An argument has a true conclusion if it is sound. If an argument is invalid, then it has a false conclusion. If an argument has a false conclusion, then it is invalid. An argument is both sound and unsound. Thus, an argument has true conclusion if and only if it has a true conclusion.
Paper topic 3Please put the following argument in standard logical form:
If
an argument is valid and has a true conclusion, then it is sound. An argument is unsound only if it is invalid. An argument has a true conclusion if it is sound. If an argument is invalid, then it has a false conclusion. If an argument has a false conclusion, then it is invalid. An argument is both sound and unsound. Thus, an argument has true conclusion if and only if it has a true conclusion.
Please evaluate this argument. Is it valid? Explain in terms of a full truth table. If one premise is a contradiction, is the argument valid? if the conclusion is a tautology, is the argument valid? (Explain these last two points in terms of a truth table that includes only the last premise and the conclusion. This truth table should only have four rows.) Is the argument sound? Can any argument with a contradiction as a premise be sound? Explain why each premise is true or false. Explain why the conclusion is true or false.
Hints
1. When you put this argument in standard logical form, you will provide a dictionary and symbolize the argument. This argument is not a sorites. It is one argument. Reread the material in 2.12 of the textbook.
2. You only need three statement letters to symbolize this argument. If you use P=an argument has true premises, you can use ~P to stand for âan argument has false premises.
3. If you find your big truth table distracts from the main text of your paper, you may place it in an appendix at the end of your paper (and your big truth table is the ONLY thing that belongs in the appendix). The big truth table will include every premise of the argument and the conclusion. It will only have 8 rows. You should not have multiple truth tables, one for each statement. You need one big truth table in order to see the relation of the premises to the conclusion. The smaller truth table, the one that includes only the last premise and conclusion, can go in the main text of your paper.
4. While truth tables that show an argument is valid cannot generally determine whether an argument is sound, your two truth tables can show that this argument is unsoundâthanks to the last premise. Explain why this is the case.
5. You can use a truth table to explain why a tautology is true or a contradiction is false. But if a statement is contingent, the truth table is worthless. To determine whether the statement is actually true or false, you will need to plug in values to see what the statement actually says. Suppose you have the premise SÃ V where âSâ stands for âan argument is soundâ and âVâ stands for âan argument is validâ. To explain why âSÃ Vâ is true or false, you need to explain why if an argument is sound, then it is valid.
6. When you discuss why statements are true or false, it is better to translate them as material conditionals. Take the statement âAn argument is sound only if it has a true conclusionâ. It is better to explain why this statement is true: If an argument is sound, then it has a true conclusion. You are less likely to make a mistake. The statement âan argument is sound only if it has a true conclusionâ does not mean that the only condition needed for a sound argument is a true conclusion. Rewrite statements as âif____, then___â You are less likely to make a mistake on meaning.
7. When you explain why a premise is true or false, it is a good idea to give each statement its own paragraph. You should not discuss two or three premises in one paragraph.
8. USE EXAMPLES when relevant. For this paper, your examples will be categorical syllogisms.
9. Remember, good writing helps.
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