2.5 Augmentation

To augment an argument is to add one or more premises to it to make a new argument.

Augmentation: adding premises to make a new argument.

An argument is just a collection of sentences: a set of premises and a conclusion. So if you change the premises, you’ve changed the argument.

Nonetheless, we can ask about the relation between the two arguments. For example, say we have a valid argument and augment it. Can we ever end up with an invalid argument?

Consider an example. Here’s a valid argument:

1. Stan and Uma are innocent.
Thus,
2. Uma is innocent.

Now say we augment it with another premise, where you get to place whatever you’d like on line 2*:

1. Stan and Uma are innocent.
2*. ???
Thus,
3. Uma is innocent.

When we augment this argument, the new premise might add relevant information, such as:

1. Stan and Uma are innocent.
2*. Everyone is innocent.
Thus,
3. Uma is innocent.

But that won’t make the argument invalid.

Secondly, the new premise might be irrelevant to the conclusion:

1. Stan and Uma are innocent.
2**. Tamar is innocent.
Thus,
3. Uma is innocent.

But that also won’t make the argument invalid. The original premises already entailed the conclusion, and irrelevant information won’t change that.

Lastly, the new premise might contradict the other premises or conclusion. For example:

1. Stan and Uma are innocent.
2***. Uma is guilty.
Thus,
3. Uma is innocent.

Augmentation can never make a valid argument invalid.

If any augmentation will make it invalid, you might be thinking, that will. But this strategy will always create contradictory premises, and remember weird case of validity #2!

Once you realize that, you’ve discovered a principle or law of logic: augmentation of a valid argument can never lead to an invalid argument.

Now consider this:

There are several ways of making an invalid argument valid with augmentation. The simplest is to use weird case of validity #1: just add the conclusion as a premise. Presto!

Here is the next challenge to test your understanding on. Recall that induction is probabilistic reasoning, where the premises might support a conclusion to some degree without guaranteeing the conclusion is true.

The premises support or confirm the conclusion: the probability of the conclusion being true is greater than 50%.

In inductive logic we say that a set of premises supports or confirms a conclusion if they make the conclusion more likely than not. In probabilistic terms, the conclusion has a greater than 50% chance of being true, given the premises.

Now let’s say we have an argument in which a set of premises does support the conclusion, and we augment that argument. Can the new argument fail to support the conclusion?

For example, here’s an argument that supports the conclusion, given suitable background assumptions:

1. The bullet hole is on the north wall of the lobby.
2. There are gunpowder traces on the chair in the middle of the room.
3. ???
So:
4. The gun was fired from the south side of the lobby.

Is there anything we can put in for line 3 so that the argument no longer supports the conclusion? Here’s another way to put the question:

Consider adding this premise:

3*. The bullet ricocheted 170 degrees.

We can leave all the other information intact, yet adding that premise destroys the inductive support.

That fact helps us see a major difference between inductive support and deductive validity.

Validity is like a tipping point: once some information guarantees the conclusion is true, you can’t stop it by adding more information; only by taking some of that information away.

Validity is like a tipping point: once some information guarantees the conclusion is true, you can’t stop it by adding more information; only by taking some of that information away.

In general, inductive support isn’t like that: we can add new information to take the support away. Of course, this generalization has one exception: if the inductive support is maximal (that is, if it guarantees the conclusion) then you can’t take it away. But that’s just because that’s a case of validity!

If you’ve followed us so far, all the way through the odd and extreme cases of validity, you now have a solid and comprehensive understanding of the concept.