme but directly denies the consequent.

Not only is this a denying the consequent but Paul is also appealing to the law of non-contradiction as a contrast between the P and Q with the understanding that the law and promise cannot both acquire the same goal because they are contraries to one another. By this Paul’s conclusion is made more obvious. This also shows us how to use a contradiction or more directly a contrariety in the form of deny the consequent. Since the truth of the one means the falsity of the other then we state the one we wish to affirm in the (Q) position as false; and the false statement we place in the (P) position as a truth. Then we affirm the truth of Q by denying the false statement about it, and thus it will deny the other.

(P) For if the inheritance is of the law; (~Q) then the inheritance is no longer of promise.

~(~Q) God gave the inheritance to Abraham as a promise. ~(P) Therefore, the inheritance is not of the law.

 

(5.) Gal. 3:29

Affirming the Antecedent. # 2

Galatians 3:29, “And if you are Christ's, then you are Abraham's seed, and heirs according to the promise.”

The last part of the verse, “and heirs according to the promise,” has already been established as a point previously by Paul in verse 6-14.  That is, Abraham’s seed receives Abraham’s promised blessing. With this point already made it is best to continue the flow of logic with an obvious affirmative hypothetical.

The structure of having the conclusion of one affirming the antecedent being the first premise of one following it is able to have a similar logical effect of a simply categorical or longer sorites syllogism. 

 

(P) If you are Christ’s, (Q) Then you are Abraham’s seed.

(P) You are Christ’s. (Q) Therefore, you are Abraham’s seed.

And

(P) If you are Abraham’s seed. (Q) Then you are heirs of the blessing according to the promise.

(P) You are Abraham’s seed. (Q) Therefore, you are heirs of blessing according to the promise.

 

(6.) Gal. 4:4-7

A.A.A. Categorical syllogism & Affirming the Antecedent.

Galatians 4:4-7

But when the fullness of the time had come, God sent forth His Son, born of a woman, born under the law,

to redeem those who were under the law, that we might receive the adoption as sons.

And because you are sons, God has sent forth the Spirit of His Son into your hearts, crying out, "Abba, Father!"

Therefore, you are no longer a slave but a son,

and if a son, then an heir of God through Christ.

The conclusion is obvious. The only adjustment is the rearranging of the proper subject and predicate for correct categorical order.  The middle term is the long explanation right before the conclusion. For Paul these might be a mixture of middle term and evidence/explanation of the middle term.  I prefer for to just keep it a little wordy and put it all in for the middle term, unless it takes away from the obviousness of the category. 

First.

Major P: (Those who God has sent His Son to redeem from under the law to receive adoption and who God’s Spirit causes their hearts to cry out Father) are (no longer slaves.)

Minor P: (Those who are sons) are (those God has sent His Son to redeem from under the law to receive adoption and who God’s Spirit causes their hearts to cry out Father).

Therefore, (those who are sons) are (no longer a slaves)[1]

Second.

(P) If you are a son, (Q) then you are an heir of God through Christ.

(P) You are a son. (Q) Thus, you are an heir of God through Christ.

 

 (7.) Gal. 4:28-31

A.A.A. Categorical syllogism.

Galatians 4:28–31 (LEB)

28 But you, brothers, are children of the promise, just as Isaac. 29 But just as at that time the child born according to human descent persecuted the child born according to the Spirit, so also now. 30 But what does the scripture say? “Drive out the female slave and her son, for the son of the female slave will never inherit with the son” of the free woman.

31 Therefore, brothers, we are not children of the female slave but of the free woman.

The conclusion is obvious. Now, with the conclusion we already have the subject and predicate.  The only adjustment is the rearranging of the proper subject and predicate for correct categorical order.  Also, I substituted, “brothers” for “presently children of God.” The middle term is found in the first verse, and then next two verses are a defense for the middle term (verses 29-30).

Major: (Those who are children of the promise and blessing, just as Isaac was), are (presently children of God.)

Minor: (Those who are not children of the female slave (law), but of the free woman (promise)), are (children of the promise and blessing, just as Isaac was).

Therefore: (Those who are not children of the female slave (law), but of the free woman(promise)) are (presently children of God.)

 

 

(8.) Gal. 5:1

A.A.A. Categorical syllogism.

Galatians 5:1 (LEB)

For freedom Christ has set us free. Stand firm, therefore, and do not be subject again to a yoke of slavery.”

 

In this simple categorical syllogism, the conclusion is made known by this typical “therefore,” except this time because of a literacy device, the “therefore,” is placed in the middle of the sentence. In addition, the subject of the conclusion is a silent understood “you.” “Therefore, “you” stand firm and do not place yourself under slavery.” With this completed conclusion we have our subject of the minor premise, and we have the predicate of the major. The middle is conveniently given to us in a short sentence right before the conclusion.  Also for clarification I added the phrase “in the category of,” in the minor premise. Hint. This can sometimes help when doing, categorical syllogisms.

 

Major P: (The church whom Christ has set free, to be free) are (those who stand firm and do not subject themselves to slavery).

Minor P: (You, oh Christian) are (in the category of, the church whom Christ as set free, to be free.)

Therefore: (You oh Christian) are (to stand firm and do not subject yourself to slavery). 

 

(9.) Gal. 5:25

Affirming the Antecedent.

Galatians 5:25 (LEB)

If we live by the Spirit, we must also follow the Spirit.”

Here we have a simple hypothetical syllogism, affirming the antecedent.  If P, then Q. P, therefore, Q.

 

(P) If we live by the Spirit, (Q) then we must also follow the Spirit.

(P) We do live by the Spirit. (Q) Therefore, we must also follow the Spirit.

 

 

(10.) Gal. 6:8-10

Affirming the Antecedent & A.A.A. Categorical syllogism.

Galatians 6:8–10 (LEB)

The one who sows to the Spirit will reap eternal life from the Spirit. And let us not grow weary in doing good, for at the proper time we will reap, if we* do not give up.

So then, as we have opportunity, let us do good to all people, and especially to those who belong to the household of faith.

 

The conclusion starts with “so then. The subject for this is found in the “we” and “us.” There are many names for God’s chosen people given in Scripture, however, when choosing a particular one for a syllogism we want to find one that is most closely related to the context. Here they are called the “household of faith.” And so, this becomes our subject. This puts the sentence into categorical form. Also, the middle term it is found verse 9. Now we have a syllogism.

Did you notice? There is a hypothetical syllogism in verse 9, which is actually at the same time the middle term for our categorical syllogism. This is an Affirming the Antecedent. The order of the “if … then” is backwards as it is found in its literary form.  All we need to do is put it back in logical order.

 

Affirming the Antecedent.

(P) If we do not give up, (Q) then we will reap the good we have sown(ing).

(P) We are not giving up, (Q) therefore, we will reap the good we have sown(ing).

 

Categorical

Major P: (Those who are sowing good and who will reap good) are (those who use opportunity to do good, particularly to the household of faith).

Minor P: (Those of the household of faith) are (Those who are sowing good and who will reap good).

Therefore: (Those of the household of faith) are (those who use opportunity to do good, particularly to the household of faith).

 

(11.)  Gal. 6:6-8

A.A.A. Categorical Syllogism.

Galatians 6:6–8 (LEB)

Now the one who is taught the word must share in all good things with the one who teaches. 7 Do not be deceived: God is not to be mocked, for whatever a person sows, this he will also reap, 8 because the one who sows to his own flesh will reap corruption from the flesh, but the one who sows to the Spirit will reap eternal life from the Spirit.

The conclusion on this one is a little more difficult to find without the typical, therefore, so then/that, (etc.). However, the word, “for” as in verse 7 can be, as in this case, is an indicator of a premise that supports a conclusion. In this case, it is an indicator for the middle term that belongs to a syllogism. The way verse 7 starts with, “Do not be deceived,” is written so that it carries a “therefore,” force to it. In other words, it is just a more interesting way to say, therefore. Now, we need the subject for the conclusion which his simply the implied subject of God Himself. And more particular it is about God the judge, and so we will word the syllogism from this relative viewpoint. We now have a completed conclusion, and we also already know the middle term.

 

Major P: (He who insures mankind will reap what they sow) is (He who will not be mocked).

Minor P: (God who is Judge over all things) is (He who insures mankind will reap what they sow).

Therefore: (God who is Judge over all things) is (He who will not be mocked).



[1] i.e. in a positive affirmation a more precise way to say the predicate would be non-slaves. And so, it is fine to say it as I did above as long as it is clear that it is a positive affirmation (S is non-P) and not “No S is P.” Euler circles makes this distinction clear. 

 
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