Strong, Weak, Cogent

Question 1

Strong, Weak

Answer 1

To determine if an Inductive argument is Strong, ask: if the premises are TRUE, do they make the conclusion more than 50% likely to be true ? Is it more probable than not that the conclusion follows from the premises?

To determine if an Inductive Argument is Weak, ask if the premises are TRUE, do they make the conclusion 50% or less likely to be true ? Is it not more probable the conclusion follows from the premises?

Question 2

Cogent

Answer 2

An argument is cogent if it is a strong inductive argument with true premises.

Now we are going to work a few more details here to get the hang of this:

You can never have a weak cogent argument

Question 3

Example 1

Answer 3

Is the following argument Strong or Weak? Is it Cogent?

1) 75% of dogs drool.
2) Poppy is a dog.
3) Thus, Poppy probably drools.

This argument is STRONG since the premises guarantee the conclusion by more than 50%. That is, if it is true that 75% of dogs drool and we know that Poppy is a dog, then there is a 75% chance that she drools. That 75% is more than 50%, so the argument is STRONG.

Is this argument COGENT? Remember, this asks if a STRONG argument is actually true. Well, is it true that 75% of all dogs drool? How do we decide this? It’s tough to say. When evaluating Inductive arguments, statistics and data become very important.

Question 4

Example 2

Answer 4

Is the following argument Strong or Weak? Is it Cogent?

1) This barrel contains 100 bananas.
2) 84 bananas selected at random were ripe.
3) Thus, probably all 100 bananas are ripe.

This argument is STRONG since the premises guarantee the conclusion by more than 50%. Think about it this way, we want to see if the bananas in the barrel are ripe, every banana that we pull out that is ripe increases the chance that all 100 of them are ripe. Likewise, when if we pull out an unripe banana, then the likelihood gets a bit lower.

Is this argument COGENT? Remember, this asks if this is actually true. We would have to check out the rest of the barrel to find out for sure.

Question 5

Example 3

Answer 5

1) Every U.S. President has been over 40.
2) The next U.S. President will probably be over 40.

This argument is STRONG since the premises guarantee the conclusion by more than 50%. There have been (as of this writing) 46 presidents. Because every single one has been over 40, the remainder is likely to be so also.

This argument is COGENT since it is actually true that every president has been over 40 years old.

Not like flipping a coin. But what if (random thought here) You flipped a coin 46 times and it always landed on tails. But that doesn’t make it any more likely that it’s going to land on tails next time right? It’s always a 50% chance. So just because there’s a pattern, it doesn’t mean that it’s more likely. There could be another factor (like the limiting and uncontrolled equal chance of flipping a coin).

Question 6

Example 4 (tricky)

Answer 6

1) Every U.S. President has been a woman.
2) The next U.S. President will probably be a woman.

This argument is STRONG since the premises guarantee the conclusion by more than 50%. Remember, a strong argument is an argument where the premises, if true, guarantee the conclusion by more than 50%.

This argument is NOT COGENT since it is not actually true that every president has been a woman.

This whole concept is similar to validity and soundness

Validity - conclusion logically follows the premise
Soundness - if it is valid and all premises are actually true

At first I thought if the conclusion was true but it’s talking about premise I think