Chapter 3 – Clarity 2023 with verified questions and answers

3.1 Clear inferences - correct answerWhen our reasoning is muddled, we're not sure exactly why we have the beliefs we do, or make the decisions that we make. When our reasoning is crystal clear, we can identify how our beliefs are supported, and which facts we take to support them Inference - correct answerWhen I arrive at a belief because I take it to be supported by other beliefs, I've made an inference. Suppose I come to believe that a certain star in the sky is the North Star because I have two other beliefs: -Alice said so -Alice is an expert on stars Analyze this - correct answerIn this case, neither of my supporting beliefs provides much support for the new belief all by itself. Alice's opinion is not very strong support unless her views on stars are reliable. And her expertise is irrelevant unless she said something about that particular star. It is only taken together that these two beliefs provide strong support for my new belief that the star I have in mind is the North Star. Argument - correct answerIf someone asks me why I think it's the North Star, I can express my inference in the form of an argument—which, as we saw in the last chapter, is a series of claims presented as support for a conclusion I could say, "Alice said that's the North Star. And she's an expert on stars. So that's the North Star." Premises and conclusions - correct answerThe statements that express my supporting beliefs are called premises, and the statement that expresses the belief they are supporting is called the conclusion. To state an argument clearly - correct answerTo state an argument clearly requires making the premises and conclusion clear, and also making it clear how the premises are supposed to support the conclusion (at least, if it's not already obvious). When can you begin to asses how good an argument is? - correct answerOnce we are clear about the premises and conclusion of an argument, we can begin to assess how good the argument is: that is, how well does it support its conclusion? Thinking of an argument analogy - correct answerIt's useful to think of an argument as similar to a building supported by pillars. A building like that needs solid pillars as well as good structural integrity connecting the pillars to the rest of the building. It's crucial to notice that both of these attributes are needed for the building to be strong. If the pillars aren't solid, they could collapse under the weight of the building. But it's not enough to have solid pillars; they also need to be properly arranged and connected so that they can bear the weight of the structure. Otherwise, no matter how solid they are, the rest of the structure can still collapse around them. What do we look for in an argument - correct answerpremises that are true premises that are properly connected to the conclusion suppositional strength - correct answerHow well the premises are connected to the conclusion—so that they can properly support it if they are solid—is called the argument's suppositional strength. A suppositionally strong argument is like a structure - correct answerlike a structure in which the support is properly distributed to the pillars. As long as the pillars are solid, we can be confident that the structure is strong. So what does it take for a conclusion to be well-connected to the premises? - correct answerIt means that if we could be sure that the premises were true, we'd be fairly safe in accepting the conclusion. In other words, suppositional strength is a matter of how much evidence the premises provide for the conclusion if we suppose they are true. An argument whose premises are questionable can be suppositionally strong All giraffes can fly. I am a giraffe. So: I can fly - correct answeran argument can be suppositionally strong even if its premises are questionable—indeed, even if they are obviously false. All giraffes can fly. I am a giraffe. So: I can fly This argument is suppositionally as strong as any argument can be—we can see that if we suppose the premises are true, we have to accept the conclusion as well. If we grant the premises, there is no way to avoid the conclusion. Still, this is not a good argument, because we all know the premises are false. The conclusion is perfectly bolted to the premises, but the premises themselves are no good. All cats are mammals. Some mammals bark. So: some cats bark. - correct answerThere are also arguments that have clearly true premises, but the premises are not well-connected to the conclusion. That's like having pillars that are solid but aren't well-connected to the rest of the building, so they can't support it properly and it might just collapse around them In this case, it's easy to see that the argument is suppositionally weak. We know that the premises are true, and yet they don't give us any reason to think that some cats bark. Even if we had no idea whether cats have fins, learning that cats are mammals and some mammals have fins wouldn't give us much reason to think that cats have fins. Now consider this similar argument with a true conclusion: All cats are mammals. Some mammals bite. So: some cats bite. - correct answerIt's easy to get distracted by the fact that this time the conclusion happens to be true. But actually that's completely irrelevant to whether this argument is suppositionally strong. The question is whether the argument gives us a reason to accept the conclusion. And it doesn't. If we had no idea whether any cats bite, learning that cats are mammals and that some mammals bite wouldn't give us much reason to think that cats do. In fact, the "bite argument" is suppositionally weak for exactly the same reason that the "bark argument" is. (You'll see why if you compare the arguments!) the truth of the premises and/or conclusion is irrelevant to - correct answerto an argument's suppositional strength. If we happen to know the premises of an argument are false, - correct answerwe have to set that aside and remember that the argument can still be suppositionally strong, as long as if the premises were true, they would provide good reason to accept the conclusion. f we know the premises of an argument are true, - correct answerwe have to set that aside and remember that the argument can still be suppositionally weak, if the premises don't actually support the conclusion. Implicit premises - correct answerSometimes the suppositional strength of an argument depends on information that is taken for granted but not stated. For example, consider this one-premise argument: Fido is a dog. So: Fido has a tail. Learning that Fido is a dog gives us a reason to think that Fido probably has a tail, but that's only because we already know that most dogs have tails. In a conversation where we can assume that everyone knows that most dogs have tails, someone presenting this argument can just leave that fact unspoken. When some claim is being taken for granted in this way, we can treat it as part of the argument for purposes of assessing the argument's suppositional strength. Implicit Premises definition - correct answerThings do not always work out so well. We might take something for granted in making an argument without realizing that it's not known by everyone in the intended audience. Or we might skip over a premise because it's questionable and we're hoping no one notices! In any case, when we leave a claim unspoken but take it for granted in making an argument, it's called an implicit premise Deductive vs inductive - correct answer Entail - correct answerWe say that the premises of an argument entail the conclusion when they guarantee it completely: if the premises were true, the conclusion would have to be true. No exceptions: there is no possible way that the conclusion could be false and the premises true But again, even arguments with the highest level of suppositional strength can be terrible arguments - correct answerAll giraffes can fly. I am a giraffe. So, I can fly. There's no way for the premises to be true and the conclusion false: the premises entail the conclusion. But the argument is still not going to convince anyone, because its premises are obviously false. Deduction - correct answerThe process of arriving at a conclusion because we accept some premises that entail the conclusion, we call that deduction Deductive argument - correct answerWhen an argument is presented as entailing its conclusion, we say the argument is deductive. (We call it that even if the premises don't actually entail the conclusion—for example if the speaker is making a logical mistake. Deductively valid argument - correct answerAnd when an argument's premises actually do entail it conclusion, we'll say that the argument is deductively valid. However, most arguments that people give in real life are not intended as - correct answerdeductive. Usually, the truth of the premises is not supposed to guarantee the truth of the conclusion. Instead, the premises are just intended to provide support for the conclusion—perhaps a great deal of support, but not so much that the conclusion follows with the certainty of mathematical proof. Induction - correct answerWhen we arrive at a conclusion because we accept some premises that merely support the conclusion, we call that induction. Inductive Arguments - correct answerAnd arguments presented as merely supporting their conclusions are called inductive arguments. (The Fido argument is one example.) Trade-offs - correct answerAll ravens are black. so, if there is a raven in that tree, it's black. All ravens I have observed so far have been black. So, if there is a raven in that tree, it's black One has a doubtful premise that would guarantee its conclusion if it were true; the other has a well-supported premise that does not guarantee the conclusion. This comparison illustrates the fact that, when we are deciding how to formulate an argument, there is often a trade-off between suppositional strength and how much support the premises have. The Ground Floor - correct answerWe've been focusing on the second requirement, but haven't said much about the first. How do we know the premises are true? If our premises support our conclusion, what supports our premises? For example, consider again the argument that a certain star is the North Star. The premises were: Alice said so; and she's an expert on stars. But why should I think the premises are true? Maybe she wasn't talking about the same star. Or maybe she's only pretending to be an expert. It seems that my two supporting beliefs also require support. The ground floor analogy - correct answerBut, of course, the lowest floor of such a structure is supported directly by the ground. This raises the question: what would correspond to the ground floor of a well-built structure of beliefs? These would be beliefs that don't require support from other beliefs, or maybe don't require any support at all. Let's consider two sorts of beliefs that seem to fall in this category. directly perceptual beliefs. - correct answerFirst, there are beliefs that are supported directly by perception, rather than by other beliefs. These are directly perceptual beliefs. If I look up and see an apple on the table in front of me, I will form the belief that there is an apple there. If someone asks, "Why do you think there is an apple there?", I will say "Because I see it." My belief that there's an apple on the table doesn't seem to be based on any other beliefs—except maybe the belief that apples look like this and I seem to see this. Of course, it's possible that there's no apple at all. Maybe someone spiked my breakfast with LSD, and I'm hallucinating. In that case, I seem to see an apple but there is no apple at all. But I would have to be pretty unlucky for that to happen. If I have a history of reliable sense-perception, and no reason to think anything strange is going on, then just accepting what I clearly perceive with my senses is a fairly reliable method of forming beliefs. Self-evident beliefs - correct answerAnother traditional category of beliefs that can be treated as on the ground floor of our belief structures are self-evident beliefs. These are beliefs that are so obviously true that we don't know how we would even go about supporting them with evidence. For example: 1 + 1 = 2. Green is a color If someone was murdered, they died. If x is taller than y, and y is taller than z, then x is taller than z. 3.2 Clear interpretation - correct answerGetting clear about our own reasoning requires understanding exactly what it is that we believe, and what the structure of our beliefs is. Likewise, we should be clear when we express our reasoning in the form of arguments. This means we should: -state every premise and the conclusion in clear language -make the structure of the argument clear Premise indicators - correct answerCertain expressions often function to indicate the presence of a premise: since, given that, seeing as, after all. These are called premise indicators. Why aren't premise indicators completely reliable? - correct answerbecause they can be used in other ways as well. For example, in the sentence: Since Alice is happy, her team must have won the game the word "since" is used as a premise indicator. The fact that Alice is happy is being offered as a reason to think that her team must have won the game. But in the sentence: Since yesterday, I've had a terrible headache the word "since" is not a premise indicator; it just indicates the duration of the headache. The only general way to tell when such words are being used as premise indicators is to think about the role they are playing in their context. Conclusion indicators - correct answerLikewise for conclusion indicators like therefore, so, thus, and as a result. For example, "so" is obviously not being used as a conclusion indicator when it is used as an intensifier, as in "I am so-o-o done with this crap about indicators." Standard Form - correct answerP1. If it's morning, then the direction of the sun is east. P2. It's morning. C1. The direction of the sun is east. (from P1 & P2 by deduction) P3. We should be going east. C2. We should be going in the direction of the sun. (from C1 and P3 by deduction) This way of laying out an argument is called standard form. As you can see, this argument has two steps. First there is a mini-argument establishing C1, and then there is another mini-argument that uses C1 as a premise to argue for C2. This makes C1 an interim conclusion For each conclusion, there is a remark in parentheses that tells us which premises (or previous conclusions) directly support that conclusion, and whether the support they provide is inductive or deductive. Note that while P1, P2 and P3 all support C2 when taken together, the first two do so only indirectly by way of supporting C1. Since their support for C1 has already been noted, we don't list them again as directly supporting C2. if any of the inferences in a multi-step argument is inductive - correct answerif any of the inferences in a multi-step argument is inductive, the argument as a whole is inductive, because the final conclusion is not guaranteed by the argument's premises taken collectively Principle of charity - correct answerWhen interpreting someone's argument, we should always try to identify the best version of the argument that the author could plausibly have intended to put forward. This is known as the principle of charity. The point is not just that finding the best version of the argument is a nice thing to do. If we are genuinely curious about the truth, good arguments are far more useful to us. We are far more likely to learn something from a good argument than a bad one. In order to be as charitable as possible - correct answerIn order to be as charitable as possible when reconstructing someone's argument in standard form, we sometimes have to look beyond what they say explicitly. In ordinary conversation, we often take things for granted because we think they are obvious or not worth saying. As a result, interpretive charity requires us to try to identify the most helpful implicit premises that could plausibly have been intended by the speaker. Often it requires careful attention to the context of an argument to figure out what a speaker or writer might have been assuming that would improve the quality of the argument. What else does need to be aware of? - correct answerWhether someone's argument is deductive or inductive Suppose Alice says, "My pets are acting scared. And they get scared whenever it's thundering. So it must be thundering out." Alice may intend this as a deductive argument, but it's not suppositionally strong enough to be a good deductive argument: the premises could be true even if the pets are actually afraid of something else instead. It may be that she is confused about the form of the argument: the premises would entail the conclusion if her second premise was reversed: "Whenever they are scared, it's thundering". On the other hand, it's also possible that Alice's argument was intended as an inductive argument. Maybe she does not intend the conclusion to be absolutely guaranteed by the premises: she just thinks the premises provide good reason to accept the conclusion. If we interpret her argument that way, it is much more plausible. (should say it could be thundering out) Reconstruction - correct answer"God must be the cause of the universe. After all, everything with a beginning has a cause. And what else could have caused the universe except God?" To reconstruct this in standard form requires first identifying the conclusion. The argument is attempting to establish that God created the universe, so even though that is the first line, it is still the conclusion of the argument. The first premise is also clear: everything with a beginning has a cause. Next, the author asks a rhetorical question. A question isn't a statement about how things are, so it can't be a premise in that form. But from context, we know that we are supposed to give the answer "nothing", which gives us a premise we can write down: "Nothing could have caused the universe except God." Now how does this relate to the first premise? The author is taking for granted the premise that the universe has a beginning. That is an implicit premise that should be explicitly stated in our reconstruction. We now have: Everything with a beginning has a cause. The universe has a beginning. ... Nothing could have caused the universe except God. So, God is the cause of the universe. But something else is missing. If everything with a beginning has a cause, and the universe has a beginning, then we can conclude that the universe has a cause. This time the implicit item is an interim conclusion, and we should state it. This gives us our full form: P1. Everything with a beginning has a cause. P2. The universe has a beginning. C1. The universe has a cause. (from P1 & P2 by deduction) P3. Nothing could have caused the universe except God. C2. So, God is the cause of the universe. (from C1 & P3 by deduction) What makes the previous reconstruction plausible? - correct answerBut it is a plausible reconstruction of what was intended by that argument, and it clarifies the structure of the argument so that we can begin to evaluate its strengths and weaknesses. The premises clearly entail the conclusion, so its suppositional strength is impeccable. Those who reject the conclusion typically reject at least one of the three premises, usually the first and third. 3.3 Clear Language - correct answer Lexical Ambiguity - correct answerhe word ambiguity is sometimes used for any situation lacking clarity; we can say that the end of a movie is ambiguous if it's unclear what really happened. But we are using ambiguity in a more technical sense to refer to cases where two words or sentences share the same written and/or spoken form. When this happens at the level of individual words, it's called lexical ambiguity. This can make for some terrible jokes: I still miss my ex-husband, but my aim is improving. Cannibals were not so bad; they only wanted to serve their fellow men. The absent-minded professor was arrested for not finishing his sentence. When else does Lexical ambiguity arise? - correct answerLexical ambiguity can also arise when we just leave a word out, and it is unclear which word was supposed to fill the gap. A major source of this kind of ambiguity occurs in English when we make claims about groups of people or objects and we omit terms that clarify quantity, like all, some, the, a, most, or three. All dog's bark --> dogs bark syntactic ambiguity - correct answerEven when it's clear which individual words are being used in sequence, there can be ambiguity about which sentence structure is intended. This is called syntactic ambiguity. Jokes based on this kind of ambiguity were a favorite of Groucho Marx—for example, "One morning I shot an elephant in my pajamas. How he got in my pajamas, I don't know." Vagueness - correct answer Borderline cases - correct answerAs a result, there are borderline cases where the word (mountain) doesn't clearly apply, but also doesn't clearly not apply. What actually defines a mountain? Illustrating the difference between vagueness and ambiguity - correct answerTo illustrate the difference, suppose we have many different objects of all kinds depicted on a piece of paper, and we are supposed to draw a circle around all the things that bat applies to. Because of the ambiguity of bat, we want to draw two circles: one around all the baseball bats, and a different one around all the little flying mammals. But if we are given a vague term like red, we want to draw a single circle with a fuzzy border—at least if the paper has both clear and borderline cases of red objects. Some objects clearly belong inside the circle and others clearly belong outside it, but there are also objects on the fuzzy border between them. Generality - correct answerIt's also worth distinguishing both ambiguity and vagueness from a third feature of words, namely generality. What makes an expression more general than another is simply that it applies to more things. So, for example, land formation is more general than mountain, because all things that are mountains are land formations, but not vice versa. Likewise cutlery is more general than fork, child is more general than toddler, etc. But just because one word is more general than another doesn't mean that it is more vague. To return to our example of drawing circles around objects: generality has to do with how many objects are in the circle, vagueness has to do with how many objects are on the borderline, and ambiguity has to do with how many different circles we need vagueness neglect - correct answerAssuming that real and useful categories can't have borderline cases is a fallacy we'll call vagueness neglect. For example, consider this argument: There is no such thing as friendship really, because you can't draw the line where two people suddenly become friends as they get to know and like each other more. The mistake here is to assume that there must be a sharp border between relationships that are friendships and those that are not. And that would be to neglect the fact that the word friend is vague, and so is the category it expresses. But friendship is still a useful category that we can use to make distinctions and convey information, and there are many clear examples people who are