11.1 The Extraction Method
Extracting arguments is the culmination of the skills which we have studied up to this point in the course. ‘Extracted’ or ‘reconstructed’ arguments are easy to understand, make every premise explicit, and make clear which premises need to be defended.
Table of Contents
- 11.1 The Extraction Method
11.1.1 Overview of Extractions
Extractions create a bridge to link premises to conclusions.
What is an Extraction?
‘Extracting’ an argument means charitably reconstructing an informal argument as a formal argument, making sure all the inferences are valid. The informal argument may come from a conversation, from a bit of prose, or from your own thoughts. A formal argument fits the structure which we have been studying so far in this class: numbered premises, followed by a conclusion, each of which is a single sentence. The premises in the argument which are inferred from others are labeled clearly with rules of inference, like (1, 2 MP); the premises in the argument which are not inferred from others are labeled (Basic), to indicate that they are claims which need to be defended outside of the argument.
For example, most college students living in Western cultures have, at some point in their life, encountered some version of the teleological argument for the existence of God, the idea that the natural world exhibits a kind of intrinsic order and purpose, and that this had to come from the intentions of a creator or designer. Because this is a controversial topic, it makes for a perfect example of the usefulness of formal logic in evaluating controversial issues more objectively. An extracted version of the argument might go like this:
- The natural world has order and purpose. (Basic)
- Everything which has order and purpose was created with an intention in mind. (Basic)
- The natural world was created with an intention in mind. (1, 2 UI)
- If the natural world was created with an intention in mind, then God exists. (Basic)
- God exists (3, 4 MP)
Lines 1, 2, and 4 are noted “(Basic)”, since they would have to be defended outside of the argument (and they are, no doubt, highly controversial). Line 3 follows from lines 1 and 2 by the rule of UI, and line 5 follows from 3 and 4 by MP, so this is labeled.
Why Extract Arguments
Extracting an argument neither counts for nor against the argument.
Somebody might extract the argument above because they accept it and want to know which basic premises they need to defend: premise 1, 2, and 4. They would want to give reasons to believe each of those premises. For instance, premise 1 seems true because many natural things, like flowers and kidneys and eyes, all have purposes: producing seeds, purifying the blood, and seeing, respectively. Premise 2 seems true because many of the things we observe as having order and purpose are things which were also designed with some intention in mind, from computers and clocks to roads and buildings. Premise 4 might be defended on the basis that the word “God” here simply means some creator or designer outside of nature.
Somebody might, on the other hand, extract the argument above because they reject it and want to know what kinds of objections to raise against it. For instance, they might object to premise 1, the claim that the natural world has order and purpose, because the appearance of order and purpose might be the product of a human interpretation of nature, not part of nature in itself. They might object to premise 2, the claim that all order and purpose requires intentions, because it might be that a process that involves no overarching intentions, like an evolutionary process of natural selection, can produce order and purpose. Alternatively, someone might object to premise 4, because even if intentions were behind the natural world, those intentions might belong to a team of gods, or to ancient aliens, or to the mind of the cosmos itself.
Extracted arguments don’t settle debates. What they do is make what is being debated clear. Here are six reasons why extracted arguments are helpful:
- They are simpler to understand than paragraph after paragraph of prose. The structure is clear, and the claims are short and succinct. There is less risk of misunderstanding, or of using language to obscure what is really being said.
- There are no hidden assumptions in an extracted argument. Every premise which is necessary for the argument to be valid is part of the extracted argument. There are no hidden claims that aren’t open to being challenged.
- They ensure the inferences are valid which are made in an argument. Every inference must use a valid rule of inference, so there is no risk of jumping to conclusions. The premises of the argument must guarantee the conclusion is true.
- They make clear what to defend. If someone wants to defend the argument, then they need only to give evidence for each of the premises of the argument.
- They make clear what to object to. If someone doesn’t agree with the conclusion of an argument, rather than raising objections to the conclusion, they need to raise objections to the premises. Some premises are likely to be potential weak points in the argument, and so that is where somebody who disagrees needs to raise objections.
Extracted arguments are useful not only for vexing philosophical topics, but for anything else which you might want to persuade somebody to do or believe something using reason. For instance, a salesperson trying to persuade a client, or an employee trying to persuade their supervisor, or a CEO trying to persuade a board of directors, or a lawyer trying to persuade a judge: all of these are cases where persuasion is important. If the person who needs to be persuaded is themselves a sound reasoner (which is not always the case), then extracting the argument one wants to make before making it will help with being more persuasive. We’ll practice a number of tools and techniques for extracting arguments in this module, to help you get better and quicker at this valuable skill.
11.1.2 Identifying Premises and Conclusions
Extracting an argument requires sifting through prose to spot premises.
Extractions in 3 Steps
There are three basic steps involved in extracting an argument. They are:
- Identify the Conclusion
- Identify the First Premises
- Repair the Argument to make it Valid
Step 1: Identify the Conclusion
The first step to extracting an argument is knowing what the argument is for. What is the claim that the argument is trying to demonstrate or prove? State the claim as a single, simple, concise sentence. For instance, what claim is being made in the following paragraph?
“Everybody who knows anything knows that we can’t continue the way we’ve been going. Gun violence is a problem that we must stop, and the only way to do that is licensing and registration for firearms. Simply trusting that the good guys will get the guns hasn’t worked for us. Simply hoping that crazy people with guns will disappear has failed. But when we license gun owners, we know the people who are armed can be trusted.”
There are many claims made in the paragraph. The conclusion of the paragraph is the claim that everything else in the paragraph is meant to support. Most of the other claims are reasons to believe the conclusion. Which one is the conclusion?
Let’s start by identifying claims in the paragraph which are not part of the conclusion:
- When we license gun owners, we know the people who are armed can be trusted. This is the last sentence in the paragraph, but that’s no reason to think it is the conclusion. The other sentences in the paragraph do not all aim to give a reason to think this sentence is true. This sentence is actually meant to be a reason to believe something else in the paragraph.
- Everybody who knows anything knows that we can’t continue the way we’ve been going. This sentence is rather vague, and it is hard to say what exactly the claim is. It seems more like a rhetorical flourish than something than a claim to be defended as either true or false.
- Gun violence is a problem that we must stop. This seems closer to the conclusion, but this hardly seems like the main claim in the paragraph. Consider that somebody who disagrees with most of the paragraph, like somebody who opposes any form of gun control, might still agree that gun violence is a problem that we must stop. The conclusion will be something that an opponent would disagree with.
- The only way to do that [stop gun violence] is licensing and registration for firearms. This is probably the closest statement to the conclusion. It isn’t the conclusion, though. It only says that there is no other way to stop gun violence, but doesn’t actually say that we must license and register firearms.
The conclusion of this argument is unstated. Nonetheless, once it’s stated, it shouldn’t be hard to recognize. It’s something like:
- We must stop gun violence by licensing and registering firearms.
Everything else in the paragraph is meant to support, or give a reason to believe, this claim. The paragraph is written by somebody who is advocating for licensing and registering firearms.
We should simplify the conclusion, though, by removing unnecessary complexity, and removing anything that properly belongs in a premise. That we must stop gun violence is itself a reason to believe the conclusion, not part of the conclusion. So, we can simplify the conclusion and state it in this way:
- We must license and register firearms.
Step 2: Identify the First Premises
Now that we know the conclusion, we need to identify our premises. There are many reasons given in the paragraph which are meant to support the conclusion, such as:
- Gun violence is a problem which we must stop.
- The only way to stop gun violence is licensing and registration of firearms.
- When we license gun owners, we know the people who are armed can be trusted.
- Simply trusting that the good guys will get the guns hasn’t worked for us.
- Simply hoping that crazy people with guns will disappear has failed.
One very tempting thing, which we should not do, is to list all five of these as the starting premises in the argument. First, the more numerous and complicated the premises, the more difficult it is to make an argument valid. Second, very often there are multiple, distinct reasons given in a paragraph for a conclusion, and each of these could be the source of its own argument. There are at least two different chains of reasoning in the paragraph: the first is that all options except licensing and registration have failed, and the second is that licensing will allow us to know that armed people can be trusted. Often a paragraph will give three or four distinct reasons to believe a conclusion. It is better to put these into separate, distinct arguments, rather than combine them all into one single argument.
Instead, it’s best to pick one main reason to believe the conclusion is true, and make that the first premise. For instance, that gun violence is a problem which we must stop seems like the most important reason given by the person making the argument. So, we might give this argument:
1. Gun violence is a problem which we must stop. (Basic)
C. We must license and register firearms.
We can rephrase the first premise to make it more concise:
1. We must stop gun violence. (Basic)
C. We must license and register firearms.
On the other hand, somebody else might instead think that a different reason is more important to the argument. So, this first premise would be perfectly fine also:
1. When we license gun owners, we know the people who are armed can be trusted. (Basic)
C. We must license and register firearms.
Here, we can rephrase the first premise both to make it more concise, and to reveal its logical structure (it is really a conditional claim):
1. If we license gun owners, then we can trust armed people. (Basic)
C. We must license and register firearms.
Of course, neither of these is a complete or valid argument. Both are a clear, concise starting place. Making the argument valid is the next step.
Step 3: Repair the Argument to Make it Valid
The last step is the most difficult, and we’ll discuss how to do it more on the next page. Repairing an argument means adding premises in order to make it valid. The premises we add will involve both claims we know from context are required to bridge the gap to the conclusion, as well as statements that we can use a rule of inference with to reach the conclusion. First, we know from context that two other claims are part of the argument we started earlier:
1. We must stop gun violence. (Basic)
2. Simply trusting that the good guys will get the guns hasn’t worked for us. (Basic)
3. Simply hoping that crazy people with guns will disappear has failed. (Basic)
C. We must license and register firearms.
Again, let’s simplify the language, aiming for consistency:
1. We must stop gun violence. (Basic)
2. Hoping that only good guys will have guns does not work. (Basic)
3. Hoping that no crazy people will have guns does not work. (Basic)
C. We must license and register firearms.
Now, how can we use rules of inference to make this argument valid? Well, it looks like the argument is suggesting there are 3 options, and that 2 of those options have failed. So, the argument makes use of something like a process of elimination, a rule we know as disjunctive syllogism:
1. We must stop gun violence. (Basic)
2. Hoping that only good guys will have guns does not work. (Basic)
3. Hoping that no crazy people will have guns does not work. (Basic)
4. Either we must license and register firearms, or hoping that no crazy people will have guns works; or else, hoping that only good guys will have guns works.
5. Either we must license and register firearms, or hoping that no crazy people will have guns work (2, 4 DS)
C. We must license and register firearms. (3, 5 DS)
Now, we notice two loose ends: line 4 doesn’t come from any prior line, and line 1 hasn’t been used in the argument. We know how to get one claim from another, though, using a conditional and the rule of modus ponens. Of course, we also have to renumber the argument:
1. We must stop gun violence. (Basic)
2. Hoping that only good guys will have guns does not work. (Basic)
3. Hoping that no crazy people will have guns does not work. (Basic)
4. If we must stop gun violence, then: either we must license and register firearms, or hoping that no crazy people will have guns works, or else, hoping that only good guys will have guns works. (Basic)
5. Either we must license and register firearms, or hoping that no crazy people will have guns works; or else, hoping that only good guys will have guns works. (1, 4 MP) 6. Either we must license and register firearms, or hoping that no crazy people will have guns work (2, 5 DS)
C. We must license and register firearms. (3, 6 DS)
Repairing arguments isn’t an easy task. We’ll turn now to some strategies for repairing arguments.
11.1.3 Repairing Arguments
Repair arguments to make the bridge to the conclusion valid.
Repairing an Argument
Repairing an argument means taking an argument which is invalid, and making the argument valid by adding additional premises. The added premises are supposed to be consistent with the principle of charity: the idea that when interpreting someone else’s argument, we should try to represent their thoughts as fairly and rationally as possible.
For example, this is an invalid argument.
1. The kitchen smells bad.
2. If no one has taken out the trash, then the kitchen smells bad.
C. No one has taken out the trash.
This argument is invalid because there is a possibility that the conclusion could be false even though the premises are true. For instance, it could be the case that the kitchen smells bad because someone has burnt a loaf of bread in the oven, or because the sink is full of dirty dishes. The premises don’t rule out these possibilities. However, what premises could we add to make the argument valid? Well, we need to think to ourselves: what counterexamples do I need to rule out? Add in premises which rule out all of the counterexamples, and the argument will be valid. For instance, perhaps we need to add that nothing else is causing the bad smell, and that if nothing else is causing the smell, then no one has taken out the trash. Note that the premises we add should plausibly represent somebody’s reasoning. For instance, the argument would technically be valid if we added the premise, “Either 2+2=5 or no one has taken out the trash”, but most humans would not use or follow that reasoning.
Symbolizing
Making use of symbolization and rules of inference can help with recognizing what is needed to make an argument valid. Let:
B = The kitchen smells bad
T = Someone has taken out the trash (so, ~T = no one has taken out the trash)
C = Something else is causing the smell (so, ~C = nothing else is causing the smell)
Now, let’s symbolize the original argument:
1. B
2. ~T => B
C. ~T (???)
This is invalid; specifically, it’s an instance of affirming the consequent. Let’s try to repair the argument by adding the premise that nothing else is causing the smell:
1. B
2. ~T => B
3. ~C
4. B & ~C (1, 3 &I)
C. ~T (???)
This argument is still invalid, but now it may be clearer what we need to do. What rule could we use to derive the conclusion? One familiar rule is modus ponens:
1. B
2. ~T => B
3. ~C
4. B & ~C (1, 3 &I)
5. (B & ~C) => ~T
C. ~T (4, 5 MP)
Now the argument is valid! But we also have one premise that isn’t necessary. Notice that we cite lines 1, 3, 4 and 5, but we never make use of line 2. So, there is no reason to include line 2 in the argument. We can delete it and renumber the premises:
1. B
2. ~C
3. B & ~C (1, 2 &I)
4. (B & ~C) => ~T
C. ~T (3, 4 MP)
Translating this back into English
1. The kitchen smells bad.
2. Nothing else is causing the bad smell.
3. The kitchen smells bad and nothing else is causing the bad smell (1, 2 &I)
4. If the kitchen smells bad, and nothing else is causing it, then no one has taken out the trash.
C. No one has taken out the trash. (3, 4 MP)
Now, we have a valid, extracted argument!
Steps to Repairing an Argument
- Step 1. Add any premises which, intuitively, would be needed to ‘fill in the gaps’ in reasoning. For instance, intuitively we recognized in the argument above that we needed to include that there were no other causes of the bad smell in the kitchen.
- Step 2. Symbolize the argument so that you can recognize its form. Use simple rules of inference when it might help to have all of the premises on the same line, as we used &E above.
- Step 3. Identify a Rule which would allow you to validly bridge the gap between the premises and the conclusion using one of the 3 key strategies: conditional rules, disjunction, or categorical syllogism. We will study these strategies in the next sub-module. Above, we used a conditional strategy, with modus ponens.
- Step 4. Add what the rule requires as an additional premise. For instance, above we added “(B & ~C) => ~T” to allow us to use modus ponens.
- Step 5. Subtract any premises which don’t contribute to the validity of the argument, and renumber the premises. For instance, in the original argument, the premise “if no one has taken out the trash, then the kitchen smells bad” did not contribute to the validity of the argument, so we removed it.
- Step 6. Translate the result back into English. The result is a valid extracted argument, which you can then explain and evaluate
Submodule 11.1 Quiz
Licenses and Attributions
Key Sources:
- Watson, Jeffrey (2019). Introduction to Logic. Licensed under: (CC BY-SA).
Next Page: 11.2 Tricks and Shortcuts