LPS 29 Lecture Notes - Lecture 3: Modus Tollens, Modus Ponens, Sentence Clause Structure

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LPS 29 - Lecture 3 Propositional Logic
3.1 Argument Forms
Formal Logic: the study of argument forms, abstract patterns of reasoning shared by
many different arguments
Disjunctive Syllogism:
o Either P or Q
o It is not the case that P
o Q
o In this case, P and Q serve as something called sentence letters.
Example: Either Sally took the apple or Roger did.
Roger didn’t take the apple
Sally took the apple
Modus Ponens/ assertive mode
o If P, then Q
o P.
o Q
Example:
If he is going to the beach, then I will go to the beach.
He is going to the beach.
I will go to the beach.
Modus Tollens/ denying mode
o If P, then Q
o It is not the case that Q
o It is not the case that P
In some cases:
o If P and Q, then R
o It is not the case that R
o It is not the case that P and Q
Both cases of Modus Ponens and Modus Tollens are valid.
However, a form called affirming the consequent is not always valid
o If P, then Q
o Q.
o P.
Example:
If you are against me, then you are in trouble
You are in trouble
You are against me
In this example, the argument above is invalid, because you can
be in trouble for other matters other than being against me.
3.2 Logical Operators
Logical Operators/ Connectives
o “it is not the case that” (~)
Negation: sentences that express an opposition
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Ex: He is not a soccer player.
Ex: He was uncomfortable/ it is not the case that he was comfortable
o “and” (as well as ‘yet’ ‘although’ ‘but’) (&)
binary operator
conjunction: the compound sentence
conjuncts: the two parts of the compound sentence
goes by first conjunct, and second conjunct
Ex: Sally and Jane are going to the party today
o “either…or” (V)
binary operator
disjunction: the compound sentence
disjuncts: the two parts of the compound sentence
goes by first disjunct, and second disjunct
Note that ‘either’ will not always be in the sentence
Ex: I want either a cat or a dog. OR: I want a cat or a dog
o “if…then” ()
binary operator
conditional: the “if…then” statement
antecedent: the “if” part of the statement
consequent: the “then” part of the statement
Note that ‘then’ will not always be in the sentence
o “if and only if” ()
binary operator
biconditionals: the “if and only if” statement
left-hand side: the part of the sentence that comes before the “if and only
if”
right-hand side: the part of the sentence that comes after the “if and only
if”
Left and right hand sides do not matter
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find more resources at oneclass.com