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Missing parts

How do we tell if part of an argument is missing?
© Patrick Girard, University of Auckland
Sometimes when people give you arguments, they will leave out parts of the argument. This may be because those parts are things that we all know, or maybe they think they don’t need to state every single reason explicitly, or maybe they have rhetorical reasons for leaving parts out.
If in some part of my argument, I need something simple like
  • The Moon is not a planet.
I don’t really need to say this, because I know that you know this. And it would be pedantic or perhaps insulting to tell you. And sometimes, it’s more effective to leave it out.
Here’s an example of an argument with missing parts, taken from the cabaret song Maybe This Time:
Everybody loves a winner, so nobody loves me.
The conclusion of this argument is “nobody loves me”. Why? The only reason provided is that “everybody loves a winner”, but something is missing.
What do you think is missing?
Answer: a premise is missing:
  • I’m not a winner.
When the part of an argument that is missing is a premise, we call that statement a ‘suppressed premise’. The argument in standard form, including the suppressed premise, is:
\(\begin{array}{ll} \text{P1} & \text{Everybody loves a winner.}\\ \text{P2} & \text{[I’m not a winner.]}\\ &\text{Therefore,}\\ \text{C} & \text{Nobody loves me.} \end{array}\)
Notice how we put the second premise in brackets in the standard form to indicate that the premise is suppressed.
One word of advice about suppressed premises: be economical! Don’t add suppressed premises unless they’re really obvious. You only want to include a suppressed premise in an argument when it is required for the argument, and it’s obvious that it has been left out on purpose.
Sometimes, another part of an argument that may be missing is the conclusion. We then say that the argument has a suppressed conclusion. An argument has a suppressed conclusion if it’s not explicitly stated. For example:
Recently, whilst I was on sabbatical in Scotland, I thought I saw the Loch Ness Monster. Turns out that all the sightings of the Loch Ness Monster are actually people mistaking logs for non-logs.
What do you think the conclusion is?
  • I did not see the Loch Ness Monster.
You might have been tempted to say “the Loch Ness Monster does not exist”, but that would not be right, as the premises do not seem to provide enough reason for that conclusion.
In standard form, the argument looks like this:
\(\begin{array}{ll} \text{P1} & \text{Whilst I was on sabbatical in Scotland, I thought I saw the }\\ & \text{Loch Ness Monster.}\\ \text{P2} & \text{All the sightings of the Loch Ness Monster are actually }\\ & \text{people mistaking logs for non-logs.}\\ &\text{Therefore,}\\ \text{C} & \text{[I did not see the Loch Ness Monster.]} \end{array}\)
As above, we put the conclusion in brackets to indicate that it was suppressed.
You need to be careful when formulating the suppressed conclusion. You want to find a conclusion that matches the reasons. You don’t want to put in a conclusion that wouldn’t be supported by the premises. This is not always easy, and we’ll have a chance to come to examples with suppressed premises and conclusions.
© Patrick Girard, University of Auckland
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Logical and Critical Thinking

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