The Language of Argument

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B a s i c P r o p o s i t i o n a l C o n n e c t i v e s

Process of Elimination

Using only negation and disjunction, we can analyze the form of one

common pattern of reasoning, which is called process of elimination or, more

technically, disjunctive syllogism. As an example, consider this argument:

She is sitting alone and talking, so she must be either talking on a phone

I don't see or talking to herself. She is clearly not talking to herself, since

she's not crazy. So she must be talking on her phone.

After trimming off assurances and subarguments that support the premises,

the core of this argument can be put in standard form:

(1) She is either talking to herself or talking on a phone.

(2) She is not talking to herself.

∴(3) She is talking on a phone. (from 1–2)

This core argument is then an instance of this argument form:

1. p ∨ q
   ~p
   ∴ q
   It does not matter if we change the order of the disjuncts so that the first
   premise is “She must be either talking on a phone or talking to herself.”
   Then the argument takes this form:


2. p ∨ q
   ~q
   ∴ p
   Both of these argument forms are valid, so the core of the original argument
   is also valid.

than one way, symbolize each interpretation and describe a context in which it

would be natural to interpret it in each way.

1. It won’t rain tomorrow.


2. It might not rain tomorrow.


3. There is no chance that it will rain tomorrow.


4. I believe that it won’t rain tomorrow.


5. Joe is not too smart or else he’s very clever.


6. Kristin is not smart or rich.


7. Sometimes you feel like a nut; sometimes you don’t. (from an advertisement
   for Mounds and Almond Joy candies, which are made by the same
   company and are exactly alike except that only one of them has a nut)

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