the study of the methods and principles of reasoning.
An argument uses a set of facts or assumptions, called premises, to support a conclusion.
An argument uses a set of facts or assumptions, called premises, to support a conclusion.
fallacy
a deceptive argument—an argument in which the conclusion is not well supported by the premises.
Appeal to Popularity
Many people believe p is true; therefore…p is true.
False Cause
A came before B; therefore…A caused B.
Appeal to Ignorance
There is no proof that p is true; therefore…p is false.
Hasty Generalization
A and B are linked one or a few times; therefore…A causes B (or vice versa).
Limited Choice
p is false; therefore…only q can be true.
Appeal to Emotion
p is associated with a positive emotional response; therefore… p is true.
Personal Attack
I have a problem with the person or group claiming p; therefore… p is not true.
Circular Reasoning
p is true. p is restated in different words. (The argument states the conclusion.)
Diversion (Red Herring)
p is related to q and I have an argument concerning q; therefore…p is true.
Straw Man
I have an argument concerning a distorted version of p; therefore…I hope you are fooled into concluding I have an argument concerning the real version of p.
A Set
A collection of objects
If A is a subset of B, then all members of A are also members of B.
If A is disjoint from B, then the two sets have no members in common.If A and B are overlapping sets, then the two sets share some of the same members.
Statement: “Some dogs can swim.”Rephrase to:
“Some dogs are animals that can swim.”
Inductive Reasoning
specific premises → general conclusion
Deductive Reasoning:
general premises → specific conclusion
An inductive argument does not prove its conclusion true, so it is evaluated based on its strength.
An argument is strong if a compelling case is made for its conclusion.
An argument is weak if the conclusion is not well supported by its premises.
Applytwo criteria to evaluate a deductiveargument
The argument is valid if its conclusion follows necessarily from its premises, regardless of the truth of the premises or conclusion.
The argument is sound if it is valid and its premises are all true.
The following tests the validity of a deductive argument with a Venn diagram:
1. Draw a Venn diagram that represents all the information contained in the premises.
2. If the Venn diagram contains the conclusion the argument is valid; otherwise, it is not.
Affirming the Hypothesis (antecedent):
If one gets a college degree, then one can get a good job.
Marilyn has a college degree
Marilyn can get a good job. (VALID)
Affirming the Conclusion (consequent):
If one gets a college degree, then one can get a good job.
Marilyn gets a good job.
Marilyn has a college degree. (invalid, inverse fallacy)
Affirming the Conclusion (consequent):
If one gets a college degree, then one can get a good job.
Marilyn gets a good job.
Marilyn has a college degree. (Invalid, inverse fallacy)
Denying the Hypothesis (antecedent):
If one gets a college degree, then one can get a good job.
Marilyn does not have a college degree.
Marilyn cannot get a good job. (inValid inverse fallacy)
Denying the Conclusion (consequent):
If one gets a college degree, then one can get a good job.
Marilyn does not have a good job.
Marilyn does not a college degree (valid)
To convert from one unit to another, we need to know the ______between the two units.
Conversion factor
The conversion factor between feet and inches is
1 ft = 12 inches
Currency conversion - dollars per foreign
dollars divided by foreign
Absolute change
absolute change = new value - reference value
relative change
rel chg=abs. chng= new value-ref value
ref value ref value
Absolute difference
actual difference between the compared value and the reference value:
absolute dif = compared value-ref value
relative difference
describes the size of the absolute difference as a fraction of the reference value
rel dif=ab dif = comp value - ref value
ref value ref value
Of vs more than (or less than)
If the compared value is P% more than the reference value, it is (100 + P)% of the reference value.If the compared value is P% less than the reference value, it is (100 + P)% of the reference value.
Don't average percentages
beware of shifting reference values
Scientific notaion
a format in which a number is expressed as a number between 1 and 10 multiplied by a power of 10.