I think about presenting arguments a lot. Arguments are best represented in DAG form; mostly a tree structure, although some premises might support multiple conclusions so it's inherently graph-based (graphical data structure). Because some conclusions are often lemmas supporting further conclusions, arguments can go several levels deep.
I like envisioning them with the conclusion on the top and the premises on the bottom, although people often visualize them flipped in another direction.
But the trick comes in presenting the argument to someone else, verbally, in a presentation, or through writing. What is the best way to do it?
Because your goal isn't just to impart information; it's also to be convincing and to hope that your counterparts get invested in the conclusion.
I find that if the conclusion is counterintuitive, then starting with the conclusion can create resistance. People love to interrupt and argue against something they disagree with even if they haven't thought it through.
On the other hand, starting with a bunch of premises devoid of context can just feel unrooted.
I guess I generally try to analyze the argument to find the highest (closest to conclusion) points that are not controversial, start with those, and then try to talk about the surprising conclusion that they imply. It can be a real workout, though, trying to anticipate responses, being open to feedback while still working towards your conclusion.
I wonder if this sort of thing is related to any algorithmic concepts, like most efficient ways to walk a DAG.
Sustaining interest is also important. If you look at stories and stand up sets, there's an alternation between tension and release. In an argument, a challenging statement creates tension; resolving it is release. Meanwhile, with each such scene or joke, background is implicitly built up for a larger payoff later on.
Another aspect of this is explicitly addressing counter-arguments that arise in the reader's mind. If left dangling too long, the doubt is annoying for the reader. One problem is you don't know which specific counter-argument each specific reader is thinking of. So you corral them. You implicitly provoke this counter-argument, so when you address it, it's satisfying for the reader. By deliberately leaving open this specific counter-argument, and subtly suggesting it, you only have to deal with that specific one, at that point, for all readers. You lead them to objections, then resolve them.
Finally, if you finish a "scene" with another question, it propels the reader into the next stage of the argument.
BTW if you're not writing, but talking to one person, a crucial part of leading them to your conclusion is to find out where they are. Like giving directions to someone who's lost, they won't make sense if you don't know where they are. For an argument, it's their current view, what issues concern them, what perspective they have, and perhaps what misunderstandings they have. To convince, you should listen more than talk.
NB. All this is a lot of work, and mostly I can't be bothered.
I conceptualise arguments in the same way. I think the requirement of serialising arguments and evidence is bogus for the age we live in and would much rather just give the whole graph to an audience to play with, and then elaborate and discuss as needed. Or heaven forbid the reader could have write access!
In the end you have to examine the arguments in some order. By deciding the order you are reducing work for the reader in finding a pleasant traversal of the graph.
Maybe you're increasing the work by deciding an order. I've testing this approach several times of actually laying out complex arguments graphviz-style and watching people's eyes as they review it. Everyone seems to traverse the graph differently, depending on which parts challenge them.
Toulmin's model (data, warrant,backung,claim,rebuttal) reminds us that arguments are generally expressed with qualifiers and rebuttals rather than asserted as absolutes. This lets the reader know how to take the reasoning, how far it is meant to be applied,
I think there is certainly room to present graphs replete with pleasant and unpleasant traversals highlighted. It should also be possible to deconstruct misleading traversals.
I've been trying to develop a kind of argument map for mathematical proofs. Most proofs I come across are fairly ill-structured, especially from the point of view of someone with programming experience (a proof is just a program which operates on truths!). I'm still not sure about the grammar of these arguments, but some experiments are
The idea is that arguments supporting claims are indented, so you can read off the structure of the proof easier. Also, to keep nesting down, there is the convention that variables can be introduced with an implicit "for all" surrounding all of the following steps in a branch (using "suppose" or "for all"). Finally, proofs by contradiction are just case enumeration where some cases reach an impossibility.
I could see something like this being used for non-mathematical arguments. It would need a better way of having multiple arguments for claims, something math doesn't need. At some point I was thinking about a forum for arguments for facts/claims, where arguments can depend on these facts/claims. The idea would be that positions can be pulled up as a graph to see how strong or weak they are, or see where further arguing is needed. Perhaps something like this could improve political discourse.
A bit OOT: representing arguments as trees and computing which argument is the "best" is one research area in AI/KR, which I am currently doing for my univ's FYP. (if you're interested, check "Argumentation Framework" on Wikipedia and "Assumption-based Argumentation" on Google Scholars)
Proofs should be in DAG form, but starting a presentation from first principles seems like overkill. If your audience isn't at least as interested already interested in your side, they aren't going to be baby stepped through ever layer, especially when the first layers are the lowest levels.
Probably the same still holds if you flip the DAG and start with the conclusion, as you've already mentioned. People are going to tune out if you are presenting an opposing argument.
I don't think there's a great formula for arguments. You have to know your audience and pick your battles. Maybe the next best thing is making clear what you want/don't want and making clear what you believe others want/don't want and trying to find options that maximize as many of those constraints as possible. I think a lot of arguments stem from people who are already in agreement about most things.
> conclusion on the top and the premises on the bottom, although people often visualize them flipped in another direction.
In my own writing, my first draft seems to end with whatever should have come first. My second draft starts with that, and becomes shorter and clearer.
I like envisioning them with the conclusion on the top and the premises on the bottom, although people often visualize them flipped in another direction.
But the trick comes in presenting the argument to someone else, verbally, in a presentation, or through writing. What is the best way to do it?
Because your goal isn't just to impart information; it's also to be convincing and to hope that your counterparts get invested in the conclusion.
I find that if the conclusion is counterintuitive, then starting with the conclusion can create resistance. People love to interrupt and argue against something they disagree with even if they haven't thought it through.
On the other hand, starting with a bunch of premises devoid of context can just feel unrooted.
I guess I generally try to analyze the argument to find the highest (closest to conclusion) points that are not controversial, start with those, and then try to talk about the surprising conclusion that they imply. It can be a real workout, though, trying to anticipate responses, being open to feedback while still working towards your conclusion.
I wonder if this sort of thing is related to any algorithmic concepts, like most efficient ways to walk a DAG.