Argument Form
As we discussed in previous lessons, the “superpower” of validity is that it allows us to study arguments based on their form. To do this effectively, it is helpful to symbolize statements, and as usual, we will return to our favorite example:
- If you hear barking, then there must be a dog.
- You heard barking.
- There must be a dog. (1, 2)
To symbolize the argument above: Let “B” represent the statement “I heard barking”, “D” represent the statement “there must be a dog”, “B → D” represent “If you hear barking, then there must be a dog.”
- B → D
- B
- D (1)
Note: The first premise includes a logical connective known as the implication, if you are unfamiliar with it, do not worry; we will cover it in a later lesson–the point of this lesson is solely on symbolizing statements and generalizing them into forms.
Now that we have symbolized our statements, it is easier to recognize the form of the argument. To generalize a form, we use variables, which can be thought of as placeholders for statements and are represented with lowercase letters.
a → b
a
b
Note: Forms do not contain line numbers. This is to convey that premise order does not matter. For example, if line numbers 1 and 2 were switched in the previous argument, so that “B” was line number 1 and “B → D” was line number 2, it would still follow the above form.
With its form identified, we can easily parallel an argument, which means to generate another argument that follows the same form. Let us use: “If it is raining (R), you need an umbrella (U). It is raining (R). So, you need an umbrella (U)”.
- R → U
- R
- U
We can immediately recognize that “R” is in the place of “a” and “U” is in the place of “b”, so this argument follows the previously mentioned form. Now what if we had something like “If it is raining, you need an umbrella. You need an umbrella. So, it is raining.”?
- R → U
- U
- R
This is NOT the same form. Instead, it follows the form:
- a → b
- b
- a
This slight difference is the difference between modus ponens and the fallacy of the converse. The first being one of the most common valid argument forms and the second being one of the most common invalid forms–or fallacies–in formal logic. There is much more to be said about the two aforementioned argument forms and their differences. However, before we can dive into studying argument forms, we still need to know the difference between an affirmed or negated statement.
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app now:
As we discussed in previous lessons, the “superpower” of validity is that it allows us to study arguments based on their form. To do this effectively, it is helpful to symbolize statements, and as usual, we will return to our favorite example:
- If you hear barking, then there must be a dog.
- You heard barking.
- There must be a dog. (1, 2)
To symbolize the argument above: Let “B” represent the statement “I heard barking”, “D” represent the statement “there must be a dog”, “B → D” represent “If you hear barking, then there must be a dog.”
- B → D
- B
- D (1)
Note: The first premise includes a logical connective known as the implication, if you are unfamiliar with it, do not worry; we will cover it in a later lesson–the point of this lesson is solely on symbolizing statements and generalizing them into forms.
Now that we have symbolized our statements, it is easier to recognize the form of the argument. To generalize a form, we use variables, which can be thought of as placeholders for statements and are represented with lowercase letters.
a → b
a
b
Note: Forms do not contain line numbers. This is to convey that premise order does not matter. For example, if line numbers 1 and 2 were switched in the previous argument, so that “B” was line number 1 and “B → D” was line number 2, it would still follow the above form.
With its form identified, we can easily parallel an argument, which means to generate another argument that follows the same form. Let us use: “If it is raining (R), you need an umbrella (U). It is raining (R). So, you need an umbrella (U)”.
- R → U
- R
- U
We can immediately recognize that “R” is in the place of “a” and “U” is in the place of “b”, so this argument follows the previously mentioned form. Now what if we had something like “If it is raining, you need an umbrella. You need an umbrella. So, it is raining.”?
- R → U
- U
- R
This is NOT the same form. Instead, it follows the form:
- a → b
- b
- a
This slight difference is the difference between modus ponens and the fallacy of the converse. The first being one of the most common valid argument forms and the second being one of the most common invalid forms–or fallacies–in formal logic. There is much more to be said about the two aforementioned argument forms and their differences. However, before we can dive into studying argument forms, we still need to know the difference between an affirmed or negated statement.
Want an interactive way to learn logic?
Enhance your critical thinking skills with Symbols Logic. Unlock access to the first studycard and the first level of all activities for free. Get the app now: