ch 8-9 continued Flashcards
A graphic means of representing a categorical claim or categorical syllogism by assigning classes to overlapping circles is called a
Venn Diagram
Venn diagrams exactly represent the ______.
four standard-form categorical claim types
In Venn diagrams the circles represent what?
the classes named by the terms
Colored areas in Venn diagrams represent what?
areas that are empty
Areas containing X’s in Ven diagrams represent?
areas that are not empty-that contain at least one item
An area in a Venn diagram that is blank is one that
the claim says nothing about; it may be occupied or empty
A claim that INCLUDES one class or part of one class within another are _______.
Affirmative Claims
A claim that EXCLUDES one class or part of one class from another are _______.
Negative Claims
A- and I-Claims are examples of what claims
Affirmative
E- and O-Claims are examples of what claims
Negative
The main idea of ________ is to take an ordinary claim and turn it into a standard-form categorical claim that is exactly equivalent.
Translation into Standard-Form
We’ll say that two claims are _______ ______ if and only if they would be true in all and exactly the same circumstances-that is under no circumstances could one of them be true and the other false.
Equivalent claims
basically they are saying the same things
Every X is a Y translates to
A-Claim: All X’s are Y’s
Minors are not eligible translates into
E-Claim: No minors are eligible people
We translate: “ There were creatures weighing more than four tons that lived in North America” to
I-Claim: Some creatures that lived in North America are creatures that weighed more than four tons
When looking at a claim you do two things first
- identify the terms
- identify whether its an A-E-I-O-Claim think carefully about what relation between classes is being expressed and then decide how that relation can be turned into standard form.
identify the terms and what type of claim this is:
“Only sophomores are eligible candidates”
Terms: Sophomores and eligible candidates
A-Claim: but there are two possibilities
-All sophomores are eligible candidates
-All eligible candidates are sophomores<—–this best represents
All claims that are “Only X’s are Y’s” should be translated as
All Y’s are X’s
What word plays a crucial role in claims making us treat the claims differently
only
With the claim, “The only people admitted are people over twenty-one” what is the subject class?
In this case a restriction is being put on the class of people admitted we’re saying that nobody else is admitted except those over 21. Therefore PEOPLE ADMITTED is the subject class
The only people admitted are people over 21 is translated to
All people admitted are people over 21
All claims of the sort, “The only X’s are Y’s” should be translated
All X’s are Y’s
The word ONLY used by itself introduces the _____ ___ of an A-Claim
predicate term
The phrase THE ONLY introduces _____ ___ of an A-Claim
subject term
Only matinees are half-price shows translates to
All half-price shows are matinees
Matinees are the only half-price shows translates to
All half-price shows are matinees
“I always get nervous whenever I take a logic exam.” What is the claim
The claim is about times.
I always get nervous whenever I take a logic exam translates to
All times I take logic exams are times I get nervous
Whenever is a word that indicates
that you are talking about times or occasions as well as that you’ll have an A-or E-Claim
Whenever can indicate times or occasions as well as ___
places
“He makes trouble wherever he goes” translates to
All places he goes are places he makes trouble
Categorical claims are always about ___ classes
two
Why is “Aristotle is a logician” hard to translate into standard form?
Because this claim specifies logicians as a class and aristotle as part of that class but categorical claims are always about two classes and aristotle isn’t a class. (we certainly don’t talk about some of aristotle being a logician).
Translate “Aristotle is a logician”
All people identical with Aristotle are logicians
Claims about single individuals should be treated as ___-claims or ___-claims
A-Claims or E-Claims
People aren’t the only things that crop up in individual claims. What else does
objects, occasions, places, and other kinds of things.
Other claims that cause translation difficulty contain what are called ____ ___
mass nouns
Boiled okra is too ugly to eat- can be translated to
All examples of boiled okra are things that are too ugly to eat
If the claim “Socrates is Italian” is false, then, providing there is such a person as Socrates the claim “Socrates is not Italian” is
true
A false A implies a true E and vice versa but only when
the claims are individual claims being treated as A- and E-Claims
Translate: Every salamander is a lizard
A-claim: All salamanders are lizards
Translate: Not every lizard is a salamander
O-claim: Some lizards are not salamanders
Translate: Only reptiles can be lizards
A-Claim: All lizards are reptiles
Translate: Snakes are the only members of the suborder Ophidia
A-Claim: All members of the suborder Ophidia are snakes
Two categorical claims ___ to each other if they have the same subject term and the same predicate term
correspond
A table of the logical relationships between two categorical claims that have the same subject and predicate terms.
square of opposition
The A-and E-claims across the top of the square from each other can both be false, but they cannot both be true which makes them ___ claims
contrary claims
The I- and O-claims across the bottom of the square from each other can both be true, but they cannot both be false which makes them ___ claims.
subcontrary claims
The A-and O-claims and the E-and I-claims which are at opposite diagonal corners from each other are ___ ___ because they never have the same truth values.
contradictory claims
