Logic and Logicians: A Few Things to Know Before Jumping In

Logicians are funny people. Many have Ph.D.'s in mathematics, and this both serves them well in some ways, and harms them in others. Some have dual degrees, perhaps one of them taken in the sciences. It is interesting to note -- and a man named Thomas Kuhn DID note this about scientists (and I will extrapolate his claims to include logicians) -- that the kind of logic they prefer, and the way they go about critiquing the works of others, depends a great deal on the formal training they have received.

I say this not because it is something brand new to say, but because it carries a truth so important that it bears repeating. Learning logic is learning the systems of logic so far produced. And these vary one from another in their most basic axiom sets or assumptions about what kind of world this is, how we know what we know, and how we should live our lives. Logicians, believe it or not, even have political views -- some vote democrat.

This means that when you learn logic, one must take care to watch just what he is learning and ask, "That's nice Gottlob, but is your system of mathematical logic BIBLICAL?" How many students today think that a system of logic developed by pagans will -- by valid inferences --imply all the truths of the Bible -- raise your hand please? NO hands? So far so good.

Logic can tell you which conclusions follow from which beginnings by logical necessity. It cannot tell you what sorts of things to believe in the beginning. The Bible can. Only by beginning with the whole of the Bible as a set of ONLY and ALL true premisses, can one reason in a way that has valid and SOUND conclusions only.

A sound argument has only true premisses and its conclusions follow in a "straight line" (called "validity") from its premisses. An argument may be valid, but not sound. In any theoretical or logical system (for that matter any ideology), one cannot validly deduce MORE propositional content than that which already exists in the premisses or axioms to begin with.

This is Van Til 101 applied to the study of Logic.

This means, "Go ahead and learn the subject of logic, but keep one eye open the entire time, and with your learning retain a healthy measure of skepticism about the axioms chosen at the outset, not only for what textbooks include, but also what they leave out. Keep your eye on the Bible, because there is a whole lot of ax grinding going on in any textbook written by those with no respect for the Word of God.

Questions For Today:

1. How might the political views of logicians affect the way they think about logic?

[one possible answer: The material a logician chooses to critique as an example might come from a political argument offered from a political position he does not like. While fewer critiqued examples may come from the party he particularly likes. Rarely will a man take potshots at his own team. This will -- as much by omission as not -- leave students with the impression that **his** political party has the better platform. Go team.]

2. What is logic, and what does it have to do with the Bible?

[One possible answer: Whatever the Bible suggests (implies) is true is as much the Word of God as what it says outright (explicitly). This is why Christians believe in the doctrine of the Holy Trinity. There is no ONE passage which commands us to believe this doctrine. We infer it from many and various passages scattered throughout the Bible.

This means God expects men and women to reason from His Word, and to reach only valid and sound conclusions. Jesus and the apostles did this often. And we must follow their example.]

3. Are the axioms logicians choose to start off their systems of reasoning chosen from the Bible carefully? How does this affect their own views? What does it SHOW about their outlook on life?

Answer: Not on your life. Most logicians, like most other professors in the academic arena show a marked dislike of what the Bible teaches. Some textbooks even purport to show errors in the Bible itself. This means that they choose axioms without the least concern of whether or not these mesh with what the Word of God says, or else enjoy showing students how to rebel against its teachings.

4. If a logician chooses a passage from the Bible and critiques it, finding some fault with it, what does this tell you about the logician's own reasoning?

Answer: his reasoning is hostile in principle to the Word of God. This means he will necessarily be incorrect at various points in his arguments, no matter how intelligent he may be. It also means students must be on the guard to critique from the word all they are told to the best of their (developing) abilities. On this blog, I will occasionally offer the challenges of logicians and others to the Word and give them a significant dose of their own medicine.

5. Logicians are trained using textbooks not written by Christians. How will this affect the axioms they pick to start off the reasoning process?

Answer: Thomas Kuhn -- I'll be mentioning him later in a separate post (if the Lord wills) -- has answered this one for us. One's academic training sets the pace for, not only the value system that blossoming scholars tend to adopt, but for their picture of the world as well. Their textbooks will tend to bias them against the Word of God over time, as they get more consistent -- as logicians are wont to do -- with their non-Christian textbooks and counter-biblical axioms (or even simply non-biblical axioms).

The Bible construes what is not warranted by the Bible as the same as that which is hostile to the Bible in principle, though perhaps not in attitude or tone. Jesus said "Whoever is not for me is against me, and he who does not gather with me scatters." This means neutrality in matters of covenants -- and I will later show (if the Lord wills) that logic is clearly a covenantal matter -- is not only undesirable -- it is impossible.

God is gracious and does not require us to know it all at once, but gives us time to work out from his Word what are our duties and privileges so that we can glorify him by learning what the Bible implies over time. Logic is necessary for working out your salvation with fear, trembling and consistency. For God is not a God of disorder, but of peace.