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### Introduction to Logic III

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Deductive Argument
if the premises are true, the conclusion must be true (it is impossible for the conclusion to be false)
inductive argument
if the premises are true, then the conclusion is probably true (it is improbable for the conclusion to be false)
when is an argument said to be valid?
if and only if it is impossible to have all true premises and a false conclusion
the conclusion
if all premises of an argument are true, what else must be true
when is an argument sound?
if and only if we know that all the premises are in fact true and its form is valid
draw a venn diagram of an "A" proposition
(two circles, left circle filled in with blank in the middle)
(two circles, x in the middle section)
draw a venn diagram of a "I" proposition
(two circles, middle section filled in)
draw a venn diagram of an "E" proposition
(two circles, x in the left circle)
draw a venn diagram of an "O" proposition
All countries identical to Costa Rica are beautiful countries.
Translate into standard form: Costa Rica is a beautiful country.
All dogs are creatures bound for heaven.
Translate into standard form: It is false that some dogs are not creatures bound for heaven.
All philosophers are lovers of wisdom.
Translate into standard form: Only lovers of wisdom are philosophers.
Some students are not lazy people.
Translate into standard form: It is false that every student is a lazy person.
Translate into standard form: She is always happy.
All persons identical to her are persons that are always happy.
All places that have smoke are places that have fire.
Translate into standard form: Wherever there is smoke, there is fire.
All eligible voters are citizens.
Translate into standard form: None but citizens are eligible voters.
Some students are students who sneezed.
Translate into standard form: A student sneezed.
All persons admitted are persons over 21.
Translate into standard form: The only people admitted are over 21.
Some men are jerks.
Translate into standard form: It is false that no men are jerks.
Some students are students who were snoring.
Translate into standard form: Several students were snoring.
contradictories
cannot both be true and false
contraries
cannot both be true
subcontraries
Two statements are blank if and only if both can be true but both cannot be false.
subalternation
subaltern comes from superaltern
conversion
switch the subject and predicate terms
obversion
change the quality of the proposition (affirmative or negative)
contraposition
switch the subject and predicate terms
major term
the predicate of the conclusion and is used in one premise of a syllogism
minor premise
the premise containing the minor term
middle term
term found once in each premise
AE/EO
acronym for remembering the distributed terms
fallacy of the undistributed middle
what is it called when the middle term isn't distributed in at least one premise?
fallacy of the illicit major/minor
what is it called when a term is distributed in the conclusion, but not in the premise in which it occurs?
fallacy of exclusive premises
what is it called when a conclusion follows from a syllogism with two negative premises?
fallacy of drawing a negative conclusion from affirmative premises
what is it called when a negative conclusion follows from a syllogism with two affirmative premises?
the fallacy of drawing an affirmative conclusion from a negative premise
what is it called when an affirmative conclusion follows from a syllogism with a negative premise?
what is the 6th rule?
two universal premises cannot have a particular conclusion
the existential fallacy
what is it called when two universal premises have a particular conclusion?
in the middle circle
in a triple venn, where does the middle term go?
in the left circle
in a double venn, where does the minor term go?
in the right circle
in a double venn, where does the major term go?
the dot
how do you symbolize "and"?
the horseshoe
how do you symbolize "if then"?
the vee
how do you symbolize "but?"
the triple bar
how do you symbolize "if and only if"?
truth table for "and"
p q p and q
truth table for "or"
p q p v q
truth table for "if then"
p q p כq
p q p ≡ q
truth table for "if and only if"
p ~ p
truth table for "not"
Negation
Adding "not" or removing it
conjunction
Two statements joined by the word AND. Only true when both statements are true.
disjunction
Two statements joined by the word OR. Only false when both statements are false.
conditional
an if-then statement
Biconditional
Conditional statement where both the converse and inverse are true and uses the phrase "if and only if"
Argument
set of statements, one of which appears to be implied or supported by the others
simple proposition
a simple proposition is one that cannot be broken down into other propositions without losing its meaning
compound proposition
a compound proposition can be broken down into meaningful simple components
truth-functionial compound proposition
a compound proposition is truth-functional if and only if there is a rule that determines when that proposition is true or false based solely upon the truth or falsehood of the simple propositions that make it up
consistency
propositions which have a form such that it is possible for them to all be true under the same circumstances (or in the same possible worlds).
validity
an argument is an instance of a valid argument form.
what is logical space of a proposition?
the conjunction of simple propositions create a larger number of possible situations.
Non-argument
A set of sentences where an inference cannot be drawn between premisses and a conclusion
Premiss
A sentence that is offered as evidence in an argument
Conclusion
Tells if your hypothesis was correct; supported or not supported
Missing premiss
An unstated premiss that is necessary in order to support a conclusion
Indicator words
Words commonly used to signal premisses or conclusions of arguments.
Conclusion indicator words
Hence, thus, therefore, and so, it follows that, for that reason
Assertion
A statement; all conclusions are assertions but not all assertions are conclusions (they can also be premisses)
Inference
To conclude form something known or assumed.
implication
the truth of one statement requires the truth of another
Universal Generalization
A sentence that states that all or none of the members of one class are members of another class
Statistical generalization
A sentence that states that some proportion of members of once class are members of another class
Ambiguity
The capacity of being understood in two or more ways-can occur at any meaningful level of language
Vagueness
If borderline cases for a word's application occur
Use vs. Mention
Using words to refer to their meaning vs. talking about the words themselves
Ostensive Definition
Defining words by pointing them out or displaying them
Nonverbal extensional definition
Includes ostensive definitions.
Verbal Extensional definition
Defining a term by listing or naming members of extension (pointing out a list of types of dogs)
Extension
the sum of all the individual objects described by it
Intension
the sum of all common attributes denoted by the term
Explicit intensional definition
Defining a term by stating the properties a thing mus possess for the term to apply. All are verbal.
Lexical definition
A definition that states the set of properties possessed by all things to which the term applies that is neither too broad nor too narrow
Circular definition
A definition incorporating the term being defined
stipulative definition
definition of a new word or existing word that is applied in a new way
precising definition
Reducing the vagueness of a term (usually for legal and policy)
Syntactic
Terms without an intension or or extension that for indicating syntactic or grammatical roles in language
Operational definition
A type of definition that specifies a publicly observable and repeatable operation with a specified outcome