Standard Logical Form & Propositional Arguments

Put the following argument in standard logical form as a propositional argument. If an argument is valid and has a true conclusion, then it is sound. An argument is sound only if it has a true conclusion. The conclusion is false if the argument is invalid. If an argument is valid, then it must have a true conclusion. An argument is neither sound nor unsound. Therefore, an argument is valid if and only if it is valid. Please evaluate this argument. Is it valid—explain in terms of a full truth table (do not omit the initial set-up). If a premise is a contradiction, can the argument ever be invalid? If the conclusion is a tautology, can the argument ever be invalid? Provide a small truth table that has only the last premise and conclusion. You can use the little truth table to explain why a contradiction as a premise and a tautology as a conclusion guarantees validity. Explain why every premise and the conclusion is either true or false. Explain why a contradiction as a premise guarantees that the argument is unsound. Additional Instructions: 1. You want to rewrite the argument in standard logical form. This means that you will provide a dictionary (make sure that the dictionary consists of complete sentences) and you will symbolize the argument. Pay attention to the material in 2.12 of the textbook. 2. You only need three statement letters. To keep down the number of statement letters, rely on the judicious use of negation (~). If you use ‘V’ for ‘an argument is valid’, use ‘~V’ for ‘an argument is invalid’ 3. If you find that the big truth table (the one with all the premises and the conclusion) distracts from the main text of your paper, you may place it in an appendix at the end of the paper (and this this the only material that belongs in the appendix). You are allowed to handwrite the large truth table. The small truth table—the table with just the last premise and conclusion should go in the main text. You are using this table to explain why a contradiction as a premise and a tautology as a conclusion guarantees validity. You should be very suspicious if the last premise is not a contradiction and the conclusion is not a tautology. 4. The truth table will tell you whether the argument is valid or invalid. In this case, it will tell you that the argument is unsound. This is because one premise is a contradiction. 5. If a statement is contingent, the truth table will not tell you whether the statement is true or false. You will have to use the dictionary and plug in the values. Suppose you have this as a premise ‘SV’ in which S=an argument is a syllogism and V=an argument is valid. To explain why SV is false, you need to explain that just because an argument is a syllogism does not mean it is valid (an example should be used). The fact that ‘SV’ is contingent in the truth table is irrelevant. 6. When you discuss why the premises are true or false, it is a good idea to treat them as conditional statements of the form “if____, then____”. It is easier to explain why “If S, then V” is true or false than it is to explain why ‘S only if V’ or ‘V if S’ is true or false. (The statement ‘S only if V’ does not mean that the only way to have S is to have V.) 7. When you discuss why the premises are true or false, it is a good idea to provide a paragraph to each premise. This way, you are less likely to skimp on the discussion. 8. Use examples when relevant. 9. It is a good idea to keep an extra copy of your paper.