I tend to do this often as part of serving as a 'moderator' of discussions/arguments, even when it's just me and another. It's useful to perceive the other party's (parties') argument as merely a podium upon which their belief rests, and then endeavor to identify, with specificity, their belief or position. Colloquially, the result would be something like:
Not you: "I think that, it just doesn't seem right, that, even without being given even a chance, the baby just dies. It's not right how they have no say at all, you know?"
You: "So, your position is..." In verbal communications you can at this point briefly pause as if you're carefully considering your words in order to allow an opportunity for their interjection of a more lucidly expressed position. "...that the fetus (and I'm just using the scientific terminology, here), has value equal to that of a grown person in moral considerations? [If confused:] I mean, that when thinking about an abortion, the fetus' rights are equal to that of the mother's?"
[As shown above, clarify one point at a time. Your tone must be that of one asking for clarification on a fact. More, "The tsunami warning was cancelled before or after the 3/14 earthquake hit?" than, "You've been wrong before; you sure?"]
Not you: "Yea, such is mine position."
You: "And, due to the fetus' having equal moral standing to the mother, abortions thus are an unjust practice?"
Not you: "Aye."
Be careful with these clarification proceedings, though. If by framing their arguments you happen to occlude the actual reasoning of their argument, due to them not knowing it themselves or otherwise, the entire rest of the argument could be a waste of time predicated upon a falsely framed position. Suggestions of possible solutions include:
From then on, you now have at your disposal vetted statements of their position that are intricate with their arguments. Subsequent arguments can then be phrased as hypotheticals: "What if EEG scans, which monitor brain waves, only showed the fetus as having developed brain activity akin to that of a grown person (the mother, say) at four months? Would that mean that at four months the fetus becomes developed enough to be considered equal to the mother?"
This way you can inquire after their exact position, why they hold that position, and without taking a side gather whether they're open to accepting another position whilst presenting viable alternatives in a reasoned and unobtrusive fashion. If you wish to defuse an argument, simply pointing out that party X holds to alternative II, and asking whether they can understand why party X holds to alternative II, should be enough to at least start smothering the fuse.
Note: The use of 'should' when expressing ideals implies a position of righteous power, and should (please decry me if I am unjustified in taking on this position of righteous power) never be used in an argument, regardless of whether it's self contained within a hypothetical. In my experience its use tends to only reinforce beliefs.
"...that the fetus (and I'm just using the scientific terminology, here), has value equal to that of a grown person in moral considerations?
Well now, this technique is straight-out dishonesty. You're not "just using the scientific terminology". You have a reason for rejecting the other person's use of "baby", and that reason is that you want to use words to draw a moral line in reality at the point of birth. Notice that you also increased the distance by comparing the "fetus" not to a newborn baby but to an adult. But...
We've all had arguments that seemed like a complete waste of time in retrospect. But at the same time, arguments (between scientists, policy analysts, and others) play a critical part in moving society forward. You can imagine how lousy things would be if no one ever engaged those who disagreed with them.
This is a list of tips for having "productive" arguments. For the purposes of this list, "productive" means improving the accuracy of at least one person's views on some important topic. By this definition, arguments where no one changes their mind are unproductive. So are arguments about unimportant topics like which Pink Floyd album is the best.
Why do we want productive arguments? Same reason we want Wikipedia: so people are more knowledgeable. And just like the case of Wikipedia, there is a strong selfish imperative here: arguing can make you more knowledgeable, if you're willing to change your mind when another arguer has better points.
Arguments can also be negatively productive if everyone moves further from the truth on net. This could happen if, for example, the truth was somewhere in between two arguers, but they both left the argument even more sure of themselves.
These tips are derived from my personal experience arguing.
Keep it Friendly
Probably the biggest barrier to productive arguments is the desire of arguers to save face and avoid publicly admitting they were wrong. Obviously, it's hard for anyone's views to get more accurate if no one's views ever change.
Inquire about Implausible-Sounding Assertions Before Expressing an Opinion
If someone suggests something you find implausible, start asking friendly questions to get them to clarify and justify their statement. If their reasoning seems genuinely bad, you can refute it then.
As a bonus, doing nothing but ask questions can be a good way to save face if the implausible assertion-maker turns out to be right.
Be careful about rejecting highly implausible ideas out of hand. Ideally, you want your rationality to be a level where even if you started out with a crazy belief like Scientology, you'd still be able to get rid of it. But for a Scientologist to berid themselves of Scientology, they have to consider ideas that initially seen extremely unlikely.
It's been argued that many mainstream skeptics aren't really that good at critically evaluating ideas, just dismissing ones that seem implausible.
Isolate Specific Points of Disagreement
Stick to one topic at a time, until someone changes their mind or the topic is declared not worth pursuing. If your discussion constantly jumps from one point of disagreement to another, reaching consensus on anything will be difficult.
You can use hypothetical-oriented thinking like conditional probabilities and the least convenient possible world to figure out exactly what it is you disagree on with regard to a given topic. Once you've creatively helped yourself or another arguer clarify beliefs, sharing intuitions on specific "irreducible" assertions or anticipated outcomes that aren't easily decomposed can improve both of your probability estimates.
Don't Straw Man Fellow Arguers, Steel Man Them Instead
You might think that a productive argument is one where the smartest person wins, but that's not always the case. Smart people can be wrong too. And a smart person successfully convincing less intelligent folks of their delusion counts as a negatively productive argument (see definition above).
Play for all sides, in case you're the smartest person in the argument.
Rewrite fellow arguers' arguments so they're even stronger, and think of new ones. Arguments for new positions, even—they don't have anyone playing for them. And if you end up convincing yourself of something you didn't previously believe, so much the better.
If You See an Opportunity To Improve the Accuracy of Your Knowledge, Take It!
This is often called losing an argument, but you're actually the winner: you and your arguing partner both invested time to argue, but you were the only one who received significantly improved knowledge.
If you're worried about losing face or seeing your coalition (research group, political party, etc.) diminish in importance from you admitting that you were wrong, here are some ideas:
Some of these techniques may seem dodgy, and honestly I think you'll usually do better by explaining what actually changed your mind. But they're a small price to pay for more accurate knowledge. Better to tell unimportant false statements to others than important false statements to yourself.
Have Low "Belief Inertia"
It's actually pretty rare that the evidence that you're wrong comes suddenly—usually you can see things turning against you. As an advanced move, cultivate the ability to update your degree of certainty in real time to new arguments, and tell fellow arguers if you find an argument of theirs persuasive. This can actually be a good way to make friends. It also encourages other arguers to share additional arguments with you, which could be valuable data.
One psychologist I agree with suggested that people ask
If folks don't have to drag you around like this for you to change your mind, you don't actually lose much face. It's only long-overdue capitulations that result in significant face loss. And the longer you put your capitulation off, the worse things get. Quickly updating in response to new evidence seems to preserve face in my experience.
If your belief inertia is low and you steel-man everything, you'll reach the super chill state of not having a "side" in any given argument. You'll play for all sides and you won't care who wins. You'll have achieved equanimity, content with the world as it actually is, not how you wish it was.