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Level 147

Introduction to Logic II


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formal logic
deals with proper modes of reasoning
statement
sentence that is either true or false
square of opposition
diagram of the basic relationship between categorical statements with the same subject and predicate
Tautology
statement that is always true by logical structure
consistent
two statements can both be true at the same time
exhaustive
no other types exist
Species
term that is more specific, narrow, or concrete than the original term and in included by it
apparent disagreement
difference of opinion or perception
term
An element or number in a sequence.
Argument
set of statements, one of which appears to be implied or supported by the others
Conclusion
Tells if your hypothesis was correct; supported or not supported
premises
the statements that imply the conclusion
categorical syllogism
syllogism consisting of three statements in categorical form
major term
the predicate of the conclusion and is used in one premise of a syllogism
minor term
the subject of the conclusion and is used in the other premise of a syllogism
middle term
term found once in each premise
major premise
the premise containing the major term
minor premise
the premise containing the minor term
schema
representation of a syllogism, having statements in standard order with standard abbreviations of its terms
mood
three letter description of the types of categorical statements a syllogism contains when arranged in standard order
figure
a number from 1 to 4 identifying the placement of the syllogism's middle term
form
the mood and figure of a syllogism
valid
a syllogism is blank if and only if the premises imply the conclusion
sound syllogism
a blank is valid and has true premises
counterexample
An example that proves a conjecture false
distributed term
term that, within a statement, refers to all members of its category
immediate inference
statement that can be inferred directly from another statement
Converse
(noun) A statement that switches the hypothesis and conclusion
obverse
statement of the opposite quality with a negated predicate. It is valid for all statements.
complement
set of all terms not included in the given term. Thus the BLANK of the term is P is non-P.
Contrapositive
when the hypothesis and the conclusion of a converse of a conditional statement are negated
inclusive
word, often a relative pronoun or adverb, that refers to a broad range of things and times.
exclusive
words that set boundaries, referring only to a limited class of things
What is a logical argument?
A set of statements, one of which appears to be implied or supported by the others.
What is a premise?
Premises are those statements in a logical argument that support or imply the conclusion.
words such as since, because, for and given that.
What are some words that introduce a premise in a logical argument?
What is a conclusion?
the statement that appears to be implied by the other statements in the argument (implied by the premises).
words such as therefore, thus, so, and consequently.
What are some words that introduce a conclusion in a logical argument?
What is a syllogism?
A logical argument consisting of two premises
What is a categorical syllogism?
A syllogism consisting of three statements in categorical form.
Major term (P), minor term (S), and middle term (M).
What are the three terms in a syllogism and what initial do we use to signify them?
Where is the major term found in the conclusion? Where else will you find it?
The major term (P) is the predicate of the conclusion. It is also used in the major premise.
Where is the minor term found in the conclusion? Where else will you find it?
The minor term (S) is the subject of the conclusion. It is also used in the minor premise.
Where is the middle term found?
The middle term (M) is found in both of the premises, but not the conclusion. It is used to connect the premises together.
The premise that contains the major term.
What is the major premise of a syllogism?
The premise that contains the minor term.
What is the minor premise of a syllogism?
What is the mood of a syllogism?
The mood is a three-letter description of the types of categorical statements it contains when arranged in standard order. It refers to the various possible combinations of A, E, I and O.
What does the figure of a syllogism identify?
It is a number from 1 to 4, identifying the placement of the middle terms.
4
How many different figures can a syllogism have?
M is P
What is the placement of the middle term in figure 1?
P is M
What is the placement of the middle term in figure 2?
What is the form of a syllogism?
the mood and figure of a syllogism listed together.
256
How many different forms of syllogisms exist?
24
How many different forms of syllogisms are actually valid?
Yes.
Can the statements in a syllogism be false?
Yes.
Can the statements in an invalid syllogism be true?
What is a sound syllogism?
A syllogism that is valid and has true premises.
NOTE on truth and validity:
Statements are true or false, arguments are valid or invalid.
Yes. Certain forms are always valid. Certain forms are always invalid.
Does the validity of a syllogism depend solely on the form of a syllogism?
What should you assume if you cannot find a counterexample?
Either the form is valid or you have not been creative enough.
Where should you start when developing a counterexample?
Start by making the conclusion obviously false and then attempt to find a middle term that makes the premises true. Make sure to create a syllogism with the same exact form.
How does a syllogism show a form to be invalid?
A form is shown invalid if the premises are both true and the conclusion is false. You cannot have true premises lead to a false conclusion.
What is a distributed term?
A term that, within a statement, refers to all members of its category. We can tell if a term is distributed or not simply by its placement in a categorical statement.
What types of statements distribute their subjects?
Universal (A and E) statements distribute their subjects.
What types of statements distribute their predicates?
Negative (E and O) statements distribute their predicates.
I statements.
What type of statement does not distribute the subject or the predicate?
Test it with the five rules of validity.
How do you establish the validity of a syllogism beyond doubt?
Which rules of validity involve distribution of terms?
Rule 1 (middle term) and Rule 2 (if distributed in the conclusion, it must be distributed in the premise)
Which rules of validity involve quality of the statement?
Rules 3 - 5: A valid syllogism cannot have two negative premises, it cannot have a negative premise with an affirmative conclusion, and it cannot have two affirmative premises and a negative conclusion.
Hint for evaluating validity regarding quality.
The number of negative premises must match the number in the conclusion. If conclusion is affirmative, then both premises must be affirmative. If the conclusion is negative, then 1 premise must be negative. Two negative premises are not allowed.
Note of caution:
Make sure the statements in the syllogism you are evaluating are in standard categorical order.
universal
idea of a category
particular
refers to the actual individual thing that make up the category
genus
term that is more general, broad, or abstract that the original and includes it