3.2: Missing Assumptions

We need to be able to identify (and then to incorporate into our argument maps) assumptions that are part of the argument, but that weren’t explicitly stated. These are called Hidden Premises, Missing Assumptions, Suppressed Premises/Assumptions, etc. Regardless of the name, these are cases where an argument in fact relies on a claim that it doesn’t state as a premise. There is a claim that must be true if the inference is to make sense, but isn’t explicitly claimed to be true by the argument as it is written or spoke.

Identifying Hidden Assumptions

It’s a bit tricky, but it might be one of the most important and practical skills you’ll learn in this class. How do we figure out when an argument has one or more hidden premises and how do we identify what those premises are?

Well, one answer is simply that formal logic does the job for us when we’re dealing with deductive arguments. This is the math-like system of argument analysis we’ll learn later in the semester. But for now, we need some informal tools to allow us to identify hidden premises or assumptions. This is not only a skill you can build without knowing logic, but is also a skill that extends to inductive reasoning as well and so is far more broadly applicable.

Check out this argument:

Flowers smell nice

???

\(\therefore\) Let’s plant some flowers

[that little triangle of dots is a “therefore” sign]

We can’t quite get from “smelling nice” to “things we’ll plant” without an assumption which links these two ideas. Notice how flowers are in both the premise and the conclusion, so we don’t need to link the topic of flowers together with the topic of flowers.

Abstractly, is A is related to B, and C is related to B, then what we need is something linking A and C so that we can bridge the gap between A and B being associated with one another to C and B being associated with one another.

Less abstractly, if we have three topics: flowers, smelling nice, and things to plant; then we need something linking smelling nice and things to plant so that we know the fact that flowers smell nice is a compelling reason to think that flowers are the kind of thing we should be planting. We know that flowers smell nice and we’re trying to get to flowers should be planted. Any idea what the hidden link might be?

The hidden assumption is something like “we should plant things that smell nice.” Can you see how that completes the inference? Check out some more examples and see if you can figure out what is going on in each example: why do we need the extra premise for the inference to work?

These wildfires are out of control! So global warming is real.

The hidden assumption is something like “global warming is the best explanation for an increase in wildfires.”

We should believe only what is reasonable, so we should reject theism.

The hidden assumption is something like “belief in theism is unreasonable.”

No one believes the Earth is flat anymore, so it’s a silly belief.

The hidden assumption here is something like “any belief that no one currently holds is a silly belief.”

Here’s a step-by-step process for identifying hidden assumptions:

A step-by-step process:

1. First, identify the inference or sub-inference with the hidden assumption

• Which one is “incomplete”?

2. Then, look at the premises of the inference and identify the “terms” or topics discussed in each premise

• Each premise is usually a claim which links two topics together.

3. Then, ask how we can link the terms that aren’t yet linked.

• This requires a bit of imagination and instinct, but you can do it!

4. Finally, write the assumption that links the unlinked terms.

Now that you’ve identified a hidden assumption or more, perform the following two steps:

5. Check to be sure your argument now works

• Does the argument now have a link between each topic? Is there a path from the topics in the premises to the topics in the conclusion?

6. Perform the “negative test” on your assumption

• If you negate your hidden assumption, you should end up with an argument that makes no sense. If the argument with the negated premise makes sense, then you haven’t identified a hidden assumption (i.e. the argument was fine without your assumption).

Let’s take a look at how this works with some real arguments.

I think we should invade North Korea. Look, the Kim Jong dynasty is simply never going to give up on their goal of being a nuclear power.

Okay, this inference is really “fast” meaning that it skates over a few hidden assumptions and so doesn’t seem to work all by itself. It’s like it rushes straight to the finish line without actually running the course. Let’s break it down step by step.

Step 1

There’s only one apparent premise and one apparent conclusion, so identifying the inference in question is easy.

Step 2

The “terms” or topics of this inference are:

A. We should invade

B. North Korea

C. Kim Jong dynasty

D. Nuclear Arms

Step 3

How do we connect these topics? First, we need to connect “North Korea” with the “Kim Jong dynasty”.

Then we’ll need to connect “being a nuclear power” with “we should invade.”

Step 4

Let’s try these assumptions and see how the argument works out:

1. The Kim Jong dynasty is never going to give up on their goal of being a nuclear power.

2. The Kim Jong dynasty is going to lead North Korea for the foreseeable future.

3. Any country that aspires to be a nuclear power is one we should invade.

4. Therefore, we should invade North Korea.

This inference is more complete and connects the topics together more completely, but it rests on one very shaky premise. Can you identify which one?

Yes, that’s right. You are very smart. Premise 3 is pretty wacky, right? What if Argentina decided it wanted to be a Nuclear Power? Should we invade them? I would hope not. They’re a pretty harmless nation at the moment.

So, we have a choice. Either decide that the argument is pretty weak and reject it out of hand, or we can exercise the Principal of Charity to try to interpret the argument to be as plausible as possible. We should always interpret arguments—especially the ones we’re skeptical of or disagree with—to be as rational and plausible as possible.

With that in mind, let’s change this argument up a bit so that it makes a bit more sense. We might not agree with the argument in the end, but at least we will have understood the argument in the best possible light. We will have seen what the most plausible argument for that conclusion on the basis of similar premises is.

If we ignore premise 3, the weak premise, and try to replace it with a few premises which make more specific and believable claims, we’ll be in a better spot. We’ll need to tie together some new topics. Premise 3 was supposed to make a link between “aspires to be a nuclear power” and “we should invade.” There’s a bit of conceptual “distance” between these ideas, though, so we shouldn’t just posit a principle like premise 3 above which directly links them. That would be too easy a principle to reject. Instead, we’ll travel the distance between these ideas in a few steps rather than a giant leap.

How about we connect “aspires to be a nuclear power” to “they’re dangerous”?

Then we can get from “they’re dangerous” to “we should invade.” That sounds more plausible, right?

1. The Kim Jong dynasty is never going to give up on their goal of being a nuclear power.

2. The Kim Jong dynasty is going to lead North Korea for the foreseeable future.

3. North Korea under Kim Jong rule would be an immediate existential danger to its neighbors and the rest of the world if they ever became a nuclear power.

4. If we invade North Korea, then we prevent that danger.

5. Therefore, we should invade North Korea.

Now the argument seems to hang together a bit more clearly. We have a clear path from the Kim Jong dynasty through to a nuclear North Korea, to the danger that poses and therefore a motivation for invading, all the way to the claim that we should invade. It’s still shaky reasoning, but it’s approaching the strongest version of the original argument.

There’s still technically something missing. Between 4 and 5 we’ve missed a premise.

In order to get from an “is” claim to an “ought” claim, often you’ll need a general normative principle. That is, we need a general rule which allows us to move from a simple statement of supposed fact (premise 4) to a prescription for what we should do (the conclusion, #5). This one will do:

4a. If we can prevent immediate existential danger to whole countries then we must/should act so as to prevent that danger.

That actually seems pretty plausible, right? So in this case the missing premise wasn’t so shaky (you might disagree, though).

We can then perform the negative test on our hidden assumptions and figure out if the argument falls apart without them. If we deny 4a, then we can’t get from 4 to 5. Does that make sense? If so,

Mapping Hidden Assumptions

Mapping Hidden Assumptions is relatively simple.

A hidden assumption will always offer conjoint support for its conclusion/sub-conclusion.

Think about it: if hidden assumptions are things that must be true for an inference to work, and conjoint premises are premises that must all be true for the inference to work, then it makes sense that any hidden premise will offer conjoint support.

The only difference will be that we’ll use dotted circles instead of regular:

, or , etc.

A few complete examples:

Example \(\PageIndex{1}\)

1. We have a right to bodily autonomy

2. Hidden Assumption: (Abortion restrictions infringe on a right to bodily autonomy)

3. Therefore, we have a right to freedom from abortion restrictions

The inference from 1 to 3 makes some sense because we’re all familiar with the abortion debate by now. What we do to make it make sense of it for ourselves, though, is implicitly add in premise two in understanding the inference from 1 to 3.

Example \(\PageIndex{2}\)

(1) We’ll never stop climate change, (2) Hidden Assumption: Climate change will intensify fires and storms, so (3) we’re going to have much more fires and storms. (4) Our current system can’t handle even basic disasters. Furthermore, (5) state disaster relief funds are insufficient without help from FEMA’s overburdened funds. So, (6) we need to reform and enhance funding for FEMA immediately.

The inference from 1 to 3 makes little sense if it’s not true that climate change is connected to fires and storms, so we need premise 2 to make that connection.

3, 4, and 5 are independent because each by itself makes sense as a premise for 6.