What does "the appearances" mean in this passage?
Does it mean superficial features or arguments that appear to support a particular opinion on a surface level, but have no substantial value upon closer examination?
But, some one may say, "Let them be taught the grounds of their opinions. It does not follow that opinions must be merely parroted because they are never heard controverted. Persons who learn geometry do not simply commit the theorems to memory, but understand and learn likewise the demonstrations; and it would be absurd to say that they remain ignorant of the grounds of geometrical truths, because they never hear any one deny, and attempt to disprove them." Undoubtedly: and such teaching suffices on a subject like mathematics, where there is nothing at all to be said on the wrong side of the question. The peculiarity of the evidence of mathematical truths is, that all the argument is on one side. There are no objections, and no answers to objections. But on every subject on which difference of opinion is possible, the truth depends on a balance to be struck between two sets of conflicting reasons. Even in natural philosophy, there is always some other explanation possible of the same facts; some geocentric theory instead of heliocentric, some phlogiston instead of oxygen; and it has to be shown why that other theory cannot be the true one: and until this is shown, and until we know how it is shown, we do not understand the grounds of our opinion. But when we turn to subjects infinitely more complicated, to morals, religion, politics, social relations, and the business of life, three-fourths of the arguments for every disputed opinion consist in dispelling the appearances which favour some opinion different from it.
---J.S. Mill from On Liberty https://www.gutenberg.org/files/34901/34901-h/34901-h.htm