When is "Strong" Both Good and Bad?


”I’ve heard you use the term "strong" in ways that seem contradictory to me. On the one hand, you call an argument "strong" when the logic is good but not valid. On the other hand, you say that an argument can be weakened if the premises are "too strong". So being strong is a good thing in the first case, but a bad thing in the second case. I'm confused."


Great question. It gives me an excuse to clarify a distinction that can cause headaches when you're first introduced to these concepts.

The confusions arises from the fact that the word "strong" has a couple of specialized uses in logic and argumentation. It has a meaning in which it's used to describe the logical properties of whole arguments, and it has another meaning in which it's used to describe the plausibility of individual claims.

We need to distinguish these two senses and realize that they’re saying different things about arguments.

“Strong” as a Property of Whole Arguments

A central question for logical analysis is, if we assume that the premises are all true, how confident can we be that the conclusion is also true?

If the answer is that we can be 100 percent confident, because the conclusion follows necessarily from the premises, then we have a name for these kinds of arguments -- they're called 'valid'.

Here’s an example:

1. All mammals are warm-blooded.
2. Tigers are mammals.
Therefore, tigers are warm-blooded.

Arguments can be valid even if the premises are false:

1. All fish are less than 2 feet long.
2. All dolphins are fish.
Therefore, all dolphins are less than 2 feet long.

The premises and conclusion are all false, but the logic of this argument is still valid, because IF those premises WERE true, the conclusion would have to be true as well.

In logic the term “strong” is used to describe an an argument for which the conclusion doesn't follow with certainty, but it does follow with sufficiently high probability that we would agree that IF the premises were true, then we would have good reasons to believe the conclusion is true. Not conclusive reasons, you could still be wrong; but the inference is strong ENOUGH to make it reasonable to accept the conclusion.

One of the examples I give in the video lectures is, if you believe that, say, 90% of human beings are right-handed, and you point to a random person and infer that that person is right-handed, then while this conclusion isn't guaranteed, it's still very likely true. In a world in which 90% of people are right-handed, then it's reasonable to think that any randomly selected person is going to be right-handed.

And so we say that this is a "strong" inference -- not deductively valid, but strong enough to warrant accepting the conclusion, on the assumption that the premises are in fact true.

So in this sense, calling an argument "strong" is a good thing -- it's a way of saying that it's an argument that succeeds in providing reasons to accept the conclusion.

“Strong” as a Property of Individual Claims

In argumentation the word “strong” can also be used to describe the plausibility of claims that are not obviously true; claims that, in advance of being given reasons to think they're true, we would be surprised to find out that they were true.

So, using this language, a weaker claim is one that is less surprising; we already have a some confident that it's true. A stronger claim is one that is more surprising.

This is how we’re using the term when we say something like “You've made a very strong claim, sir. I hope you have the evidence to back it up."

Note that these judgments are always relative to one’s background knowledge. What would be surprising to one person may not be surprising to another.

For example, let's consider the range of claims that you might encounter about the causes of the 9-11 attack that caused the Twin Towers of the World Trade Center to fall, and ask ourselves how surprised we would be if they turned out to be true.

1. "The attack was orchestrated by al-Qaeda under the leadership of Osama Bin Laden."

2. "Members of the Bush Administration had good reason to think that the attack was coming, but did nothing to prevent it, because they saw that it would create an opportunity to marshall public support for a military intervention in the middle east, which they had been wanting to do for some time.".

This is an exactly of what is sometimes called an 'advanced-knowledge conspiracy theory' -- the most famous of these is that officials in the Roosevelt administration had advanced knowledge of the Japanese attack on Pearl Harbor, and intentionally did nothing to prevent it, because they wanted the US to intervene in the war in Germany.

3. "George Bush himself was aware of the attack in advance, and agreed to let it happen, for the same reasons."

That would be like saying that Roosevelt himself knew about the attack on Pearl Harbor and did nothing to prevent it.

4. "Members within the Federal Government conspired to manufacture this event by planting explosives in the buildings themselves, and then framing al-Qaeda, to generate a pretext for going to war."

In conspiracy circles, they would call this a "false flag" event.

5. "Bush himself was aware of these plans to demolish the World Trade Centers and okay'd them".

6. "9-11 was orchestrated by a shadowy group of international elites to perpetuate a state of conflict among global powers".

This is a common claim of so-called New World Order conspiracy theorists.

For me, these go from least surprising to most surprising. In this context I would say that the weakest claim is the first and the strongest claim is the last. The stronger the claim is, the stronger the evidence must be to convince someone that it's true. Weaker claims require much less evidence to convince someone that they're true.

Arguments that rely on very strong premises, in this sense, are open to criticism for this very reason, that they assume more than most audiences are willing to grant.

Strategically, when you're crafting an argument, it's almost always a good idea to look for the weakest premises that logically entail the conclusion you're going for.

Why? Because by definition, audiences are more willing to grant a weaker premise. In this sense, weakening the premises in your argument is a way of removing barriers for your audience -- you're giving them fewer reasons to reject the argument.

For example, consider an argument for vegetarianism based on the claim that animals suffer a great deal in the food industry and it's a good thing to reduce suffering whenever possible, and compare that with an argument for vegetarianism based on the assumption that animals have divine souls and God thinks it's wrong to kill them for food.

The first argument makes much weaker assumptions than the second.

I hope it's a bit clearer now how, on the one hand, you can say that it's a good thing for an argument to be strong, as opposed to weak, in the sense of having strong logic; but it's a bad thing for an argument to rely on strong premises that your audience is unlikely to accept.