Critical thinking

premises, without references to any external information
Deductive proof: demonstrating that

a particular conclusion logically follows from certain premises, and that this conclusion must be true if these premises are true
Truth-preserving: when used correctly, deductive

 

I can’t stand any kind of physical activity. Sailing is

a physical activity, so…
2. There is no such thing as a magnetic plastic. My plate is plastic, so…
3. Anyone ignoring me while speaking on their phone is irritating. You are ignoring me while speaking on your phone, so…

diet and inactivity in elderly patients leads to memory loss.

George (not his real name) is inactive and eats a poor diet. Barbara (not her real name) is inactive but eats well. Thus, we predict that…

out the logical conclusion of your premises
Invalid reasoning: incorrectly applying

deductive reasoning so that your conclusion does not logically follow from your premises
Unwarranted: a conclusion that is not supported by the argument

if they wish to attend the workshop. I wish to

attend the workshop. Therefore, I must register.
2. There is no such thing as a purple monkey. This creature is purple, so it can’t be a monkey.
3. Purple monkeys are difficult to spot. This creature is difficult to spot, so it must be a purple monkey.
4. We always need the permission of human volunteers if our experiments on them are to be ethical. We do not yet have permission from these subjects, so we cannot yet experiment on them in an ethical manner.
5. We always need the permission of human volunteers if our experiments on them are to be ethical. We do not yet have permission from these subjects, so we can only experiment on them if they don’t know what we are doing

syllogism with one hidden premise

consequent
If A, then B.
Not B.
Therefore, not A.

Create examples!
Affirming the antecedent
All

sailors drink heavily.
He is a sailor.
Therefore, he drinks heavily.
Denying the consequent
All politicians lie.
She doesn’t lie.
Therefore, she is not a politician.

B. (Wrong!)
Affirming the consequent
If A, then B.
B.
Therefore, A. (Wrong!)

Create examples!
Denying

the antecedent
All sailors drink heavily.
He is not a sailor.
Therefore, he does not drink heavily.
Affirming the consequent
All politicians lie.
She lies.
Therefore, she is a politician.

is a poet.
Conclusion: Mayakovsky is English.
Argument invalid, conclusion true
All poets

are English.
Mayakovsky is English.
Conclusion: Mayakovsky is a poet.
Validity + truth: a sound argument.

has true premises, meaning its conclusion must also be true
Unsound:

an argument that does not meet the standard of soundness, either because it is invalid or because one or more of its premises is untrue, or both
THINK ABOUT THIS
Can you think of a deductive argument in common use that is valid but unsound? What kind of premises can we be certain are true? What kinds of deductive argument may never be sound, because their premises can’t be proven as true?

editor from a Central Plaza store owner.
"Over the past two

years, the number of shoppers in Central Plaza has been steadily decreasing while the popularity of skateboarding has increased dramatically. Many Central Plaza store owners believe that the decrease in their business is due to the number of skateboard users in the plaza. There has also been a dramatic increase in the amount of litter and vandalism throughout the plaza. Thus, we recommend that the city prohibit skateboarding in Central Plaza. If skateboarding is prohibited here, we predict that business in Central Plaza will return to its previously high levels."
Write a response in which you discuss what questions would need to be answered in order to decide whether the recommendation is likely to have the predicted result. Be sure to explain how the answers to these questions would help to evaluate the recommendation.