Ask Westerners if they think that the earth is spherical or if vaccines can prevent major diseases, and they will likely answer "Yes" without any hesitation. There are some who insist that scientific evidence indicates the opposite, but they are not representatives of Western culture at large. Ask Westerners if the laws of logic are verifiably true, however, and many of the same people who would answer the previous question(s) in the affirmative may suddenly say they are uncertain--if they even understand what logic is in the first place.
Thoroughly asking people about their stances on epistemology and metaphysics, even if those words are never used, is all that must be done to reach these conversational results. In fact, mockery might be directed at people for simply asking questions about contemporary scientific paradigms, whereas a denial of the self-evidence of the laws of logic is often met not with laughter or refutation, but with agreement. Although the external world metaphysically relies on logic and scientific results cannot be analyzed apart from logic, the reputations of reason and science are often the inverse of what they should be.
There are three distinct errors that many people in the Western world profess to believe about science. First, they believe that science necessarily reveals mind-independent facts about the external world, when science can only inform one about one's perceived surroundings. Second, they believe that past examples of specific events consistently leading to other particular events mean that scientific correlations will not change in the future. Third, they believe that correlations prove exact causal relationships if the correlations are repeatably demonstrable.
Rather than believe anything about science that involves these three logical and epistemological errors, a rational person sees that it is logical truths, not scientific concepts, that are verifiable in an ultimate sense. Logic cannot be false, but almost any scientific idea is potentially false the moment it is taken to be a true description of how the external world operates beyond the veil of sensory perception. Nevertheless, logic and science are often treated as if the opposite was true in both cases!
That anti-vax claims are often thought of as more asinine than a denial of self-verifying logical truths illustrates just how backwards a non-rationalistic society can be. On one hand, many Westerners seem to think their culture is rational simply for accepting the heightened role scientific developments play in modern life. On the other hand, they are typically very ignorant about the nature of logic itself, either focusing on science more than on reason or dismissing logic as something that may or may not be valid. As a conversation with the average Westerner can show, denial of the nature of logic is far more serious and widespread than the denial of today's scientific ideas.
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