Structure and Logic

21 Jul

I always wondered how the Problem Solution Consequences structure matches with logic. The reason is that, at first sight, it doesn’t really seem to align. What you would expect is that the case you are making, ie the solution, would be the conclusion of your meta-argument, with your arguments being the premises that, when true, necessarily lead to your solution being true. There are two problems with that. The first is that while premises in the logical structure work closely together, are even dependent on each other. Consequences appear to be independent of each other. You can have positive and negative consequences and still feel the solution is “true”. I say “true”, because the second problem is that there isn’t really a necessary truth coming from consequences, or at least not one that is obvious. Most policy solutions have positive and negative consequences. They also often have nuances and other difficulties that don’t really seem to sit well with formal logic. And then I haven’t even discusses the role of ‘the problem’ in this structure yet. Well, in this post I will try to tackle all three issues and try to marry the powerful PSC structure with formal logic.

Working together: If we look at the traditional logical argument example: C: Aristotle is mortal, P1:  Aristotle is a man, P2: All men are mortal. Then what we are looking at is what I would like to call sequential argumentation. What we do in sequential argumentation is to build a logical pyramid that supports the conclusion. First you have your conclusion, which is supported by premises, then you support these premises by further premises, etc. This pyramid is on the one hand very strong, but also very unstable. It is very strong, because the conclusion can be based on a very deep argumentation line, giving it argumentative strength. All the sub-sub-sub premises work together to ultimately support the main conclusion. However, if you can show that one of the premises, or one of its sub-sub premises is false, then the whole argumentative pyramid falls as a house of cards. The reason is that in this case if one of the premises is false, necessarily the conclusion must be false also. For example, suppose we support P1: Aristotle is a man, by arguing that “Man by definition is a rational creature” and “Aristotle is rational”. Now suppose someone could somehow show us that Aristotle isn’t rational, then by this logical pyramid, he isn’t a man and therefore isn’t mortal. Thus the conclusion is false, or at least the conclusion isn’t necessarily true.

This is for example how skeptics in philosophy deny us access to an objective truth. They go down the argumentative pyramid deep enough to find a premise that we cannot know for sure and therefor say we cannot say a certain claim is necessarily true.

There is, fortunately, a way of arguing, that (at least in real life) will prevent the weakness of the sequential argument. This I would call parallel argumentation. It is best explained with an example. Suppose I want to argue the conclusion that C: I wasn’t at the Zoo yesterday. I could support that by saying: P1: I don’t like going to the zoo, or P2: The Zoo was closed yesterday, or P3: I was abroad yesterday, or P4: I’m forbidden from going to the Zoo. Now some of these premises aren’t that strong, others are, but the good thing is, that even if one of the premises is proven false, the other premises are still valid and independently are able to support the conclusion. Even if only P3 is true, then it still necessarily follows that the conclusion is true.

Now the observant reader will have noticed that I left out all the hidden premises. If we would add those hidden premises (try it for yourself), then you would see that all the premises are actually different arguments that share the same conclusion. So what happens is that instead of having one argumentative pyramid, you now have several. If you collapse one of the pyramids, then the others are still standing strong, making it much more difficult to show that your conclusion is false. Parallel and sequential argumentation or not mutually exclusive. Each parallel argument is ultimately in itself a sequential argument, or could have parallel sub argumentation contained, which then ultimately lead to sequential sub-argumentation. This way we can build lovely intricate and complex arguments. Which we don’t have time for in an actual debate anyway, but it’s good to know. The reason parallel argumentation is so difficult to refute is why in debating you should always aim for parallel argumentation. That way, if your opponent disproves one of your arguments, your whole case doesn’t fall apart.

There is a school of thought in modern debating that says that one beautifully thought out sequential argument is more convincing than three superficial parallel arguments (given time restraints, you need to choose between width and depth). I agree to some extent, but it carries a big risk. It makes refutation much easier than in the case of parallel argumentation. So unless you are very confident about that single argument, I wouldn’t go for it. And it’s definitely not suitable for the beginner.

Necessary truth?: So how do consequences lead to the necessary, or at least the likely truth of your solution? The problem is that consequences do not have your solution as their conclusion. Take the case: “The death penalty should be abolished”. One of the consequences of the death penalty is that invariably an innocent person will be sentenced to die. In that argument the solution is not the conclusion of your argument. The conclusion of your argument/consequence is the consequence itself: “Invariably an innocent person will be sentenced to die if the death penalty is in force”, the premises support that the consequence exists. So in order for parallel argumentation to support your solution, we need a level of argumentation between the solution and the consequences. There is an implicit argument that does this: C: we should implement this solution, P1-5: there are positive consequences (1-5), P6: whichever solution has the most positive consequences should be implemented. Or alternatively, P6 :  whichever solution for which the positive consequences outweigh the negative consequences should be implemented. Potentially this could lead to a whole new level of argumentation that the opponent could challenge. Fortunately P6 is so ingrained in our thinking (it makes sense after all) that it is almost never challenged. That is why the Problem, Solution, Consequences structure is so powerful. It is based on a generally accepted meta-structure and forces you to use parallel argumentation.

Problem: But how about the problem. How does that fit into all of this. Well it fits into the debate in two ways. The removal of your problem is going to be the biggest consequence in your case. But that doesn’t explain why we mention it before the solution. The second reason does that and this second reason is that the problem also serves to justify the relevance of the debate. This is however technically a different debate. You can accept the solution as being true, but still consider it an irrelevant topic to discuss. So in that sense the problem, logically, is not part of your structure. It has no function, other than convincing your audience that this is an important subject to discuss. The PMC structure thus gives you two conclusions: 1) this solution is worthy of debate, 2) the solution should be implemented. Therefore my suggestion in previous posts that you should never spend too much time on the problem. Its only use is to get people’s attention. The moment you’ve gotten that, move on.

This explanation is my own and a bit of a hobby subject, but then again so is this entire blog. If you have any other theory on this subject I would be very interested to know. Hope you enjoyed this academic side step. Next post will be on finding arguments for your case, or how to brainstorm effectively.

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