Basic Logic
Phil 101: Introduction to Philosophy 
Jeremy Anderson, Ph.D.



Putting an Argument in Standard Form
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Jeremy Anderson



Introduction to standard form

Philosophers usually present their arguments in prose. It is often helpful to take an argument from its original prose statement and lay out its premise(s) and conclusion(s) -- i.e., to put it into standard form, because then its reasoning (whether good or bad!) may be seen more clearly. 

Here's a simple argument in standard form.

1. Humans are mortal.
2. Socrates is human.
3. Therefore, Socrates is mortal (by 1 and 2).

From this, we can see the few simple rules of standard form:
  • The argument is written as a list of numbered steps.
  • Each step contains only one proposition -- a single declarative sentence. That proposition may be a premise, a conclusion, or both the conclusion of one argument and a premise of another.
  • Premises come before the conclusions they are supposed to support.
  • Conclusions are signaled by words like “Therefore...” or “So...” or sometimes three dots in a triangle: .:
  • We say which premises are supposed to support each conclusion.
Also, in work submitted for credit, academic integrity is important. (Here are the academic integrity instructions for this course and DePauw's academic integrity policy). So, if you are putting an argument in standard form for a something you will submit for credit, there's one more rule:
  • Cite the argument's source and, if you use an author's words, put them within quotation marks.

First example: a relatively easy case

Here is an example of how to convert a relatively simple prose argument into standard form.
 
Let’s take a sample from Andrew Bailey’s discussion of inductive arguments. We will be careful to keep the author's words within quotation marks whenever we use them:

“The biological world is a highly complex and inter-dependent system. It is highly unlikely that such a system would have come about (and would continue to hang together) from the purely random motions of particles. It would be much less surprising if it were the result of conscious design from a super-intelligent creator. Therefore, the biological world was deliberately created (and therefore, God exists)” (Bailey, xx).

To start, let’s break this text down into a numbered list of separate propositions. To do this, we go through Bailey's paragraph and start a new line after each claim, and then number the resulting list. Some correction of punctuation is needed:

1. “The biological world is a highly complex and inter-dependent system.”
2. “It is highly unlikely that such a system would have come about (and would continue to hang together) from the purely random motions of particles.”
3. “It would be much less surprising if it were the result of conscious design from a super-intelligent creator.”
4. “Therefore, the biological world was deliberately created.”
5. “[T]herefore, God exists” (Bailey, xx).
 
Notice that we have kept Bailey's words in quotation marks and kept the citation. These are needed to maintain academic integrity. Also, notice how this example follows the other rules of standard form:
  • We now have a series of numbered steps.
  • Each step contains only one proposition: one premise or one conclusion (with step #4 being both a conclusion and a premise, but it is one proposition so it is placed in one numbered step).
  • The premises come before the conclusions they are supposed to support. We didn't have to re-order of the statements because the prose argument was written that way.
  • The conclusions are signaled (by "therefore").
But we are not yet finished. Our last task is to indicate which premises support each of the conclusions. Here is the final version of the argument, which now follows all the rules of standard form:

1. “The biological world is a highly complex and inter-dependent system.”
2. “It is highly unlikely that such a system would have come about (and would continue to hang together) from the purely random motions of particles.”
3. “It would be much less surprising if it were the result of conscious design from a super-intelligent creator.”
4. “Therefore, the biological world was deliberately created” (by 1, 2, 3).
5. "[T]herefore, “God exists” (by 3, 4; Bailey, xx).
 
Now, we might wonder whether 5 could follow merely from 4, rather than both 3 and 4. The mention of "super-intelligent" seems to be a feature attributed to God that is not apparent from 4 alone, so I think 5 is meant to follow from both 3 and 4.

That was fairly easy.

Second example: a more challenging case

Let’s take a more challenging example from our textbook. This argument is about whether "vital spirit" exists -- that is, whether there is some spiritual substance in the universe, in addition to matter, which makes things alive. The author here argues that denying "vital spirit" is self-defeating (or "self-refuting"): 

“The anti-vitalist says that there is no such thing as vital spirit. But this claim is self-refuting. The speaker can be taken seriously only if his claim cannot. For if the claim is true, then the speaker does not have vital spirit and must be dead. But if he is dead, then his statement is a meaningless string of noises, devoid of reason and truth” (Bailey, xx-i).
 
Again, we start by breaking the text into a numbered list of propositions. Again, we just go through the text and start a new line for each claim, and then number them. Some correction and clarification are needed, both to make each step a grammatically correct proposition and to ensure the meaning of each step stays clear:

1. “The anti-vitalist says that there is no such thing as vital spirit.”
2. “But this claim [that there is no such thing as vital motion] is self-refuting.”
3. “The speaker can be taken seriously only if his claim cannot.”
4. “For if the claim is true, then the speaker does not have vital spirit” [yes, an if-then statement is generally one step]
5. Someone who does not have vital spirit “must be dead.”
6. “But if he is dead, then his statement is a meaningless string of noises, devoid of reason and truth” (Bailey, xx-i).
 
That last step, #6, is tricky. Notice that two sorts of accusations are being made about the anti-vitalist's statement: (a) that it "is a meaningless string of noises" and (b) that it is "devoid of reason and truth." These two accusations are separated by a comma, which leaves it unclear how (a) and (b) are supposed to relate to each other. Perhaps (b) is meant to be a mere restatement of (a), so that step #6 could read like this:

6'. "But if he is dead, then his statement is a meaningless string of noises"; in other words, it is "devoid of reason and truth."

Or is (b) perhaps a consequence of (a)? In other words, maybe the author is saying that the anti-vitalist's statement is "devoid of reason and truth" because it is "a meaningless string of noises." If so, (a) and (b) make an argument, with (a) as the premise for conclusion (b). Then the rules of standard form would require us to restate #6 in two parts, maybe like this:

6''. "But if he is dead, then his statement is a meaningless string of noises."
7. Therefore, his statement is "devoid of reason and truth" (by 6''). 

What should we do here? Should we stay with the original, #6, or use 6', or use 6'' plus 7? Here is my suggestion: if we use either 6' or 6'' plus 7, we risk putting words into the author's mouth which the author did not intend. But if we stay with the original 6 we do not risk such misinterpretation. Also, if we stay with 6 the argument seems clear enough; we do not need to figure out what that comma means in order to understand the argument. Moreover, we can evaluate the argument without knowing which of these the author meant. So I would stay with the original, 6.

However, before we are finished we need to re-order the statements to put the conclusions after their premises. Notice that steps 4, 5, and 6 are premises, but no conclusions appear after them. (This is especially obvious with 4 and 6, which start with “For” and “But”: these words signal that those statements are premises.) So the conclusions that 4, 5, and 6 are supposed to support must be above. Let's rearrange the propositions into logical order, with premises prior to conclusions and conclusions indicating which premises support them. We correct the statements’ grammar where needed, and here is the finished version:

1. “The anti-vitalist says that there is no such thing as vital spirit.”
2. “If the claim [that there is no such thing is vital spirit] is true, then the speaker does not have vital spirit.”
3. Someone who does not have vital spirit “must be dead.”
4. “But if he is dead, then his statement is a meaningless string of noises, devoid of reason and truth.”
5. Therefore, “The speaker can be taken seriously only if his claim cannot” (by 1, 2, 3, and 4).
6. Therefore, the claim that there is no such thing as vital motion “is self-refuting” (by 5) (Bailey, xx-i).

We have retained the italics for "dead" because quotations must be accurate. Notice that we have kept the author's words in quotation marks throughout the argument and given the citation, as we would if this were for an assignment submitted for credit.


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