Mr Fundie and the Logic of Circles and Spirals

I was walking across campus today when I ran into a swarm of Fundie Christians (I might be getting the technical term wrong here; it could be something like plague or nest or hive--I'm really not good with the terms for groups of bugs). Their approach was to hand out pamphets bearing the cover "I used to be a drug addict" and tell passer-bys "Jesus loves you". Normally I lack the inclination to argue with these people, but their intellectually dishonest marketing (and the fact that I had time before my next class, and was not hurrying) prompted me to engage, rather than flippantly flip them off.

So I argued with Mr Fundie. Mr Fundie who used to be a drug addict and drink a lot but has been sober for five years because he found god and Jesus loves him and he loves Jesus. We went through the usual loops of illogic and fallacious reasoning, but I noticed one fallacy that I hadn't really thought about before: the confusion of circular reasoning and recursive reasoning. Unfortunately, he ignored my attempt to explain the difference (to be fair, I wasn't doing my best at explaining).

The specific form of this was Mr Fundie arguing that fossil dating using circular logic. Paraphrased somewhat, "they know how old fossils are from the layer they're in, and they know how old the layers are from where the fossils are--that's circular reasoning!" Well, no. Not at all. It's recursive reasoning.

The analogy I thought of 90 minutes too late was circles and spirals. Traversing along a circle does not approach any one point; it repeats. Traversing a spiral tends towards one point: the origin of the spiral. Circular logic is obviously the circle; it repeats the exact points ad infinitum. Recursive logic is like the spiral. There are similar points made, but they are not the same, and there is a basis for the rest of it at the origin. (Spirals could be looked at to go in the opposite direction, towards infinity, which, in this analogy, would be infinite recursion.)

Looking at the details of the logic (or lack thereof) behind both is much more enlightening that flawed analogies. Circular logic asserts the following: A is true because B. B is true because A. Therefore A ((inclusive) or B).* In symbols, B->A. A->B. Therefore, A (or B). This is blatantly invalid reasoning. It is interesting to note, however, that the premises of a circular argument form a biconditional, A<->B. The Qur'an is completely and literally true iff Allah exists. A lot of these religious arguments make equivalent statements. So by the logic of the fundie, if their god existing and their holy book having every word be literally true are equivalent, then to disprove their god, it is sufficient to show their holy book is flawed, which is usually incredibly easy to do (unfortunately, at this point, they reject their previous logic, but it's still amusing).

Recursive logic is different. We have something like the following: A1->B1. B1->A2. A2->B2. B2->A3. A3->B3. A1. Therefore, B3. We have a set of similar arguments (A1, A2 and A3, and B1, B2, and B3) that point to each other in a nonclosed manner, and a base case. Valid reasoning. A1 may be similar to A3, or a subproblem, or a different instance of the same general idea, but it's not circular.

Let us return to Mr Fundies hang up with this. For his claim to be true, scientific methods would have to be claiming something like the following: We know Fossil A is X years old because it is in Layer P. We know Layer P is X years old, because it contains Fossil A, which is X years old.* Fortunately, this is not what is being claimed.

What is being said is something more like this (with numbers pulled out of my ass for illustrative purposes). Fossil A is in Layer 0A, which we currently don't know the age of (sedimentary rock, which lends itself well to the creation of fossils, does not lend itself well to direct dating). Layer 1A, which is rock we can measure the age of, is about 4 million years old. Layer -1A, below Layer 0A, is about 5 million years old. From this we conclude Fossil A is about 4-5 million years old.

In another part of the world, we find Fossil B, which from the same species of Fossil A. As we know Fossil A is about 4-5 million years old, Fossil B much be about the same age. Fossil B is in Layer 0B. Above Layer 0B are Layers 1B, which we can't directly measure the age of, and 2B, which is about 3 million years old. As Layer 0B is about 4-5 million years old, and Layer 2B is about 3 million years old, Layer 1B is somewhere between 3 million years old and 4-5 million years old.

And so forth.

Fossils being used to show the age of geologic layers and geologic layers being used to show the age of fossils is circular logic if and only if the a fossil is being used to show the age of a layer, which is then being used to show the age of that same fossil. And even if there existed some instances of this happening, it would have to be the only method of dating used. Otherwise, the most that could be shown is that one (or more) specific instance of a dating method used on one fossil was invalid, while everything else is fine.

*Of course, circular logic can and often does involve more steps, but for the point of illustration I'm sticking with two. "A->B. B->C. C->D. D->E. E->F. F->G. G->H. H->I. I->J. J->K. K->A. Therefore A." is just as invalid, but it takes too long to write more than once.