“There is no royal road to geometry.”
…said Euclid to King Ptolemy. The King was trying to learn mathematics from Euclid, but he found it too difficult and had asked Euclid for an easier way to learn it.
And of course, Euclid was right. There’s no secret easy method for understanding math. But this observation applies more broadly than to just mathematics. As Charles Sanders Pierce later said:
“There is no royal road to logic, and really valuable ideas can only be had at the price of close attention.”
The point is that there are no oracles, no shortcuts to knowledge, no quick trick for telling a truth from a lie. There is no substitute for an actual understanding of a subject. And an understanding is what entitles one to an opinion.
As is often the case, the phrase “entitled to your opinion” can be used in more than one sense. The phrase is often used in the context of an argument by someone who feels that they are being attacked for their opinion, and who feels that their right to hold that opinion is being violated. And in one sense, they’re right. No matter how crazy or wrong or repulsive an opinion is, the right to privately hold that opinion is something that is worth protecting. In that sense people are entitled to their opinions. Regardless of what those opinions are, the rest of us shouldn’t punish them just for having them.
But being entitled to an opinion in that sense doesn’t oblige others to agree with it, nor does it mean it’s correct. Yet, the phrase “I am entitled to my opinion” is often used as if to assert that the speaker is rationally entitled to their opinion, but without appealing to any observations or reasoning.
To claim that you are entitled to your opinion isn’t even an argument; it invokes no observation or evidence, no logic or reasoning. It’s an entirely irrelevant point, a logical fallacy known as a red herring. Despite this, it’s the kind of phrase often used to justify rejecting the opinions of experts who have spent decades thinking about a topic and forming an understanding based on a critical analysis of mountains of data in favor of an opinion picked up from some inflammatory YouTube comment.
“A probable inference…is one entitled on the evidence to partial assent.”
There’s only one thing that can rationally entitle you to an opinion: the evidence and reasoning supporting it. The rules of probability and logic determine the extent to which a given opinion is justified by a particular state of knowledge. To ignore these rules is like trying to ignore any of the other rules of the universe. Someone could also claim to be “entitled” to violate Newton’s first law of motion, and in one sense they are “entitled” to…because nobody would try to stop them if they tried.