Can I be justified in believing in a proposition X through a justification that doesn't meet the standards of the scientific method? What sorts of beliefs would be justifiable in this way (non-scientifically), and what would a non-scientific justification look like?
Are there illustrative examples discussed in the academic literature of beliefs that can be justified non-scientifically?
Ethical and moral beliefs are justified but they are non scientific. Aesthetic beliefs , metaphysical beliefs , epistemological beliefs , religious beliefs , intuitive beliefs , cultural and social beliefs , existential beliefs are all justified but are non scientific.
There are no universally acceptable criteria for justifying our beliefs. If there had been, we would all agree on which beliefs are justified.
In principle, though, everybody would probably agree that it is justified to believe whatever is consistent with our personal perception of the world. What else?
The problem of course is that we cannot always all achieve the same perception of whatever aspect of the world we are considering, and that we often have to take a decision as to what justification is acceptable. We often cannot wait for everybody to agree. For instance, we cannot reasonably wait for everybody to agree with us before acting on our belief that vaccination is effective in saving lives. This seems reasonable but remember this also works the other way around.
So, what constitute a justification of our beliefs usually comes down to what . . . we believe (about various purported justifications).
People who cannot see things like I do from my own perspective, are in effect proving my point.
There is no easy or simple answer to that question, possibly the question needs more focus to be answerable.
The area of philosophy dealing with this is called Epistemology. It provides significant definitions such as belief, truth, justification, knowledge.
Can I be justified in believing...
Every belief is justified. There are just weak and strong justifications, and some justifications are also knowably wrong.
More interesting questions to ask would be: How can I self-improve my own beliefs? How can I make my beliefs consistent? Where do my least justified beliefs come from? How can I become more resilient to weakly justified beliefs?
(And my answer is via education and skepticism)
Are there illustrative examples discussed in the academic literature of beliefs that can be justified non-scientifically?
An illustrative example might be the Mind-Body problem, about which science has no answer (yet), so different schools of thought have come up with different beliefs having justifications.
It's one of 30 questions in philosophy that have no answer and on which multiple schools of thought exist, which were asked to contemporary philosophers in 2009 for a paper called "What do Philosophers believe?"
Those have no scientific answer (yet), but they have a lot of books written about them, so I guess they should be illustrative.
Can I be justified in believing in a proposition X through a justification that doesn't meet the standards of the scientific method?
This is dependent on your notion of justification, though given a colloquial understanding of justification, the answer seems to be yes. All forms of apriori reasoning do not follow the scientific method (observation, hypothesis, experiment, conclusion), and one would be quite hard-pressed to object to all forms of apriori reasoning.
What sorts of beliefs would be justifiable in this way (non-scientifically), and what would a non-scientific justification look like?
The most obvious example of a category that would fit this description would be mathematical theorems, they are justified via logical proofs, either following directly from the axioms one is working with or by contradiction.
There isn't a categorical difference between science and non-scientific sensory experiences.
For the purposes of this question, science can broadly be thought of as the process of refining, testing and expanding our experiences to reach reliable conclusions (thanks to a reliable process).
We can also reach reliable conclusions without explicitly following the scientific method - we have a pretty good idea of when our sensory experiences are and are not reliable (it's unreliable when you're in bed in the middle of the night, when you have certain mental conditions, when you're on drugs, etc., and we also know that memory can be unreliable with respect to significant details of single events). We've figured some of this out through science, and some of it is fairly obvious (dreams seemingly tend to not correspond to anything real in the world outside of our own brains).
Although we also implicitly and informally follow the scientific method in day-to-day life. If you have some food and you observe that you get a stomach ache, you may come up with the hypothesis that said food gave you a stomach ache. You might then create an experiment of sorts, where you test that hypothesis by trying to have the food again. That's pretty much what the scientific method is, it just does that more formally and robustly.
See also: Reliabilism.
If your goal is to believe as many true things and as few false things as possible, then you can't do much better than a justification of reliability - that's pretty much what reliability is.
I'd also argue many other goals circle back to reliability, because if your beliefs more reliably correspond to reality, you'd be better able to predict the outcomes of your actions, and thus achieve what you try to achieve.
* There's also a cost-benefit tradeoff - for mundane beliefs that have no effect on your life, less reliable justifications (e.g. 1 person said it) may be good enough.
If you get into more metaphysical beliefs like whether there exists a world outside of your own mind, or whether things beyond what we can perceive (e.g. what people might call "supernatural"), you can't directly invoke reliability, because you can't check the reliability (of course you can potentially reject anything for which you don't have a reliable process, but that leaves you potentially unable to evaluate certain claims). But we can invoke other principles and ideas like Occam's razor, explanatory power and coherence (and one can potentially argue for the reliability of those principles).
In any case, there are also other views on what a good justification is, but (at least in my view) that tries to draw some dubious distinctions (e.g. one can conceivably, within certain bounds, measure the reliability of any proposed source of justification, even "internal" ones, but reliabilism is categorised as an "external" source of justification) and it seems to concern itself mostly with abstract considerations, or mentions merely conceivable sources of justification. Meanwhile, I take a much more pragmatic view in focusing on what the actual point of justification is: what is the goal you hope to achieve through justification. More broadly, one might ask what the practical use of epistemology is. And that brings us back to where I started: reliability is focused on the goal of believing as many true things and as few false things as possible. That's the best goal I can find, but others are welcome to argue for a different goal.
The challenge, "For what?" is often issued on this site to any request for or issuance of a definition, rule, concept, etc. Because, it is the important aspect of those things. One part of it is the balance of risk and reward. Poorly justified beliefs often share the characteristic that there is basically no risk to believing, but some potential reward, so in Game Theory, that would look like an unbalanced payoff matrix, but with a low probability of getting the reward.
It costs nothing to believe for example, that the Earth is flat. You won't fall off, or lose your job, your refrigerator won't stop keeping food cold. Believe it if it makes you feel good because it has no effect one way or the other. Playing the Lottery is another. While it is true that "you can't win if you don't play", it is about equally true that you won't win if you do play. ("Lotteries are a tax on people who are bad at math.")
Many religious beliefs similarly have no cost for belief, but potential payoffs. Anyone can say anything similar and be equally 'justified' (zero) but people will sign up if it strikes their fancy. This makes the "cost of entry" for religion very low, just charisma basically.
It could be helpful to examine why one began believing something, "For what?" It might help in choosing future beliefs and evaluating justifications.
Justification is supposed to be a process that shows some idea to be true or good or assign some positive status to it. Any argument uses assumptions and rules that are supposed to give true results when applied to those assumptions. There is no way to guarantee the correctness of the assumptions and rules. So there is no way to show that the conclusion of an argument is actually good: justification is impossible. Knowledge can be created instead by looking for problems with existing ideas, proposing solutions to those problems and adopting solutions for which you can't find problems. This was pointed out by Karl Popper in On the Sources of Knowledge and of Ignorance, which is in his book "Conjectures and Refutations", and in "Realism and the Aim of Science" Part I, Chapter I.
Scientific knowledge is knowledge that can be criticised by doing experiments whose results could be incompatible with that knowledge. Non-scientific knowledge is knowledge that can't be tested by doing experiments.
Some examples of non-scientific knowledge include epistemology and the idea that objective reality exists. It could be the case that the world stops existing when you don't look at it and it just acts as if it exists when you turn your back. Or god could have created the world five minutes agowith all your memories and the fossil record and so on. No experiment could distinguish between such theories and our current scientific knowledge. Nevertheless we know that such alternatives to current scientific knowledge are bunk because they amount to sticking a label on parts of science saying they are false but we'll use the results anyway. See "The Fabric of Reality" by David Deutsch Chapter 4 for more explanation.
For some philosophy that tries to build on and improve Popper's ideas see
https://criticalfallibilism.com/introduction-to-critical-fallibilism/
Additionally to the provided answers:
All knowledge derived from Holism. excerpt from Wikipedia: "Holism in all contexts is often placed in opposition to reductionism, a dominant notion in the philosophy of science".
It can explain the biological concept of life (the fact of being alive), as the result of a high degree of organization of material elements.
All (valuable) knowledge derived from Serendipity. There are hard problems, such as the Millennium Prize Problems awaiting to be solved (the prize is US$1 million). Many of them are conjectures. Suppose you find by serendipity a counterexample, solving the problem. Of course the counterexample can be scientifically validated, but it was not found by scientifical means.
Science is descriptive, not prescriptive. It tries to explain how things actually are, not how they should be. So any beliefs about how things should be will need something more than scientific justification (science may provide some useful input).
I think, therefore I am.—— René Descartes
