Step 2. Identify whether the argument is valid or invalid

Since the terms "valid" and "invalid" mean something different in the world of logic than in ordinary conversation, let us first define each and then discuss how knowing this aspect of an argument allows one to better analyze it.

An argument is said to be valid if the truth of its premises guarantee the truth of the conclusion. Another way of saying this is that an argument is valid if it is (logically) impossible to have a false conclusion and all true premises.

If an argument is valid and actually has all true premises, then the argument is called sound.

 

 

Sound arguments must have true conclusions, no matter what.

 
 
  

 

On the other hand, an argument is said to be invalid if it is possible to have a false conclusion and all true premises (no matter how remote that possibility may be).

Before turning to some examples, two points of common confusion should be mentioned now.

The term valid does not mean true, and invalid does not mean false. These terms describe instead possible truth conditions for an argument's conclusion, given the assumption that all of the premises are true. What this means in turn is that the terms valid and invalid describe arguments, not single statements.

And recall finally that an argument consists of a conclusion and supporting premises.

With this said, re-read the above definitions one more time.

Another common misconception is to think a valid argument has a true conclusion. This is only partially correct. A valid argument must have a true conclusion only if every single premise is actually true. On the other hand, an invalid argument need not have a true conclusion, even if every single premise is true. This information is summarized in the following table:

 

Premises

Conclusion

Argument is valid

Argument is invalid

All true

Must be true

Need not be true

Not all true (at least one is false)

Need not be true

Need not be true

 

The natural question now is how does one determine whether an argument is valid or invalid? Unfortunately a complete answer to that question goes well beyond the scope of this introductory guide. That said, one way to discover whether an argument is invalid is to just pretend for a second that all the premises are actually true – then ask yourself if the conclusion can be false without making one of the premises false at the same time. If the answer is no, then you have at least a reason to suspect the argument is valid. On the other hand, if the answer is clearly yes, then you have a sufficient reason to conclude the argument is invalid.

So how does this help with argument analysis? Well, if one knows an argument is valid, and yet suspects the conclusion to be false, the only hope one has of showing that the conclusion is false is to show at least one of the argument's premises is false. On the other hand, if an argument is valid and one wishes to argue for it, one need only provide reasons why the premises are actually true, since if they are, the conclusion must then be true.

Here is a very simple example of a valid argument:

If it is Friday, then interstate traffic will be terrible.

But interstate traffic is not terrible.

Hence it is not Friday.

Recall, we are keeping the example as simple as we can, and for the moment we are going to ignore the ability to just look at a calendar or your cell phone to check the day of the week. Now the argument is valid, but suppose you wish to argue that it is not Friday (in other words, you wish to argue against the argument's conclusion). Since the argument is valid, the only way you can do so is to somehow show either the interstate traffic really is terrible or that the connection between Friday and interstate traffic being terrible is false. In other words, you cast doubt on the second premise, the first premise, or both.

On the other hand, if you wish to agree with the argument's conclusion, since the argument is valid all you need to do is to give reasons why the premises really are true, since their truth guarantees the truth of the conclusion as that is the very definition of a valid argument.

In comparison if an argument is invalid to argue against it one can point out the conditions that would allow for all true premises and false conclusion, and show that those conditions are indeed reasonable (in the sense of "likely to be true"). On the other hand, if you wish to support the conclusion of an argument which is invalid, you need to show that the conditions that would result in all true premises and a false conclusion are quite rare. Again, we look at a simple example of an invalid argument..

If it rains, then the streets are wet.

It has not rained.

Therefore the streets are not wet.

In this case, since the argument is invalid, to argue against the conclusion all one needs to do is point out a plausible or likely scenario where the premises are still true but the conclusion is false. One such scenario might be, "It snowed last night, and warmed up today which caused the snow to melt, making the streets wet". On the other hand, if you wished to argue for the conclusion, you point out that the conditions that might normally make the premises true but the conclusion false rarely occur. For example, one might note that it is summer and hence the streets can't be wet due to snow melt. To be really successful, each reasonable possibility that would result in wet streets without rain would be addressed and rebuffed.

These observations lead to the following useful information concerning arguments.

 

Fact 1. If an argument is valid and actually has all true premises, then new information can not make the conclusion false, unless part of that new information makes at least one existing premise false.

Example. If John wins the lottery, then we will all go on a trip around the world. We did not go on a trip around the world. Therefore John did not win the lottery.

As long as new information does not change the truth of the premises, then the conclusion that John did not win the lottery stands as long as the premises are all true.

Fact 2. If an argument is invalid and actually has true premises, then new information can change the truth of the conclusion, even if the new information does not make at least one existing premise false.

Example. Thousands of airplanes take off and land without incident or crashing on a daily basis. Hence the airplane we are on will take off and land without crashing.

In this case, if one looks out the window and sees the wing on the airplane engulfed in flames, then this new information does not make the single premise (that thousands of airplanes take off and land without incident or crashing on a daily basis) false, but does lead to the very real possibility that the conclusion that this particular flight will take off and land without crashing turns out to be false.