Argument Mapping PDF

CHAPTER OVERVIEW 3: Argument Mapping 3.1: The Basics 3.2: Missing Assumptions 3.3: Objections 3.4: More Complex Arguments 3.5: Argument Mapping Conclusion 3.6: Beginning to Evaluate Arguments 3.7: Chapter 3 - Key Terms 3.E: Chapter Three (Exercises) This page titled 3: Argument Map...

CHAPTER OVERVIEW 3: Argument Mapping 3.1: The Basics 3.2: Missing Assumptions 3.3: Objections 3.4: More Complex Arguments 3.5: Argument Mapping Conclusion 3.6: Beginning to Evaluate Arguments 3.7: Chapter 3 - Key Terms 3.E: Chapter Three (Exercises) This page titled 3: Argument Mapping is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 1 3.1: The Basics So far, we’ve discussed the basic ideas behind arguments or inferences. Each argument has premises which are the assumptions or the support of the argument. Each argument also has usually one, but sometimes more conclusions. The conclusion is the main point of the argument. The goal of any argument is to offer reasons for believing the conclusion. The reasons are the premises and the claim that you are supposed to accept if you agree with the argument is the conclusion. So far so good. But there’s a lot more that we can say about arguments. Ideally, when we’re trying to understand an argument fully—long before we decide whether or not we agree with the argument or whether or not it’s a good argument—we have a full grasp of the structure of the argument. That is, we need to know which premises go with which other premises, whether each premise is supposed to directly demonstrate the conclusion or is merely indirect support for the conclusion, etc. In short, we need a map or a diagram of the argument before we can decide whether or not it’s a good argument. Simple arguments are called syllogisms: 2 premises and 1 conclusion and immediate inferences: 1 premise and 1 conclusion. Like: I like all vegetables Carrots are a vegetable So I like Carrots Or: I like all vegetables So, there aren’t any vegetables I don’t like. But normal arguments (arguments you’d find in a letter to the editor or in a social media post or on the radio or tv) aren’t like that —they have more premises, some of which don’t directly support the conclusion, but instead support other premises. It’s like a big complex argument that’s actually made out of smaller arguments. So, if you want to understand how a complex argument in the real world hangs together, you need to be able to construct a map or diagram of that argument. We’ll need to find out two things about each premise: 1. What kind of support does it offer for its conclusion? Does it support its conclusion in conjunction with other premises? Or does it instead form an argument by itself for the conclusion? 2. Does it support the main conclusion directly? Or does it instead support the conclusion indirectly by offering support for another premise, which in turn supports the main conclusion? How do we go about actually building an Argument Map? Well, we could choose any convention at all, so we have to decide on what sorts of shapes, labels, symbols, etc. we’ll use for the sake of this course. The first thing to note is that some people teach argument mapping going in an upwards direction—meaning that the conclusion would be on top and the premises for the conclusion would be below it. But we’re going to go a different way so that our argument maps more clearly track the usual format of an argument: the premises on top and the conclusion on bottom. Here are some basic concepts and the associated conventional symbols and shapes: We use arrows to signify Inferential Links or support. Every arrow means “implies that” or Paradigm Example: “therefore”. Read backwards (upwards), this (1) We can go now, because diagram to the right means: “1 is true” “why?” (2) the car is packed. “because of 2”. Or “Given that 2 is true, 1 follows.” 3.1.1 https://human.libretexts.org/@go/page/223814  Paradigm Example: Sometimes, we might find that a premise offers (1) I know that Voodoo is real, because indirect support for the main conclusion of the (2) My cousin saw someone take on the argument. In that case, we have to build a characteristics, personality, and voice of a vertical pattern into our argument map that spirit during a ceremony. might look something like the diagram to the (3) My cousin told me that she saw this last left. week. Conjoint vs. Independent Support We need to be able to decide (once we’ve sorted out which are premises for which conclusion) what kind of support a set of premises provide for their conclusion. It’s independent support when each premise seems like it’s an argument for the conclusion on its own. It’s conjoint support when a premise doesn’t seem to support the conclusion without the help of the other premises. A good test for conjoint support is to pretend one of the premises is false. Does this affect the inference(s) from the other premise(s) to the conclusion? Labradors are gentle, but they aren’t very aggressive, so they wouldn’t make good guard dogs. This feels like independent support because each inference makes sense on its own: Labradors are gentle, so they wouldn’t make good guard dogs. Labradors aren’t very aggressive, so they wouldn’t make good guard dogs. Let’s look at another: Vegetables are healthy and tomatoes are vegetables, so tomatoes are healthy. Since 1 is a general principle and 2 is an instance of that general principle (or something like that), it makes sense to think that they’re conjoint. Any time you see this pattern—where one premise is a definition or general claim and another premise is a more particular claim that falls under that definition or general claim—you’ll think that those premises are likely conjoint.  The "General-Specific Pattern When you see two premises where one premise is a general definition, a generalization, a hypothetical or conditional, or a general principle, and the other premise is a specific claim about an individual under that generalization, those are almost certain to be conjoint premises. Examples A motorbike is any two-wheeled motor-driven vehicle and that moped has two wheels that are driven by a motor, so... If anyone goes to the amusement park, they’re going to be exhausted at the end of the day; and Cheri went to Six Flags today, so... Lying is wrong, but getting out of trouble would require me to lie, so.... If we try negating 2, then the inference doesn’t make any sense: Vegetables are healthy and tomatoes are not vegetables, so tomatoes are healthy. What???? If we try negating 1, the inference falls apart again: Vegetables are unhealthy and tomatoes are vegetables, so tomatoes are healthy. 3.1.2 https://human.libretexts.org/@go/page/223814 What?????? Let’s try one more slightly more complex conjoint support example:  Example 3.1.1 Gina told me the Earth is round and Gina wouldn’t lie to me, and furthermore Gina is an astrophysicist, so the Earth is round. Let’s try the negation test on 1: Gina told me the Earth is flat and Gina wouldn’t lie to me, and furthermore Gina is an astrophysicist, so the Earth is round. What??? Let’s try it on 2: Gina told me the Earth is round and Gina often lies to me, and furthermore Gina is an astrophysicist, so the Earth is round. What???? Let’s try it on 3: Gina told me the Earth is round and Gina wouldn’t lie to me, and furthermore Gina is not an astrophysicist, so the Earth is round. Well... this isn’t as incoherent as the other examples. But why mention that Gina is an astrophysicist at all if it doesn’t at least help 1 and 2 demonstrate the conclusion that the Earth is round? With the negation of 3 as part of the argument, it seems thoroughly awkward that we should be talking about Gina being or not being an astrophysicist at all. If anything, it seems to work against the inference. What’s the lesson here? The negation test isn’t perfect, but it does almost always reveal when you’ve got a premise that seems to work together with other premises. In the Gina case, we’ve got a premise that is closely related in subject matter and so we’ve got some reason to conjoin it with 1 and 2. Here’s how we go about mapping conjoint vs. independent support once we’ve decided what sort of support is involved. Mapping Independent Support  Example 3.1.2 We use multiple arrows to signify multiple independent inferences. So, we have many premises which do not work together to demonstrate the conclusion. Each premise offers its own reason for accepting the conclusion. Paradigm example: (1) This test is easy. (2) Tetsuo got an A on the test and (3) Xochitl got an A on the test and (4) Francisco got an A on the test. If the other premises were not there, the argument would not fall apart. The premises don’t need each other to be true to support the conclusion. “Given 2, 1 follows, and given 3, 1 follows, and given 4, 1 follow.” 3.1.3 https://human.libretexts.org/@go/page/223814 Independent support is really like having multiple inferences. So the map above seems to tell us that there are three separate inferences that just happen to have the same conclusion. Mapping Conjoint Support  Example 3.1.3 We use brackets to signify a single inference with many conjoint or mutually dependent premises. The premises work together to support the conclusion. Without the other conjoint premises, it would be unclear why one conjoint premise should be taken as a reason for accepting the conclusion. Paradigm example: (1) You are behaving unfairly. (2) You’re giving more to some than to others and (3) giving more to some than to others isn’t fair. If any one of them is false or wasn’t there to begin with, the inference falls apart. “Given 2, 1 doesn’t follow unless we also have 3 (and 4, 5, 6,...).” Deductive arguments are more often than not conjoint support. This is just a rough and ready rule, but the way standard Deductive arguments (without extra irrelevant premises) work is that the premises are all necessary for the inference to demonstrate the conclusion. So it makes sense that they would be conjoint premises. Here’s a complete example of a problem like you might see on a quiz or exam (though they’ll usually be less complex than these, at least to start out).  Example 3.1.4 (1) Government mandates for zero-emission vehicles won’t work because (2) only electric cars qualify as zero-emission vehicles, and (3) electric cars won’t sell. (4) They are too expensive, (5) their range of operation is too limited, and (6) recharging facilities are not generally available. 3.1.4 https://human.libretexts.org/@go/page/223814 Adding in 3 makes the inference make sense again (Oh, I see, electric cars won’t solve our problems). You can do the same by taking 2 away. Wait, we’ll say, what about other zero-emission vehicles??? Adding 2 back in makes sense of the inference. 4, 5, and 6 are independent because they don’t have much to do with one another. The inference from 4 to 3, 5 to 3, and 6 to 3 all makes sense. “They’re too expensive, so they won’t sell.” (makes sense). “Their range is limited, so they won’t sell” (makes sense). “There aren’t enough recharging facilities, so they won’t sell” (makes sense!).  Example 3.1.5 We also use downward braces if there are more than one conclusion for any given inference. This is called Multiple Conclusions. Example: (1) The president may have her faults, but (2) she is an outstanding leader and (3) we should reelect her. (4) Her foreign policy has brought about respite from violence in various war torn regions as (5) she sent in troops to protect refugees in Rwanda and (6) she negotiated an armistice between Egypt and Israel. (7) Her economic policy has also been largely successful in that (8) a potential recession has been avoided for now. (9) She is also a great moral leader as (10) hers is a model family and (11) she demonstrates true integrity daily. Notice how 1 isn’t actually part of the argument: it just introduces the topic but isn’t a premise or conclusion. 2 and 3 are both conclusions (notice the “and”, which often links premises to premises and conclusions to conclusion) because neither is a premise/evidence for the other and both are implied by the rest of the argument (4, 7, and 9). Why did we go with independent support for all of the top-most premises? Try to reason through it on your own. Terminology Let’s introduce some new terminology so we can have a common language with which to talk about arguments: A “level” or “layer” of an argument map is one horizontal row of a carefully-drawn argument map. Notice how the previous argument map above is drawn so that even though there’s a lot going on in the argument, we can see 3 distinct layers or horizontal rows? A Main Conclusion is the final conclusion of the argument. It doesn’t serve as a premise/support for any other proposition in the complex argument. It’s always in the bottom-most layer A Main Premise is one among the set of premises that directly support the main conclusion. It’s always in the layer that’s the second from the bottom. A Sub-Inference is an inference from a premise to another premise. The conclusion of a sub-inference is never in the bottom- most layer. A sub-premise is a premise in a sub-inference. 3.1.5 https://human.libretexts.org/@go/page/223814  A sub-conclusion is a conclusion in a sub-inference. (Note that a sub-conclusion is always a premise itself, and that it is usually one of the main premises unless the argument gets really complex). So here it is, the anatomy of a typical 3-layer argument diagram: The following excerpt from Knachel’s text covers some of the same ground we just covered, but sometimes it’s helpful to see a different explanation of the same thing: From: Knachel, Matthew, "Fundamental Methods of Logic" (2017). Philosophy Faculty Books. 1. http://dc.uwm.edu/phil_facbooks/1 Creative Commons Attribution 4.0 International License V. Diagramming Arguments Before we get down to the business of evaluating arguments—of judging them valid or invalid, strong or weak—we still need to do some preliminary work. We need to develop our analytical skills to gain a deeper understanding of how arguments are constructed, how they hang together. So far, we’ve said that the premises are there to support the conclusion. But we’ve done very little in the way of analyzing the structure of arguments: we’ve just separated the premises from the conclusion. We know that the premises are supposed to support the conclusion. What we haven’t explored is the question of just how the premises in a given argument do that job—how they work together to support the conclusion, what kinds of relationships they have with one another. This is a deeper level of analysis than merely distinguishing the premises from the conclusion; it will require a mode of presentation more elaborate than a list of propositions with the bottom one separated from the others by a horizontal line. To display our understanding of the relationships among premises supporting the conclusion, we are going to depict them: we are going to draw diagrams of arguments. Here’s how the diagrams will work. They will consist of three elements: (1) circles with numbers inside them—each of the propositions in the argument we’re diagramming will be assigned a number, so these circled numbers in the diagram will represent the propositions; (2) arrows pointed at circled numbers—these will represent relationships of support, where one or more propositions provide a reason for believing the one pointed to; and (3) horizontal brackets—propositions connected by these will be interdependent (in a sense to be specified below). Our diagrams will always feature the circled number corresponding to the conclusion at the bottom. The premises will be above, with brackets and arrows indicating how they collectively support the conclusion and how they’re related to one another. There are a number of different relationships that premises can have to one another. We will learn how to draw diagrams of arguments by considering them in turn. Independent Premises Often, different premises will support a conclusion—or another premise—individually, without help from any others. When this is the case, we draw an arrow from the circled number representing that premise to the circled number representing the proposition it supports. Consider this simple argument: 3.1.6 https://human.libretexts.org/@go/page/223814 1 Marijuana is less addictive than alcohol. In addition, 2 it can be used as a medicine to treat a variety of conditions. Therefore, 3 marijuana should be legal. The last proposition is clearly the conclusion (the word ‘therefore’ is a big clue), and the first two propositions are the premises supporting it. They support the conclusion independently. The mark of independence is this: each of the premises would still provide support for the conclusion even if the other weren’t true; each, on its own, gives you a reason for believing the conclusion. In this case, then, we diagram the argument as follows: Intermediate Premises Some premises support their conclusions more directly than others. Premises provide more indirect support for a conclusion by providing a reason to believe another premise that supports the conclusion more directly. That is, some premises are intermediate between the conclusion and other premises. Consider this simple argument: 1 Automatic weapons should be illegal. 2 They can be used to kill large numbers of people in a short amount of time. This is because 3 all you have to do is hold down the trigger and bullets come flying out in rapid succession. The conclusion of this argument is the first proposition, so the premises are propositions 2 and 3. Notice, though, that there’s a relationship between those two claims. The third sentence starts with the phrase ‘This is because’, indicating that it provides a reason for another claim. The other claim is proposition 2; ‘This’ refers to the claim that automatic weapons can kill large numbers of people quickly. Why should I believe that they can do that? Because all one has to do is hold down the trigger to release lots of bullets really fast. Proposition 2 provides immediate support for the conclusion (automatic weapons can kill lots of people really quickly, so we should make them illegal); proposition 3 supports the conclusion more indirectly, by giving support to proposition 2. Here is how we diagram in this case: Joint Premises Sometimes premises need each other: the job of supporting another proposition can’t be done by each on its own; they can only provide support together, jointly. Far from being independent, such premises are interdependent. In this situation, on our diagrams, we join together the interdependent premises with a bracket underneath their circled numbers. There are a number of different ways in which premises can provide joint support. Sometimes, premises just fit together like a hand in a glove; or, switching metaphors, one premise is like the key that fits into the other to unlock the proposition they jointly support. An example can make this clear: 1 The chef has decided that either salmon or chicken will be tonight’s special. 2 Salmon won’t be the special. Therefore, 3 the special will be chicken. Neither premise 1 nor premise 2 can support the conclusion on its own. A useful rule of thumb for checking whether one proposition can support another is this: read the first proposition, then say the word ‘therefore’, then read the second proposition; if it doesn’t make any sense, then you can’t draw an arrow from the one to the other. Let’s try it here: “The chef has decided that either salmon or chicken will be tonight’s special; therefore, the special will be chicken.” That doesn’t make any sense. What happened to salmon? Proposition 1 can’t support the conclusion on its own. Neither can the second: “Salmon won’t be the special; therefore, the special will be chicken.” Again, that makes no sense. Why chicken? What about steak, or lobster? The second proposition can’t support the conclusion on its own, either; it needs help from the first proposition, which tells us that if it’s not salmon, it’s chicken. Propositions 1 and 2 need each other; they support the conclusion jointly. This is how we diagram the argument: The same diagram would depict the following argument: 1 John Le Carre gives us realistic, three-dimensional characters and complex, interesting plots. 2 Ian Fleming, on the other hand, presents an unrealistically glamorous picture of international espionage, and his plotting isn’t what you’d call immersive. 3.1.7 https://human.libretexts.org/@go/page/223814  3 Le Carre is a better author of spy novels than Fleming. In this example, the premises work jointly in a different way than in the previous example. Rather than fitting together hand- in-glove, these premises each give us half of what we need to arrive at the conclusion. The conclusion is a comparison between two authors. Each of the premises makes claims about one of the two authors. Neither one, on its own, can support the comparison, because the comparison is a claim about both of them. The premises can only support the conclusion together. We would diagram this argument the same way as the last one. Another common pattern for joint premises is when general propositions need help to provide support for particular propositions. Consider the following argument: We shouldn’t elect someone who has proven an incompetent business leader. Candidate Z has proven an incompetent CEO. So, we shouldn’t elect Candidate Z. These premises will be mapped with conjoint support since the premises need to work together to show the conclusion. One general principle about who we shouldn’t elect, and one particular claim about Candidate Z. End Knachel Text Examples Let’s walk through a few examples of arguments that need mapping:  Example 3.1.6 She's the best girlfriend ever. She bought me a new backpack for Christmas, she's never late for a date, and she always treats me with care. Solution First, we need to identify each proposition—that is, each claim that can be true or false independently of the other claims. This is a bit interpretive, so sometimes there aren’t hard and fast rules that produce one particular right answer, but generally we can all come up with the same propositions: (1) She's the best girlfriend ever. (2) She bought me a new backpack for Christmas, (3) she's never late for a date, and (4) she always treats me with care. What a nice young person! Next, we need to decide what the conclusion is and which propositions are premises. A nice test that often helps is to read all of the premises and then say “therefore...” and then read what you think is the conclusion. It should make sense as an inference if you do this properly. For instance, this is clearly not so good: She’s the best girlfriend ever, she bought me a new backpack, and she always treats me with care, therefore she’s never late for a date. Uhhhhh...what? This one sounds a lot more sensical: She bought me a new backpack, she’s never late for a date, and she always treats me with care, therefore she’s the best girlfriend ever. It seems like the three premises are evidence for the claim that she is the best girlfriend ever. The thing we’re being asked to believe as a result of this reasoning is that she’s the best girlfriend ever. So that is the conclusion of the inference. Now we’ve already basically ruled out that 2, 3, and 4 have any inferential relationship between them. They all seem to give us reasons for believing the conclusion directly. Furthermore, none of them seems to give us reason for believing any other. Maybe 4 could be the conclusion of 2, but that’s a real stretch. So based on all of this, we can reasonably conclude that 2, 3, and 4 are all on the same level and are all main premises for the conclusion. Next, we need to decide if these are conjoint or independent premises. What do you think? 3.1.8 https://human.libretexts.org/@go/page/223814  How do we decide? Using the negation test. If negating or saying the opposite of one premise doesn’t make the inference fall apart, then the premises are not conjoint—they’re independent. Let’s try it here: She bought me a new backpack, she’s sometimes late for a date, and she always treats me with care, therefore she’s the best girlfriend ever. I mean, it is a bit weird, but it’s not nonsense. Sure, she’s sometimes late for a date, but the inference still makes sense. She hasn’t bought me a new backpack, but she’s never late for a date, and she always treats me with care, therefore she’s the best girlfriend ever. Again, it’s strange, but not nonsensical. We wonder why the backpack thing is brought up in the first place, but we don’t immediately think “oh, well, she can’t be the best girlfriend ever if she hasn’t bought you a backpack!” Instead, we just think, “she’s clearly an excellent partner, backpack or none.” The last one is a bit stranger: She bought me a new backpack, she’s never late for a date, but she doesn’t always treat me with care, therefore she’s the best girlfriend ever. Interesting...the case is definitely pretty weak for her being the bester girlfriend ever at this point, but the inference hasn’t utterly fallen apart. An opposite conclusion doesn’t now follow, we just have weaker reason for accepting the conclusion than we had before. This test reveals how strong a piece of evidence proposition 4 was for the conclusion in the original argument, but it doesn’t tell us that 4 is conjoint—the argument didn’t fall apart. With all of this in mind, the premises appear to be independent reasons from one another for accepting the conclusion that she is the best girlfriend ever. So the argument map looks like so: How about another example? This time I’ve skipped right to numbered propositions:  Example 3.1.7 (1) Obama was the best President in American history. (2) He protected people with pre-existing medical conditions from certain financial ruin or death by passing the Affordable Care Act, and (3) that feat was among the greatest legislative victories an American President has ever known. (4) He was able to topple the head of Al-Qaida and the mastermind of the 9/11 attacks, and (5) he oversaw the recovery from the largest economic disaster since the Great Depression. (6) Anyone who could bring us back from the brink of global economic meltdown to a stable and healthy economic like we had at the end of his tenure must be a truly great president. Solution Before we ever get to the question of whether or not this is a good argument, or what’s wrong with it if anything, or whether or not the conclusion is true, we must understand the argument. In particular we must understand the structure of the argument. This argument is complex, so what’s going on here? What’s the conclusion? It’s probably somewhat obvious here. There’s one claim that seems like the kind of claim someone might have as a thesis statement, or might defend in an Oxford-style debate. There’s one claim that seems to unify the rest of the propositions: everything is meant to justify or defend the claim that Obama was the best President in American history. With a longer argument like this, sometimes it is best to simply work sentence-by-sentence. 2 and 3 are part of the same sentence. The “and” tells us that there probably is no inferential link between 2 and 3. “and” is usually not interchangeable with “therefore”. When we read the content of 2 and 3, furthermore, 3 makes reference to 2. Often when a premise makes 3.1.9 https://human.libretexts.org/@go/page/223814  reference to another premise we can conclude that they are conjoint premises. Not always, mind you, and often that means that one is a subpremise for the other. Nevertheless, in this case the reference to “that feat” in 3 ties 3 to 2 conjointly. We can run the negative test to be sure we’re correct here: (1) Obama was the best President in American history. (2) He protected people with pre-existing medical conditions from certain financial ruin or death by passing the Affordable Care Act, and (3) that feat was an unremarkable legislative accomplishment. Now I’m unclear why we should think he’s the best president in history if the reason we’re being given is that he passed an important, but unremarkable piece of legislation. Not convincing. If anything, it seems to suggest that he was a fine, but unremarkable president. (1) Obama was the best President in American history. (2) He didn’t protect people with pre-existing medical conditions from certain financial ruin or death by passing the Affordable Care Act, and (3) that feat would have been among the greatest legislative victories an American President has ever known. Ummm...no. His not passing landmark legislation doesn’t make him the best president. This is one way you know you’re dealing with conjoint premises: if one premise explains how the other premise supports the conclusion. So these two premises are conjoint. What about 4? It’s part of the same sentence as 5, but the topics are so wildly different that it’s hard to see how they could be conjoint premises. Instead, it seems safe to assume they’re independent and that they’re independent from 2 and 3 for the same reason. They do, however, appear to be premises for the main conclusion (1) and so appear to belong on the second level with the other main premises 2 and 3. The last proposition, though, seems to essentially be about the same topic as 5 and furthermore seems to be the reason 5 supports the conclusion. This is one way you know you’re dealing with conjoint premises: if one premise explains how the other premise supports the conclusion. So 6 and 5 appear to be conjoint. If you ran the negative test, you’d soon learn that the negated inferences make no sense. As a result, the whole argument map, which is a bit strange looking, looks like this: This page titled 3.1: The Basics is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 3.1.10 https://human.libretexts.org/@go/page/223814 3.2: Missing Assumptions We need to be able to identify (and then to incorporate into our argument maps) assumptions that are part of the argument, but that weren’t explicitly stated. These are called Hidden Premises, Missing Assumptions, Suppressed Premises/Assumptions, etc. Regardless of the name, these are cases where an argument in fact relies on a claim that it doesn’t state as a premise. There is a claim that must be true if the inference is to make sense, but isn’t explicitly claimed to be true by the argument as it is written or spoke. Identifying Hidden Assumptions It’s a bit tricky, but it might be one of the most important and practical skills you’ll learn in this class. How do we figure out when an argument has one or more hidden premises and how do we identify what those premises are? Well, one answer is simply that formal logic does the job for us when we’re dealing with deductive arguments. This is the math- like system of argument analysis we’ll learn later in the semester. But for now, we need some informal tools to allow us to identify hidden premises or assumptions. This is not only a skill you can build without knowing logic, but is also a skill that extends to inductive reasoning as well and so is far more broadly applicable. Check out this argument: Flowers smell nice ??? ∴ Let’s plant some flowers [that little triangle of dots is a “therefore” sign] We can’t quite get from “smelling nice” to “things we’ll plant” without an assumption which links these two ideas. Notice how flowers are in both the premise and the conclusion, so we don’t need to link the topic of flowers together with the topic of flowers. Abstractly, is A is related to B, and C is related to B, then what we need is something linking A and C so that we can bridge the gap between A and B being associated with one another to C and B being associated with one another. Less abstractly, if we have three topics: flowers, smelling nice, and things to plant; then we need something linking smelling nice and things to plant so that we know the fact that flowers smell nice is a compelling reason to think that flowers are the kind of thing we should be planting. We know that flowers smell nice and we’re trying to get to flowers should be planted. Any idea what the hidden link might be? The hidden assumption is something like “we should plant things that smell nice.” Can you see how that completes the inference? Check out some more examples and see if you can figure out what is going on in each example: why do we need the extra premise for the inference to work? These wildfires are out of control! So global warming is real. The hidden assumption is something like “global warming is the best explanation for an increase in wildfires.” We should believe only what is reasonable, so we should reject theism. The hidden assumption is something like “belief in theism is unreasonable.” No one believes the Earth is flat anymore, so it’s a silly belief. The hidden assumption here is something like “any belief that no one currently holds is a silly belief.” Here’s a step-by-step process for identifying hidden assumptions: A step-by-step process: 1. First, identify the inference or sub-inference with the hidden assumption Which one is “incomplete”? 2. Then, look at the premises of the inference and identify the “terms” or topics discussed in each premise Each premise is usually a claim which links two topics together. 3.2.1 https://human.libretexts.org/@go/page/223815 3. Then, ask how we can link the terms that aren’t yet linked. This requires a bit of imagination and instinct, but you can do it! 4. Finally, write the assumption that links the unlinked terms. Now that you’ve identified a hidden assumption or more, perform the following two steps: 5. Check to be sure your argument now works Does the argument now have a link between each topic? Is there a path from the topics in the premises to the topics in the conclusion? 6. Perform the “negative test” on your assumption If you negate your hidden assumption, you should end up with an argument that makes no sense. If the argument with the negated premise makes sense, then you haven’t identified a hidden assumption (i.e. the argument was fine without your assumption). Let’s take a look at how this works with some real arguments. I think we should invade North Korea. Look, the Kim Jong dynasty is simply never going to give up on their goal of being a nuclear power. Okay, this inference is really “fast” meaning that it skates over a few hidden assumptions and so doesn’t seem to work all by itself. It’s like it rushes straight to the finish line without actually running the course. Let’s break it down step by step. Step 1 There’s only one apparent premise and one apparent conclusion, so identifying the inference in question is easy. Step 2 The “terms” or topics of this inference are: A. We should invade B. North Korea C. Kim Jong dynasty D. Nuclear Arms Step 3 How do we connect these topics? First, we need to connect “North Korea” with the “Kim Jong dynasty”. Then we’ll need to connect “being a nuclear power” with “we should invade.” Step 4 Let’s try these assumptions and see how the argument works out: 1. The Kim Jong dynasty is never going to give up on their goal of being a nuclear power. 2. The Kim Jong dynasty is going to lead North Korea for the foreseeable future. 3. Any country that aspires to be a nuclear power is one we should invade. 4. Therefore, we should invade North Korea. This inference is more complete and connects the topics together more completely, but it rests on one very shaky premise. Can you identify which one? Yes, that’s right. You are very smart. Premise 3 is pretty wacky, right? What if Argentina decided it wanted to be a Nuclear Power? Should we invade them? I would hope not. They’re a pretty harmless nation at the moment. So, we have a choice. Either decide that the argument is pretty weak and reject it out of hand, or we can exercise the Principal of Charity to try to interpret the argument to be as plausible as possible. We should always interpret arguments—especially the ones we’re skeptical of or disagree with—to be as rational and plausible as possible. 3.2.2 https://human.libretexts.org/@go/page/223815 With that in mind, let’s change this argument up a bit so that it makes a bit more sense. We might not agree with the argument in the end, but at least we will have understood the argument in the best possible light. We will have seen what the most plausible argument for that conclusion on the basis of similar premises is. If we ignore premise 3, the weak premise, and try to replace it with a few premises which make more specific and believable claims, we’ll be in a better spot. We’ll need to tie together some new topics. Premise 3 was supposed to make a link between “aspires to be a nuclear power” and “we should invade.” There’s a bit of conceptual “distance” between these ideas, though, so we shouldn’t just posit a principle like premise 3 above which directly links them. That would be too easy a principle to reject. Instead, we’ll travel the distance between these ideas in a few steps rather than a giant leap. How about we connect “aspires to be a nuclear power” to “they’re dangerous”? Then we can get from “they’re dangerous” to “we should invade.” That sounds more plausible, right? 1. The Kim Jong dynasty is never going to give up on their goal of being a nuclear power. 2. The Kim Jong dynasty is going to lead North Korea for the foreseeable future. 3. North Korea under Kim Jong rule would be an immediate existential danger to its neighbors and the rest of the world if they ever became a nuclear power. 4. If we invade North Korea, then we prevent that danger. 5. Therefore, we should invade North Korea. Now the argument seems to hang together a bit more clearly. We have a clear path from the Kim Jong dynasty through to a nuclear North Korea, to the danger that poses and therefore a motivation for invading, all the way to the claim that we should invade. It’s still shaky reasoning, but it’s approaching the strongest version of the original argument. There’s still technically something missing. Between 4 and 5 we’ve missed a premise. In order to get from an “is” claim to an “ought” claim, often you’ll need a general normative principle. That is, we need a general rule which allows us to move from a simple statement of supposed fact (premise 4) to a prescription for what we should do (the conclusion, #5). This one will do: 4a. If we can prevent immediate existential danger to whole countries then we must/should act so as to prevent that danger. That actually seems pretty plausible, right? So in this case the missing premise wasn’t so shaky (you might disagree, though). We can then perform the negative test on our hidden assumptions and figure out if the argument falls apart without them. If we deny 4a, then we can’t get from 4 to 5. Does that make sense? If so, Mapping Hidden Assumptions Mapping Hidden Assumptions is relatively simple. A hidden assumption will always offer conjoint support for its conclusion/sub-conclusion. Think about it: if hidden assumptions are things that must be true for an inference to work, and conjoint premises are premises that must all be true for the inference to work, then it makes sense that any hidden premise will offer conjoint support. The only difference will be that we’ll use dotted circles instead of regular: , or , etc. A few complete examples:  Example 3.2.1 3.2.3 https://human.libretexts.org/@go/page/223815  1. We have a right to bodily autonomy 2. Hidden Assumption: (Abortion restrictions infringe on a right to bodily autonomy) 3. Therefore, we have a right to freedom from abortion restrictions The inference from 1 to 3 makes some sense because we’re all familiar with the abortion debate by now. What we do to make it make sense of it for ourselves, though, is implicitly add in premise two in understanding the inference from 1 to 3.  Example 3.2.2 (1) We’ll never stop climate change, (2) Hidden Assumption: Climate change will intensify fires and storms, so (3) we’re going to have much more fires and storms. (4) Our current system can’t handle even basic disasters. Furthermore, (5) state disaster relief funds are insufficient without help from FEMA’s overburdened funds. So, (6) we need to reform and enhance funding for FEMA immediately. The inference from 1 to 3 makes little sense if it’s not true that climate change is connected to fires and storms, so we need premise 2 to make that connection. 3, 4, and 5 are independent because each by itself makes sense as a premise for 6. This page titled 3.2: Missing Assumptions is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 3.2.4 https://human.libretexts.org/@go/page/223815 3.3: Objections This is the final skill in argument mapping that we’ll discuss. It’s very important to be aware of because without it we can only ever map parts of a discussion which agree with one another. Meaning that if someone has an objection to an argument, we won’t be able to pinpoint where the disagreement is on our argument maps. Our argument maps are more expressive and powerful if we can diagram disagreements as well as agreements, so let’s discuss how to map disagreements! We need to have a tool to map objections to an argument that we’ve already mapped so we can see where those objections are “putting pressure” or what exactly they’re trying to critique. We use either hashed arrows or dotted arrows to signify relations of objection. They mean “objects to” or “rejects”. These are the only arrows in our system which point up. There are two kinds of objections: 1. Objections to a proposition Analyst A: (1) Building this highway would threaten the existence of the species of fairy shrimp that inhabits the proposed route, so (2) we must reroute the highway. Analyst B: I understand your concern for the fairy shrimp, but (3) the proposed route is not the only habitat for the fairy shrimp in this area, so it wouldn’t threaten their existence.  Note Note that the arrow is pointing to the Premise. 2. Objections to an inference Obama said that (1) people who were brought here illegally as children shouldn’t be punished for the choices of their parents, because (2) their parents made the decision and not them. But that doesn’t follow because (3) we’re not punishing them, instead we’re just enforcing our laws. 3.3.1 https://human.libretexts.org/@go/page/223816   Note Note that the arrow is pointing to the other Arrow. Could have also used a dotted arrow. Diagramming Tip Here’s a weird case, so that you can see what sorts of situations you might get into when trying to map objections: Notice how objection 7 has to cross over an inference to point to the inference from 3 to 1. That’s okay. But it helps to keep your argument maps a bit larger and as clear as possible. You want to be able to clearly decipher what’s going on in the argument map as you go along. This page titled 3.3: Objections is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 3.3.2 https://human.libretexts.org/@go/page/223816 3.4: More Complex Arguments Here is a description of complex argument diagramming from Matthew Knachel. From: Knachel, Matthew, "Fundamental Methods of Logic" (2017). Philosophy Faculty Books. 1. http://dc.uwm.edu/phil_facbooks/1 Creative Commons Attribution 4.0 International License The arguments we’ve looked at thus far have been quite short—only two or three premises. But of course some arguments are longer than that. Some are much longer. It may prove instructive, at this point, to tackle one of these longer bits of reasoning. It comes from the (fictional) master of analytical deductive reasoning, Sherlock Holmes. The following passage is from the first Holmes story—A Study in Scarlet, one of the few novels Arthur Conan Doyle wrote about his most famous character—and it’s a bit of early dialogue that takes place shortly after Holmes and his longtime associate Dr. Watson meet for the first time. At that first meeting, Holmes did his typical Holmes-y thing, where he takes a quick glance at a person and then immediately makes some startling inference about them, stating some fact about them that it seems impossible he could have known. Here they are—Holmes and Watson—talking about it a day or two later. Holmes is the first to speak: “Observation with me is second nature. You appeared to be surprised when I told you, on our first meeting, that you had come from Afghanistan.” “You were told, no doubt.” “Nothing of the sort. I knew you came from Afghanistan. From long habit the train of thoughts ran so swiftly through my mind, that I arrived at the conclusion without being conscious of intermediate steps. There were such steps, however. The train of reasoning ran, ‘Here is a gentleman of a medical type, but with the air of a military man. Clearly an army doctor, then. He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin, for his wrists are fair. He has undergone hardship and sickness, as his haggard face says clearly. His left arm has been injured. He holds it in a stiff and unnatural manner. Where in the tropics could an English army doctor have seen much hardship and got his arm wounded? Clearly in Afghanistan.’ The whole train of thought did not occupy a second. I then remarked that you came from Afghanistan, and you were astonished.” (Also excerpted in Copi and Cohen, 2009, Introduction to Logic 13e, pp. 58 - 59.) This is an extended inference, with lots of propositions leading to the conclusion that Watson had been in Afghanistan. Before we draw the diagram, let’s number the propositions involved in the argument: 1. Watson was in Afghanistan. 2. Watson is a medical man. 3. Watson is a military man. 4. Watson is an army doctor. 5. Watson has just come from the tropics. 6. Watson’s face is dark. 7. Watson’s skin is not naturally dark. 8. Watson’s wrists are fair. 9. Watson has undergone hardship and sickness. 10. Watson’s face is haggard. 11. Watson’s arm has been injured. 12. Watson holds his arm stiffly and unnaturally. 13. Only in Afghanistan could an English army doctor have been in the tropics, seen much hardship and got his arm wounded. 3.4.1 https://human.libretexts.org/@go/page/223817  Lots of propositions, but they’re mostly straightforward, right from the text. We just had to do a bit of paraphrasing on the last one—Holmes asks a rhetorical question and answers it, the upshot of which is the general proposition in 13. We know that proposition 1 is our conclusion, so that goes at the bottom of the diagram. The best thing to do is to start there and work our way up. Our next question is: Which premise or premises support that conclusion most directly? What goes on the next level up on our diagram? It seems fairly clear that proposition 13 belongs on that level. The question is whether it is alone there, with an arrow from 13 to 1, or whether it needs some help. The answer is that it needs help. This is the general/particular pattern we identified above. The conclusion is about a particular individual—Watson. Proposition 13 is entirely general (presumably Holmes knows this because he reads the paper and knows the disposition of Her Majesty’s troops throughout the Empire); it does not mention Watson. So proposition 13 needs help from other propositions that give us the relevant particulars about the individual, Watson. A number of conditions are laid out that a person must meet in order for us to conclude that they’ve been in Afghanistan: army doctor, being in the tropics, undergoing hardship, getting wounded. That Watson satisfies these conditions is asserted by, respectively, propositions 4, 5, 9, and 11. Those are the propositions that must work jointly with the general proposition 13 to give us our particular conclusion about Watson: Next, we must figure out how what happens at the next level up. How are propositions 4, 5, 13, 9, and 11 justified? As we noted, the justification for 13 happens off-screen, as it were. Holmes is able to make that generalization because he follows the news and knows, presumably, that the only place in the British Empire where army troops are actively fighting in tropics is Afghanistan. The justification for the other propositions, however, is right there in the text. Let’s take them one at a time. First, proposition 4: Watson is an army doctor. How does Holmes support this claim? With propositions 2 and 3, which tell us that Watson is a medical and a military man, respectively. This is another pattern we’ve identified: these two proposition jointly support 4, because they each provide half of what we need to get there. There are two parts to the claim in 4: army and doctor. 2 gives us the doctor part; 3 gives us the army part. 2 and 3 jointly support 4. Skipping 5 (it’s a bit more involved), let’s turn to 9 and 11, which are easily dispatched. What’s the reason for believing 9, that Watson has suffered hardship? Go back to the passage. It’s his haggard face that testifies to his suffering. Proposition 10 supports 9. Now 11: what evidence do we have that Watson’s arm has been injured? Proposition 12: he holds it stiffly and unnaturally. 12 supports 11. Finally, proposition 5: Watson was in the tropics. There are three propositions involved in supporting this one: 6, 7, and 8. Proposition 6 tells us Watson’s face is dark; 7 tells us that his skin isn’t naturally dark; 8 tells us his wrists are fair (light- colored skin). It’s tempting to think that 6 on its own—dark skin—supports the claim that he was in the tropics. But it does not. One can have dark skin and not visited the tropics, provided one’s skin is naturally dark. What tells us Watson has been in the tropics is that he has a tan—that his skin is dark and that’s not its natural tone. 6 and 7 jointly support 5. And how do we know Watson’s skin isn’t naturally dark? By checking his wrists, which are fair: proposition 8 supports 7. So this is our final diagram: And there we go. An apparently unwieldy passage—thirteen propositions!—turns out not to be so bad. The lesson is that we must go step by step: start by identifying the conclusion, then ask which proposition(s) most directly support it; from there, work back until all the propositions have been diagrammed. Every long argument is just composed out of smaller, easily analyzed inferences. This page titled 3.4: More Complex Arguments is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 3.4.2 https://human.libretexts.org/@go/page/223817 3.5: Argument Mapping Conclusion Theoretically, you could have a very complex argument map which traces lines of disagreement through multiple stages. We have a sophisticated enough argument mapping system now that we would be able to map even absurdly complex disputes. As a little practice, try to identify each component here and then try to figure out which numbers would belong to which of two people in a dispute that has this map. This page titled 3.5: Argument Mapping Conclusion is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 3.5.1 https://human.libretexts.org/@go/page/223818 3.6: Beginning to Evaluate Arguments Before I said that we use argument mapping to understand an argument before we do any evaluation of those arguments as good or bad arguments, valid or invalid, cogent or uncogent, sound or unsound, and so on. But the process of identifying hidden assumptions is in itself a sort of evaluative process: we must identify the need in the argument for another claim to be true—we have to declare that an argument is incomplete and therefore faulty before we can talk about the argument needing an extra premise. So if we’ve already done a bit of evaluating of arguments in identifying hidden premises, perhaps those tools that we gained when we were identifying hidden assumptions will help us in trying to evaluate an argument as a good or bad argument. Let’s explore how helpful those tools are. Recall that the central idea in the process of identifying hidden assumptions is the idea that a good, complete argument has a series of topics or terms that are linked together in the right way. This is a really informal and incomplete version of what you might learn if you learn Categorical or Aristotelian Logic. That’s the study of how categories or terms must be linked for an argument to be deductively valid. Let’s look at how this informal idea can help us determine whether we’ve got a good or bad argument. Here’s an example to consider—it’s something you might see on social media and in the wording that one might actually find there: If you don’t want an abortion, don’t have one. [Implied conclusion: Abortion should remain legal and available]. Hopefully it’s relatively clear that this argument needs a tune up—not because it is wrong-headed (it might not be) or because its conclusion is wrong (it might be true), but because it’s unclear what the actual argument is: what are the premises and how do they support the conclusion? First, we should try to interpret the argument in a way that makes the process of identifying topics easier. This process is already a bit evaluative in that we are interpreting the argument charitably: we’re trying to understand the most rational version of the argument without changing its essential content. Maybe something like: Abortion rights aren’t abortion mandates, so there’s no reason to oppose abortion rights. Making abortion legal doesn’t mean requiring (mandating) anyone to have an abortion. This is already starting to look more complete, and it’s already beginning to look like a serious philosophical argument. We’ve taken it out of the format of a slogan and interpreted it as an argument. The next step is to identify the topics being discussed: a. Abortion rights laws b. Abortion mandates c. Reason to oppose things Once we’ve identified these terms, we can think about the argument in terms of a series of propositions which connect them together. 1. Abortion Rights laws aren’t abortion mandates [Links (a) to (b)] 2. So, There’s no reason to oppose abortion rights [Links (c) to (a)] We’ve got some of the tools now to recognize that there’s a missing premise here. Can you find it? Ummm....There’s no link between Reason to oppose things and Abortion mandates, so the inference has a gap in it. Right-o! Good work. We’ve linked a to b, and a to c, but not b to c. This is why the argument feels a bit gappy and incomplete. What, then, might our hidden premise be? We need to link “Abortion mandates” with “reason to oppose things.” Any ideas? 3.6.1 https://human.libretexts.org/@go/page/223819 Yeah. Why not something like “There’s no reason to oppose abortion mandates.” Well...not quite. That’s a pretty clearly false, statement right? Lots of people want to have children and lots of other people are morally opposed to abortions, so it makes little sense to say there’s no reason to oppose mandating everyone has an abortion, right? Oh...yeah. What about “If something isn’t a mandate, then there’s no reason to oppose it.” Now we’re talking! That’s a really general claim: it applies to everything (or at least every public policy or law) that isn’t a mandate. So maybe we’d want something more restrictive. Nevertheless, this is a good start. So here’s our complete argument: 1. Abortion rights laws aren’t abortion mandates [Links (a) to (b)] 1a. If something isn’t a mandate, then there’s no reason to oppose it [Links (b) to (c)] 2. So, There’s no reason to oppose abortion rights laws [Links (c) to (a)] This process is tricky and interpretive. When we get to Aristotelian Logic, we’ll cover some tools that make this a more strict and formalized process. For now, though, we’re sticking with intuitively understanding arguments and how they hang together. This is an incredibly valuable skill in all aspects of life: when is an inference making an implicit assumption? People make loads of implicit assumptions all of the time. Okay, so the goal in this section was to start to evaluate arguments using some of the tools we’ve picked up so far. Here’s how this might go: The first claim in this argument is that Abortion rights aren’t abortion mandates. This is clearly true. No law or policy securing abortion rights (within the realm of reasonable laws) would require that people have abortions. So there’s no problem with the first claim. The second (hidden) claim in the argument is that If something isn’t a mandate, then there’s no reason to oppose it. This, as I said before, is very broad. It seems easy to come up with a counterexample. In this case, a counterexample would be something that isn’t a mandate, but which we would have reason to oppose. Can you think of a possible law that doesn’t put a requirement on citizens, but nevertheless is a law we’d want to oppose? I can think of thousands. A law allowing murder. A law allowing ritual human sacrifice. A piece of legislation requesting that the President strongly consider nuking the moon....the list goes on. So this seems like a bad principle: one shouldn’t be opposed to something that doesn’t bring a mandate with it. In other words: if it doesn’t interfere with you, then leave it alone. That’s not how a civil society, works though. We take an interest in each other’s lives for the sake of having a healthy society and protecting one another. As I said a few paragraphs back: this hidden premise we inserted completes the argument fairly directly, but might be too general. More general than we need, in fact. We might consider something more specific like “If a law doesn’t require people to do something immoral, then there’s no reason to oppose it.” But that is refuted by the same counterexamples I listed above. We could try over and over to find more specific premises to complete the argument, but honestly at some point we have to admit that the argument as we’ve reconstructed it probably rests on a false general premise. So in reconstructing this argument and identifying what hidden premise it rests on, we have set ourselves up to evaluate whether or not this is a good argument. You might disagree, but this seems like a bad argument for abortion rights. Best to go looking elsewhere for good arguments for abortion rights (they’re out there! Philosophers like Judith Jarvis Thomson, Mary Anne Warren, and Rosalind Hursthouse have interesting arguments indeed). This page titled 3.6: Beginning to Evaluate Arguments is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 3.6.2 https://human.libretexts.org/@go/page/223819 3.7: Chapter 3 - Key Terms Conjoint Support Independent Support Hidden Assumption/ Suppressed Premise Sub-Inference Sub-Conclusion Sub-Premise Main Inference Main Premise Main Conclusion Objection to a Premise Objection to an Inference This page titled 3.7: Chapter 3 - Key Terms is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 3.7.1 https://human.libretexts.org/@go/page/223820 3.E: Chapter Three (Exercises) How can I tell one from the other? Objections to inferences usually use phrases like “that doesn’t follow,” or “even if we accept x, we need not accept y.” The objection is that the inference itself is incomplete or weak or invalid or simply doesn’t make any sense. An objection to a hidden premise is actually an objection to an inference: you’re claiming that the inference rests on a weak hidden premise and so is an incomplete inference. Objections to propositions/premises will always be arguing that some proposition is false rather than that a conclusion doesn’t follow. The objection is that some particular claim is false or at least is likely or plausibly false.  Exercise 3.E. 1 : Conjoint vs Independent Support For each, determine whether the support offered by the premises is conjoint or independent. Deploy the negative test when you’re unsure. A. Eating healthy food is important and Figs are super healthy, so we should eat more figs. B. I have to have a steady income to support my family, I already have a stable job, and grad school would require me to quit my job, so I shouldn’t go to grad school. C. All of the nurses have gone on the strike, the custodial staff is threatening the same, and the doctors are demanding better legal support. This hospital is in trouble right now. D. He is ten years younger than you and no one should date anyone ten years younger, so you can’t date him! E. An ergonomic desk can prevent permanent injury, is more comfortable to use, and is cost-effective, so can I please buy one for my office? F. A robust economic recovery will require higher taxes on the wealthy, and we need to have a strong recovery to prevent melt downs in the near future, so we must raise taxes on the wealthy. G. We’ve always been honest with each other and the honest thing to do right now is to tell you that that outfit is terrible, so I need to tell you the truth about that outfit.  Exercise 3.E. 2 : Terminology Fill in the blank labels using one of each of the following key terms: (A) Sub-Conclusion, (B) Sub-Premise, (C) Main Premise, (D) A premise on level 4 of the argument map, (E) A premise on level 2 of the argument map, (F) Conjoint Premise, (G) Independent Premise. 3.E.1 https://human.libretexts.org/@go/page/223821  Exercise 3.E. 3 : Simple Argument Maps For each, create an argument map. Be sure to distinguish between conjoint and independent support. A. (1) Eating healthy food is the most effective weight-loss strategy, since (2) the amount of calories one takes in while eating even small snacks takes a long time to burn off by exercising, and (3) almost no one can afford to spend hours and hours exercising throughout the day. B. (1) We’ve been out here in the sun all day, and (2) being in the sun for too long is unhealthy, so (3) let’s go inside. C. (1) He’s so popular. (2) Everyone wanted to be invited to his birthday party and (3) he had five people invite him to the dance. D. (1) We should ban all guns. (2) Guns are especially effective killing machines for mass killings. Also, (3) children often have fatal accidents with guns. Furthermore, (4) guns don’t have a non-violent use. E. (1) Having intercourse before 18 is wrong because, (2) you are not emotionally mature enough to deal with the awkwardness and intimacy of the situation, and (3) you are not mature enough to deal with the potential consequences of the situation (pregnancy or STIs). F. (1) Treating others with respect is important, so (2) we should all respect each other, and (3) we should try to teach our children to respect others. G. (1) Oreos aren’t healthy, since (2) Nabisco products generally aren’t healthy. Think about it: (3) Pringles aren’t healthy, (4) Pop Tarts aren’t healthy, and (5) neither are Chips Ahoy. H. (1) People are starting not to like you. (2) Tina said she wasn’t your friend anymore, (3) Beto said he doesn’t like you, and (4) I certainly don’t want to be around you.  Exercise 3.E. 4 : More Complex Argument Maps For each, create an argument map. Be sure to distinguish between conjoint and independent support. A. (1) I know that Sally went to the park with Billy because (2) Sally said she’d go with him if he asked, and (3) Billy likes Sally (so he wouldn’t ask her as a prank) and (4) Billy asked Sally to go to the park. B. (1) Eating any meat is wrong because, (2) most meat is produced in factory farms, (3) animals in factory farms suffer greatly, and (4) even ‘free range’ and ‘organic’ meat causes animal suffering. 3.E.2 https://human.libretexts.org/@go/page/223821 C. (1) We already have almost all of the technology needed to clone dinosaurs and (2) human beings tend to do whatever they find they can do. (3) So, killer dinosaurs will roam the Earth one day. And since this is true, we can expect two things: (4) an armed response leading to the loss of innocent life, and (5) movie producers trying to buy the rights to the story. D. (1) Burning fossil fuels like petrol, coal, and natural gas contributes to global warming. (2) According to experts, the combustion reaction releases free molecules of CO2 into the atmosphere, and (3) Scientists wouldn’t lie about this. Think about it: (4) there’s no profit incentive for scientists to lie about this, but (5) there is a profit motive for other people to deny that it is true. E. The Republicans have argued repeatedly that (1) the Affordable Care Act is in a death spiral. Because, they say, (2) premiums are getting higher, and (3) as premiums get higher, the people will stop purchasing policies and (4) if the people stop purchasing policies, then the insurance companies will pull out of the exchanges, and (5) if that happens, then the whole system collapses. F. (1) We need to protect the environment, since (2) biodiversity is necessary to protect future food sources and (3) biodiversity is sustainable only in a relatively healthy global environment. Furthermore, (4) We take great pleasure in the natural wonders that the Earth has to offer (5) [suppressed premise]  Exercise 3.E. 5 : Even More Complex Argument Maps For each, create an argument map. Be sure to distinguish between conjoint and independent support. A. (1) We need to buy a new trampoline, since (2) our son almost hurt himself really badly when this one broke last week, and (3) I don’t want to risk it again. (4) Even if you’re able to fix it, there’s no guarantee that it will be as safe as a new one. Think about it: (5) older trampolines like ours don’t have a net around them, and (6) the net makes it less likely that a kid will bounce off onto the ground and hurt themselves. Finally, (7) older trampolines like ours don’t have good spring covers, and (8) without spring covers, the risk of pinching oneself or falling through the springs and breaking a limb are very high. B. (1) Eating kale is sometimes unsatisfying, but the fact is that (2) Kale has countless health benefits. (3) It is rich in folate and (4) folate helps guard against bad epigenetic changes. (5) It has more minerals and vitamins than most meat sources and (6) vitamins and minerals got from whole food sources are better than those got from multivitamins and other supplements since (7) whole foods contain more bioavailable forms of vitamins and minerals. C. (1) We’ve already been in Afghanistan for over a decade and (2) no other American war has lasted this long, so (3) Afghanistan is the longest running American war. (4) We’ve shown little sign of progress in the past few years, and (5) we’ve sunk countless dollars into Afghan infrastructure and security projects with little to show for it. Given all of this, (6) we should pull out of Afghanistan and (7) we should divest interest in the Afghan society. (8) Since we’ve already tried so hard to fix it, (9) we should let them try to solve their own problems! D. (1) Epigenetics is the most important frontier in genetic research. (2) Countless traits and processes depend not on genetic changes, but on epigenetic changes, (3) epigenetic changes are easier to induce through therapies, chemicals, and other interventions in a clinical setting, and (4) we already know the basic rules of genetics, but are far behind in our understanding of epigenetics. Given all that, it follows that (5) we should shift the balance of funding in favor of epigenetic research and (6) we should fund more PhD’s in epigenetics as well. E. (1) We should put more direct emphasis in school and college on thinking clearly and critically. (2) The most important skill in life is thinking well. I think this because (3) other important skills like decision making and communication rely centrally on thinking well, and (4) a good citizen, employee, and overall person is one who can think clearly and rationally. (5) Citizens must weigh complex values in voting on candidates and referenda, (6) employees must make decisions in the workplace based on complex policies and competing needs, and (7) people in general need to have habits of self-critical and careful thinking in order to live good lives.  Exercise 3.E. 6 : Hidden Assumptions For each inference, identify the most direct hidden assumption. A. Moby Dick is a whale. So Moby Dick is a mammal. B. Giving students a fail grade will damage their self-confidence. Therefore, we should not fail students. 3.E.3 https://human.libretexts.org/@go/page/223821  C. It should not be illegal for adults to smoke pot. After all, it does not harm anyone. D. There is nothing wrong with texting during lectures. Other students do it all the time. E. Traces of ammonia have been found in Mars' atmosphere. So there must be life on Mars. F. I don't like people who spit on the sidewalk, so littering should be illegal. G. No one even cares what you think, so what you think isn't important. H. Americans believe in freedom, so any law that restricts our freedom should be abolished. I. Trees are beautiful, so we should plant more of them. J. Carbon emissions contribute to global warming, so we should tax them.  Exercise 3.E. 7 : Mapping Hidden Assumptions For each inference, identify the hidden assumption and then create a map of the inference including the hidden assumption. A. The truth is, (1) we can’t vote for the Republican candidate. (2) She doesn’t believe in global warming. B. (1) Nobody has ever been there and come back, and (2) I have children, so (3) I’m not going. C. (1) Freedom isn’t free. (2) So, someone has to pay the price for freedom. (3) The way people pay the price of freedom is by serving in the armed forces. (4) So we should institute a draft. [at least two hidden assumptions] D. (1) Nobody has ever seen a dinosaur, so (3) dinosaurs don’t exist. E. (1) We should reduce the penalty for drunken driving, as (2) a milder penalty would mean more convictions. (3) The only way to reduce the penalty is to elect more liberal judges and prosecutors, so (4) we should elect liberal judges and prosecutors. F. (1) Never again should we bow to tyrants, because (2) tyranny has been the mark of rule throughout human history, (3) as has cruelty and abject want. It follows that (4) we must rebel against the Imperial rule of England. G. (1) Only real marriages should be recognized by the state, so (2) polygamist marriages shouldn't be recognized by the state. (3) Any marriage not recognized by the state should be illegal. So (4) polygamist marriages should be illegal. (5) Another reason they should be illegal is that, polygamist marriages often result in abusive situations. [the hidden assumption is between 1 and 2] H. (1) No one believes in Odin anymore, so (2) why should anyone believe in God? [this is a rhetorical question, which is a claim that is disguised as a question. The claim appears to be "no one should believe in God”]. (3) If no one should rationally believe in something, then we should actively fight against belief in it. It follows that (4) we should actively fight against belied in the existence of God. (5) A world without believers would be a better world to live in. [the hidden assumption is between 1 and 2] I. (1) We can't let terrorists live here with us in Pakistan, so (2) we should expel all Christians from our country. (3) Christians also don't contribute to the economy and (4) could potentially be spies for the Americans. [Where's the most blatant hidden assumption? There are more than one, but one in particular is relatively clearly a missing assumption of the argument]  Exercise 3.E. 8 : Identifying Types of Objections Identify which type of objection is illustrated: an objection to a premise or an objection to an inference (including pointing out that there’s a hidden premise and/or rejecting a hidden premise)? A. I agree with your conclusion, but it doesn’t follow from your assumptions. B. Interesting argument, but what I don’t understand is your claim that every case of tyranny is a case of injustice. That doesn’t seem quite right. C. You claim that there isn’t a threat to the Amazon. On the contrary, there are countless threats, one of which is people claiming that there isn’t a threat to the Amazon! D. So if I accept all of your assumptions, it doesn’t seem to me that I must accept your conclusion. 3.E.4 https://human.libretexts.org/@go/page/223821  E. If I have it right, it seems to me that your inference rests on a hidden assumption that we ought to do whatever is in our national interest. That’s not clearly true. Think about cases of humanitarian aid that only very indirectly if at all are in our national interest. F. I think I understand the general thrust of this argument, but one claim makes me uncomfortable. Your inference rests on the claim, as you stated it, that Great Britain is to blame for more historical atrocities than any other European nation. That’s not clearly right. G. I don’t think this is a good argument. We won’t clearly advance well beyond where we are today in terms of computing power because of the physical limits of the hardware we have available.  Exercise 3.E. 9 : Mapping Ojections Identify which kind of objection is illustrated and then map the objection along with the original argument. A. Person A: (1) Edward Snowden released petabytes of classified data. (2) He should be convicted of treason. Person B: Wait a minute! (3) We shouldn’t just convict anyone who releases that much data of treason! Person A: (4) If we don’t, then we’ll be opening the door to more dangerous leaks. Person B: (5) Actually, come to think of it, I don’t think he did release petabytes. I think it was only Terabytes. B. The Republicans have argued repeatedly that (1) the Affordable Care Act is in a death spiral. Because, they say, (2) premiums are getting higher, and (3) as premiums get higher, the people will stop purchasing policies and (4) if the people stop purchasing policies, then the insurance companies will pull out of the exchanges, and (5) if that happens, then the whole system collapses. But their conclusion doesn't follow, since (6) people need health insurance and won't stop purchasing it if prices continue to rise incrementally. C. Person A: (1) College isn't designed around the goal of producing good plumbers and electricians and welders. (2) Furthermore, college is expensive and (3) college is time-consuming. So (4) we shouldn't expect everyone to go to college. Person B: I understand your inference, but (5) college does make one a better plumber, electrician, and welder because it gives you a host of intellectual resources to bring to bear on solving the many unforeseen problems that arise on jobs like that. Person C: I actually take issue with the inference here from your first claim to your conclusion, since (6) college isn't about job training, but is instead about creating a well-informed citizenry that can make rational and informed decisions at the voting booth. D. Obama argued that (1) we should pass the ACA, claiming that (2) there is an epidemic of chronically-ill citizens without health insurance due to their pre-existing conditions and that (3) many citizens simply can’t afford health insurance. But (4) the ACA won’t provide health insurance to a large group of relatively poor Americans. E. Her argument was as follows: “(1) No one wants to be put in the position where they are faced with a deadly intruder without the proper means to protect theirself and their family. (2) Gun laws make it probable that someone will end up in that situation. (3) Therefore, we can’t enact gun control legislation.” But that argument isn’t convincing. (4) Even if we accept the premises, we need not accept the conclusion. After all, there are reasons to pass gun control that must be addressed.  Exercise 3.E. 10 : Hidden Assumptions and Objections Identify the hidden assumptions in the first argument and then map both the argument and the objections. Remember that objections to hidden assumptions are objections to inferences and so they should be mapped as such. A. Frank: (1) We'll never make it to the party on time, so (2) let's just turn around and head home. (3) Samir and Imani live miles away and (4) we can't go very fast in this traffic. Margaret: That's ridiculous, we'll absolutely make it on time. First, (5) we have 30 minutes to get there and also (6) we could be 15 minutes late and still be "on time" since it's a party. 3.E.5 https://human.libretexts.org/@go/page/223821  B. Tamil: (1) We need to protect the environment, since (2) biodiversity is necessary to protect future food sources and (3) biodiversity is sustainable only in a relatively healthy global environment. Furthermore, (4) we take great pleasure in the natural wonders that the Earth has to offer (5) [suppressed premise] Jamal: (6) I agree with your conclusion, but even if we accept that biodiversity is necessary and that protecting the environment is necessary for protecting biodiversity, we need not accept your conclusion. C. (1) Counting Crows wrote and performed Mrs. Robinson, so (2) They’re the best band ever. Ummm... (3) they wrote and performed “Mr. Jones”, not Mrs. Robinson. And either way (4) neither song would make them the best band ever. D. He said “(1) I need some space, so (2) we need to break up.” But (3) he doesn’t need space. And either way, (4) needing space isn’t a good enough reason to break up with someone. E. She said “(1) Potato chips are high in saturated fat and salt, and so (2) they should be consumed very sparingly.” But that’s a bad inference since (3) dietary research is overturning the idea that saturated fat is bad for humans and (4) humans need salt to maintain proper blood volume and electrolyte concentrations. F. Pablo: (1) We shouldn’t eat even fake animal meat since (2) we wouldn’t think it’s okay to eat fake human meat. Afterall, (3) eating fake human meat would be tacitly affirming that cannibalism is morally acceptable. Marisela: I disagree, (4) there’s a faulty hidden premise there: that eating fake animal meat is analogous to eating fake human meat. Furthermore, (5) the other inference for the claim that eating fake human Meat is wrong has a hidden assumption as well and I’m not so sure it’s correct. This page titled 3.E: Chapter Three (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 3.E.6 https://human.libretexts.org/@go/page/223821