UnApologetic

Christian Theology and Apologetics

Logic and Scripture

GamalielLogic is simply the study of appraising arguments. When someone uses logic, he is trying to clarify reasoning and separate good arguments from bad ones. We use arguments every single day, though we may not realize this; with a little introspection anyone can begin to notice how day to day deliberation often follows the rules of logic. This is true today, and it was true for folks in ancient times as well, some of these arguments were captured in the pages of the New Testament.

Luke records Gamaliel’s reasoning:

34 But a Pharisee named Gamaliel, a teacher of the Law, respected by all the people, stood up in the Council and gave orders to put the men outside for a short time.
35 And he said to them, “Men of Israel, take care what you propose to do with these men.
36 “For some time ago Theudas rose up, claiming to be somebody, and a group of about four hundred men joined up with him. But he was killed, and all who followed him were dispersed and came to nothing.
37 “After this man, Judas of Galilee rose up in the days of the census and drew away some people after him; he too perished, and all those who followed him were scattered.
38 “So in the present case, I say to you, stay away from these men and let them alone, for if this plan or action is of men, it will be overthrown;
39 but if it is of God, you will not be able to overthrow them; or else you may even be found fighting against God.” (Acts 5:34-39)
Essentially, Gamaliel’s argument was thus:
The apostles’ teaching either comes from God or is of human origin.
If it’s of human origin, then it’ll collapse of its own accord.
If it’ll collapse of its own accord and we kill the apostles, then our killings will be unnecessary.
∴ If we kill the apostles, then either our killings will be unnecessary or we will be fighting God.

Put into symbolic logic the argument looks like this:

(G v H)
((G ∙K) ⊃ F)
(H ⊃ C)
((C ∙ K) ⊃ U)
∴ (K ⊃ (U v F))

At first glance, an argument this complex can be a little intimidating; many of us are used to much simpler arguments such as the Kalam or the Moral argument which have fewer propositions and premises. With arguments this complex one needs a test to determine whether the argument is logically valid; the formal proof is one of the quickest and most effective ways to do this.

In his book “Introduction to Logic, 2nd ed.,” Harry Gensler gives a three step strategy for testing
1. Block off the conclusion and assume its contradictory. Blocking reminds us not to use the premise to derive other conclusions.
2. Go through Simplification and Inference rules until a contradiction is reached (14 contradicts15). Once a complex premise is used to derive another one make a mark to remind yourself not to use it to derive further conclusions. I’ve highlighted the used premises.3. Apply reductio ad absurdum, which is when an assumption is made that leads to a contradiction , that assumption must be false. arguments:
(G v H)
((G ∙K) ⊃ F)
(H ⊃ C)
((C ∙ K) ⊃ U)
[∴ (K ⊃ (U v F))
5. [ asm ~ (K ⊃ (U v F))
6. ∴ K [from 5]
7. ∴ ~ (U v F) [from 5]
8. ∴ ~ U [from 7]
9. ∴ ~ F [from 7]
10. ∴ ~ (G ∙ K) [from 2 and 9]
11. ∴ ~ (C ∙ K) [from 4 and 8]
12. ∴ ~ G [from 6 and 10]
13. ∴ H [from 1 and 12]
14. ∴ C [from 3 and 13]
15. ∴ ~ C from 6 and 11]
16. ∴ (K ⊃ (U v F)) [from 5; 14 contra15]
Simplification (S-rules)

(P ∙ Q) → P, Q
~(P v Q) → ~P, ~Q
~(P ⊃ Q) → P, ~Q

~ ~ P → P

(P ≣ Q) → (P ⊃ Q), (Q ⊃ P)
~(P ≣ Q) → (P v Q), ~ (P ∙ Q)
Inference (I-rules)

~(P ∙ Q), P → ~Q
~(P ∙ Q), Q → ~P

(P v Q), ~P → Q
(P v Q), ~Q → P

(P ⊃ Q), P → Q
(P ⊃ Q), ~Q → ~P

So, by using the formal proof, we’ve demonstrated that this argument put forth by Gamaliel is a logically valid airtight argument. Moreover, we know that the premises were proved true because the apostles’ teaching did not collapse of its own accord as the other teachings had; Christianity spread throughout the region and eventually the world and has survived over two thousand years of testing and hasn’t collapsed. Interestingly enough, the previous movement mentioned by Gamaliel ended at the death of the founder after his followers dispersed from the area. The difference between that movement and Christianity is simple, Theudas remained in the grave, and Christ did not, he rose from the grave and that made all the difference to his followers.

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