4.3 Clarifying Claims
A claim is a proposition which someone asserts, either so that you will believe the claim, or so that you will have a reason to believe some other claim: it is the premise of an argument. In addition to being relevant to the conclusion, there are four other virtues that we want premises or claims to have in an argument. We want premises to be precise, concise, explicit, and to involve methodical reasoning.
Table of Contents
4.3.1 More Precisely
Precision means reducing vagueness and ambiguity.
Making Claims Precise
In the previous module we discussed the difference between vagueness, ambiguity, and relativity, and the importance of reducing vagueness and relativity when possible. This is especially important when preparing the premises of an argument for symbolization. Although symbolization ignores the content of an argument and emphasizes its structure, if the content which we symbolized is ambiguous, relative, or vague, then an argument which has a valid form can still turn out to be an instance of the fallacy of equivocation, because one of the terms has a “double meaning”. Here are a couple of examples.
First, suppose we want to translate the sentence, “Alex is an incompetent driver”. We could interpret “incompetent” as just meaning “not competent”, and symbolize the sentence as ~A, where A = “Alex is a competent driver”. The following argument would be valid:
- ~~A (“Alex is not an incompetent driver”)
- A (1, DN) (“Alex is a competent driver”)
Competence is vague, however. Alex might be one of those drivers who can be trusted on surface streets but not on freeways during rush hour. So it might be that “incompetent” means something like “dangerous” or “far from competent”. Now the argument above will be a fallacy, because Alex might not be dangerous or far from competent, without actually qualifying as competent.
Second, suppose that we want to translate the sentence, “9pm is not late at night”. From the perspective of most college students, this is true. From the perspective of most preschool students, however, this is false. Suppose we translate this as ~L, where L = “9pm is late at night”. We get the following truth table:
| L | ~L |
| T | F |
| F | T |
Since ~L is true from the perspective of most college students, the truth table demonstrates that L will be false from the perspective of most college students. But we need to be careful not to switch the context in the middle of the truth table. The fact that ~L is true for most college students does not mean that “9pm is late at night” is false for most preschool students.
Even when the meanings of words are perfectly precise, there can be ambiguity in the structure of a sentence. For example, consider this sentence:
“Sue will pay and Freddy will eat or Drew will be upset.”
Think carefully about this sentence. Would it be true or false if Sue didn’t pay and Drew was upset? There are two readings:
“Sue will pay, and either Freddy will eat or Drew will be upset.”
On this interpretation, the sentence would be false if Sue didn’t pay, even if Drew was upset. On the other hand:
“Either Sue will pay and Freddy will eat, or else Drew will be upset.”
On this interpretation, the sentence would be true so long as Drew was upset, even if Sue didn’t pay. So, it is necessary to make use of punctuation and words like ‘both’, ‘either’, ‘also’, ‘additionally’, or ‘else’ to help clarify the structure of a sentence.
4.3.2 More Concisely
Being concise means saying no more than necessary.
Concise Translations
“Concise” means that something is not excessively wordy. When trying to make a complicated sentence more concise for the purpose of symbolizing sentences or making a formal argument, you need to ignore and delete anything in the sentence which would not change the truth value of the sentence or which is irrelevant to the argument. For example, suppose we have this argument:
- Laura’s old, calloused hands, revealing a lifetime of struggle, clicked ‘Send’, and struck the crucial blow against her oppressor by revealing the rancid stink of corruption at the FBI.
- If Laura’s old, calloused hands, revealing a lifetime of struggle, clicked ‘Send’, and struck the crucial blow against her oppressor by revealing the rancid stink of corruption at the FBI, then Laura was a whistleblower.
- Laura was a whistleblower.
Is everything in premise (1) relevant to the conclusion that Laura is a whistleblower? This might be interesting information about Laura’s context, but would it change the truth of premise 1? Does it matter that her hands were old or calloused? Does it matter that they revealed a lifetime of struggle? Does it even matter that it was a crucial blow against her oppressor? Does it matter that she clicked ‘Send’ as opposed to ‘Submit’? Does it matter how metaphorically bad the corruption smelled? What actually matters to her being a whistleblower? Isn’t it just that she revealed corruption at the FBI?
- Laura revealed corruption at the FBI.
- If Laura revealed corruption at the FBI, then Laura was a whistleblower.
- Laura was a whistleblower.
Although the premise may not be as descriptive, it is much more useful for the purpose of argument. Other kinds of language that are common to add to premises but which aren’t relevant to an argument are those which communicate something about the mind of the person who wrote the premise, as opposed to the truth of the conclusion. For instance:
It’s unrealistic to expect everybody in this whole beautiful country to care about our precious environment.
My humble opinion is that people need more than food and water to live, they also need friendship.
These two claims communicate a lot of information about the mind of the person who wrote them, like that they think the environment is “precious” and that the country is “beautiful”, or that their opinion is “humble”, but that information isn’t necessary to determine whether the core claims being made are true or false. We might rephrase them more concisely as:
Not everyone in this country cares about our environment.
People need friendship to live.
Now they should be easy to symbolize:
~C = “Not everyone in this country cares about our environment”, where C = “Everyone in this country cares about our environment”
F = “People need Friendship to live”
4.3.3 More Explicitly
Say what you really mean. Don’t beat around the bush.
Literally Speaking
Sometimes people say things in a “roundabout” way. Their words indirectly imply or suggest certain things, but without saying it outright. For example, if you want someone to stop talking and let you go home, you might not say “I would like you to stop talking so that I can go home”, but out of politeness you’ll say, “Well, it is certainly getting late!” What you said implicates something that you didn’t say. This is an indirect way of speaking. Indirect speech, or implicature, involves “flouting” the rules of quantity, quality, manner, and relevance discussed in the previous module.
When you are creating the premises of an argument, you want to make sure that you focus only on the literal, explicit meaning of the statements themselves, and not on implicatures, or non-literal meanings that are suggested by the act of making the statement. This is especially important with the logical operators “not”, “some”, “and”, “or”, “all”, and “if…then”.
- “Not P” often implicates that the opposite of P is true, but it doesn’t literally mean that. For instance, “John is not rich” might implicate that John is poor, but literally speaking it could be true that John is upper-middle class. Similarly, “Alice is not happy” might implicate that “Alice is unhappy” or “Alice is sad”, but literally speaking Alice could be not happy and yet also not be sad.
- “Some As are Bs” often implicates “more than one A is a B”, but literally speaking, it only means “at least one A is a B”. So, even if only one person is happy, “some people are happy” is true. Even if only one mouse likes cheese, “some mice like cheese” is true.
- “Some As are Bs” often implicates “not all As are Bs”, but literally speaking, a predicate can be true of both “some” and “all” of something. For example, all physical objects are subject to the law of gravity, but “some physical objects are subject to the law of gravity” is also true. If everyone is having fun at the party, then “some people are having fun at the party” is also literally true, even if it falsely implicates that some people are not having fun.
- “Every A is B” or “All As are Bs” implicates that there is at least one thing which is A and B, but it is true in a vacuous way that “every A is B” when nothing is A. For example, suppose somebody gives you the instruction to go to the store and buy every Hershey’s bar in the store, but the store is out of Hershey bars. You still followed their instructions and bought every Hershey’s bar in the store if there were no Hershey’s bars. Again, a paranoid city council might give the police the assignment to arrest all of the Martians in the city. The police arrested all the Martians in the city even if the arrested none, provided that there were no Martians in the city.
- “P and Q” often implicates that Q happened after P. For instance, “I brushed my teeth and I woke up” implicates that I brushed my teeth and then I woke up, because it is a strange order to put things in. Literally speaking, though, “I woke up and I brushed my teeth” means the same thing as “I brushed my teeth and I woke up”.
- “P or Q” often implicates that only one choice is available, that it can’t be both P and Q. For instance, “either you have the fish or you have the chicken” implicates that you can’t have both the fish and the chicken. It doesn’t literally mean that, though. “Either you pay your bill or you don’t get to eat the food” is true, but you could both pay the bill and eat the food.
- “P or Q” also often implicates that there is some genuine possibility of Q, but “P or Q” can be true even if Q is impossible. For example, it is true that either the Eiffel Tower is in Paris or I am a banana, even though it is impossible that I am a banana.
- “If P then Q” often implicates that P causes Q, as in “If you run over a nail, then you will have a flat tire.” This is not, however, part of what “if” and “then” mean. “If you woke up this morning, then you fell asleep last night” is true, even though waking up doesn’t cause falling asleep; “If school is out, then it is over 100 degrees outside” is true in any place where the summers are hot and the schools close for the summer, but it’s not that schools closing causes the temperature to go up. What makes “If P then Q” true is that either P is false, or Q is true, or both P is false and Q is true. Either you didn’t wake up this morning, or else you fell asleep last night (or both); either school isn’t out, or it is over 100 degree outside (or both).
4.3.4 More Methodically
Slower thinking is often smarter thinking.
Rules for Thinking Slower
Although we often associate “thinking quickly on your feet” with being smarter or winning a debate, one effect of studying logic is to make it take longer to come to conclusions and to help us think slower. By forcing our thinking to conform to fixed rules or patterns of logic, instead of just an intuitive sense that something “makes sense” or “seems to follow”, we slow down our thinking. Thinking slower is actually thinking smarter, because it tends to be more accurate and avoid fallacies and common biases.
Some psychologists believe we have two distinct cognitive systems: System 1, which produces intuitive judgments rapidly, and System 2, which involves careful deliberation and analysis. The rules of Logic force us to use System 2: they encourage us to be slow, careful, systematic, and methodical in our thinking.
Step by Step
We want the premises of an argument to show methodical, step-by-step thinking. It is tempting to want to skip steps in an argument because they seem obvious, but laying out each step makes it easy to catch if there is an error that we otherwise might miss. The rules of inference which we are learning force us to lay out each step.
For instance, here is an argument which is valid, but not as methodical as it could be:
- Either Shawn shows up, or else if Andre leaves then Drew leaves.
- Drew doesn’t leave.
- Andre leaves.
- Shawn shows up.
Here is the same argument: a bit more tedious, but also more methodical:
- Either Shawn shows up, or else if Andre leaves then Drew leaves.
- Drew doesn’t leave.
- Andre leaves.
- Assume Shawn doesn’t show up
- Then, If Andre leaves, then Drew leaves. (1, 4 DS)
- Drew doesn’t leave. (2, Reit.)
- So, Andre doesn’t leave (5, 6 MT)
- So, if Shawn doesn’t show up, then Andre doesn’t leave. (4-7 CP)
- Andre doesn’t not leave. (3, DN)
- So, Shawn shows up (8, 9 MT)
It will take several modules to learn all of the rules of inference used in the argument above. You already recognize Reit. and DN, but you will eventually learn MT, DS, and CP. For now, notice the value in laying out the steps of an argument step-by-step using rules of inference, citing the prior lines and the rule used to derive each line, instead of going with a feeling that an argument seems or doesn’t seem valid, in that it forces us to slow down our reasoning.
Submodule 4.3 Quiz
Licenses and Attributions
Key Sources:
- Watson, Jeffrey (2019). Introduction to Logic. Licensed under: (CC BY-SA).
Next Page: 4.4 Modeling Validity