Chapter 4 Notes: Some Valid Argument Forms
I. Sentential Form
A. Form and Variables
One premise can be a conditional sentence (“If…then…”)
The second premise is the same as the clause the comes after the “if” in the conditional
The conclusion is the same as the clause that follows the “then” in the conditional
Sentential Form- when letters replace the simple sentences that make up compound
Sentential Variables- stand for any sentence that might be substituted with them
If P, then Q
Therefore, Q (3 dots or line above)
We can use symbols to replace ordinary connective words like “and”, “or”, and “if…
They should be regarded as representing the logical function performed by a number of
phrases that have a common role, rather than a translation
Ordinary Words Symbol Name
Either….or… v Disjunction
Either it is a cat or it is a dog.C v D
And, but, yet • Conjunction
It is a dog, and it bites. D B
If it bites, then you should be waBy. W
In a conditional/hypothetical sentence, the component immediately following the if is
called the antecedent.
The component sentence following the then is the consequent.
A symbol is used to show the denying of a claim. It is like putting, “It is not the case that”
before a sentence.
It is not a dog. D
You can also add another symbol to deny the negative variable. D. An Example of Symbolizing
Sentences are easier to deal with if we consider their constituent parts one at a time
If cigarette advertising leads teenagers to smoke, and advertisers lie about their aims,
then either cigarette advertising should not be allowed or it should be strictly regulated.
Cigarette advertising leads teenagers to smoke, and advertisers lie about their aims.
Either cigarette advertising should not be allowed or it should be strictly regulated.
A v R
(C L) ( A v R)
Hints on Symbolizing Complex Sentences:
1. Identify the simple component sentences – those that are not made up of further
sentences and connective phrases
2. Identify the main connective. This is the connective phrase that holds the whole
3. Try to symbolize the components that are connected by the main connective as
separate sentences. This involves applying Steps 1 and 2 again to these
subcomponents of the sentence. II. Valid Argument Forms
1. Modus Pones (MP)
If P, then Q P Q
Therefore, Q Q
If Manning is healthy, then the Colts will win.
Manning is healthy.
The Colts will win.
Complex as well as simple sentences can occupy the places of P and Q.
Components can be negative sentences.
The order in which the premises are given does not matter.