Task 7 - Categorical Propositions - chapter 4 Flashcards
Proposition
a sentence that is either true or false
Categorical proposition
a proposition that relates two classes, or categories
- the classes in question are denoted respectively by the subject term and the predicate term
Standard-form categorical proposition
A categorical proposition that expresses there relations with complete clarity
Quantifiers
words such as "all", "no" and "some" - they specify how much of the subject class is included in or excluded from the predicate class
Copula
the words “are” and “are not”
- they link the subject term with the predicate term
Proposition
All S are P
Every member of the S class is a member of the P class; that is, the S class is included in the P class
Proposition
No S are P
No member of the S class is a member of the P class; that is, the S class is excluded from the P class
Proposition
Some S are P
At least one member of the S class is a member of the P class
Proposition
Some S are not P
At least one member of the S class is not a member of the P class
Attributes of categorical propositions
Quality and quantity
Quality
it is either affirmative or negative depending on whether it affirms of denies class membership
- affirmative and negative propositions
Quantity
it is either universal or particular, depending on whether the statement makes a claim about every member or just some member of the class denoted by the subject term
- Universal Propositions
“all S are P” and “No S are P” - Particular Propositions
“some S are P” and “some S are not P”
the universal affirmative
A proposition (“All S are P”)
the universal negative
E proposition (“No S are P”)
particular affirmative
I proposition (“Some S are P”)
particular negative
O proposition (“Some S are not P”)
Distribution
attribute of the terms (subject and predicate) of propositions
- (A and E)
- A term is said to be distributed if the proposition makes an assertion about every member of the class denoted by the term
Distribution for A, E, I, O
- For any A proposition, the subject term is distributed and the predicate term is undistributed.
- For any E proposition both the subject term and the predicate term are distributed.
- For any I proposition neither the subject term nor the predicate term are distributed.
- For any O proposition the predicate is distributed and the subject is undistributed
If term distributed in a proposition
it simply means that the proposition says something about every member of the class that the term denotes
If a term is undistributed,
the proposition does not say something about every member of the class
Aristotelian standpoint
existential import
- a statement has this when the subject terms donate actually existing things
Boolean standpoint
“closed” to existence
- when things exist the boolean standpoint does not recognise their existence, and universal statements about those things have no existential import
Modern square of opposition
it arises from the modern (or Boolean) interpretation of categorical propositions
Contradictory relation
if two propositions are related through this, they necessarily have opposite truth value
Logically undetermined truth value
like all propositions they have a truth value, but logic alone cannot determine what it is
Vacuously true
their truth value results solely from the fact that the subject class is empty, or void of members
Immediate inferences
are arguments that have only one premise
Unconditionally valid
arguments that are valid from the Boolean standpoint are said to be this because they are valid regardless of whether their terms refer to existing things
Existential fallacy
from the Boolean standpoint is a formal fallacy that occurs whenever an argument is invalid merely because the premise lacks existential import
Conversion
the simplest of the three – it consists of switching the subject term with the predicate term
Obversion
(1) changing the quality (without changing the quantity),
(2) replacing the predicate with its term complement
Term complement
it is the word or group of words that denotes the class complement
Contraposition
(1) switching the subject and predicate terms
(2) replacing the subject and predicate terms with their term complements
Traditional square of opposition
it is an arrangement of lines that illustrate logically necessary relations among the four kinds of categorical propositions
Contradictory relation
is the same as found in the modern square, thus it expresses complete opposition between propositions
Contrary relation
differs from the contradictory in that it expresses only partial opposition and applies only the A and the E propositions
Subcontrary relation
it also expresses a kind of partial opposition, but only for the I and the O statements
Subalternation relation
it is represented by two arrows: a downward arrow marked with the letter T (true), and an upward arrow marked with an F (false)
Illicit contrary
committed If an inference depends on an incorrect application of the contrary relation
Illicit subcontrary
committed if an inference depends on an incorrect application of the subcontrary relation
Illicit subalternation
committed if an inference depends on an incorrect application of the subalternation relation
Existential fallacy
committed from the Aristotelian standpoint when and only when contrary, subcontrary, and subalternation are used to draw a conclusion from a premise about things that do not exist
Conditionally valid
applies to an argument after the Aristotelian standpoint has been adopted and we are not certain if the subject term of the premise denotes actually existing things
Mathematical logic
abstracts from concepts having a content
Classical logic
only abstracts from the specific content, while insisting that there must be a content, that is, each concept signifies a characteristic of a possible reality
