All dogs are mammals.
Fido is a mammal.
So Fido is a dog.
Shakespeare was a woman.
So Shakespeare was female.
To cure this patient we must use surgery or chemo.
We have used surgery.
So this patient does not need chemo.
You can practice medicine in Texas only if you have graduated from an
approved medical school.
John has graduated from an approved medical school.
So John can practice medicine in Texas.
We will have a picnic if it doesn't rain.
It is raining.
So we won't have a picnic.
Only BMWs have side airbags.
This car is a BMW.
This car has side airbags.
St. Augustine is a kind of grass.
Healthy grass is green.
So healthy St. Augustine grass is green.
Sarah owns a TV.
So John owns a TV.
Probability of the conclusion is high. (maybe over 95%)
BUT the argument is very weak!
The issue is NOT the probability of the conclusion.
The issue is how much does the reason raise the probability
of the conclusion.
Vagueness and precision do not indicate validity of an argument.
The first arguement below contains a vague word: 'disgusting', but it is
valid. The second one has very precise numbers but it is invalid.
Liver is disgusting.
People don't enjoy disgusting food.
So people don't enjoy liver.
The velocity of the satellite is 35.471 ft./sec.
If the launch is normal the velocity is 35.471 ft./sec.
So the launch is normal.
Requirements for a good inductive argument.
a) There must be enough cases.
b) Cases must be representative of the whole.
24 of 25 balls in the bag are red.
The balls were thoroughly mixed.
So the next ball I chose will be red.
This argument has enough cases to be strong (better than 95% chance
This penny came up heads 3 times in a row.
So on the next throw it will be heads.
Ask yourself: how often does a fair penny come up heads
three times in a row? Since it is 1 in 8 there are not enough
cases for a strong argument.
For a strong inductive argument you usually need at least 12 cases to
draw a general conclusion about a group.
The Importance of a Representative Sample
Of the 1000 people polled by phone 60% were for Dewey.
So Dewey will win conformably.
This arguemnt was incorrectly used to predict a win for Dewey. The problem was that the (phone) sample was not representative since at the time, farmers (who had few phones at the time) tended to be for Dewey.
17 of 18 patients were cured of herpes when treated by light.
2 of 11 patients were cured of herpes when given a placebo.
So light cures herpes.
Controls: (The sample must be representative.)
Nothing other than the light treatment must vary.
1. Patient knows what treatment is being received.
2. Doctor knows what treatment is being received.
3. Patients in two groups should should be in the same physical shape.
4. The ratio of males/females old/young etc. should be the same.
Reading ability of children in Federally funded reading programs is
consistently below average.
So those programs cause poor reading ability.