Translate each into symbolic form and then use the first


The following dialogue contains eight arguments. Translate each into symbolic form and then use the first thirteen rules of inference to derive the conclusion of each.

With This Ring
"Hi. I didn't expect to see you here," says Ken as he catches sight of Gina on the steps of the church. "You must be friends with the bride." "I am," she says, "and are you a friend of the groom?" "A friend of a friend of the groom," he replies. "So I don't know too many people here." "Well, I'll be happy to keep you company until the ceremony starts," Gina says. "And it looks like things are running late, so we'll have a few minutes." She looks around and sighs.

"Every time I attend a wedding," she says, "I feel sad for a lesbian couple I know who would give just about anything to get married. Unfortunately this state doesn't allow same-sex marriage." "Well, I don't think that's unfortunate," says Ken. "If marriage is sacred, then we shouldn't tamper with it; and if that's the case, then we shouldn't allow same-sex marriage. And I do think marriage is sacred, so we shouldn't allow same-sex marriage." Gina looks shocked. Ken continues. "Look," he says, "the Bible condemns homosexuality. If either Leviticus or Romans is true, then homosexuality is an abomination and it must be avoided.

And if it must be avoided or it's contrary to nature, then if it's a sin, then it must not be allowed. Now, we know that Romans is true, and if the Bible condemns homosexuality, then it's a sin. Thus, same-sex marriage must not be allowed." "Obviously you're injecting religion into the issue," Gina responds, as she waves to a friend in the gathering crowd. "But the First Amendment to the Constitution says that the state must not act either to establish a religion or to interfere with religious practices. If the state bars same-sex marriage for your reasons, it acts to establish a religion. So, it must not bar same-sex marriage for your reasons." Ken opens his mouth to object, but this time it's Gina who's on a roll.

"Also," she continues, "our country is based on the principle of equality. If straight couples can get married, and obviously they can, then either same-sex couples can get married or same-sex couples are not equal to straight couples. And if same-sex couples can get married, then our law has to change and other state laws have to change as well. Now, if our country is based on the principle of equality, then same-sex couples are equal to straight couples. Thus, our law has to change." "Look," says Ken, "Marriage has always been between a man and a woman. And if that is so and tradition is worth preserving, then if we allow same-sex marriage, then the very concept of marriage will change and gender roles will switch.

Now tradition is worth preserving and gender roles shouldn't switch. Thus, we cannot allow same-sex marriage." "Ha!" says Gina. "I can see why you don't want gender roles to switch. You can't see yourself in the kitchen preparing meals and washing dishes." "Well, I don't really relish the idea," Ken admits. "I think God wants us to keep things the way they are. But here's another reason. One of the chief purposes of marriage is raising children, and if that is so, then it's important that the children grow up well adjusted. But if the children are to be well adjusted, then they must have both a male role model and a female role model. If the parents are both men, then the children will have no female role model; if they're both women, then the children will have no male role model. Clearly if the marriage is a same-sex marriage, then the parents are either both men or they are both women. Therefore, the marriage must not be a same-sex marriage." "Your reasoning is a bit shortsighted," Gina says.

"In a same-sex marriage with children, the parents are either both men or they are both women. This much I grant you. But if they are both men, then surely they have close female friends, and if that is so, then the marriage has both male and female role models. If the parents are both women, then surely they have close male friends, and if that is so, then the marriage has both female and male role models. If a marriage has both male and female role models, then the children will be well adjusted. Therefore, in a same-sex marriage with children, the children will be well adjusted. What do you think of that?" "Well," says Ken, as he scratches his head, "I wonder if those surrogate role models would be as effective as male and female parents.

But in either event there is the option of civil unions. Why won't that satisfy you?" "Civil unions fall short of marriage in too many ways," Gina replies. "They're valid only in the state in which they are performed, and they don't allow the partners either to file a joint federal tax return or to receive Social Security survivor benefits. If they're valid only in the state in which they're performed, then if the couple moves to a different state, then if one partner is hospitalized, the other partner will have no visitation rights. If the partners can't file a joint federal tax return, then they must file as single taxpayers.

And if that is so, then they might pay much more in taxes. If the partners don't receive Social Security survivor benefits, then if a partner receiving Social Security benefits dies, then the other will not receive anything as a survivor. Suppose that two partners in a civil union move to a different state, and that one partner, who receives Social Security benefits, is hospitalized and eventually dies. The conclusion is that the other partner will not have either visitation rights while the hospitalized partner is alive or survivor benefits after that partner dies, and the partners might pay much more in taxes.

Does that seem like a fair substitute for marriage?" "Maybe not," Ken says, as he stretches to see above the crowd. "But I still think there's something unnatural about same-sex marriage. Anyway, here are the bride and groom. Let's go inside." "Good, let's go," says Gina.

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Basic Statistics: Translate each into symbolic form and then use the first
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