The problem there, is figuring out what "simplest" means. To many people, "God" seems like the simplest explanation for the universe, even though what the word implies is very complex. It's the same phenomenon as people who say, "Scientists can't explain magnets, the liars!" Magnets seem like a magical extra, but it turns out that electromagnetism is a fundamental. It's a rock sitting on a tabletop that's complex and turns out to need explanation.
Eg. If you take as axioms that it is always wrong to end life, and life begins at conception, abortion is wrong is a sound logical conclusion.
Do note that often in this kind of controversial topics, the axioms are not held consistently by a given side (or the actual axioms are hidden and differ from the stated ones). For example, "it's always wrong to end a life [except when bombing abortion clinics | except when it's a death row immate]". Then the ad hoc provisions start, "oh, I meant an innocent life" ("but how can a nonsentient being be called innocent in any meaningful way?"), etc, etc. The debate then becomes anything but grounded on well defined axioms.
When I have an argument, I find it most productive to first seek out to understand how the other person feels. Peoples' feelings are rarely "incorrect", and usually align with my own feelings at some fundamental level, although perhaps with different intensities. I then try to work with them to put our brains and experiences together to find a more solid understanding for why we feel that way.
I will definitely concede that the logic people use on a day-to-day basis is much fuzzier than an analytic might prefer, and that there's much greater allowance for contradiction (see the phenomenon of Cognitive Dissonance). But I do think that most people argue from their own first principles, consciously or not. There are rare cases where you can convince someone of something when you discover and correct a logical flaw they have made. More often than not, though, a 'logical argument' is a veiled battle of dogma; both participants are moderately rational, and share the same rules of logic, but their axioms are so alien to eachother that what is plain as day to one is a violation of human decency to another. I'd reckon that in reality, it's rare that two people are actually even arguing about the same thing, even though they may be using some of the same words.
So... what's the state of the art?
This makes me imagine putting people through a trolley problem where you have a serial killer on one side and an 8 week old fetus [1] on the other. That said, many of the people I've known simply argue against the death penalty instead. This may be biased by knowing Catholics, though.
[1] https://www.babycenter.com/fetal-development-images-8-weeks
yes, and you'd also end up with an outright ban on civilian ownership of automatic weapons, amongst other safety measures. But you don't often see those two together. I think that the axioms are a layer or two below that, and might involve concepts like "individual responsibility" and "greater good"
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0. there are, of course, different sets of axioms that arrive at superficially similar conclusions. For example, the category of pacifist that believes that any loss of life is not justifiable; this kind of person will reject both abortion and ownership of weapons, war, etc.
Funny enough, this conversation could also be a form of abductive reasoning. We're inferring that people are using abductive reasoning because people often hold conflicting moral views, though using abductive reasoning wouldn't necessarily guarantee conflicting views.
Second, the goals of abductive reasoning are different than philosophical or mathematical proof. Often we need to make decisions on incomplete information, and it's a philosophy to help one do so.
For example, juries are supposed to make a decision based on a preponderance of evidence or beyond a reasonable doubt. Convictions would be rare if the standard were incontrovertible truth.
Also, while abductive reasoning is (a bit) different from inductive reasoning, they have the same underlying epistemological justification. In discussions of epistemology you often don't see abductive reasoning mentioned, as it falls under the general framework of inductive reasoning.
Even if we're able to reduce our competing models to Turing machine implementations, we're only able to calculate their complexity relative to some defined collection of models, which in turn depends on what kind of low-level logical formalism we're using.
In practice, of course, we can't parse out all these formal details for every decision, but I think it's helpful to at least be aware of the inherent problems with naive Occam's Razor.
https://en.wikipedia.org/wiki/Occam's_razor
tends to be a valid approach, generically speaking.
https://en.wikipedia.org/wiki/Abductive_reasoning
It's important to keep the Münchhausen trilemma and abductive reasoning in mind when discussion controversial issues where one side feels they have proof and the other side is ignorant or duped. Often the difference is something like whether emergent behavior or a conspiracy feels like a simpler explanation.