Brookdale Community College Valid Sound Strong & Cogent Discussion Paper 1 There was once an outlaw named Fred who had robbed 24 banks successfully. On th

Brookdale Community College Valid Sound Strong & Cogent Discussion Paper 1 There was once an outlaw named Fred who had robbed 24 banks successfully.

On the way to rob his 25th bank, Fred said to himself: “I have robbed 24 banks, and every single time, I got away unharmed with the money. Therefore, when I rob this bank today, I will get away unharmed with the money.”

But on this day, Fred was ambushed by many citizens and shot to death.

What Fred said to himself was an argument. Was that argument deductive or non-deductive?

If you said deductive, was it valid or invalid?

If you said non-deductive, was it strong or weak?

– Give reasons for both your answers.

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In your reply post to another student, give reasons why you don’t agree with their answer(s), or give reasons why you do agree with their answer(s).

When you respond to a fellow student’s response, you need to dispute some point that another student made, and to give reasons for your response. Don’t just say something like “I disagree with his or her response.” Be respectful: the goal is to have an enlightening debate

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As we have already discussed, the difference between a deductive argument and a nondeductive argument has to do with the intended relationship between the premises and the
conclusion. A deductive argument intends for the premises to guarantee the conclusion. A nondeductive argument intends for the premises to make the conclusion likely, not guarantee it.
As we saw in the lesson on Deductive vs Non-Deductive, when the premises of a deductive
argument do actually succeed at guaranteeing the conclusion, the argument is said to be valid. If
the premises of a deductive argument don’t succeed at guaranteeing the conclusion, the argument
is said to be invalid or not valid. In logic, the terms ‘valid’ and ‘invalid’ are technical terms.
They apply just to the relationship between the premises and the conclusion, not to the question
whether the premises are true. If a deductive argument is valid, then the premises are properly
related to the conclusion.
But it doesn’t follow that a valid deductive argument is good. In order for a deductive
argument to be good, the premises have to be true as well. We will now introduce a new term. If
you have a deductive argument that has all true premises and is also valid, then the argument is
said to be ‘sound’. That means that if you have a deductive argument that is invalid or has at
least one false premise, the argument is said to be ‘unsound’.
(You may now wonder if all sound arguments have true conclusions. Yes, they do. A sound
argument has true premises, and because it is valid, the premises cannot be true while the
conclusion is false; so that means it has a true conclusion.)
Here is an example of a sound deductive argument:
All humans are mortal. The President of the United States is a human.
So the President of the United States is mortal.
This deductive argument is sound, because both its premises are true and the argument is
valid.
Here is an example of an valid deductive argument that is unsound.
1. All humans are fast swimmers.
2. My uncle is a human.
So, my uncle is a fast swimmer.
This deductive argument is unsound because the first premise is false. Not all humans are
fast swimmers. Although the argument is unsound, it’s still a valid argument, because the
premises do guarantee the truth of the conclusion. In other words, if the premises were true, then
the conclusion would also have to be true. Remember that validity only applies to the
relationship of the premises to the conclusion; it does not require that the premises be true.
Here is an example of an invalid deductive argument (and that makes it unsound too).
All dogs are mammals.
Monty is a mammal.
So Monty is a dog.
This deductive argument is unsound because it’s invalid. It’s logically possible that even if
the premises were true, the conclusion could be false. Yes, all dogs are mammals. But that does
Valid, Sound, Strong, Cogent
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not entail that all mammals are dogs! There are many non-canine mammals. Monty could be a
cat (or a human) and the premises would still be true. But the conclusion would be false.
The previous example illustrates an informal way of telling whether a deductive argument
is valid or invalid.
– Try to imagine a scenario in which all the premises of the argument are true, but the
conclusion comes out false. (In our example, the scenario was that Monty was a cat.)
– If you can imagine such a scenario, you should say the argument is invalid.
If you cannot imagine the premises being true while at the same time the conclusion
is false, you should say the argument is valid.1
– If you determine that the argument is valid, you then ask whether the premises are in
fact true. If they are, then the argument is sound. If the argument is either invalid or
there is at least one false premise, the argument is unsound.
We covered many examples that illuminate the meaning of “valid” in the lesson on
Deductive vs Non-Deductive. Please review them before you tackle the Practice Quiz and the
Quiz for this week.
__________________________________________________________
NON-DEDUCTIVE ARGUMENTS:
Now let’s turn to Non-Deductive arguments. When the premises of a non-deductive
argument do succeed in making the conclusion likely,2 the argument is said to be ‘strong’. If the
premises don’t succeed in making the conclusion likely, the argument is said to be ‘weak’.
No non-deductive arguments are valid. But this is not a criticism of a non-deductive
argument, because the premises of a non-deductive argument aren’t intended to guarantee the
conclusion, as they are in a deductive argument. In logic, the terms ‘strong’ and ‘weak’ are
technical terms that apply to the relationship between premises and conclusion in a nondeductive argument. The strength of a non-deductive argument comes in degrees. The more
likely the conclusion to be true, supposing the truth of the premises, the stronger the argument. In
contrast, the strength of the relationship between the premises and conclusion in a deductive
argument does not come in degrees. Rather, it’s an all-or-nothing matter, valid or invalid. If a
non-deductive argument is strong, then the premises are properly related to the conclusion.
Putting all this together, what is a one-sentence definition of “strong”?
A non-deductive argument is strong
if the conclusion follows with a greater-than-50% probability
from the supposition that the premises are true.
Note the impact of this definition. When assessing strength, we must “give the premises a
chance” by supposing that they are true, and see if the conclusion is rendered probable by that
supposition. While assessing strength we don’t worry about whether the premises are actually
true in our world: just what a world would probably be like if they were true in it.
1
Actually, the word “imagining” here is not as subjective as it might sound. What we really mean is “asserting
without contradiction”. When an argument is valid, you will find that if you assert that the premises are true and
the conclusion is false, you will find that you are caught in a contradiction.
2
Recall that by “likely” or “probable”, we refer to a probability greater than 50%.
Valid, Sound, Strong, Cogent
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But a strong argument may not be good overall. In order for a non-deductive argument to
be good, the premises have to be true as well. When a non-deductive argument passes this test, it
is said to be cogent. Thus cogency includes two separate conditions:
1. the argument must be a strong non-deductive argument
2. the premises must be true.
That means that true premises alone do not make a non-deductive argument cogent. And being
strong doesn’t do the trick either. The argument must have both. If it doesn’t satisfy both
conditions, it is said to be uncogent (or not cogent). Therefore, if you have a non-deductive
argument that is weak or has at least one false premise or both, the argument is uncogent.
Here is an example of a cogent non-deductive argument:
1. Most American adults have eaten at least one hamburger.
2. James Franco is an American adult.
So it’s likely that James Franco has eaten at least one hamburger.
It’s true that most American adults have eaten at least one hamburger. It’s also true that James
Franco is an American adult. Do the premises guarantee the conclusion? No. It’s logically
possible that James Franco has not eaten a single hamburger in his life. But the premises of a
non-deductive argument are not intended to guarantee the conclusion. They are only intended to
make the conclusion likely. And in this case, they do that, so the argument is strong. This nondeductive argument is therefore cogent, since its premises are true and the argument is strong.
Here is an example of a strong, yet uncogent, non-deductive argument.
1. Most American adults have never eaten a hamburger.
2. James Franco is an American adult.
So it’s likely that James Franco has never eaten a hamburger.
This non-deductive argument is uncogent because the first premise is false. Although the
argument is uncogent, it’s still a strong argument, because if both premises were true, the
premises would make the conclusion likely. Remember that “strong” only applies to the
relationship of the premises to the conclusion; it does not apply to the truth of the premises.
Here is an example of a non-deductive argument that is uncogent only because it is weak.
Sharks and shrimp both live in the ocean.
So I’ll bet that sharks taste like shrimp.
The premise of this non-deductive argument is true. But it’s an uncogent argument, because it
has a weak relationship between its premise and conclusion. In other words, the truth of the
premise does not make the conclusion likely. If you recall, this argument also commits the
fallacy of false analogy.
Here’s an informal way of telling whether a non-deductive argument is strong or weak.
• First, try to imagine a scenario in which all the premises of the argument are true.
• Second, ask yourself whether, in this scenario, the conclusion is rendered likely
(remembering that by ‘likely’ we mean: “having a probability greater than 50%”).
Valid, Sound, Strong, Cogent
•
•
•
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If you think the conclusion is made likely, given the scenario in which you imagine
the premises being true, you should say the argument is strong.
If you think the conclusion fails to be made likely given the scenario in which you
imagine the premises being true, you should say the argument is weak.
If you determine that an argument is strong, you should then ask whether the
premises are in fact true. If all the premises are true and the argument is strong, then
the argument is cogent. If either at least one premise is false or the argument is
weak, the argument is uncogent.
SOUND and COGENT:
You will be asked on the quiz to assess soundness and cogency.
And here is the crucial point for the quiz:
There are four possible scenarios for a deductive argument:
1. invalid with at least one false premise
2. invalid with true premises
3. valid with at least one false premise
4. sound (valid with true premises)
Thus there are three different ways of being unsound, shown in options 1, 2, and 3.
Here is a good way to choose among these four options:
• first, figure out if the argument is valid, by supposing the premises are true and seeing if
that forces you to grant the conclusion’s truth
• then look at whether its premises are true.
– If you decided the argument is valid, then it could be sound if you found true premises, or
valid with at least one false premise if you found at least one false premise.
– If you decided that the argument was invalid, then it could be invalid with at least one false
premise or invalid with true premises, depending on whether you found all premises to be true.
A similar logic applies with non-deductive arguments, to the question of cogency.
With non-deductive arguments, first see if the argument is strong. Then see if its premises are
true.
There are four possible scenarios for a non-deductive argument:
1. weak with at least one false premise [weak just means not strong]
2. weak with true premises
3. strong with at least one false premise
4. cogent (strong with true premises)
→ See the next page for some examples to work through, with explanations given after you
do.
Be sure to go through these examples before you tackle Practice Quiz 12.
Valid, Sound, Strong, Cogent
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For each of the following arguments, say whether it is deductive or non-deductive.
If it is deductive, say whether it is valid.
If it is non-deductive, say whether it is strong.
[Correct answers, with explanations, are on the next page.]
1.
Bradford, who is twenty-five, has never had a speeding ticket in his life.
Therefore it is likely that Bradford will never, ever get a speeding ticket.
DEDUCTIVE? ______
VALID? ______
NON-DEDUCTIVE? ______
STRONG? ______
2.
If Jessica is in New Orleans, then Jessica is in Louisiana.
Jessica is in New Orleans.
So, Jessica is in Louisiana.
DEDUCTIVE? ______
VALID? ______
NON-DEDUCTIVE? ______
STRONG? ______
3.
I had my flu shot on New Year’s Eve.
I got sick on New Year’s Day with a fever.
So it’s clear the flu shot gave me the flu.
DEDUCTIVE? ______
VALID? ______
NON-DEDUCTIVE? ______
STRONG? ______
4.
There are 7 kids and 2 adults in the van.
So, there are exactly 8 people in the van.
DEDUCTIVE? ______
VALID? ______
NON-DEDUCTIVE? ______
STRONG? ______
5.
90% of the 300 Republicans I’ve talked to recently are pro-life.
Therefore most Republicans are pro-life.
DEDUCTIVE? ______
VALID? ______
NON-DEDUCTIVE? ______
STRONG? ______
→ On the next page are answers with explanations.
Valid, Sound, Strong, Cogent
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ANSWERS, WITH EXPLANATIONS:
1. Bradford, who is twenty-five, has never had a speeding ticket in his life.
Therefore it is likely that Bradford will never, ever get a speeding ticket.
DEDUCTIVE? ______
VALID? ______
NON-DEDUCTIVE? Yes
STRONG? No
EXPLANATION: This argument is not meant to guarantee its conclusion, so it is nondeductive.
But the premise is based on too small a sample – Bradford does not have enough of a track
record yet as a driver – so the conclusion is not rendered likely. That means the argument is not
strong.
_________________________________________________________
2. If Jessica is in New Orleans, then Jessica is in Louisiana.
Jessica is in New Orleans.
So, Jessica is in Louisiana.
DEDUCTIVE? Yes
VALID? Yes
NON-DEDUCTIVE? ______
STRONG? ______
EXPLANATION: Could the premises be true and yet the conclusion be false?
No. If you suppose the premises both true, it follows necessarily that the conclusion is true. So
the argument is valid, and that makes it deductive.
________________________________________________________
3. I had my flu shot on New Year’s Eve.
I got sick on New Year’s Day with a fever.
So it’s clear the flu shot gave me the flu.
DEDUCTIVE? ______
NON-DEDUCTIVE? Yes
VALID? ______
STRONG? No
EXPLANATION: this is clearly intended to be a Causal Argument, which we have seen is an
example of Inference to the best Explanation, a non-deductive argument form.
However, the sequence of “took-flu-shot, then got-sick” is an example of the Post Hoc fallacy:
just because the speaker got sick after having the flu shot does not mean the shot caused the
illness.
So the argument is weak (not strong): the premises do not make the conclusion likely.
________________________________________________________
→ see next page
Valid, Sound, Strong, Cogent
page 7
4. There are 7 kids and 2 adults in the van.
So, there are exactly 8 people in the van.
DEDUCTIVE? Yes
VALID? No
NON-DEDUCTIVE? ______
STRONG? ______
EXPLANATION: As we said in the lesson on Deductive vs Non-Deductive, mathematical
reasoning is usually deductive, because its results are intended to be certain, not just probable.
The arguer here is clearly trying to do a simple piece of addition, but gets it wrong.
So the argument is deductive, but is invalid.
___________________________________________________________
5. 90% of the 300 Republicans I’ve talked to recently are pro-life.
Therefore most Republicans are pro-life.
DEDUCTIVE? ______
NON-DEDUCTIVE? Yes
VALID? ______
STRONG? Yes
EXPLANATION: this argument is an inductive generalization, a pattern we know is nondeductive. The conclusion uses the word “most”, which is a mark of a generalization (along with
“all”).
Is this argument strong? Yes, for two reasons:
• the sample is quite large
• the conclusion does not say “all Republicans”; it says “most”, so it is easier to make that
probable.
Nicole Edwards
Tuesday
I would consider Frank’s argument to be non-deductive. Although the premises may have been true they did
not guarantee the conclusion that since he got away with 24 bank robberies he would get away with 25.1
thought that this was a strong argument. While I don’t think it was logical to think that you can rob banks as
many times as you want and not get caught I though the argument was strong. Getting away with robbing a
bank 24 times would make someone think that they could get away with it 25 times. Even though the argument
is not guaranteed I think that the argument was strong.
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