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 one-way 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 non-mortal
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 non-P is non-S
What is the contrapositive of;
E: No S is P-
O: Some non-P is not non-S. (by limitation)
What is the contrapositive of
O: Some S is not P
O: Some non-P is not non-S
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;
Conversion
Contraposition
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 A-I or E-O
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
A------E; Now can be both true.
I------O; can both be False now
A-----O; Contradictories
I------E; Contradictories
Symbolic Representation of All S is P;
S bar P = 0
The class of things that are both S and non-P 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 non-P 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
