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Conversion, Obversion, and Contraposition
5
Logical Operators
Conversion, Obversion, and Contraposition.
Aristotle
Figure 1
Author
Conversion, Obversion, and Contrapostion build off of the well know square of opposition (Figure 1) developed by Aristotle.
These operators allow us to change propositions from one categorical statement to another (under certain rules).
Overview of Rules
A quick refresher on the rules of these operators.
Rules
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Rules of Conversion
Conversion is the process of swapping the position of the Subject and the Predicate within a proposition.
Conversion only holds truth value if it is used on an E or an I proposition, A and O propositions will produce a different meaning than the original proposition.
Conversion
Obversion Rules
Obversion is the process of negating both the Subject and the Predicate.
Obversion holds truth value in all propositions no matter what categorical statement.
Obversion
Rules of Contraposition
Contraposition uses the rules of both Conversion, and Obversion to complete it's operation.
To Contrapose a proposition, you must first obvert (Negate S and P), then Convert (swap positions of S and P), finally Obvert Again. Your result should be a proposition with both S and P negated, and swapped positions. Only A and O propositions hold truth value (opposite of conversion).
Contrapostion
Understanding Operations
During my time of repeatedly writing these in my BNR, I learned a couple of tricks that helped me to really understand and optimize this logic.
Uderstanding the Operations
Venn Diagrams with Operators
A=Subject
B=Predicate
Dashed lines=Empty
X=Existence
Examples:
All men are mortals. (A Prop)
Some plants are nonroses. (I Prop)
Venn Diagrams
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Formal Language for these Operations
Categories of the Proposition (placed at the beggining):
Formal Language
5
Conversion Example
Original: Some non-Fords are nonautomobiles.
Translated: I-x+y
Converted: Iy+-x
Translated Back: Some nonautomobiles are non-Fords
Conversion Example
Obversion Example
Original: Some Las Vegas casinos are not places likely to increase your wealth.
Translated: Ix-+y
Obverted: Ix(--)+-y
Translated Back: Some Las Vegas casinos are non-places likely to increase your wealth.
Obversion Example
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Contraposition Example
Original: All college students are entities having IQs of at least 100
Translated: Ax+y
Contraposed:
Obverted: Ex+-y
Converted: E-y+x
Obverted: A-y+-x
Translated Back: All non-entities having IQs of at least 100 are non-college students
Contraposition Example
Works Cited
Copi, Irving et al. "Essentials Of Logic", Routledge, 2016.
Smith, Robin. "Aristotle’s Logic", Stanford Encyclopedia of Philosophy, 2000 Mar 18.
Venn, John “I. On the diagrammatic and mechanical representation of propositions and reasonings.” Philosophical Magazine Series 1 10: 1-18.