Exam 2 Prep

PHIL 115 Exam 2 Prep
(for Fri., Nov. 20)

Know and be able to do anything on HW4 or HW5 or HW6 or HW7 or in-class quizzes, including but not limited to the following concepts:

Chapter 4 Categorical Propositions
4.1 Components of Categorical Propositions
Categorical Propositions
Standard Form
Subject term
Predicate term
Quantifiers ("all," "no," "some")
Copula ("are," "are not")
4.2 Quality, Quantity, and Distribution
Quality (affirmative, negative)
Quantity (universal, particular)
A, E, I, O
Distribution of terms

Proposition	Letter Name	Quantity	Quality	Terms Distributed
All S are P.	A	universal	affirmative	S
No S are P.	E	universal	negative	S and P
Some S are P.	I	particular	affirmative	none
Some S are not P.	O	particular	negative	P

4.3 Venn Diagrams and the Modern Square of Opposition
Aristotelian and Boolean standpoints
Venn diagrams (shading to indicate empty area, "x" to indicate at least one)
Modern square of opposition
Contradictory relations (A-O, and E-I)
Logically undetermined relations (all others)
Testing immediate inferences (Venn diagrams or the modern square)
Unconditional validity
How to say that a categorical proposition is false
Existential fallacy
4.4 Conversion, Obversion, Contraposition
Conversion consists in switching the subject and predicate terms
E and I propositions are logically equivalent to their converses
(To be logically equivalent is to necessarily have the same truth value)
Illicit conversion (formal fallacy) - arguing from an A or O proposition to its converse
Obversion consists in changing the quality of a proposition and then replacing the predicate term with its term complement
Class complement
Term complement
Scope of discourse (a.k.a. universe of discourse or u.d.)
Each proposition is logically equivalent to its obverse
Contraposition consists in conversion of a proposition followed by replacing the subject and predicate terms with their term complements
A and O propositions are logically equivalent to their contrapositives
Illicit contraposition (formal fallacy) - arguing from an E or I proposition to its contrapositive
4.5 Traditional Square of Opposition
Aristotelian standpoint
Contrary (not both true) - A/E
Subcontrary (not both false) - I/O
Subalternation (truth flows down, A/I and E/O; falsity flows up, I/A and O/E)
Formal fallacies: illicit contrary, illicit subcontrary, illicit subalternation
Existential fallacy: using contrary, subcontrary, or subalternation (otherwise correctly) with propositions about things that do not exist
Conditional validity and unconditional validity
4.6 Venn Diagrams and the Traditional Standpoint
Using the circled X in A and E propositions
3 step procedure for testing immediate inferences from the Aristotelian standpoint:
1. Reduce the inference to its form and test from the Boolean standpoint. If valid, stop - it is unconditionally valid.
2. If invalid from the Boolean standpoint, adopt the Aristotelian standpoint and employ the circled X if applicable and retest.
3. If conditionally valid, determine whether the circled X represents something that exists. If so, the inference is valid from the Aristotelian standpoint. If not, the inference is invalid and it commits the existential fallacy from the Aristotelian standpoint.
4.7 Translation
See many examples and hints in the book, especially the box on p. 239
Chapter 5 Categorical Syllogisms
5.1 Standard Form, Mood, Figure
Categorical Syllogisms
Major Term (predicate of the conclusion)
Minor Term (subject of the conclusion)
Middle Term (occurs in each premise but not the conclusion)
Standard Form defined (4 clauses, p. 244)
Mood (EIO, AAI, etc.)
Figure (1, 2, 3, 4)
Form (AAA-1, OAE-4, etc.)
Tables and poem for validity
Unconditional and conditional validity
5.2 Venn Diagrams
7 guidelines (pp. 253-4)
3 more steps for the Aristotelian standpoint (p. 259)
5.3 Rules and Fallacies
These are 5 rules that a categorical syllogism must comply with, in order to be valid
If a categorical syllogism breaks none of the rules, it is unconditionally valid
If it breaks one of the first four rules, it is invalid
If it breaks rule 5 only, it is invalid from the Boolean standpoint, and conditionally valid from the Aristotelian standpoint, conditional upon the non-empty extension of a critical term
Rule 1: The middle term must be distributed
Fallacy: Undistributed middle
Rule 2: If a term is distributed in the conclusion, it must be distributed in a premise
Fallacy: Illicit major, or illicit minor, as the case may be
Rule 3: Two negative premises are not allowed
Fallacy: Exclusive premises
Rule 4: A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise
Fallacy: Drawing an affirmative conclusion from a negative premise, or drawing a negative conclusion from affirmative premises, as the case may be
Rule 5: If both premises are universal, the conclusion cannot be particular
Fallacy: Existential fallacy
5.4 Reducing the number of terms
Conversion, obversion, and contraposition may be used to reduce the number of terms to three
5.5 Ordinary Language Arguments
This section is a rehash of Section 4.7
5.6 Enthymemes
An enthymeme is an argument expressible as a categorical syllogism, but with one of the statements (premise or conclusion) missing
The reader must determine what is missing (premise or conclusion), and then supply the missing statement with the aim of converting the enthymeme into a good argument (p. 278)
Any enthymeme that contains an indicator word is missing a premise