Nice to see you back, Ella.
I am still limiting what kinds of posts I make and what I reply to. I realize that I cannot figure out how to improve myself through pure introspection alone and I think I've come as far as I can there, so I'm metaphorically dipping my toes back into the water in order to collect more data.
I did stray from practicing mindfulness and I think that might be partially responsible for my brief emotional reactivity. I have to remember to react by calming down and pausing to think through my next response, if any, and compare my potential response to my standard of behavior before I put it into action. Mindfulness helps with this process.
I'm also working on maintaining my focus on my higher values so that I stop placing so much emphasis on small matters that either do not matter in the greater scope of things or that are actively counter-productive to focus on. I think this is a key feature of wisdom. I know that nobody is perfect at this, and I am still rather young and most of the people I know who are even a few years older than me come to me for advice on this, but I am still painfully aware of how much progress I still have to make on this virtue.
You are probably the one person I feel like I owe an explanation, and you might be the only person on this site that I think will actually hear me out, too. But I'm glad to address this a bit more out in the open after I have had some time to think about it.
If it's premises are true, and its logic is sound, reason unfailingly leads us to the truth. Granted, sometimes those are big asks, but (hey) it can be done and has been done many times. Reason fails us when we make bad assumptions. The case of luminiferous ether in 19th century science is a great example of reason leading us astray. But once scientists figured out that they were (erroneously) assuming that all waves need a medium to travel through, the logical proposition was recognized as false.
(Actually, I think it happened the other way around: luminiferous ether was disproven, thus showing scientists that waves don't need a medium through which to travel.)
To nitpick a bit here, this is a purely deductive approach to reason that assigns binary true/false values to the premises. I think that is an important aspect to reason and it's often what people think about when they mention logic as a formal discipline.
The problem is, of course, as you say, the truth of the premises isn't necessarily something we can always assume or be certain of. Some statements are probably true or probably false. In fact, I would probably argue that most of our practical, everyday reasoning relies on this sort of fuzziness. Decision theory is tied closely to probability theory, for instance, and science and engineering of course deal with statistical analyses frequently.
That's why the Bayesian approach is so important, which is where we are constantly putting new data back into our analysis and changing the conclusion. This is what I mean when I refer to reason as a process that approximates truth rather than leading to absolute truth.
Deductive logic only works for constructed languages like mathematics, symbolic logic, or computer languages. It has some practical application, but this is mostly for the sake of communication. I do think that's a kind of truth, but only under a coherentist model of truth.
By contrast, inductive reasoning tells us about the external world around us, and it might be the closest we have to a way of approximating truth according to the correspondence theory of truth. If we're going to say that our truths are actually objectively true independent of linguistic constructs and independent of a subjective agent to perceive them, and that they correspond to an actual mind-independent reality, then it's inductive reasoning that we have to rely on, not deduction.
At least, that's how I see it, and I am open to arguments to the contrary.
Notably, it's not that the inference rules of deduction are removed from inductive reasoning. It's just that the premises cannot be assigned as pure truth or pure falsity. The process of "reason" is the same for deduction and induction, it's just that induction is more nuanced and adaptable for real-world applications.
What are these paradoxes? And how specifically do they relate to the ethical matters we are discussing? (I could, of course, Google them to find out what they are, but I figured I'd be "old school" and ask a friend.)
Both of the paradoxes deal with inductive reasoning, so they might not be the best examples to dive into until the above points are hashed out a bit more. That's why I've moved this to the bottom of my reply.
The Raven's Paradox is the idea that a green apple, for instance, is evidence that the statement "All ravens are black" is true. When one is first learning about induction, this normally feels "wrong" intuitively, which has lead to a number of arguments against the paradox by a number of philosophers on that basis.
However, if we take a moment to step back and think, the Raven Paradox begins to make more sense. We can imagine two categories of objects, "black" and "non-black." When we say "All ravens are black" we are saying that there is a third category, ravens, which exist entirely within the black category and does not overlap with the non-black one; that is to say, we are saying that no ravens are a non-black object. "No ravens are not black" necessarily describes the data implied by "All ravens are black."
If we constrain our statement to a smaller scale, say, to a room, then the reason that green apples can be evidence for all ravens being black begins to become more clear. If we sort every object into the room into black and non-black, which is a finite set, then we begin to notice something.
Take, for instance, this hypothetical assortment of objects:
-A blackberry
-A black raven
-A green apple
-An orange
There are 4 things total. When we discover that 1 of these things is both non-black and not a raven, that means there are only 3 things left that could be a non-black raven, which literally lowers the odds that one of the remaining objects is a non-black raven. When we have the room completely sorted and all non-black things in the room are in a single corner, separated from the black things on the other end, we merely need to look over all of the non-black things we collected to see if there is a raven.
Since the only non-black things in the room are a green apple and an orange, we have proven that there are no non-black ravens in the room, which would be necessary if "No ravens (in this room) are non-black," which is necessarily true if "All ravens (in this room) are black." The only requirement to prove the latter statement from the former statement is to demonstrate that the former is not a vacuous truth by showing that there is, indeed, an existent raven which is black (or "not non-black.")
But if we did come across an albino raven when sorting the room, then we would falsify the statement that "All ravens are black." A white raven is stronger evidence that "All ravens are black" is false than a green apple is evidence that "All ravens are black" is true. This does line up with our intuition because, in the real world, sorting all non-black objects in existence is infeasible. The counter-intuitive part is that a green apple is evidence at all, though, even if it is very weak evidence.
There are situations where the Raven Paradox is more apparent, such as in the above case when I limited the statements to be about objects within a certain room in order to make processing those objects more feasible. In the real world, situations like my constrained example do appear from time to time, so properly understanding the truth at hand might require double-checking our initial intuitions.
Does the raven paradox apply to ethics? It can if you support ethical naturalism, especially if it takes on a form such as evolutionary ethics where it relies on a scientific field for its conclusions. It also matters in the case of consequentialism, because information that might directly or indirectly tell us what the consequences of our actions might be can sometimes take this form.
It is not as readily applicable to deontology and virtue ethics, but I think there are arguments to be made there, too. Deontology often argues that we should imagine what would happen if we generalized our patterns of behavior into rules that everyone followed, for example, which can invoke the Raven Paradox in some circumstances. In virtue ethics, likewise, the virtues themselves are often supported by various observations about how people behave.
There is some amount of induction in all of these philosophies, so paradoxes of induction such as the Raven Paradox can be very relevant.