Week 2 Prompt Option #4: Finding the Argument Form
One of the ways that we can determine whether a deductive argument is valid or not is based on its logical form. The first step in being able to make this determination is to be able to determine the logical form of the argument. This discussion allows you to get practice determining the logical form of various arguments. Once you get the hang of it, you might even find that discovering argument forms is fun.
Prepare: To prepare to respond to this question, read the required sections from Chapter 3 and Chapter 4, paying special attention to those sections that explain categorical argument forms (in Chapter 3) and propositional argument forms (in Chapter 4).
Reflect: Choose an argument from the list below. To find the argument’s form, leave in the logical terms in the argument and replace the other terms with variables. In the categorical examples, the logical terms are ‘all’, ‘no’, ‘some’, ‘only’, and ‘not’, and the variables are letters like A, B, and C.
Here is an example of finding the form of a categorical argument: Take the argument, “Some dogs are brown. Only brown things are mammals. Therefore, Some dogs are mammals.” What we do is replace the non-logical terms with variables (capital letters). We can use ‘D’ for dogs, ‘B’ for brown things, and ‘M’ for mammals. The result, in standard form, is that the argument has the form:
Some Ds are B.
Only B are M.
Therefore, Some D are M.
In the propositional examples, the logical terms are ‘and’, ‘or’, ‘not’, ‘if … then’, ‘only if’ and ‘if and only if’, and the variables, letters like P, Q, and R, represent the simplest component sentences. You may use the following simplified symbols: The symbol for ‘and’ is ‘&’, the symbol for ‘or’ is ‘v’, the symbol for ‘not’ is ‘~’, the symbol for ‘if … then …’ is ‘–>’, and the symbol for ‘if and only if’ is <–>’ (Don’t forget to use parentheses to clarify the grouping in complex statements).
Here is a propositional example: Take the argument, “If you don’t like cabbage, then you should eat the peas. You like the cabbage, so you should not eat the peas.” We’ll use the letter ‘C’ for the sentence “You like cabbage” and the letter ‘P’ for “You should eat the peas.” The result, in standard form, is:
~C –> P
Write: Choose an argument from the list below. Make sure not to pick one that someone else has used. Paste the argument at the beginning of your post, then use standard form to present its logical form, as with the examples above. Make sure to provide a key indicating what each letter symbolizes. Next, provide a brief discussion of whether the argument form is valid and why. If it is valid, try to explain why the conclusion must be true provided that the premises are. If it is not valid, try to explain how it would be possible for the premises to be true and the conclusion false.
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