How to structure long, intricate arguments?
November 8, 2015 11:15 AM Subscribe
I'm looking for inspiration for how to structure a long, intricate deductive argument. Can you help me find examples of arguments like this?
I'm not looking for clever arguments; I'm looking for deductive arguments where lots and lots (and lots) of premises and perhaps intermediate conclusions need to be juggled, yet it's still (relatively) easy to follow the argument. This could be because of formatting (hierarchies, labeled premises...) or some other means?
Has any argument (essay, book) struck you as being like this? And/or, are you aware of any general resources that help with this? Thank you.
I'm not looking for clever arguments; I'm looking for deductive arguments where lots and lots (and lots) of premises and perhaps intermediate conclusions need to be juggled, yet it's still (relatively) easy to follow the argument. This could be because of formatting (hierarchies, labeled premises...) or some other means?
Has any argument (essay, book) struck you as being like this? And/or, are you aware of any general resources that help with this? Thank you.
Response by poster: Educated people who don't have a lot of background but are willing to put in the work to actually trace the argument and accept or reject the conclusion.
posted by zeek321 at 11:22 AM on November 8, 2015
posted by zeek321 at 11:22 AM on November 8, 2015
Best answer: Legal writing is somewhat like this. Check out The Winning Brief by Bryan A. Garner. Reading past U.S. Supreme Court decisions may help as well.
posted by melissasaurus at 11:26 AM on November 8, 2015 [4 favorites]
posted by melissasaurus at 11:26 AM on November 8, 2015 [4 favorites]
Philosophy is the first place to look for this in general - check out the top search results for "writing a philosophy paper" - eg Jim Pryor has a good guide, but there are many.
But if you're writing something like a blog post for a general audience, it may be somewhat trickier since you can't assume familiarity with argumentative moves like reductio.
In a philosophy context, it would be normal to lay things out in explicit numbered premises, so you can refer back to prior segments of the argument, definitions, etc. Math proofs look similar, spelling out exactly what result they're aiming to prove, what falls out as a corollary, etc. Do you think your readers would put up with that? Or do you want to write it in a more conversational, paragrapphy way?
posted by LobsterMitten at 11:27 AM on November 8, 2015 [1 favorite]
But if you're writing something like a blog post for a general audience, it may be somewhat trickier since you can't assume familiarity with argumentative moves like reductio.
In a philosophy context, it would be normal to lay things out in explicit numbered premises, so you can refer back to prior segments of the argument, definitions, etc. Math proofs look similar, spelling out exactly what result they're aiming to prove, what falls out as a corollary, etc. Do you think your readers would put up with that? Or do you want to write it in a more conversational, paragrapphy way?
posted by LobsterMitten at 11:27 AM on November 8, 2015 [1 favorite]
Correcting a previous wrong link: Here's Jim Pryor on Writing a Philosophy Paper (when I say 'philosophy' I mean in the analytic/Anglo-American tradition.) The core is: be really explicit about structural guideposts, tell me where we're going, say only exactly what you mean and don't dress it up with extra stuff.
posted by LobsterMitten at 11:34 AM on November 8, 2015
posted by LobsterMitten at 11:34 AM on November 8, 2015
Best answer: Oh man. You definitely want The Problem of Political Authority. It is exactly what you're looking for.
posted by sevensnowflakes at 12:02 PM on November 8, 2015
posted by sevensnowflakes at 12:02 PM on November 8, 2015
Some of the proofs for Arrow's theorem would fit your bill, I think. I *think* there's on in Ordeshook's _Game Theory and Political Theory_ or _The Political Theory Primer_ that's good at leading the reader through, but those are either in the office (or maybe chucked) so I can't verify right now.
posted by ROU_Xenophobe at 12:11 PM on November 8, 2015
posted by ROU_Xenophobe at 12:11 PM on November 8, 2015
Look at Spinoza's Ethics. Take it either as inspiration or as a warning.
posted by meese at 12:36 PM on November 8, 2015
posted by meese at 12:36 PM on November 8, 2015
If you happen to follow developments in computer science, you may be aware that deductive arguments turn out in specific ways to be equivalent to functions in computer programs.
The basic idea is that the statement P → Q corresponds to the type of a function that takes a P and gives back a Q; and that a proof of that statement corresponds to a correct implementation of such a function.
This is known as the "Curry-Howard equivalence."
I spied briefly on your comment history only to scan for mentions of programming, and indeed found one, and so I suggest that whatever you have learned about how to organize programs to be understandable, may offer inspiration for structuring your argument.
Sadly, programs tend to be extremely difficult to follow, using lots of non-local effects, implicit state, unclear modularity, excessive abstractions, and so on...
Of course the most fundamental principle of program organization is to "divide and conquer" your problem into coherent subproblems. You want to construct P → Q but to get from P to Q you need many steps. Some are parallel, some are sequential. If you clearly identify the necessary subproblems A → B, B → C, and C → D, you can work on them independently, and the reader can assure herself of the correctness of each step independently. Maybe B → C turns out to be complex in its own right, and deserving of a separate "module."
Since the relation between proofs and programs is an equivalence, you can think in terms of either, but if you hadn't made the connection intuitively already, maybe thinking about this for a while might let you reuse some of your neural networks dedicated to structuring programs.
posted by mbrock at 1:26 PM on November 8, 2015 [1 favorite]
The basic idea is that the statement P → Q corresponds to the type of a function that takes a P and gives back a Q; and that a proof of that statement corresponds to a correct implementation of such a function.
This is known as the "Curry-Howard equivalence."
I spied briefly on your comment history only to scan for mentions of programming, and indeed found one, and so I suggest that whatever you have learned about how to organize programs to be understandable, may offer inspiration for structuring your argument.
Sadly, programs tend to be extremely difficult to follow, using lots of non-local effects, implicit state, unclear modularity, excessive abstractions, and so on...
Of course the most fundamental principle of program organization is to "divide and conquer" your problem into coherent subproblems. You want to construct P → Q but to get from P to Q you need many steps. Some are parallel, some are sequential. If you clearly identify the necessary subproblems A → B, B → C, and C → D, you can work on them independently, and the reader can assure herself of the correctness of each step independently. Maybe B → C turns out to be complex in its own right, and deserving of a separate "module."
Since the relation between proofs and programs is an equivalence, you can think in terms of either, but if you hadn't made the connection intuitively already, maybe thinking about this for a while might let you reuse some of your neural networks dedicated to structuring programs.
posted by mbrock at 1:26 PM on November 8, 2015 [1 favorite]
Check out a random entry of the Stanford Encyclopedia of Philosophy (or browse by topic).
posted by John Cohen at 2:23 PM on November 8, 2015
posted by John Cohen at 2:23 PM on November 8, 2015
A Socratic dialogue would seem to be an example of one Classic approach.
posted by XMLicious at 3:43 PM on November 8, 2015
posted by XMLicious at 3:43 PM on November 8, 2015
George Lakoff is generally very good at this. I was a fan of his linguistics work and when he turned his attention to helping Democrats frame their arguments in the post 9/11 era I happily followed along.
posted by cleroy at 4:00 PM on November 8, 2015
posted by cleroy at 4:00 PM on November 8, 2015
how to write a proof is ostensibly about structuring mathematical proofs, but the guidance is more general.
i feel there should be something more along graphical lines, as you suggest in the question. the closest i can think of are the arguments in edward tufte's books (the most famous example is this map) but they are more about presenting data than complex arguments.
posted by andrewcooke at 4:08 PM on November 8, 2015
i feel there should be something more along graphical lines, as you suggest in the question. the closest i can think of are the arguments in edward tufte's books (the most famous example is this map) but they are more about presenting data than complex arguments.
posted by andrewcooke at 4:08 PM on November 8, 2015
Response by poster: Ahhhhh this is all so good; thank you everyone. Still watching this thread.
posted by zeek321 at 9:30 PM on November 8, 2015
posted by zeek321 at 9:30 PM on November 8, 2015
Personally I love Virginia Woolf's Three Guineas. Not only long arguments, but beautiful and evocative writing. Three intertwined essays.
posted by chapps at 11:37 PM on November 8, 2015
posted by chapps at 11:37 PM on November 8, 2015
Best answer: Yeah, as melissasaurus said, complicated legal writing fits the bill. Garner is the go-to source for "how to" instruction. If you're looking for things written by excellent, excellent legal writers (and arguers), look no further than the Office of the Solicitor General; it's the office that argues the United States' position before the United States Supreme Court, and nobody spends more time in front of the Supreme Court than they do. Their briefs are considered the gold standard, at least when it comes to appellate brief writing and argument. Here is a searchable database of their briefs.
posted by craven_morhead at 8:12 AM on November 9, 2015
posted by craven_morhead at 8:12 AM on November 9, 2015
Best answer: Seconding LobsterMitten on Jim Prior's advice about writing philosophy. There are other resources for philosophy students which are similar to Prior's advice (are lot are listed at the end of this list of 'tips for philosophy students' by Douglas Portmore).
I tell (and teach) students to explicitly number their premises, and to refer back to earlier premises / line numbers in later premises, so that the links are laid out and obvious. Here's one I've just been discussing in an email (asking for feedback), a reconstruction of an argument from Plato's Phaedo:
What's nice is that in the next semester we pick up these students' arguments from this course and get them to translate them into a formal logical language and test the arguments for validity. What might interest you is that there are several formats for doing natural deduction in formal logic which try to 'keep score' of how the arguments are adding up. So, for example, Paul Tomassi's textbook Logic [a google search for name name title just got me a .pdf of this immediately] has not only 'line numbers' for each premise, but also 'dependency numbers' for working out what each subsequent line is ultimately 'depending' upon (see p.47 onwards). Premises are claims that you bring to the table, so they take their own line-numbers as 'dependency numbers' - they don't depend on anything outside the argument. Subsequent lines in the deduction which have relied upon those premises will feature those line numbers in their dependencies. Let's put line numbers at the front, then the claims / sentences which make up the argument, then in squiggly brackets at the end we'll list what they're dependent upon:
posted by Joeruckus at 9:37 AM on November 9, 2015 [1 favorite]
I tell (and teach) students to explicitly number their premises, and to refer back to earlier premises / line numbers in later premises, so that the links are laid out and obvious. Here's one I've just been discussing in an email (asking for feedback), a reconstruction of an argument from Plato's Phaedo:
1. Indeterminate things are essentially unknowable.This one isn't finished, there's more work to be done to make it all clear and explicit ['appearances are deceptive / unreliable' could be a line by itself, instead of featuring in both 5 and 9] etc., but it's certainly standard in philosophy (at least when it's being taught/learnt) to have arguments set out in this premise1, premise2, premise 3 ... : conclusion form. One reason I get students to do this from day one is so that they get used to seeing how deductive arguments add up, and so that they can start wondering about which of the links they want to focus on (here, most of them just go straight for premise 1, but some have decided that they want to direct their attention to the logical space in premises 4 and 5 that while it might be that Heraclitus' view is incomplete, we still might not need to go all the way Platonic and invoke a further realm of unshifting eternal perfection).
2. If Heraclitus’ view of the world is right (that everything we encounter is always changing, always shifting, perpetual flux) then by premise 1 it follows that no-one can know anything.
3. But we do know things.
4. So Heraclitus’ view must be wrong or incomplete.
5. So not all of reality can be constantly changing (it might seem to be, but appearances ≠ reality, appearances are deceptive / unreliable).
6. So there must be a part of reality which must be unchanging (eternal, perfect, immutable etc), let's call this the 'World of the Forms'.
7. If the World of the Forms is not part of the shifting, changing, physical realm that we encounter using our senses, then it's a separate domain of non-physical things, i.e. abstract objects.
8. If we know anything (and we do, see premise 3), then it's because we have knowledge of this domain of unchanging abstract objects (see premises 1 + 7).
9. We can't know about this domain of abstract objects using our bodies / bodily senses, because our bodies are physical things, constantly changing, unreliable, not the kind of thing that can interface or interact or liaise with abstract objects.
10. So there must be a part of each of us (let's call it the 'soul') which is immaterial, which can interact with the World of the Forms.
11. So we must have immaterial souls.
What's nice is that in the next semester we pick up these students' arguments from this course and get them to translate them into a formal logical language and test the arguments for validity. What might interest you is that there are several formats for doing natural deduction in formal logic which try to 'keep score' of how the arguments are adding up. So, for example, Paul Tomassi's textbook Logic [a google search for name name title just got me a .pdf of this immediately] has not only 'line numbers' for each premise, but also 'dependency numbers' for working out what each subsequent line is ultimately 'depending' upon (see p.47 onwards). Premises are claims that you bring to the table, so they take their own line-numbers as 'dependency numbers' - they don't depend on anything outside the argument. Subsequent lines in the deduction which have relied upon those premises will feature those line numbers in their dependencies. Let's put line numbers at the front, then the claims / sentences which make up the argument, then in squiggly brackets at the end we'll list what they're dependent upon:
1. Spud plays records {1}In line 5, we don't list 3 in the dependencies, because 3 was just derived from 1 and 2 - so we just transfer the dependencies - we pool them together. The advantage of having this 'score keeping' is that way we can see at a glance which claims are crucially contributing to the truth of line 5 (or the eventual conclusion).
2. If Spud plays records then Tom will buy a dress {2}
3. So Tom will buy a dress {1,2}
4. If Tom will buy a dress then Juliun will ride a bike {4}
5. So Juliun will ride a bike {1, 2, 4}
posted by Joeruckus at 9:37 AM on November 9, 2015 [1 favorite]
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posted by LobsterMitten at 11:20 AM on November 8, 2015