Logic

My wife knows when I want to eat. When she says, “I bet you want something to eat,” I don’t wonder if she has some weird link to my hypothalamus. She has reasoned. She bases this on many things that she knows about me. Among those things: 1) When I don’t eat for a while, I get hungry; 2) I hate bananas.

—Logically:

Premise 1: He wants to eat something when he doesn’t eat for several hours.
Premise 2: He hasn’t eaten for several hours.
Conclusion: He wants to eat something.

—And:

Premise 1: He does not like to eat things that have bananas.
Premise 2: This item has bananas.
Conclusion: He will not want to eat this item.

What, then, would my wife say if I have not eaten for 10 hours and there is only banana cake? If I am hungry enough, perhaps I will eat even the dreaded banana. Would that mean that the second principle and syllogism are false? No, they are still true, but in a relative sense. I don’t like bananas—generally. In fact, both conditions (“time since eating” and “amount of banana”) may be true to a greater or lesser extent.These conditions vary independently. They each may vary alone, together, or in opposite ways. I might have eaten minutes ago or days ago, regardless of whether the item I am offered is banana-free or 5 percent or 50 percent banana.

Neither of these principles is presented with the other as an exception. For instance, the second argument did not read:

Premise 1: He does not like to eat things that have bananas unless he is hungry.
Premise 2: This item has bananas.
Conclusion: He will not want to eat this item unless he is hungry.
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Here is a thought experiment. Imagine that you are given access to a banking machine, and told that you may withdraw in one transaction up to 500,000 dollars. You are also permitted to make subsequent withdrawals, but no withdrawal can amount to more than half of the previous withdrawal. How many withdrawals will you have to make before you have a million dollars?

The answer is that you will never reach a million—quite. Enough withdrawals, however, will bring you to within a penny of a million. If it were possible to split a penny, you could get within half-a-cent, then a quarter‐cent, and so forth. Given an infinite number of withdrawals, you could arrive at an amount that was so close to the million that no human could measure the difference. You would never get to the full million dollars, but the difference would be infinitesimal. You could approach the million asymptotically.

I have argued that necessary inferences (conclusions) drawn from Scripture are just as authoritative as the direct statements of the Bible. Necessary inferences are those that are drawn deductively through valid syllogisms. Since these inferences are drawn from true premises (what else could Scriptural premises be?), they are necessarily true, and consequently, they are necessarily authoritative.

Inferences that are reached inductively are not necessary, but merely probable. I have suggested that such inferences should be pressed no more vigorously than their probability warrants. Generally, this means that they need to be held and advocated with greater caution than necessary inferences.

Probability, however, comes in degrees. As the degree of probability increases, uncertainty over the soundness of an inference has to decrease correspondingly. At the upper end of the scale, probability may become so strong as to constitute virtual certainty.
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In Part One, I discussed Paul’s view of logic and its relation to the Word and doctrine. Paul viewed logical conclusions as fallible and submissive to the Word. Even so, Paul greatly respected logical thought. In Parts Two and Three, I want to look at a few ways Paul actually used logic.

Paul made great use of logic in his epistles. His logical thought is seen in his constant use of connecting words like “for,” “because,” “therefore,” etc.

Paul used “gar” 433 times. Gar is usually translated “for.” It is usually a conclusive term which introduces the reason for the statement that precedes it. He ate the bread for (because) he was hungry.

Paul used “oun” 116 times. Oun is usually translated “therefore.”

The second Scripture source in Part One involved Paul’s view of logizomai/logismos. Paul used logizomai 42 times (out of a total 49 in the NT), logismos (reasonable) twice (no one else uses this word).

Logizomai:

In class[ical] literature, logizomai means to “deliberate, to conclude.” Esp. in Plato it is the typical term for the non-emotional thinking of the philosopher seeking suprapersonal knowledge, in this case, the receptive apprehension of something objectively present. (Theological Dictionary of the New Testament, Kittel.)

Hence, logizomai means: (a) reckon, credit, rank with, calculate; (b) consider, deliberate, grasp, draw a logical conclusion, decide. (J. Eichler, The New International Dictionary of New Testament Theology.)

This word was used in both accounting and philosophy. That mix of ideas suggests reasoning viewed as a logical-mathematical endeavor.
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The writer to the Hebrews was distressed by the spiritual immaturity of his readers. He wanted to discuss theology with them—specifically, the calling of Christ as a high priest after the order of Melchizedek (Heb. 5:10‐14). He made it clear that the Hebrews had been saved long enough (“when for the time”) that they ought to have mastered this topic (“ye ought to be teachers”). Instead, he had to rehearse certain elementary teachings of biblical doctrine (“the first principles of the oracles of God”).

The writer’s disappointment with the immaturity of the Hebrew believers was what fueled the warning passage of chapter 6. Not until 7 did he return to the theme that Christ is a high priest after the order of Melchizedek. When he finally got back to it, however, he penned one of the most difficult and detailed arguments in all of Scripture. This argument is highly instructive in three ways. First, it is useful because of what it teaches about Christ’s high priesthood. Second, it is useful because it shows exactly how the writer arrived at his conclusions. Third, it is useful because the writer explicitly demonstrated (in Heb. 7) the very thing that he had already said the readers ought to have done for themselves (in Heb. 5:10‐14).

In other words, whatever methods are used in Hebrews 7:1‐28 are methods that any mature believer ought to master. Any conclusions that are drawn in Hebrews 7:1‐28 are conclusions that any mature believer ought to be able to draw. The writer himself rested the authority of chapter 7, not on its inspiration, but on the correctness of the inferences that he was able to draw from Scripture. He thought that his readers should have drawn them without his having to show them how.
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