What I’m saying is that both you and I accept certain propositions as objectively true solely through intuition, logical reasoning, and/or basic sense data instead of the methods of empirical science.
Some of these propositions are only contingently true in this world, meaning that you can imagine another world where it is not true (e.g. “Other minds exist besides my own” - I can imagine a world where I am literally the only mind existing).
Some other propositions are necessarily true, meaning you cannot imagine a world where they are not true (e.g. mathematical theorems such as “for any finite group G, the order of every subgroup H of G divides the order of G.”).
These facts are proof that the methods of science alone are insufficient to account for all the knowledge we hold.
Now, you’ve basically replied that non-scientific knowledge is not reliable knowledge. However, you’ve also conceded that you don’t have a rigorous definition of what reliable knowledge is. Without such a definition, it’s going to be difficult for us to come to terms on anything. (It’s also kind of ironic, because that means you’ve been using the term “reliable knowledge” in an intuitive manner during this conversation, when at the same time you’ve been criticizing intuition as a way of knowing.
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Now on to the secondary matters…
I don’t know if you can ask for further justification for people who believe morality is objective. Most people end up behaving as if they do. Do you not think that say, the 9/11 attacks were objectively morally wrong?
I can support it with argumentation, some of which is philosophical, some scientific. However, most of the things I mentioned have not traditionally been the purview of science anyway.
It’s certainly not a reason I would bring to a formal academic debate, but we hold beliefs not for strictly rational reasons, am I correct? (Of course, this is not to say that Christianity is irrational. Just that my belief in it is not reducible to a mere act of rational assent.)
Just to drive the point home again, on what rational basis do you hold the belief that other minds exist?