Traditional Logic I Chapter IX - Memoria Press
Traditional Logic I Chapter IX - Memoria Press
Traditional Logic I Chapter IX - Memoria Press
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Three Acts of the Mind<br />
Mental Act:<br />
• Simple Apprehension<br />
• Judgment<br />
• Deductive Inference<br />
Verbal Expression:<br />
• Term<br />
• Proposition<br />
• Syllogism<br />
Slide 9-1<br />
Obversion, Conversion &<br />
Contraposition<br />
The Three relations of equivalence<br />
Obversion<br />
Double Negation<br />
Conversion<br />
Contraposition<br />
Review of <strong>Chapter</strong>s 4-9<br />
Slide 9-2
Equivalence: Three ways to<br />
convert logical statements into<br />
their logical equivalents<br />
Obversion<br />
Conversion<br />
Contraposition<br />
Slide 9-3<br />
Obversion<br />
Slide 9-4<br />
Change the quality of the<br />
statement<br />
Negate the predicate
How to change the quality<br />
of a statement<br />
If the statement is affirmative, simply<br />
make it negative<br />
If the statement is negative, simply<br />
make it affirmative<br />
Be careful not to change the quantity<br />
of the statement: AE, IO<br />
Slide 9-5<br />
All S is P<br />
No S is P<br />
Examples of how<br />
to change the<br />
quality of a<br />
statement:<br />
No S is P<br />
All S Is P<br />
Some S is P Some S is<br />
not P<br />
Some S is not P Some S is<br />
P<br />
Slide 9-6
How to<br />
change the<br />
quality of a<br />
statement<br />
Simply place a ‘not’ in<br />
front of it.<br />
Slide 9-7<br />
How to<br />
obvert an A<br />
statement<br />
Change the quality:<br />
All S is P No S is P<br />
Then negate the predicate:<br />
No S is P No S is not P<br />
Slide 9-8
How to<br />
obvert an E<br />
statement<br />
Change the quality:<br />
No S is P All S is P<br />
Then negate the predicate:<br />
All S is P All S is not P<br />
Slide 9-9<br />
How to<br />
obvert an O<br />
statement<br />
Change the quality:<br />
Some S is not P Some S is P<br />
Then negate the predicate:<br />
Some S is P Some S is non-P<br />
Slide 9-10
The Rule of<br />
Double<br />
Negation<br />
A term that is not negated is<br />
equivalent to a term that is<br />
negated twice and viceversa.<br />
Slide 9-11<br />
Slide 9-12<br />
How to perform double<br />
negation<br />
1. Place two ‘not’s at the beginning of the<br />
predicate-term<br />
2. Make the second ‘not’ a ‘non’ and attach it to<br />
the predicate term with a dash<br />
3. Place an ‘im’, ‘un’, ‘in’, or ‘ir’ at the beginning of<br />
the predicate term<br />
4. Apply the rule of double negation
How to<br />
obvert an I<br />
statement<br />
Change the quality:<br />
Some S is P Some S is non-P<br />
Then negate the predicate:<br />
Some S is not P Some S is not<br />
non-P<br />
Slide 9-13<br />
Conversion<br />
Interchange the subject and<br />
predicate<br />
Slide 9-14
How to convert<br />
an E and I<br />
statements<br />
Interchange the subject and the<br />
predicate:<br />
No S is P No P is S<br />
Some S is P Some P is S<br />
Slide 9-15<br />
Partial<br />
conversion of<br />
A statements<br />
Interchange the subject and the<br />
predicate and change the<br />
quantity:<br />
Slide 9-16<br />
All S is P Some S is P
Contraposition<br />
Obvert the statement<br />
Convert the statement<br />
Obvert the statement again<br />
Slide 9-17<br />
How to convert<br />
an A statement<br />
Original Statement: All men are mortal<br />
Obvert: No men are non-mortal<br />
Convert: No non-mortals are men<br />
Obvert: All non-mortals are non-men<br />
Slide 9-18
Obversion, Conversion & Contraposition<br />
Equivalents<br />
A<br />
E<br />
I<br />
O<br />
Obversion<br />
<br />
<br />
<br />
<br />
Conversion<br />
<br />
<br />
Contraposition<br />
<br />
<br />
Slide 9-19
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