# Portfolio Project. Phil 251A Logic Fall Due: Friday, December 7

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2 2. Your representation of the argument. 3. Justification of your representation of the argument. 4. Evaluation of the argument. How you do each of these will change depending on which entry you are working on. The examples below should make clear what is expected. If you have any questions, please ask! 3 Deductive Arguments In this category you must find arguments that are plausibly represented as deductively valid arguments. However, authors rarely give arguments that are explicitly deductively valid. Often they will leave key premises implicit. For example: If we don t reform the way that money is allocated to student organizations, student government will soon run out of money and not be able to fund any organizations. So, there must be reform. This argument is not valid as stated. But it is plausible that the author intends the argument to be represented as something like the following, even though premises 3 and 4 are not explicitly stated: 1. If we don t reform the way that money is allocated to student organizations, student government will run out of money. 2. If student government will run out of money, then it will not be able to fund any organizations. 3. Failing to funding any organization is a bad thing. 4. If A implies B and B is bad, then we shouldn t do A. 5. Thus, we should not not reform the way that money is allocated to student organizations. The process of representing a real-life argument as deductively valid is deceptively difficult. There is a trade-off between writing down the author s explicit statements and rendering the argument so that it is valid. Your task is to find two arguments with which you can do this. What follows is an example of an entry in this category. 2

3 3.1 Deductive Example: Gould s Rocks of Ages Excerpt: Representation of the Argument: 1. If science and religion battle for the same turf, then Darwin would have become hostile and dismissive toward religion and cynical about life. 2. It is not the case that Darwin became dismissive toward religion and cynical about life. 3. Thus, science and religion do not battle for the same turf. 3

4 Formal Representation: B = Science and religion battle for the same turf. H = Darwin is hostile toward religion. C = Darwin is cynical about life. 1. B (H & C) 2. (H & C) 3. B Justification of Representation: Gould explicitly states premises 1 and 2. The overall context of the chapter where this is drawn from makes it clear that Gould s conclusion is what is represented in 3. This chapter of the book is where Gould is concerned to argue for his Non-Overlapping Magesteria Thesis (NOMA), which states that science and religion do not conflict with each other because they are concerned with different things. Evaluation of Argument: This argument is deductively valid. To show this, I have included the following proof: Though the argument is valid, I would argue that it is not sound. Premise 2 seems acceptable. Darwin did not become cynical about life, and he was certainly not overly hostile toward religion. However, premise 1 appears to be false. It is a conditional premise, so it can be shown to be false if we can argue that B could be true while (H & C) is false. So, suppose that science and religion really do conflict. It could be that Darwin was simply ignorant of this fact and so acted as if they did not conflict. In that case, 1 would be false. But even this objection assumes that if science and religion conflict and Darwin knew about that conflict, then he would be compelled to become hostile toward religion and cynical about life. But this doesn t seem right either. There are many things that conflict, and yet there need not be hostility between these things. For example, Republican views often conflict with Democratic views. This entails a disagreement, but it need not entail hostility. 4

5 4 Argument from Analogy and Inference to the Best Explanation In these categories you must find (i) an argument that is an argument from analogy, and (ii) an argument that is an inference to the best explanation (IBE). Unlike deductively valid arguments, these kinds of arguments are not offered with the intention that the premises guarantee the truth of the conclusion. Rather, the premises are intended to make the conclusion likely. In our unit on inductive logic we will learn more about both arguments from analogy and inference to the best explanation. One thing to notice is that, unlike the deductively valid arguments, when you present your argument from analogy or your IBE, you do not need to formalize the argument into logical notation. Each argument must still be put into a standard form (which we will learn about in class), but that form does not involve logical symbols. What follows is an entry that is an argument from analogy. Since the IBE entry will look very similar (but with a different form of argument), I do not include an example. 4.1 Analogy Example: A. J. Ayer: Knowledge of Other Minds Excerpt: Suppose someone tells me that he has had a tooth extracted without an anesthetic, and I express my sympathy, and suppose I am then asked, How did you know it hurt him? I might reasonably reply, Well, I know that it would hurt me. I have been to the dentist and know how painful it is to have a toothache stopped without an anesthetic, let alone taken out. And he has the same sort of nervous systems as I have. I infer, therefore, that in these conditions he felt considerable pain, just as I should myself. 1 Representation of the Argument: 1. I am similar to other humans in that we have the same nervous systems. 2. It is true of me that having a tooth extracted without anesthetic would cause me tremendous pain. 3. Thus, having a tooth extracted without anesthetic causes other people tremendous pain. Justification of Representation: In this section of the paper Ayer is responding someone who wonders how we can know that other people feel pain. This is the purpose of the rhetorical question at the beginning of the excerpt. The last sentence makes it clear that 1 Ayer, A. J. One s Knowledge of Other Minds. Theoria XIX (1953):

6 Ayer thinks that he can establish this via some kind of argument that others would feel pain if they were to have a tooth removed without anesthetic. He also hints that it is the similarity between himself and other people that allows him to make the argument. This suggests that an argument from analogy is being given. The representation above is the standard form for analogical arguments. Ayer explicitly states premise 1 in the penultimate sentence. Just above this, Ayer asserts something close to premise 2: that having a tooth removed without anesthetic would cause him tremendous pain. Evaluation of Argument: Arguments from analogy are evaluated based on the strength of the analogy. Ayer only mentions one way in which he is similar to other people: a shared type of nervous system. One might think, then, that the analogy is weak. However, the strength of an analogy is not determined by the number of ways in which the things being compared are similar. Rather, what matters is whether or not the similarities are relevant to the target property. In this case the target property is the feeling of pain in a certain circumstance. One kind of relevance is causal relevance. The nervous system is plausibly a key cause of the feeling of pain, thus it appears that the nervous system is causally relevant to the target property. Thus, it appears that this is a strong analogy. Despite this, more could be done to strengthen the analogy. In particular, Ayer does not say much about what it means to have the same sort of nervous system. On a very weak reading of this phrase, fish and bees and dogs all have the same sort of nervous system. On a stronger reading of this phrase, humans have the same sort of nervous system, but humans and dogs (for instance) do not. The argument is stronger if Ayer understands the same sort of nervous system in the stronger way. 5 Fallacy In this category you must find an argument that commits a fallacy. There are many different fallacies. Some deductively valid arguments commit fallacies. Sometimes a fallacy occurs because the argument appears to be deductively valid but is not. In our unit on fallacies we will learn more about how to identify such errors in reasoning. What follows is an example of an entry in this category. 5.1 Fallacy Example: Dobson s Argument Against Gay Marriage Excerpt: Why will gay marriage set the table for polygamy? Because there s no place to stop once that Rubicon has been crossed. Historically, the definition of marriage has rested on a foundation of tradition, legal precedent, theology, and an overwhelming support of the people. 6

7 After the introduction of marriage between homosexuals, however, it will be supported by nothing more substantial than the opinion of a single judge or by a black-robed panel of justices.... Given that unstable legal climate, it is certain that some self-possessed judge somewhere will soon rule that three men, or three women, can marry. Or five men and two women. Or four and four. Who will be able to deny them that right?... How about group marriage? Or marriage between daddies and little girls? Or marriage between a man and his donkey? 2 Representation of the Argument: 1. If gay marriage is made legal, then there will be an unstable legal climate. 2. If there is an unstable legal climate, then some judge will soon allow three men or three women to marry. 3. If three men or three women all allowed to marry, then five men and two women will be allowed to marry. 4. If five men and two women will be allowed to marry, then daddies will be able to marry little girls. 5. If daddies will be able to marry little girls, then a man will be able to marry his donkey. 6. Thus, if gay marriage is made legal, then a man will be able to marry his donkey. Formal Representation: 3 G = Gay marriage is made legal. U = There is an unstable legal climate. M = Three men are allowed to marry. W = Three women are allowed to marry. F = Five men and two women are allowed to marry. I = Daddies and little girls are allowed to marry. D = Men and donkeys are allowed to marry. 1. G U 2. U (M W ) 3. (M W ) F 4. F I 5. I D 3. G D 2 Quotation available at: 3 Note: a formal representation is not always needed for the fallacy entry. However, in this case, the argument is valid (see the Evaluation of Argument section), and so it is important to show that it is. 7

9 one of the premises is clearly false, so that the initial action will not lead to the alleged horrible result. With Dobson s argument, it seems plausible that this is the flaw. One could reasonably question premise 1, the claim that gay marriage will lead to an unstable legal climate. Of course, it will change the precedent that judges can appeal to, but this need not result in any instability. One might also reasonably argue that whatever instability results, it will not be enough to prompt polygamy to be legalized. But grant both of those premises. There seems to be a clear difference between allowing consenting adults to enter a marriage relationship and allowing an adult to enter a marriage with a minor. It is hard to imagine how the legal climate could be so unstable that no judge sees a relevant difference between marriage between adults and marriage between an adult and a minor. Given this, it seems that (if nothing else) premise 4 is clearly false. Thus, the argument is unsound. If the argument is simply a valid but unsound argument, why is it classified as a fallacy? It is classified as a fallacy because this kind of chain reaction, cause-and-effect reasoning can be very persuasive. The arguer proceeds by small steps from something that appears perhaps to be acceptable to something that is pretty clearly not acceptable. It is the seductive nature of such an argument that gets it classified as a fallacy. 6 Complex Argument The four types of entries above involve simple arguments, where there is one set of premises and one conclusion. But often the argument an author gives is complex. He or she may have a main argument, with several premises, but then sub-arguments supporting each of these premises. He or she may also have several distinct arguments for the same conclusion. In this category, you must find an argument that has a more complex structure like this. You will first provide a diagram of the argument to reveal its logical structure. Then, you will represent each of the sub-arguments as either a deductively valid argument or as one of the inductive argument forms we have learned about. Finally, you will evaluate each of these sub-arguments and provide an overall evaluation of the authors complex argument. What follows is an example of an entry in this category. 9

10 6.1 Complex Example: Bertrand Russell on Sense Data Excerpt: 10

11 11

12 Diagram of Argument: This is a graphical representation of what I take Russell s argument to be. The translation guide is included below. Claims that are in ovals are claims that Russell explicitly makes. Claims that are in boxes are unstated or suppressed premises. An arrow from an oval or a box to another oval indicates that the oval/box from which the arrow originates is providing a reason for the oval to which the arrow is pointing. If several arrows join up to point into one oval, this indicates that the several claims are working together to provide a reason for the conclusion. In this diagram, Russell s main conclusion is U. The argument for that consists of three explicit premises, and two suppressed premises. However, there is also a sub-argument that Russell offers on behalf of M, which operates as a premise in the main argument. Since there are two arrows in this diagram, that means that there are two arguments to analyze. Each arrow represents an argument. In the section below I have represented both of these arguments, and then formalized them into logical notation. 12

13 Representation of the Argument: 1. If you change your point of view, then you change the way that light is reflected to you. (... any change in the point of view makes some change in the way the light is reflected. ) 2. If you change the way that light is reflected to you, then you change the color the table appears to be. (... the parts that reflect the light look much brighter than the other parts. ) 3. There are many points of view. (... no two can see it from exactly the same point of view... ) 4. If there are many points of view, and if when you change your point of view you change the color the table appears to be, then the table has many colors that it appears to be. [suppressed premise] 5. Thus, the table has many colors that it appears to be. (... no two of them will see exactly the the same distribution of colors... ) 5. The table has many colors that it appears to be. 6. If the table has many colors that it appears to be, then each apparent color has an equal claim to being real. (... the other colors which appear under other conditions have just as good a right to be considered real... ) 7. If each apparent color has an equal claim to being real, then if one color is chosen as the color of the table, then this is favoritism. [suppressed premise] 8. We should avoid favoritism. (... therefore, to avoid favoritism... ) 9. If we should avoid favoritism, then favoritism is false. [suppressed premise] 10. Thus, no color is the color of the table. (... we are compelled to deny that, in itself, the table has any one particular color. ) Formal Representation: P = You change your point of view. L = You change the way light is reflected to you. T = You change the color the table appears to be. V = There are many points of view. M = There are many colors the table appears to be. 13

14 1. P L 2. L T 3. V 4. (V & (P T )) M 5. M R = Each apparent color has an equal claim to being real. U = One color is the color of the table. A = We should avoid favoritism. F = Favoritism is true. 5. M 6. M R 7. R (U F ) 8. A 9. A F 10. U Justification of Representation: It is clear that Russell s main conclusion is that it is false that the table has, in itself, any one color. This is the conclusion of my representation. I think it is also clear that Russell proceeds in two steps. First he attempts to convince us that the table appears different to different people. And from this he attempts to argue that the table therefore has no particular color. My representation makes clear this two-step process. As for individual premises, I have included the direct quotes from which I drew the premises. Often the premises I attribute to Russell do not match perfectly with what he has said. However, I believe that my representation of the premises captures Russell s meaning. For example, near the beginning of the excerpt Russell writes:... any change in the point of view makes some change in the way the light is reflected. I have represented this as: If you change your point of view, then you change the way that light is reflected to you. The representation says that if you are to change your point of view, then this will bring about a corresponding change in how light is reflected to you. This seems to capture what Russell is saying when he says that any change in point of view will bring about a change in the reflected light. I have three times attributed to Russell suppressed premises which he does not explicitly state (premise 4, premise 7, premise 9). I think that Russell would agree with each of these. Consider premise 4. It says: If there are many points of view, and if when you change your point of view you change the color the table appears to be, then the table has many colors that it appears to be. The idea here is that if there are many ways to view the table, and each one makes the table appear differently, then there are many ways the table appears to be. This seems to be Russell s line of thought. Consider premise 7. It says: If each apparent color has an equal claim to being real, then if one color is chosen as the color of the table, then this is favoritism. This seems to be just what Russell 14

15 is thinking when he admonishes us to avoid favoritism. If choosing one color as the color, even though the table appears many ways were not favoritism, then Russell s admonishment to avoid favoritism would make no sense. Finally, consider premise 9. It says: If we should avoid favoritism, then favoritism is false. This premise must be there for the argument to be valid. For choosing one color as the color of the table implies that favoritism is true (e.g., that some color is special), not that we should maintain favoritism. So, the claim that we should not maintain favoritism only helps Russell s argument if the fact that we should not maintain favoritism shows that favoritism is false. The idea seems to be that if a certain view should be avoided, then that is because that view is false. Evaluation of Argument: Each argument Russell gives is deductively valid. included two proofs: To show this, I have 15

16 Though both arguments are valid, I think that an objection can be raised against premise 9. One must always be careful arguing against a suppressed premise. Since a suppressed premise is not actually stated, the author can always maintain that he or she does not hold the premise that you are critiquing. However, in this case, I have already argued that premise 9 is essential to Russell s argument. Nevertheless, it appears to be false. Whether or not we should play favorites in choosing what color is the color of the table may come down to practical constraints. Since the table looks differently to each of us, and since we cannot see how it looks to each other, there will be no practical way of settling the question of what the color is. Such a dispute will never be resolved. Perhaps for this practical reason, we shouldn t pick out one color as the color: we ll just never agree, so it is pointless to make a decision. But that does not imply that there is not some one color that the table really has. The difficulty in knowing what the color of the table is, does not show that the table does not nevertheless have some one particular color. If that s true, then premise 9 is false, and Russell fails to establish his main conclusion. For all I ve said, however, the first sub-argument is still successful. 7 Assessment of Your Portfolio Hopefully these examples give you a good idea of what I expect from your portfolios. I will assess your portfolio by asking myself the following questions: Does each excerpt have a clear citation and does it contain an argument? Have you represented the author s argument with numbered premises and a conclusion and is it plausible that the argument you have stated is the argument the author is giving? If the argument is a deductively valid argument, have you translated it into logical form and proved it to be valid? If the argument is an argument from analogy or an IBE, have you put it into standard form? If the argument commits a fallacy have you clearly explained which fallacy it commits and why it commits this fallacy? If the argument is a complex argument, have you diagrammed the argument and have you analyzed each arrow of the diagram? Have you thoughtfully evaluated the arguments you have chosen? This requires you to both consider the strength of the inference and the truth of the premises. Have I learned something about the argument from reading your entry? Based on answers to these questions, I assign each entry a number: 16

17 4: Wow! This is outstanding! 3: Great work. 2: Average, adequate, okay. 1: Seriously flawed. 0: Missing. 8 Tips 1. You do not need to use entire articles as your excerpts. Authors often make many different arguments throughout their writing. It is acceptable to focus on a small part of an article for evaluation. 2. A frequent, serious mistake occurs when you present the argument by simply numbering many of the sentences from the source and then writing what you think is the conclusion. You need to think through the entire argument that is being given, consider whether they may be suppressed premises, and then present the clearest version that gets at the heart of the structure of the argument being made. Listing every sentence of an article as part of the argument is not a good way to understand an author s argument. 3. Another serious error occurs when you formalize an argument that is an argument from analogy or inference to the best explanation and then try to prove it to be valid. These arguments are intended to be inductively strong and so cannot be proven valid. 4. Do not forget to prove that your deductively valid arguments are valid. 5. When you are evaluating your fallacy entry, be sure to show some sensitivity to the subtlety in diagnosing a fallacy. For example, it is not the case that every argument that produces an emotional reaction is a fallacious appeal to pity. 6. It is always important that you explain why your representation of the argument you have chosen is a good representation of the author s argument. 7. I prefer to read typed material. Torn edges are a sign of sloppiness. Pages that are all the same size are a sign that you have put time into this project. Note: This assignment is loosely based on T.A. Gracyk, Critical Thinking Portfolio Newsletter of Teaching, The American Philosophical Association, Fall, 1991: Last updated: July 10,

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