Testing Logical Arguments

Synoptic Problem: Markan Priority Defies Logic (Part 4/13)

Figure 1 — Flawed Logical Argument Example

It’s Not Always Easy to Spot Logical Flaws

Logical fallacies and erroneous reasoning often present themselves in more insidious ways than the simple: all cats are blue, Fluffy was a cat, therefore Fluffy was green. The example in Figure 1 above is similar, and one that I would suspect most people reading here would spot as flawed.

Often times, the flawed argument isn’t presented in such a straight forward manner. For example, one source may make the claim that the earliest extant written authorities (e.g. “Church Fathers”) all unanimously claim that Matthew was the first Gospel. A separate source may claim that outside of early Christian sources, there is no other first or second century evidence that Matthew was first. Then perhaps this person, or another source will claim that early Christian sources are prone to mistakes and often had pro-Christian agendas. Thus, when a reader comes along later and earnestly tries to put it all together, this is what they have:

1. General Premise: The earliest extant written authorities (e.g. “Church Fathers”) all unanimously claim that Matthew was the first Gospel, but
2. Observation: Outside of early Christian sources, there is no other first or second century evidence that Matthew was first, and
3. Observation: Early Christian sources are prone to mistakes and often had pro-Christian agendas, therefore
4. Conclusion (Faulty): Matthew was not the first Gospel

Again, most astute readers would not make this faulty conclusion when the argument is presented this way. Being en garde, they’d recognize this trap and avoid it. Still, these type of reasoning is pervasive because often we’re not en garde, and we have biases, agendas, etc. It’s only made worse when one hears the conclusory: Mark was the first Gospel over and over again, and it’s easy to see how the flawed logic above can seep in without our awareness.

“Valid” Arguments vs. “Sound” Arguments

It’s important to understand what we have above. Assume the first three premises (1–3) above are true as stated. This is an oversimplification, but let’s accept them as true for argument sake. This brings us to our first key lesson in testing logical reasoning: just because the premises are true, does not mean the conclusion is true. Arguments with true premises, but faulty conclusions are invalid.

Similarly, arguments with true conclusions, but faulty premises are also invalid. This leads us to one other equally important thing to point out: just because the conclusion here fails to flow logically doesn’t mean it is false either.

It is also possible for an argument to have false premises, but with a conclusion that flows logically from those premises. Such arguments are logically valid, even if untrue. For example: all cats lack DNA, Fluffy is a cat, Fluffy lacks DNA. Here, the first premise is false but the argument is valid because the premises necessitate the conclusion. The key lesson here is that logical validity does not by itself mean an argument is true. Thus, it is essential that we examine the premises of arguments lest we fall into the trap of accidentally accepting a false argument because it’s logically valid.

Lastly, we turn to arguments where the premises are true and they necessitate a conclusion that is also true. For example: all cats have DNA, Fluffy is a cat, Fluffy has DNA. This argument has true premises and the conclusion must be true if the premises are true. Arguments such as these are called sound arguments. And these are the types of arguments we are looking to make, and identify, in our analyses.

We’ll return to the actual examination of Matthew and the Church Fathers later, but there are questions we should keep in mind generally for any claims. For example, how many early sources made this claim? Who were they? How close were they to the events? What types of errors are they prone to? Is this one of those types of errors? Were there debates about priority amongst these early sources or was there consensus? Etc. So when we talk about testing logical arguments, we’re talking about examining the evidence supporting the premises and observations underlying those arguments. And then attempting to reach conclusions that flow directly (and necessarily) from those premises — or that necessarily do not.

What Does Logical Hypothesis Testing Look Like?

Our Fluffy - Photo by Daria Datipina on Unsplash

Let’s return again to Fluffy. In this new hypothetical, Fluffy is the name archaeologists have given to remains found in a first century dig site. We’re trying to answer the following question: what color was Fluffy? Let’s say there are two competing hypotheses put forth. One argues that Fluffy was green, and the other argues Fluffy was blue. Let’s test them (assume that animals can only be one color), starting with the Green team:

Green Hypothesis

1. General Premise: All animals other than cats are green. Cats are not green, and 75% of animals are not cats. (Assume we know this from our global analysis of felines and other animals, and we’ve reached evidentiary consensus on its truth. You can see how powerful this can be if it’s wrong!)
2. Observation: Fluffy was definitely an animal. (We’ve examined the evidence, including phenotypic characteristics, behavior patterns, historical records and drawings, etc. and all point to Fluffy being some kind of animal).
3. Conclusion: Fluffy was most likely green. (Given that 75% of animals are green, and the evidence shows conclusively that Fluffy is an animal, it’s likely Fluffy was green)

With our hypothetical above, it would be reasonable to conclude that Fluffy was most likely (more probable than not) green. But “most likely” is about as far as we can go, without more. It would be fallacious to conclude that Fluffy was certainly green, however. The premises above do not necessitate that conclusion, and we should be extremely careful to avoid making that leap. Recalling our earlier discussion, we’ve arrived at this conclusion abductively. That means this is the best hypothesis of the ones available to use on this data. Arguing that Fluffy was mostly likely blue, on this data alone, is logically unreasonable.

Going further, and tweaking the testing, let’s say we now have some new data from the Blue team.

Blue Hypothesis

1. General Premise: All cats are blue. (Again, this team has new data about cats that the green team didn’t have. Assume their premise is true.)
2. Observation: Fluffy was a cat. (We’ve examined all of the new evidence and it confidently points to Fluffy being a cat)
3. Conclusion: Fluffy was blue.

You can see this argument is deductive. Thus, it is necessarily and unavoidably true that Fluffy was blue if 1 and 2 above are true. And if they are true, Fluffy cannot be green and the Green Hypothesis must fail, and does. This last point is important. Prior to the success of the Blue Hypothesis, the Green Hypothesis was viable. But the validation of the Blue Hypothesis completely eliminates the Green Hypothesis from consideration (again, so long as the premises are true).

We cannot cover all possible hypotheticals for all situations here. These illustrations hopefully paint a picture of the challenges one faces when advancing arguments, and pitfalls that should be avoided. They also highlight the importance of making sure that our “observation” step(s) is as solid as possible. And it’s on that step that we’ll spend most of our remaining time going forward.

Controversial Premises Make for Poor Arguments

Before we move one, we should go over one more point. Controversial premises should be either avoided, or proven (logical proof) before being used. If we wish to rely on a logical proof for a controversial premise, it should be solid. Because invalid and unsound proofs only make one’s case worse, and damage credibility. To be clear, if one wants to be persuasive in their logical arguments, controversial general premises should be avoided at all costs. For example:

1. General Premise: Mark was written after 70 AD
2. Observation: Peter died in 68 AD
3. Conclusion: Peter couldn’t have been the source for Mark (assume, for argument’s sake, that the source had to be alive when the Gospel was written)

You might be saying, “wait a minute, how is the general premise that Mark was written after 70 AD controversial?” You might have even “learned” this. But in this example, it goes back to a logically fallacious, and thus controversial proof similar to the below:

1. General Premise: In the Synoptic Gospels, Jesus predicts the fall of the Jewish Temple in Jerusalem
2. Observation: The temple didn’t fall until 70 AD
3. Observation: Though the fulfillment of this prophecy is never explicitly mentioned in the Synoptic Gospels (or in Acts), Jesus couldn’t have predicted this and so the fulfillment is implied by the inclusion of the prediction.
4. Conclusion: The Synoptic Gospels could not have been written until 70AD or later

There are myriad things wrong with this argument, and the analysis itself is beyond the scope right now. For our purposes here, the point is that if one chooses to make arguments with premises stemming from arguments constructed this way, those arguments will be unpersuasive and will undermine credibility. Again, to be crystal clear, none of this means that the 70AD date isn’t otherwise true. And controversial arguments like these (“Mark was written after 70 AD”) are perfectly valid for, and worthy of, scholarly debate. They simply should not premise other arguments where one is trying to argue persuasively. Instead, the lion’s share of the effort should be put toward trying to gather evidence to substantiate the premises.

Up next, we’ll turn to the evidence we have available to us in our analyses (Part 5/13).