PHIL 1010-Chapter 5
Which two standard-form categorical propositions affirm class inclusion either in whole or partial?
A and I ("AffIrmo)
What are the two types of propositions for which contraposition can be validly applied?
A and O
On the traditional square of opposition, the two pairs of contradictories are indicated by the diagonals of the square:
A and O propositions are contradictories and E and I propositions are contradictories
What trick do you use to determine the distribution of a standard-form categorical proposition?
ASEBINOP
What propositions have existential import according to Aristotle?
All propositions (A,E,I,O)
A proposition that can be analyzed as being about class, or categories, affirming or denying that one class, S, is included in some other class, P, in whole or in part. These are the fundamental elements, building blocks of arguments, in the classical account of deductive logic.
Categorical Proposition
How do you obvert a proposition?
Change the quality (from affirmative to negative or from negative to affirmative) and replace the predicate term with it complement.
The collection of all objects that have some specified characteristic in common.
Class
The traditional account of syllogistic reasoning, in which certain interpretations of categorical propositions are presupposed.
Classical or Aristotelian Logic
The collection of all things that do not belong to a given class.
Complement or complementary class
Being neither tautologous nor self-contradictory. A ______ statement may be true or false. We are to make the assumption that propositions are this...
Contingent
(Can't both be true and can't both be false) Two propositions are _______ if one is the denial or negation or the other- that is if they cannot both be true and cannot both be false. Two standard-form categorical propositions that have the same subject and predicate terms but differ in BOTH quantity and quality.
Contradictories
What are the four ways in which propositions may be "opposed"?
Contradictories Contraries Subcontraries Subalternation
A valid form of immediate inference for some, but not for all types of propositions . To make this kind of immediate inference from a given proposition its S term is replaced by the complement of its predicate term, and its predicate term is replaced by the complement of its subject term.
Contrapositive (CONtrApOsition= "change order and negate" for A and O propositions)
(Can't both be true, but can both be false) Two propositions are said to be _______ if they cannot both be true- that is, if the truth of one entails the falsity of the other- but both can be false.
Contraries
Which relationships no longer exist with Boolean Interpretation?
Contraries Subcontraries Subalternation (Contradictories is the only one that remains)
A valid form of immediate inference for some but not al types of propositions. To form this immediate inference, switch the S and P terms.
Conversion
By a combination of subalternation and conversion we advance validly from "All S is P" to "Some S is P". This pattern of inference, called __________ __ _________ proceeds by interchanging the S and P terms and changing the quantity of the proposition from universal to particular. This method of immediate inference is used to create the valid converse for a given A proposition, "All S is P".
Conversion by Limitation
What are the three other kinds of immediate inferences that can be made?
Conversion, Obversion, Contraposition
The original proposition, before undergoing conversion, is called the "________"
Convertend
Any form of the verb "to be" that serves to connect the subject term and the predicate term of a categorical proposition.
Copula
When two propositions have the same subject and the same predicate terms, and agree in quality (both affirming or both denying) but differ in quantity (one universal, the other particular), they are called ___________ __________.
Corresponding Propositions
An argument whose presmises are claimed to provide conclusive grounds for the truth of its conclusion
Deductive Argument
An attribute that descries the relationship b/t a categorical proposition and each one of its terms, indicating whether or not the proposition makes a statement about every member or the class represented by a given term.
Distribution (ASEBINOP)
Conversion is perfectly valid for all __ and __ propositions.
E and I
Which two standard-form categorical propositions deny class inclusion either in whole or partial?
E and O ("nEgO")
Any mistake in reasoning that arises from assuming illegitimately that some class has members.
Existential fallacy
T/F: With contraposition, both the quality and quantity of the original proposition is changed.
False: "Neither the quality nor the quantity of the original proposition is changed, so the contrapositive of an A prop is an A prop, the contrapositive of an O prop is an O prop and so on"
An inference that is drawn directly form one precise without the mediation of any other premise. Various kinds of _______ _______ may be distinguished traditionally including conversion, obversion, and contraposition.
Immediate Inference
When we draw a conclusion from one or more premises, some ________ must be involved.
Inference
What does the Boolean interpretation argue?
It argues that we cannot infer the truth of the particular prop from the truth of its corresponding universal prop b/c every particular prop asserts the existence of its subject class.
Any inference drawn from more than one premise. (As is the case with syllogisms)
Mediate Inference
The account of syllogistic reasoning accepted today. It differs in important ways from the traditional account.
Modern symbolic logic
Conversion is not at all valid for the ___ proposition.
O
A valid form of immediate inference for EVERY standard-from categorical proposition.
Obversion
The proposition serving as premise for the obversion is called the ______; the conclusion of the inference is called the ______.
Obvertend Obverse
What propositions have existential import according to Boole?
Only I and O
The logical relation that exists b/t two contradictories, b/t two contraries, or in general b/t any two categorical propositions that differ in quantity, quality, or other respects. These relations are displayed on the spare of opposition.
Opposition
Some, but not all, of the members of one class may be included in another class. (Thus the class of all athletes is ______ _______ in the class of all females.)
Partial Inclusion (Partially Included)
If the proposition refers only to some members of the class designated by its subject term, its quantity is:
Particular (I and O)
Which of the four kinds of standard-form categorical propositions is described here: A proposition that affirms that the relation of class inclusion holds, but does not affirm it of the first class universally- it affirms it only partially.
Particular Affirmative (I) Some S is P
Which of the four kinds of standard-form categorical propositions is described here: A proposition that does NOT affirm the inclusion of some member or members of the first class ins the second class; this is precisely what is denied.
Particular Negative (O) Some S is not P
An attribute of every categorical proposition determined by whether the proposition affirms or denies class inclusion. Thus every categorical proposition is affirmative or negative.
Quality
Each proposition has these three characteristics:
Quality Quantity Distribution
An attribute of every categorical proposition, determined by whether the proposition refers to "all" members or only to" some" members of the class designated by its subject term. Thus every categorical proposition is either universal or particular in quantity.
Quantity
A diagram in the form of a square in which the four types of categorical propositions (A,E,I,O) are situated at the corners, exhibiting the logical relations called "oppositions" among these propositions.
Square of Opposition
(Truth moves downward, and false moves upward) This opposition b/t the universal proposition and its corresponding particular proposition is known as....
Subalternation
(Can't both be false, but both can be true) Two propositions are said to be ________ if they cannot both be false, but they can both be true.
Subcontraries
In subalternation, the __________ implies the truth of the _________, but not the other way around.
Superaltern Subaltern
In any such pair of corresponding propositions, the universal proposition is called the _________ and the particular is called the ________.
Superaltern Subaltern
What characteristics of propositions remain unchanged when obverting a proposition?
The quantity (universal and particular) and the subject term.
If the proposition refers to all members of the class designated by its subject term, its quantity is:
Universal (A and E)
Which of the four kinds of standard-form categorical propositions is described here: A proposition that affirms that the relation of class inclusion holds b/t the two classes and says that the inclusion is universal.
Universal Affirmative (A) All S is P
What are the four kinds of standard-form categorical propositions?
Universal Affirmative (A) Universal Negative (E) Particular Affirmative (I) Particular Negative (O)
Which of the four kinds of standard-form categorical propositions is described here: A proposition that denies the relation of inclusion b/t the two terms, and denies it universally.
Universal Negative (E) No S is P
Contraposition is valid for E propositions only...
by limitation
The proposition that results from a proposition being converted is called the "_________".
converse
A proposition is said to have ________ ________ if the truth of the proposition requires a belief in the existence of members of the subject class.
existential import
The complement of the class designated by the term S is designated by the term______.
non-S
The ______ of any standard-form categorical proposition determines whether its predicate term is distributed or undistributed.
quality
The ______ of any standard-form categorical proposition determines whether its subject term is distributed or undistributed.
quantity
A proposition distributes one its classes if it:
refers to ALL members of that class. (Distributed vs. Undistributed)
Classical logic deals mainly with arguments based on the....:
relations of classes of objects to one another
With the Aristotelian Interpretation, the truth of a universal proposition implies.....
the truth of its corresponding particular proposition
A number of very useful immediate inferences may be readily drawn from the information found in the ......
traditional square of opposition
T/F: The Boolean Interpretation preserves most Immediate inferences including conversion for E and for I props, contraposition for A and for O props, obversion for any proposition but all cases of limitation become invalid.
True
T/F: the class-defining characteristic need not be a "simple" attribute; any attribute may determine a class.
True
There are two rival interpretations of categorical propositions: the Aristotelian which is _________ and the Boolean which is ______.
Traditional Modern
In assessing the correctness of a deductive argument, the deductive argument can either be _____ or _____.
Valid Invalid
A CHARACTERISTIC of any deductive argument whose premises, if they were all true, would provide conclusive grounds for the truth of its conclusion. Such an argument is said to be valid.
Validity
Two classes may have no members in common. (Thus the class of al triangles and the class of all circles may be said to ______ one another.)
Whole Exclusion (Exclude)
What are the three ways that two classes can be related?
Whole Inclusion Partial Inclusion Whole Exclusion
All of one class may be included in all of another class. (Thus the class of all dogs is ______ ______ in the class of all mammals.)
Whole Inclusion (Wholly Included)
