Subjectivity, Judgment, and the Basing Relationship

Moral and legal judgments sometimes depend on personal traits in this sense: the subject offers good reasons for her judgment, but if she had a different social or ideological background, her judgment would be different. If you would judge the constitutionality of restrictions on abortion differently if you were not a secular liberal, is your judgment really based on the arguments you find convincing, or do you find them so only because you are a secular liberal? I argue that a judgment can be based on the considerations the subject claims as justification even when it depends on personal traits.