PHIL 150 Chapter Notes - Chapter 5, E-G: Categorical Proposition, Baltimore Stars
10 May 2018
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PHIL Logic Reading Notes
Chapter 5 (E-G)
E. Conversion, Obversion, and Contraposition in the Modern Square
Immediate argument: an argument that has only one premise
Mediate argument: an argument that has more than one premise
Conversion: an immediate argument formed by interchanging the subject and predicate terms of a
given categorical proposition
o We start with the convertend, and after conversion, it becomes the converse
Ex: Convertend – No beer commercials are subtle advertisements. (E-prop)
o Converse – No subtle advertisements are beer commercials. (E-prop)
Obversion: an immediate argument formed by 1. changing the quality of the given proposition, and
then 2. replacing the predicate term with its complement
o Complement: the set of objects that do not belong to a given class
o The objects that belong to the non-(predicate term) class
o We start with the obvertend, and after obversion, it becomes the obverse
Ex: Obvertend – All jackhammers are weapons. (A-prop)
o Obverse – No jackhammers are non-weapons. (E-prop)
Contraposition: an immediate argument formed by 1. replacing the subject term of a given
proposition with the complement of its predicate term, and then 2. replacing the predicate term of
the given proposition with the complement of its subject term
Ex: Given proposition – All pencils are ink-free writing tools. (A-prop)
o Contrapositive – All non-ink-free writing tools are non-pencils. (A-prop)
Diagrams
o With conversion, obversion, and contraposition, if the diagram stays the same, the
transformation keeps the argument valid
o Remember if the premise and conclusion are the same, then if the premise is true, the
conclusion is also true
Conversion is valid for E- and I-propositions
Obversion is valid for A-, E-, I-, and O-propositions
Contraposition is valid for A- and O-propositions
F. The Traditional Square of Opposition and Venn Diagrams
Contraries: pairs of propositions that cannot both be true at the same time, but can both be false at
the same time
Ex: A- and E-propositions
o (1) All zoos are places where animals are treated humanely. (A-prop)
o (2) No zoos are places where animals are treated humanely. (E-prop)
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find more resources at oneclass.com
Document Summary
Chapter 5 (e-g: conversion, obversion, and contraposition in the modern square. Immediate argument: an argument that has only one premise. Mediate argument: an argument that has more than one premise. Conversion: an immediate argument formed by interchanging the subject and predicate terms of a. Ex: convertend no beer commercials are subtle advertisements. (e-prop: converse no subtle advertisements are beer commercials. (e-prop) Ex: obvertend all jackhammers are weapons. (a-prop: obverse no jackhammers are non-weapons. (e-prop) Ex: given proposition all pencils are ink-free writing tools. (a-prop: contrapositive all non-ink-free writing tools are non-pencils. (a-prop) Conversion is valid for e- and i-propositions. Obversion is valid for a-, e-, i-, and o-propositions. Contraposition is valid for a- and o-propositions: the traditional square of opposition and venn diagrams. Contraries: pairs of propositions that cannot both be true at the same time, but can both be false at the same time.
