This essay tackles the idea that many people are already made up in their beliefs and will struggle to change them for a number of reasons. Logic is something few people care to study because it's something will all already engage in. I thought it was interesting that Peirce notes the history of logic and drawing inferences; it's an art that has improved over the centuries. Every major new work of science, after a few generations, exemplifies the "defective state of the art of reasoning of the time it was written". Reasoning allows us to discover new conclusions from old data. We can be mislead from habit if it doesn't produce true conclusions from true premisses. Our daily way of dealing with things is steeped in bad logic, and this could be for practical reasons - not wanting to disturb our inner peace, not wanting to be ostracized etc. Doubt is "an uneasy and dissatisfied state" - pushing us to inquire, but preventing us from acting. Inquiry must start with a real and living doubt; from propositions that are not under doubt; and ends after doubt ends.
favourite part in the essay is when Peirce discusses the avoidance of
reasoning. "When an ostrich buries its head in the sand as danger
approaches, it very likely takes the happiest course. It hides the
danger, and then calmly says there is no danger; and, if it feels
perfectly sure there is none, why should it raise its head to see? A man
may go through life, systematically keeping out of view all that might
cause a change in his opinions, and if he only succeeds -- basing his
method, as he does, on two fundamental psychological laws -- I do not
see what can be said against his doing so. It would be an egotistical
impertinence to object that his procedure is irrational, for that only
amounts to saying that his method of settling belief is not ours. He
does not propose to himself to be rational, and, indeed, will often talk
with scorn of man's weak and illusive reason. So let him think as he
pleases." However this method may be pleasing to the ostrich-man, it may
not be obtainable as "the social impulse is against it".