I disagree that if you would be less likely to reject his ideas if X were true, that can always be usefully described as “my rejection has something to do with X”. The statement “my rejection has something to do with X” literally means “I would be less likely to reject it if X were true”, but it does not connote that.
Generally, that you would be less likely to reject it if X were true, and a couple of other ideas:
X is specific to your rejectiion—that is, that the truthfulness of X affects the probability of your rejection to a much larger degree than it affects the probability of other propositions that are conceptually distant.
The line of reasoning from X to reducing the probability of your rejection proceeds through certain types of connections, such as ones that are conceptually closer.
The effect of X is not too small, where “not to small” depends on how strongly the other factors apply.
(Human beings, of course, have lots of fuzzy concepts.)
I disagree that if you would be less likely to reject his ideas if X were true, that can always be usefully described as “my rejection has something to do with X”. The statement “my rejection has something to do with X” literally means “I would be less likely to reject it if X were true”, but it does not connote that.
All right, I can accept that. So what does it connote, by your reckoning?
Generally, that you would be less likely to reject it if X were true, and a couple of other ideas:
X is specific to your rejectiion—that is, that the truthfulness of X affects the probability of your rejection to a much larger degree than it affects the probability of other propositions that are conceptually distant.
The line of reasoning from X to reducing the probability of your rejection proceeds through certain types of connections, such as ones that are conceptually closer.
The effect of X is not too small, where “not to small” depends on how strongly the other factors apply.
(Human beings, of course, have lots of fuzzy concepts.)