11.3 Evaluating Arguments
Extracted arguments must be valid, but should have no more premises than are actually used to obtain the conclusion. They should avoid obvious fallacies. When an extraction meets these criteria, it can then be evaluated for soundness.
Table of Contents
11.3.1 Evaluating for Validity
Audit the validity of the argument. Were only valid inferences made?
Three Criteria
There are three basic criteria for a good extracted argument. First, and most basically, the argument must be valid. Second, and closely related, there should be no extra premises in the argument which are not necessary for validity, or not needed to reach the conclusion. Third, the argument should avoid fallacies, especially the “straw man” fallacy.
For every informal argument, there are many good ways to extract a formal argument. For instance, the following three extractions all make use of different rules of inference, and different strategies, but they are all equally good extractions:
1. You have teeth. (Basic)
2. Either you don’t have teeth, or you should floss (Basic)
C. You should floss. (1, 2 DS)
1. You have teeth. (Basic)
2. If you have teeth, then you should floss. (Basic)
C. You should floss. (1, 2 MP)
1. You have teeth. (Basic)
2. Everybody who has teeth should floss (Basic)
C. You should floss. (1, 2 UI)
These are good extractions because they are valid, don’t involve any unnecessary premises, and do not rely on fallacies (at least, not in any obvious way).
Invalid Extractions
So, there are going to be three ways to mess up an extraction: it can be invalid, it can include unnecessary premises, or it can involve a fallacy. (Some extractions are bad in multiple ways). Consider the teleological argument given earlier in this module, from the claim that nature has order and purpose to the claim that God exists. Earlier we looked at a valid extraction of the argument. The following would be a bad extraction of the argument, on the other hand, because it is invalid:
1. If God exists, then the natural world has order and purpose. (Basic)
2. The natural world has order and purpose. (Basic)
C. God exists. (!!INVALID!!)
The best way to ensure an extracted argument is valid is to make sure that you are using a valid rule of inference, and using it correctly. If you ever want to double-check whether or not an inference is valid, however, you can use the tools of Truth Tables and Venn Diagrams presented earlier in the class. For instance, we can use a truth table to show that this argument is invalid. First, we symbolize the argument:
G = God exists
N = The natural world has order and purpose.
1. G => N
2. N
C. G
Now, the truth table:
| G | N | 1. G => N | N | G |
| T | T | T | T | T |
| T | F | F | F | T |
| F | T | T | T | F |
| F | F | T | F | F |
The third row shows that the argument is invalid, because the first and second premise are true, but the conclusion is false.
Unnecessary Premises
A very common way in which extractions could be improved is that they include unnecessary premises, premises which are not needed in order for the argument to be valid. For instance, this argument is valid, but it includes a basic premise which isn’t used in order to reach the conclusion. Look closely. Can you spot the extra premise?
1. Either the natural world has no order and purpose, or God exists. (Basic)
2. The natural world has order and purpose. (Basic)
3. The natural world is very beautiful. (Basic)
4. The natural world does not have no order and purpose. (2 DN)
C. God exists (1, 4 DS)
You can tell that a basic premise is used to reach the conclusion when it is cited on a lower line. Line 1 is cited on line C, and line 2 is cited on line 4, but line 3 is not cited on any lower line. So, line 3 is a Basic premise which isn’t used to reach the conclusion, and the argument could carry on without it.
Sometimes a premise is clearly relevant, but needs to be incorporated into the rules used in the argument. For instance:
1. If Bob is a good business partner then Bob is reliable. (Basic)
2. Bob is a liar. (Basic)
3. Bob is not reliable. (Basic)
C. Bob is not a good business partner. (1, 3 MT)
In the argument above, premise 2 is not necessary to the argument, because the argument would be valid without it:
1. If Bob is a good business partner then Bob is reliable. (Basic)
2. Bob is not reliable. (Basic)
C. Bob is not a good business partner. (1, 2 MT)
That said, the premise that Bob is a liar is clearly relevant to the argument. What is is relevant to is establishing another premise: Bob is not reliable because Bob is a liar. So, rather than delete the premise entirely, we might instead add another premise which shows the link between the claim that Bob is a liar and the claim that Bob is not reliable.
1. If Bob is a good business partner then Bob is reliable. (Basic)
2. Bob is a liar. (Basic)
3. All liars are not reliable. (Basic)
4. Bob is not reliable. (2, 3 AUI)
C. Bob is not a good business partner. (1, 4 MT)
This argument is now one in which no premise is unnecessary. Premise 2 is needed to reach line 4, which is used to derive the conclusion. When faced with an unnecessary premise in an argument, typically it is better to delete the premise if it is irrelevant, but it is often better to find a way to incorporate it into the structure of the argument if it is relevant.
11.3.2 Evaluating for Fallacies
Are there cracks in the reasoning in the argument?
Avoiding Straw Men
Extracted arguments should avoid obvious fallacies. The most common fallacy which extracted arguments tend to follow occurs when somebody is extracting an argument for a view they disagree with, and that’s the fallacy of the “straw man”. A “straw man” argument is an uncharitable interpretation of an opponent’s argument, which characterizes their reasoning in a way in which they would not themselves accept. The most common way to engage in the straw man fallacy is to represent one’s opponent as engaging in a fallacy by extracting an obvious fallacious argument.
As discussed earlier, sound reasoning requires interpreting one’s opponent charitably, putting their best reasoning forward rather than their worst reasoning. For instance, suppose that Athena and Theo are debating the teleological argument for the existence of God. Theona believes that God exists, and Athena does not. Theona represents Athena’s reasoning in this way:
1. The whole world is completely random and purposeless. (Basic)
2. If the whole world is completely random and purposeless, then God does not exist. (Basic)
C. God does not exist. (1, 2 MP)
Athena then represents Theona’s reasoning in this way:
1. We don’t know why the natural world has order and purpose. (Basic)
2. If we don’t know why the natural world has order and purpose, then God exists. (Basic)
C. God exists. (1, 2 MP)
Both arguments are valid. But both arguments are bad extractions, because they give uncharitable interpretations of the person making the argument. Both require the person making the argument to be committed to a fallacy.
Theona’s interpretation of Athena’s argument commits Athena to a self-undermining claim. The “whole world” would include human intentions, purposes, and goals. Obviously, Athena herself has intentions, purposes, and goals, including the purpose of engaging in reasoning or making an argument, so clearly part of the world is not random or purposeless; for instance, the part which involves human actions (and other animals who form intentions). Perhaps what Athena denies is that there is an outside mind which gives an intrinsic purpose to the world, independent of anything assigned by reasoners like us. A more charitable interpretation of Athena’s argument might be this:
1. The natural world does not have intrinsic purposes independent of those given by reasoners in the world. (Basic)
2. If God exists, then the natural world has intrinsic purposes independent of those given by reasoners in the world. (Basic)
C. God does not exist. (1, 2 MT)
On the other hand, Athena’s interpretation of Theona’s argument is an example of an appeal to ignorance, a fallacy which we studied earlier. Somebody might make the argument that, because we don’t know why something is the case, therefore God must make it the case, when they aren’t reasoning at their best, but a good extraction represents what somebody ought to say, if they were reasoning at their best. A more charitable interpretation of Theona’s argument might be this:
1. The natural world has purposes independent of those given by reasoners in the world. (Basic)
2. If the natural world has purposes independent of those given by reasoners in the world, then some reasoner outside the world gives it purpose. (Basic)
3. If some reasoner outside the world give it purpose, then God exists. (Basic)
4. If the natural world has purposes independent of those given by reasoners in the world, then God exists. (2, 3 HS)
C. God exists. (1, 4 MP)
Tolerating a Little Vagueness
An extracted argument can be a good one even if there is a little bit of unclarity left in the premises, provided that the unclarity is part of the debate itself and not something caused by the extraction. Some vagueness and unclarity is inevitable. For instance, while both of the arguments given above avoid any obvious fallacies, they also make use of some vague and questionable concepts. What is “the natural world”? What does the word “God” even mean, and what does “exists” mean? What counts as a “reasoner”? Does that mean all of the natural world, or just some of the natural world? Are humans part of the natural world? Are cities natural? What exactly is a “purpose”, and how would one determine whether or not something has a particular purpose? What makes a purpose “intrinsic”? Are these even coherent concepts? Why couldn’t nature contain intrinsic purposes without the need for a reasoner? All of these are good philosophical questions.
A logic student does not need to answer all of these philosophical questions before extracting an argument, though. The unclarity comes from the concepts Athena and Theona are using, rather than from the structure of the extraction. Sometimes it is better to tolerate and allow for some vagueness or unclarity in the premises of an extracted argument in order to keep it simple. After presenting a formal argument, the person making it then has an obligation to explain what exactly the premises mean and to answer all of these questions.
A good extracted argument which meets the three basic criteria can then be explained and evaluated. Reasoning behind the premises can be given, and potential objections to each premise weighed. The goal of an extraction is to reach the point where the validity of the argument is clear, so that soundness of the argument can then be discussed.
11.3.3 Evaluating for Soundness
Truth pushes away Falsehood’s mask and tears out his double tongue.
Explaining an Argument
After extracting an argument, the next step is to explain the premises of an argument, in order to help determine whether or not the argument is sound. There are two kinds of explanation needed:
- Explaining the meaning of the premises, so that definitions are clear.
- Explaining the justification for the premises, the evidence for believing the premises to be true.
Each premise in an extracted argument needs to be explained, though some might require more explanation than others. Let’s tackle this argument:
1. School bonds lead to high taxes (Basic)
2. School bonds bring no substantial benefit (Basic)
3. School bonds lead to high taxes and bring no substantial benefit. (1, 2 &I)
4. Everything which leads to higher taxes and brings no significant benefit is something we shouldn’t vote for. (Basic)
C. We shouldn’t vote for school bonds. (3, 4 UI)
For each premise, we’ll first give definitions of the meanings of term in each basic premise, and then give reasoning which is supposed to justify each premise. Only the basic premises need explained.
- Premise 1: School bonds lead to high taxes.
- Definitions. Here some of the terms are pretty straightforward. We’ll assume “school bonds” refers to some particular set of bonds at issue in an election, and that “higher taxes” means that property tax rates will go up. “Lead to” is talking about causation.
- Reasoning. We’ll assume the reasons behind this premise are also uncontroversial. Even proponents of the bonds will agree that they have to be paid for by property taxes, and that means higher taxes than if they bonds weren’t passed. That’s how bonds work.
- Premise 2, School bonds bring no substantial benefit.
- Definitions. We’re familiar with “school bonds”, and we’ll assume “bring” also involves causation. The word “benefit” is hard to define, but the idea seems to be that a benefit involves someone’s being made better off than they would have been otherwise. But what about “no significant benefit”. We don’t want to define this in a circular way, so we can’t say “no benefit worth paying higher taxes for”, since this would beg the question. We don’t want to imply that there’s no benefit at all to the school bonds, since surely someone will get some benefit out of it. So we’ll have to acknowledge that the term “significant” is vague. It means something like “enough to be worth noticing”, but it’s hard to nail this down.
- Reasoning. Here are some reasons a person might give: education has enough money being wastefully thrown at it, education never gets better, and education won’t get better until we deprive it of money. Certainly all three of these, if they are true, give reasons to be skeptical about the benefits of the bonds. If money is being ‘wastefully thrown at’ education, then more money is likely to have the same effect. If education never gets better, then there’s no point in trying to make it better. And if education won’t get better until we deprive the system of money, passing the school bonds won’t help.
- Premise 4: Everything which leads to higher taxes and brings no significant benefit is something we shouldn’t vote for.
- Definitions. Here the only phrase in need of definition is “we shouldn’t vote for it”. We’ll assume “we” is the audience of the argument who can vote on the bonds, and we’ll assume voting is pretty straightforward. The word “should” is a difficult word, though. It seems like it isn’t so much a matter where one morally shouldn’t vote for the bonds – as though casting a ‘Yes’ vote were immoral or evil. Instead, the issue seems to be that we prudentially shouldn’t vote for the bonds – that means, we shouldn’t as a matter of our mutual self-interest.
- Reasoning. Here the premise seems to be built on a slightly deeper principle. It’s not just that we should only vote for higher taxes if they are justified by some benefit. Instead, the principle being assumed here seems to be that we shouldn’t bring about anything which will lead to a harm without more significant benefits. That is, we shouldn’t make ourselves worse off in one way (taxes) unless it’s compensated for by some benefit (a better education system). This seems like a fairly intuitive principle.
Now that we’ve explained the premises, there’s not much needed to explain the conclusion: the outcome of this argument is that one shouldn’t vote for the school bonds.
Evaluating an Argument
Now begins the fun part. Evaluating an argument requires thinking critically about the argument, and trying to think of possible objections. Objections are not raised to the conclusion, and they are not given to premises which are inferred from other premises using a valid rule of inference; rather, an objection should give a reason to doubt that one of the premises marked (Basic) is true.
- Premise 1 says that school bonds lead to high taxes. How might somebody object to this premise? The claim that school bonds lead to high taxes means that, were it not for the school bonds, taxes wouldn’t be as high. Yet, perhaps this isn’t true. Perhaps, if there were no school bonds, it would still be necessary to fund school construction in some manner, and so income taxes or sales taxes would be increased instead. Or, perhaps school bonds could be funded without increasing taxes, if existing tax revenue is enough to cover the cost of the bonds, perhaps because other expenses have decreased. So, it is possible to object to premise 1.
- Premise 2 says that school bonds bring no substantial benefit. This is probably the most controversial premise. Proponents of the bonds would certainly disagree. They would argue that the school bonds are necessary to produce the benefit of an improved and better education. They don’t think cutting school funding will force the schools to get better. Instead, they think more funds will improve the schools, by making it possible to have more resources in classrooms, having a smaller number of students per teacher, and hiring more motivated and qualified teachers. They probably don’t believe the education system is likely to waste most of the money from the school bonds. So, there are many possible objections to premise 2.
- Premise 4 says that everything which leads to higher taxes and brings no significant benefit is something we shouldn’t vote for. This premise is probably less controversial, since a proponent of the school bonds might agree with premise 4, but reject premise 2. Still, somebody could reject Premise 4 on the basis that there are some things which we should vote for out of duty, or as a matter of consistency, even if it brings no particular benefit. For instance, public holidays cost the state more money and make everything more difficult when state offices are closed. Nonetheless, somebody might vote in favor of a public holiday because it represents a day that they think should be important and significant.
Hopefully, this gives you a sense of what is involved in evaluating premises. After thinking through the justification for each premise, and the potential objections to each premise, it is time to weigh the evidence on both sides. We will look in future modules at evidence and probability, which will offer us more resources for weighing the premises of an extracted argument.
Submodule 11.3 Quiz
Licenses and Attributions
Key Sources:
- Watson, Jeffrey (2019). Introduction to Logic. Licensed under: (CC BY-SA).
Next Page: 11.4 Practice with Extractions