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Lecture 4

PHI 1101 Lecture Notes - Lecture 4: Brown Recluse Spider, Electrical Contacts, If....


Department
Philosophy
Course Code
PHI 1101
Professor
Mark Brown
Lecture
4

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PHI 1101
Chapter 4
Exam #2
Sentential Form
A) Form and variables.
Consider these arguments:
1- If the presence of the anthropologist changed the normal lifestyle of the islanders, then her
conclusions are not reliable. Her presence did cause such a change. So her conclusions are not reliable.
2- If the spider is a brown recluse, then it is dangerous. The spider is a brown recluse. Therefore, it is
dangerous.
-These arguments both contain two premises and a conclusions
-One premise is a conditional (if.....then....) sentence.
-The other premise is the same as the clause that comes immediately after the “if” in the conditional
-The conclusion is the same as the clause that follows “then” in the conditional.
---> If we use letters to replace the component sentences in either argument, we represent the form in
this way:
If P, then Q
P
therefore, Q
Sentential form: Letters replace simple sentences that make up the compound sentences of the
argument. The letters P and Q are called sentential variables.
B) Connectives
-We can simplify the representation of argument forms by using symbols to replace ordinary
connective words like “and”, “or”, and “if ..... then.....” that are used to join simple sentences.
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Ordinary words Symbol Name
_________________________________________________________________________
either... or.... V Disjunction
Either it is a cat or a dog. C. v. D.
And, but, yet . Conjunction
It is a dog, and it bites. D. .B
if...., then.... ----> Implication
If it bites, then you should be wary. B ----> W
-”If.... then....” are called conditionals or hypotheticals. In a conditional, the component immediately
following if is called the antecedent; the component sentence following then is the consequent.
C. Negation
-Symbol used to deny or negate a claim.
Not (and other ways of denying) ~ Negation
It is not a dog. ~D
-Putting a “~” before a variable forms its denial. It's like putting “it is not the case” before a sentence.
-Negative sentences (Cats do not like cream) can be denied by adding the prefix, “it is not the case
that”. We can deny a negative variable, ~C, by adding another ~. But double negatives are clumsy and
sometimes confusing (it is not the case that cats do not like cream). Instead of adding another “not” to
this sentence, we remove the one we already have. We treat the denial of negative variables in the same
way, generally using C (rather than ~~C), to deny ~C.
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