Subconscious Reasoning

We are reasoning machines, but most of the reasoning we do isn't explicit and formal. Aristotle attempted to formalize our reasoning methods by recognizing laws of logic, including syllogisms that express laws of logical inference. Using these tools in a formal way allows us to recognize and avoid making mistakes in our reasoning. It also helps us understand what people are saying and thinking if we can formalize what they say.

Consider this conversation:

Sam I Am: I may have had Covid a month ago, but I'm not sure.

Doctor: Oh, if you had Covid, you would know it.

Sam I Am: In that case, I definitely had the flu.

This conversation didn't actually happen, so there's no need to nit pick about the fact that it's possible to have Covid and not know it. That's irrelevant to the point I'm trying to make.

Anywho, it might seem like I made some big leap in logic to conclude that I had the flu from the fact that if I had Covid, I would've known it. But there's some unstated premises in my reasoning as there almost always is in our day to day conversations. If I were to formalize my reasoning, it would look like this:

1. If you had Covid, you would know it.
2. I do not know it.
3. Therefore, I did not have Covid.

1. I either had the flu, or I had Covid.
2. I did not have Covid.
3. Therefore, I had the flu.

Formalizing my reasoning reveals that I used two different kinds of syllogisms. The first one uses the modus tollens syllogism, and the second one uses the disjunctive syllogism. Notice that the second premise in my second syllogisms says the same thing as the conclusion in my first syllogism. That's why the first syllogism comes first. I have to establish that conclusion before I can use it as a premise in my next argument. To simplify this sort of thing, we can combine all the premises and inferences into one argument, which eliminates repetition. In my case, it would look like this:

1. If I had Covid, I would know it.
2. I do not know that I have Covid
3. I either had the flu or I had Covid.
4. Therefore, I did not have Covid (this follows from 1 and 2 by modus tollens).
5. Therefore, I had the flu (this follows from 3 and 4 by disjunction).

Whenever we're talking to somebody, and they seem to make a leap of logic, or they come to some conclusion we disagree with, we tend to want to fill in the gaps where they didn't explicitly state all their permises. If we're charitable, we fill the gaps with whatever we think must be assumed in order to render their argument logically valid. Often, we don't even state the premise ourselves. If we disagree with their conclusion, the reason we give is always some denial of what we think the hidden premise was.

Now consider the following conversation:

Jim: I don't think I had Covid.

Bobe: Why not?

Jim: Because if I had Covid, I would've known it.

Notice that if we tried to formalize this into a syllogism, there would be a missing premise.

1. If I had Covid, I would have known it.
2.
3. Therefore, I did not have Covid.

What is the hidden premise? It doesn't take too much creativity to recognize that Jim's reasoning assumes that he did not know he had Covid since that's the only way to render the reasoning valid. If you were trying to understand Jim, you would likely assume that's his hidden premise. He could've said something like this:

Jim: I don't think I had Covid.

Bob: Why not?

Jim: Well, I didn't have any of the symptoms of Covid.

Bob: It's possible to have Covid without having symptoms.

There are a couple of things going on in this conversation. First, Jim is making an argument to justify his conclusion that he didn't have Covid. Second, Bob is objecting to Jim's argument by denying what he takes to be Jim's hidden premise.

At first glance, Jim's argument might seem unobjectionable, but even this line of reasoning contains a hidden premise, which can be exposed by trying to formalize the reasoning into a syllogism.

1. I did not have any of the symptoms of Covid.
2.
3. Therefore, I did not have Covid.

The best candidate for the hidden premise that jumps out at us is this: If Jim had Covid, he would have had symptoms of Covid. If that were the hidden premise, the conclusion would follow by modus tollens. Since that's the only premise Bob can immediately come up with, he fills in the gap and denies that premise. If the hidden premise is false, then Jim's argument is unsound even if it's logically valid.

Notice that Jim and Bob had this conversation without either of them ever stating the hidden premise in Jim's argument. This sort of thing happens every day. It happens in regular conversation, in heated arguments, and in civil debate and discussion.

There is a danger in filling in the gaps when somebody else delivers an argument with hidden premises. The danger is that you will fill the gaps with the wrong premise. If you do that, and the other person notices, they will think you are misrepresenting them. They may either chalk it up to an innocent misunderstanding, or they may think you're misrepresenting them deliberately. It's hard not to want to fill the gaps when the missing premise seems obvious, but we sometimes fill the gaps with whatever jumps out at us even if there are other options. We do this because we're hasty and sometimes uncharitable.

When I've had formal debates, I've tried two different tactics when responding to my opponent's argument. One tactic is to acknowledge that there's a hidden premise. I'll say something like, "Your argument assumes such and such because that's the only way to make the argument go through." Another tactic I use is to formalize their argument, leave one of the premises blank, and say that unless my opponent fills in the blank, his argument is invalid. I can only remember using that second tactic one time in a debate. I'm reluctant to use that in a formal debates because it requires more back and forth before getting to the point, and there are limited rounds. Usually, I make my best guess at the hidden premise. To avoid being accused of strawmanning their position, I make it known that I'm only guessing what their hidden premise is. Then I'll say something like, "If I've understood you correctly, here's the issue I have with your arugment. . ."

It is interesting to me that in most debates, arguments, and discussions I've seen or been involved in, the disagreements seem to hinge on the hidden premises rather than the explicitly stated premises. It is also interesting to me to recognize that a lot of reasoning - even valid reasoning - happens without even exlpicitly thinking about all the premises we're invoking. We just jump from one fact or observation to our conclusion without explicitly thinking about the hidden premise or the logical rule of inference we used to draw the conclusion from the stated and hidden premise. In many, and possibly most, cases, we reason subconsciously. But formalizing our reasoning can help us be more clear. Formalizing our buddy's reasoning can help us understand him. Formalizing our reasoning can help us recognize and avoid mistakes in thinking. It can also improve our reading compreshension.

We should be thankful for Aristotle.