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Traditional Logic:
 Concerns categorical propositions and categoricalpropositions affirm/deny the relationship between class and objects.
 (Class of humans, call of mortals)

4 kinds of categorical propositions
 1. Universal affirmative prop. All S is P.
 2. Universal negative prop. No S is P
 3. Particular affirmative prop. Some S is P
 4. Particular negative prop. Some S is not P

Categorical Proposition
a proposition that asserts a relationship between one category and some other category.

Universal Affirmative Proposition (A propositions)
 Prop. that assert that the whole of one class is included or contained in another class.
 All S is P.
 Example: All politicians are liars.

Universal Negative Proposition (E propositions)
 Prop that assert that the whole of one class is excluded from the whole of another class
 No S is P
 Example: No politicians are liars

Particular Affirmative Proposition (I propositions)
 Prop that assert that 2 classes have some member or members in common
 Some S is P
 Example: Some politicians are liars

Particular Negative Propositions (O propositions)
 Prop. that assert that at least 1 member of a class is excluded from the whole of another class
 Some S are not P
 Example: Some politicians are not liars

All lawyers are wealthy people
name and form;
A  Universal affimative

No criminals are good citizens
Name and form;
E  Universal negative

Some chemicals are poisons
Name and form;
I  Particular affirmative

Some insects are not pests
Name and form;
O  Particular negative

Quality
Determined by whether the proposition affirms or denies some form of class inclusion (affirmative or negative)

Quantity
Determined by whether the propositions refers to all members ("universal") or only some members ("particular") of the subject class

Distribution
 A characterization of whether terms in a categorical proposition refer to all members of the class designated by that term.
 If it makes term to all of the members distributed
 If it doesnt make term to all of the members undistributed

Distibuted vs. Undistributed
*All S are P;
 S= distributed
 P=undistributed

Distributed vs. undistributed
*Some S are P;
 S=undistributed
 P=undistributed

Distributed vs undistributed
*No S are P;
 S=distributed
 P=distributed

Any predicate will be undistributed in an ____ statement.
A

Statements are not distributed or undistributed, just
the terms S and P

______ propositions are distributed, regardless of quality.
Universal

Opposition
Any logical relation among the kinds of categorical propositions (A,E,I,O) exhibited on the Square of Op.

Contradictories
Two propositions that cannot both be false

Contraries
 Two propositions that cannot both be true; if one is true, that other must be false.
 They CAN both be false

Subcontraries
 Two propositions that cannot both be false; if one is false the other must be true.
 They CAN both be true.

Subalternation
 The opposition between a universal proposition (the superaltern) and its corresponding particular proposition (the subaltern).
 It implies the truth of its corresponding particular proposition

Square of Opposition
Diagram showing the logical relationships among the 4 types of categorical propositions

 A(all S is P)=superaltern of I; contrary of E; & contradictory of O
 E(No S is P)=Superaltern of ); contrary to A; & contradictory to I.
 I(Some S is P)=subaltern to A; contradictory to E; & subcontrary to O.
 O(Some S are not P)=subaltern to E; subcontrary to I; & contradictory to A.

If A being given is true, then
 E is false
 I is true
 O is false

E being given as true, then
 A is false
 I is false
 O is true

I being given as true, then
 E is false
 A is undetermined
 O is undetermined

O being given as true, then
 A is false
 E is undetermined
 I is undetermined

A being given as false, then
 O is true
 E is undetermined
 I is undetermined

E being given as false, then
 I is true
 A is undetermined
 O is undetermined

I being given is false, then
 A is false
 E is true
 O is true

O being given as false, then
 A is true
 E is false
 I is true

Immediate Inference
An inference drawn directly from only one premise

All S are P and No S are P are both what type of quantity?
Universal

Some S are P and Some S are not P are both what type of quantity?
Particular

Conversion
 An inference formed by interchanging the Subject and Predicate terms of a categorical proposition.
 Only works for E & I statements
 No S are P  No P are S.
 Some S are P  Some P are S
 (Some students are females  Some females are students)

Convert by Limitations
 All S are P  Some P are S
 Turn an A statement into an I statement.
 ONLY used in A statements
 Only oneway inference(cant go the other way)

Converse of: (A) All S is P;
(I): Some P is S (by limitation)

Converse of: (E) No S is P;
(E): no P is S

Converse of: (I) Some S is P;
(I) Some P is S

Converse of: (O) Some S is not P;
(I) Some P is S **Conversion is not valid

Complement of a class
The collection of all things that do not belong to that class

Obversion
An inference formed by changing the quality of a prop. and replacing the predicate term by its complement.

Obversion is done in 3 ways
 1. Change the quality of the statement
 2. Leave the subject alone
 3. Substitute the predicate with its complement
 *All S are P
 *No S are P
 *No S are NON P

OBV. All humans are mortal
No humans are nonmortal

Obverse of; (A) All S is P;
(E) No S is non P

Obverse of; (E) No S is P;
(A) All S is non P

Obverse of (I) Some S is P;
(O) Some S is not non P

Obverse of; (O) Some S is not P;
(I) Some S is non P

Contraposition
 An inference formed by replacing the subject term of a prop. with the complement of its predicate term, and replacing the predicate term by the complement of its subject term.
 Only works for A & O statements

All P are S  Contraposition
All non P are non S

Contraposition by limitation
Works only for E statements

If A being given is true, then E is;
False

If A being given is true, then I is;
True

If A is true, then O is
False

If E is true, then A is;
False

If E is true, then I is;
False

If E is true, then O is;
True

If I is true, then E is;
False

If I is true, then A is;
Undetermined

I is true, then O is
Undetermined

If O is true, then A is;
False

O is true, then E is;
Understermined

O is true, I is;
undetermined

If A is false, then o;
true

If A is false, then E is
undetermined

If A is false, then I is;
undetermined

E is false, then I is;
true

E is false, then A is;
undetermined

If E is false, then Ois;
undtermined

If I is false, then A is;
false

f I is false, then E is;
True

If I is false, then O is
true

If O is false, then a is;
true

If O is false, then E is;
false

If O is false, then I is;
true

What is the contrapositive of;
A: All S is P
A: All nonP is nonS

What is the contrapositive of;
E: No S is P
O: Some nonP is not nonS. (by limitation)

What is the contrapositive of
O: Some S is not P
O: Some nonP is not nonS

If there is just one pair of complements, then _________ will be used
Obversion

If there are two pairs of complements, then _______ will be used
Contraposition

If S and P terms need to be reversed you will use;

Boolean Interpretation
Universal propositions (A and E) are not assumed to refer to classes that have members

In the boolean interpretation what statements are said to have existential import?
I and O statements

In the Boolean Int., "Some S are P"
 1. Will be false, There are S's and none are P's. (Some Usc students are alligators)
 2. Will also be false if there are no S's (Some martians are green) There are no existing martians.

In the Boolean Int., "Some S are not P"
 1. Will be false when all S's are P
 2. Will be false if there are no S's to begin with (Some martians are not green)

In the Boolean Int., "No S are P" is true when,
 1. there are S's that are p
 2. Are no S's to begin with

Existential Fallacy
In Boolean Int. cant go from AI or EO

What still works when dealing with Boolean Interp.
 Contraposition
 Conversion
 Obversion

 All S is P
 Predicate term in NOT distributed

 No S is P
 No philosophers are idlers
 Both S and P are distributed

 Some S is P
 Both terms are undistributed

 Some S is not P
 We are told something about the entire predicate class
 S is notdistributed, P is distributed

 AE; Now can be both true.
 IO; can both be False now
 AO; Contradictories
 IE; Contradictories

Symbolic Representation of All S is P;
S bar P = 0
 The class of things that are both S and nonP is empty. (OBV= all s are p)
 (All humans are mortal)

Symbolic representation of No S is P
 SP =0
 The class of things that are both S and P is empty

Symbolic representation of Some S is P
 SP does not = 0
 The class of things that are both S and P is not empty. (SP has at least 1 member)
 "X" indicates that something is there
 (SP is the overlap in the middle of the circles)

Symbolic representation of Some S is not P
 S bar P does not = 0
 The class of things that are both S and nonP in not empty. (S bar P has atleast 1 member)

In the Boolean inter. A and E statements;
Do not have exestential import

In the Boolean Inter. I and O statements;
have existential import

Fallacies of Ambiguity
 1. Equivocation
 1. Amphiboly
 3. Accent
 4. Composition
 5. Division

Fallacy of Equivocation
An informal fallacy in which 2 or more meanings of the same word or phrase have been confused
 Words that are vague or unclear
 Example: gay

Example of the fallacy of equivocation
 All kids have four legs
 My three year old is a kid
 Therefore my three year old has four legs
(kid could mean kid or goat...)

Fallacy of Amphiboly
An informal fallacy arising from the loose, awkward, or mistaken way in which words are combined, leading to alternative possible meanings of a statement

I've looked everywhere in this area for an instruction book on how to play the concertina without success. you need no instructions. just plunge in ahead boldly.
Fallacy of amphiboly

Fallacy of Accent
 Happens when a term or phrase has a meaning in the conclusionof an argument that is different from its meaning in one of the premises.
 Difference is usually because there is a change in emphasis given to the words used

Fallacy of Composition
An inference is mistakenly drawn from the attributes of the parts of a whole to the attributes of the whole itself

...each person's happiness is a good to that person, and the general happiness, therefore, a good to the aggregate of all persons
example of fallacy of composition

Fallacy of Division
is a mistaken inference is drawn from the attributes of a whole to the attributes of the parts of the whole

"No man will take counsel, but every man will take money: therefore money is better than counself
example of fallacy of Division

