Rachels’s argument in the first chapter is, essentially, the following:
1. Partisans on both sides of the case of Baby Theresa agree that moral judgments must be (1) based on reasons and (2) impartial.
2. Partisans on both sides of the case of Jodie and Mary agree that moral judgments must be (1) based on reasons and (2) impartial.
3. Partisans on both sides of the case of Traci Latimer agree that moral judgments must be (1) based on reasons and (2) impartial.
4. If all these people, who disagree about so much, agree that moral judgments must be (1) based on reasons and (2) impartial, then moral judgments must be (1) based on reasons and (2) impartial.
5. Therefore, we can confidently conclude that moral judgments must be (1) based on reasons and (2) impartial.