When Catholics talk about “ways of knowing” different from science, what do they mean? And besides the existence of God, what is “known” that science can’t address?
The meaning of life
why we were created
Science cannot address non-tangibles; metaphysical concepts such as beauty and goodness.
Science can certainly understand aspects that cause us to perceive something as beautiful (such as facial symmetry), but it cannot explain the reality of beauty; what it is.
Science is about the study of the tangible universe. It is about measurement and dissection. Anothing that is not physical, or which has no physical dimensions, is outside of its scope.
As for other means of knowledge, I think the best would be philosophy. Philosophy is separate from science, yet we can use it to arrive at truths about the nature of reality; truths which science could not tell us.
Science has its place, and it’s great and all, but it is not all that there is.
The revelation of God. That’s what faith is: believing what God has revealed based on the authority of the revealer. Science, on the other hand, helps us obtain knowledge about the natural world that we can sense. But science cannot prove, for example, the nature of the Trinity, the truth of the hypostatic union, that if we obey the commandments, we will be saved, that our sins our forgiven in the sacrament of penance, etc., etc. We only can know these to be true because God has testified that they are.
I believe Monty Python covers these.
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