Logic Midterm Exam

How to identify conclusions

Use “the therefore test” - put what you think is the conclusion at the end and then put therefore in front of it and see if it makes sense

definition of an inductive argument

If the premises are true, the conclusion is PROBABLY true

definition of a deductive argument

If the premises are true, the conclusion MUST be true

common deductive argument forms

• based on mathematics

• arguments from definitions

• categorical syllogisms (each statement begins w/ “all” or “some” or “no”

• hypothetical syllogisms (have a conditional statement - if…then - as one of the premises)

• disjunctive syllogism (have an either / or statement as one of the premises)

common inductive argument forms

• predictions

• argument from analogy

• generalization

• argument from authority

• argument based on signs

• causal inference

deductive argument - valid or invalid

valid argument: if the premises are true, the conclusion HAS TO BE true

invalid argument: if the premises are true, the conclusion DOES NOT have to be true

* doesn’t matter if the premises are actually true, we assume they are in order to determine validity

deductive argument - valid - sound or unsound

any invalid argument is unsound

sound: argument is valid, AND the premises are TRUE

unsound: argument is valid, BUT the premises are UNTRUE

inductive argument - weak or strong

weak argument: even if the premises are true, it is not the case that the conclusion is probably true

strong argument: if the premises are true, the conclusion is probably true

inductive argument - strong - cogent or uncogent

cogent: if the argument is strong AND has TRUE premises

uncogent: if the argument is weak AND / OR has false premises

3 places premises can come from

1. common knowledge / assumed as obvious

2. report of a fact or statistic

3. conclusion of another argument

genus vs species , proximate genus

genus: larger class of things (includes the smaller class)

species: smaller class of things (included within a larger class)

proximate genus: the genus closest to what you are defining

more universal vs more particular vs individual

universal: a larger genus that applies to more things

particular: a smaller genus / species that applies to fewer things

individual: a singular thing

exhaustive vs nonexhaustive

exhaustive: when they are the ONLY options possible (no possible option left out) (*at least one has to be true)

ex: Either I go to the party or I don’t go to the party = exhaustive

vs Either I spend all night at the party or I spend all night at home = nonexhaustive

mutually exclusive vs not mutually exclusive

mutually exclusive: when both options can’t be true (*can’t both be true)

ex: Either July 4th is on a Tuesday or Thursday this year

(often implied by making an either / or statement)

Ad baculum

appeal to force - threatens to influct some kind of harm on another person if the conclusion of the argument isn’t accepted

Begging the question (3 types)

1. controversial premise left out

2. the conclusion merely restates a premise in different language

3. the argument goes in a complete circle

Suppresed evidence

• inductive argument ignores something that provides important evidence against the conclusion

Equivocation

• the conclusion of the argument depends on the fact that a word is used in 2 different sense

False Dichotomy

• the argument presents 2 alternatives as if they were the only ones possible, but there’s a 3rd option that the argument neglects to mention

Appeal to unqualified authority

• cites an authority that lacks credibility

Slippery slope

• claims an unavoidable chain reaction without sufficient evidence

Hasty generalization

• makes a generalization from an unrepresentative sample

Ad hominem (3 types)

1. Abusive - attacks character of person rather than argument

2. Circumstantial - show someone’s bias to dismiss argument

   1. Tu Quoque - “you too” - show dismisses argument bc hypocritical

Straw man

• (opposite of the principle of charity) - a response to someone’s argument where instead of criticizing the argument, you attack a caricature of the argument

Red Herring

• the arguer diverts the attention of the audience by subtly changing the subject

Ad populum

• appeals to someone’s desire to belong to a group

Appeal to pity

• attempts to support a conclusion by merely evoking pity (not relevant to conclusion)

Reductio ad absurdum and how it works

= reduction to the absurd - argues for a conclusion indirectly by showing that denying the conclusion leads to an absurdity

Method: (you want to preove that X is true)

1. assume that X is NOT true (~X)

2. use valid reasoning to show that an absurd conclusion from ~X

(absurd conclusion = contradiction or something obviously false)

3 forms of rhetoric from Aristotle’s Rhetoric

1. ethos - appeal to the character of the person arguing

2. pathos - appeal to emotion

3. logos - appeal to rational argument

definition of steamroller effect

= the person arguing pressures the reader to accept a conclusion with little evidence to avoid appearing unintelligent or immoral

convertibility of definitions

• if a definition is neither too narrow nor too broad, it is convertible, and means you can universal statements in both directions

non sequiter

= “it does not follow"

necessary, sufficient, and necessary and sufficient statements

1. necessary: required to produce X (ONLY IF)

2. sufficient: is alone enough to produce X (IF)

3. necessary and sufficient: both (IF AND ONLY IF)

structure on analogical argument

A has features x, y, z… and p

B has features x, y, z

________

B has feature p

A = primary analogue

B = secondary analogue

x, y, z = similarities

p = the feature that you know “A” has, and want to infer that “B” has

criteria for evaluating analogical arguments

1. # / relevance of similarities = strengthen

   # / relevance of differences = weaken

2. # of primary analogues

3. diversity of primary analogues

counterexample method of proving deductive argument invalid

TRUE PREMISES AND A FALSE CONCLUSION = INVALID

1. determine the form

   1. distinguish “form words” from “content words”

   2. form words: all, some, no, are, are not

   3. represent content words with uppercase letters

   4. ex: Some H are not V, some V are D ___ some H are not D

2. find counterexample

   1. find a substitution instance that has true premises and a false conclusion

   2. use the words: cats, dogs, fish, mammals, animals

varying the score / quantifiers

general rule for inductive arguments:

• if you weaken the conclusion, you strengthen the argument

• if you strengthen the conclusion, you weaken the argument

(weakening the conclusion is like lowering the bar)

• adding quantifiers makes the conclusion more precise

the principle of charity

= always interpret an argument so that

1. its the best argument possible

2. its in the original spirit of the argument