This is the first of a series of posts I will publish to aid you in understanding logic and prepare you to “argue biblically.’
In order to have a rational discussion or debate, you must be willing to agree to a certain set of ground rules, i.e., rules of engagement. This is self-evident; it’s why we have rules in sports. Football would be really unfair if the home team always got 6 points for field goals but the away team only got 3, wouldn’t it?
There exist several basic rules of logic that we must be able to agree upon in order to draw logical conclusions to our axioms or assumptions. Logic doesn’t determine truth, nor does it prove that something is true. Logic will be able to show you that which rationally can be deduced from a set of axioms, or starting points. For example, I hope we can all agree that the following is a “logically sound” argument.
If all cars are green and
my friend bought a car today
I can logically conclude, based on the assumptions made, that my friend’s car is green.
Notice that there is no actual validation that the statements are true, just that the conclusion logically follows from the assumption (all cars are green) and the facts delivered (car was purchased).
This article is intended to provide a brief overview of some rules of logic we should all follow when trying to discuss theology. I hope to provide you with enough information to help you to better discern when you are hearing a logical fallacy, and how to adequately contend for the faith once delivered unto the saints. Hopefully, when you are discussing these things with atheists, Catholics, Muslims, Jehovah’s Witnesses, Mormons, evolutionists or a member of any other cult or false religion you will be able to see if they agree to these rules of logic. If they will not, again, this would be like playing a game with them where you each had different rules for scoring.
First let’s define some terms.
1. Assumptions. Assumptions cannot be proven. There are two things that can happen when you make an assumption and follow it logically, you will either prove it to be utterly false, or you will show that it is consistent with other known facts and with itself. The assumption made in the sample above was “all cars are green.” We will be delving further into these ideas herein.
2. Axioms are like assumptions, except that to call something axiomatic ascribes to it a much greater assumption of truth. Assumptions can be tossed around and changed “for the sake of argument.” When something is referred to as axiomatic, it implies a self-evident idea with no need for proof. Axioms are ideas which, if they were not true, would completely unravel the way we see the world, or a particular problem. Axioms are “synonymous” or “equal” to many of their conclusions, in that, without one, the other could not be true and vice versa.
A great example of this is the assumption that a triangle’s internal angles will always add up to 180 degrees. I bet many of my readers did not know that this is an assumption, or rather, an axiom to what is referred to as Euclidean Geometry (what most people learn as geometry in school). But every mathematical proof that relies on this to be true cannot be proved otherwise. What I am saying is that often when we prove something in geometry, what we’ve done is show that based on the assumption that a triangle’s internal angles add up to 180 degrees, the following is true. There are valid mathematical models that deny this axiom! If this interests you, then you are a nerd. Welcome to the club.
The point is that we can modify assumptions and axioms and arrive at different, logically valid conclusions than we arrived at before denying an axiom or assumption. Most axioms are not argued, but ought to be questioned and should stand up to logical scrutiny.
3. Facts. Facts are things we know to be true, or rather, that which we perceive we can trust. Facts can be questioned though, and can be shown to truly be assumptions. What this means is that some things that people will promote as a fact are, in fact, assumptions! The fact that my friend bought a car in the example above is an example of a fact. Axioms are not facts in the sense that they are unobservable phenomena, whereas facts are observable. Axioms are abstract; facts are “material,” if you will. Facts do not change based on a change in assumptions. For example, a fossil of a dinosaur is still the same size, texture, temperature and weight, was still found in the same location next to the same other artifacts, regardless of whether you assume the world is millions of years old or thousands.
4. Conclusions. Conclusions are all the ideas that logically follow from the facts and assumptions. I can “conclude” that my friend’s car is green based on the fact and assumption provided. A conclusion’s validity is based on whether it logically follows from the facts and assumptions. A conclusion’s truthfulness is based on whether the facts and assumptions are true. Some types of conclusions are deductions, inferences and implications.
You will notice that logic is, itself, axiomatic.
We are assuming these definitions and rules of logic, and that’s OK. We can assume them all we want as long as everyone agrees to them and they don’t lead to contradiction or absurdity. Logic is axiomatic in that, we all accept it as fact or the way it is, but cannot prove it. If we could prove it, then we’d have to accept that which we relied upon to prove it as axiomatic until it could be proved…do you see now? We must appeal to an ultimate set of rules at some point axiomatically and trust that they are “true.” If we do not, then we are assuming an infinite number of iterations of “new axioms to prove” anyway, which is ultimately the same thing…reliance on unprovable axioms. It’s OK. If logic exists it must be true, and the effects of it will be consistent with the very rules we are following. It’s why we trust it so innately, and why so many people with different viewpoints on certain issues still generally agree to logic rules when it comes to debate.