Fluent Essays

read the article attached ask one question about the attached article must be at least 200 words include 1 reference  must be written in apa 7th edition form include in-text citations A Brief Guide to Logic and Argumentation When a philosopher tackles a question, her aim is not just to answer it. Her aim is to provide an argument for her answer and so to present her audience with reasons for believing what she believes. When you read a philosophical text, your main job is to identify and assess the author’s arguments. When you write a philosophy paper, your main job is to offer arguments of your own. And because philosophy is an especially reflective discipline—every question about philosophy is a philosophical question—philosophers have turned their attention to this phenomenon. What is an argument? What is a good argument? How can we tell whether an argument is a good one? The aim of this brief guide is to introduce some of the tools that philosophers have developed for answering these questions. But be warned: some of what follows is controversial, and many of the most important questions in this area remain wide open. It may be unsettling to discover that even at this elementary stage, philosophy raises questions that centuries of reflection have not resolved. But that is the nature of the subject, and you might as well get used to it. 1. WHAT IS AN ARGUMENT? An argument is a sequence of statements. The last claim in the sequence is the conclusion. This is the claim that the argument seeks to establish or support. An argument will usually include one or more premises: statements that are simply asserted without proof in the context of the present argument but which may be supported by arguments given elsewhere. Consider, for example, the following argument for the existence of God: ARGUMENT A 1. The Bible says that God exists. 2. Whatever the Bible says is true. 3. Therefore, God exists. Here the premises are (1) and (2), and statement (3) is the conclusion. Now, anyone who propounds this argument will probably realize that his prem ises are controversial, so he may seek to defend them by independent arguments. In defense of (2) he may argue: ARGUMENT B 4. The Bible has predicted many historical events that have come to pass. 5. Therefore, whatever the Bible says is true. These two arguments may be combined: ARGUMENT C 6. The Bible has predicted many historical events that have come to pass. 7. Therefore, whatever the Bible says is true. 8. The Bible says that God exists. 9. Therefore, God exists. Here the premises are (6) and (8). Statement (7) is now an intermediate conclusion, supported by premise (6), and the conclusion of the argument as a whole is (9), which is in turn supported by (7) and (8). It can be useful to make all of this explicit by writing the argument out as follows: ARGUMENT C, annotated 10. The Bible has predicted many historical events that have come to pass. · [premise] 11. Therefore, whatever the Bible says is true. · [from (6)] 12. The Bible says that God exists. · [premise] 13. Therefore, God exists. · [from (7), (8)] 14. when you are reading a philosophical text with an eye toward identifying the author’s argument, it is extraordinarily important (and often quite difficult) to distinguish the author’s premises—the propositions she takes for granted as a starting point—from her conclusions. Why is this important? If a statement is meant as a conclusion, then it is fair to criticize the author if she has failed to give a reason for accepting it. If, however, a statement is a premise, then this sort 15. f criticism would not be fair. Every argument must start somewhere. So you should not object to an argument simply on the ground that the author has not proved her premises. Of course, you can object in other ways. As we will see, it is perfectly fair to reject an argument when its premises are false, implausible, 16. r defective in some other way. The point is rather simply this: since every argu- ment must have premises, it is not a flaw in an argument that the author has not argued for her premises. · All of this is trivial when the arguments are simple and neatly packaged. But Rules of thumb: If a sentence begins with “hence” or “therefore” or “so,” that is a clue that it functions as a conclusion. If a sentence begins with “Let us assume that . . .” or “It seems perfectly obvious that . . .” or “Only a fool would deny that . . . ,” this is a clue that it functions as a premise. Exercise: Consider the following passage. What are the premises? What is the main conclusion? Everyone knows that people are usually responsible for what they do. But you’re only responsible for an action if your choice to perform it was a free choice, and a choice is only free if it was not determined in advance. So we must have free will, and that means that some of our choices are not determined in advance. 2. VALIDITY An argument is valid if and only if it is absolutely impossible for its premises to be true and its conclusion false. In our examples, argument a is clearly valid. If the premises are true—if the Bible is infallible, and if the Bible says that God exists—then God must certainly exist. There is no possible situation—no possible world—in which the premises of the argument are true and the conclusion false. Argument b, by contrast, is clearly invalid. It is easy to imagine a circumstance in which the Bible makes many correct predictions about historical events while remaining fallible on other matters. When an argument is valid, we say that the premises entail or imply the conclusion, or, equivalently, that the conclusion follows from the premises. This concept of validity is a technical one, and some of its applications may strike you as odd. Consider: ARGUMENT D All philosophers are criminals. All criminals are short. Therefore, all philosophers are short. ARGUMENT E God exists. Therefore, God exists. ARGUMENT F The moon is green. The moon is not green. Therefore, God exists. It is easy to see that argument d is valid. The premises are false, but that is ir relevant. They could have been true, and any possible circumstance in which they are true is one in which the conclusion is also true. Argument e is also valid. Since the premise and the conclusion are identical, it is clearly impossible for the one to be true and the other false. To see that argument f is valid, note that it is obviously impossible for its premises to be true together—the moon cannot be both green and not green! But this means that it is impossible for the premises to be true and the conclusion false, and that is exactly our definition of validity. As the examples show, a valid argument can be a lousy argument. Still, validity is an important property of arguments. Some disciplines—notably, mathematics— insist on valid arguments at every stage. In these areas, a good argument must be a proof, and a proof is a valid argument from premises known to be true. Philoso phy, like most disciplines, does not insist on proof. Yet philosophers often aspire to produce valid arguments for their conclusions, and there is a good reason for this. Begin by noting that it is always possible to turn an invalid argument, or an argument whose validity is uncertain, into a valid argument by adding premises. Suppose a philosopher offers the following argument: ARGUMENT G I can imagine existing without my body. (I can imagine my feet slowly and painlessly disappearing, then my knees, then my legs. . . . As my body disap pears, I lose all sensation. As my head disappears, everything goes black and silent because my eyes and ears have disappeared, but still I’m thinking about these strange events, and because I’m thinking, I must exist.) Therefore, I am not my body. It may be hard to say whether this is a valid argument, but we can easily turn it into an argument whose validity is beyond dispute: ARGUMENT H I can imagine existing without my body. If I can imagine X existing without Y, then X is not Y. Therefore, I am not my body. A philosopher who offers argument g as a proof that human beings are not identical to their bodies probably has argument h in mind. She is probably tacitly assuming the premise that is missing in argument g but that h makes explicit. For philosophical purposes, it is often important to make these tacit assumptions explicit so that we can subject them to the bright light of scrutiny. When you reconstruct the argument implicit in a philosophical text, you should set yourself the task of producing a valid argument for the author’s conclusion from the author’s stated premises, supplying any missing premises that might be necessary for this purpose, so long as they are premises that the author might have accepted. If there are many ways to do this, you will find yourself with several competing interpretations of the argument. If there is only one sensible way of doing this (as with argument g), you will have identified the author’s tacit assumptions. This is often a valuable step in your effort to assess the argument. Exercise: Spot the valid argument(s):  (i) If abortion is permissible, infanticide is permissible. Infanticide is not permissible. Therefore, abortion is not permissible.  (ii) It is wrong to experiment on a human subject without consent. · X experimented on Mr. Z. · Z consented to this experiment. Therefore, it was not wrong for Dr. X to experiment on Mr. Z. iii. I will not survive my death. My body will survive my death. Therefore, I am not my body.   (iv) Geoffrey is a giraffe. If X is a giraffe, then X’s parents were giraffes. Therefore, all of Geoffrey’s ancestors were giraffes. Exercise: The following arguments are not valid as they stand. Supply missing premises to make them valid. (v) Every event has a cause. No event causes itself. Therefore, the universe has no beginning in time.  (vi) It is illegal to keep a tiger as a pet in New York City. Jones lives in New York City. Therefore, it would be wrong for Jones to keep a tiger as a pet. (vii) The sun has risen every day for the past 4 billion years. Therefore, the sun will rise tomorrow. Check your understanding. Some statements express necessary truths: truths that could not possibly have been false under any circumstances. The truths of pure mathematics are the best examples. There is no possible circumstance in which 2 + 3 ≠ 5, so “2 + 3 = 5” is a necessary truth. With this in mind, show that an ar gument whose conclusion is a necessary truth is automatically a valid argument. 3. SOUNDNESS A valid philosophical argument is a fine thing. But if the premises are false, it cannot be a good argument. Good arguments, after all, provide us with reasons for accepting their conclusions, and an argument with false premises cannot do that. Recall argument d: ARGUMENT D 1. All philosophers are criminals. 2. All criminals are short. 3. Therefore, all philosophers are short The argument is perfectly valid, but it obviously fails to establish its conclusion. This means that when you evaluate a philosophical argument, it is never enough to show that the author’s conclusions follow from her premises. You must also ask whether the premises are true. A valid argument with true premises is called a sound argument. Check your understanding: Use the definitions of soundness and validity to show that if an argument is sound, its conclusion must be true. 4. HOW TO RECONSTRUCT AN ARGUMENT: AN EXAMPLE One of the most important skills a philosopher can acquire is the ability to extract an explicit argument from a dense block of prose. There is no recipe for doing this: it is an art. Here we work through an example to illustrate one way of proceeding. Assignment: Identify and assess the argument in the following passage. We see that things which lack intelligence, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that not fortuitously, but designedly, do they achieve their end. Now whatever lacks intelligence cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence, as the arrow is shot to its mark by the archer. Therefore some intelligent beings exist by whom all natural things are directed to their end. (Thomas Aquinas, Summa Theologica, part I, question 2, article 3) Step 1: Identify the Conclusion When you seen an argument like this, your first job is to identify the main con clusion. Unsurprisingly, this will usually come at the end, though many writers will tell you at the start what the conclusion of the argument is going to be. (This is very helpful to the reader, and you should always do it in your own writing.) In this case, the main conclusion is helpfully marked by an explicit “therefore.” (Main conclusion) Some intelligent beings exist by whom all natural things are directed to their end. Step 2: Interpret the Conclusion Now that you have identified the conclusion, your next job is to understand it. This can be difficult, especially when the text is old and the language unfamiliar. What is it for a being to be intelligent? What is a natural thing? In this case, the most pressing issue is to understand what it means for a natural thing to be “directed towards an end.” As the context makes clear, a natural thing is anything that is not a person or an artifact—an animal or a plant, or perhaps a rock. What is it for such a thing to have an end? This is in fact a profound question, but to a first approximation, the end of a thing is its purpose or function. The end of the heart is to pump blood, the end of a worker bee is to supply food for the queen, and so on. The conclusion of the argument, reformulated in more familiar terms, is therefore this: (Main conclusion, reformulated) There is an intelligent being that ensures that natural objects perform their functions. This illustrates a general point: when you analyze an argument, you are not required to employ the author’s original words in every case. It is sometimes useful to sup ply more familiar words and grammatical constructions, provided they represent a plausible interpretation of the author’s meaning. In this case, we have replaced Aquinas’s talk of “ends” with talk of “functions.” Step 3: Reconstruct the Argument Your next job is to reconstruct the argument for the main conclusion. What are the premises from which Aquinas argues? You might think that the first sentence states a premise: “We see that things which lack intelligence . . . act for an end.” But as we read on, it becomes clear that this is, in fact, an intermediate conclusion. The first sentence, taken as a whole, is itself an argument. Unintelligent things always or nearly always act in the same way, so as to achieve the best result. [premise] Therefore, unintelligent things perform a function. This is an interesting argument, but the connection between the premise and the conclusion is obscure. As it stands, the argument is not clearly valid. But we can render it valid by interpolating an unstated premise: (1) Unintelligent things always or nearly always act in the same way, so as to achieve the best result. 2. If a thing always or nearly always acts in a certain way, so as to achieve the best result, then that thing performs a function. 3. Therefore, unintelligent things perform a function. This shows the value of making unstated premises fully explicit. The unstated premise (2) contains an important idea. The function of the heart is to pump blood. How do we know? Because hearts almost always pump blood, and this is a benefit to the organism as a whole. In general, when we see a natural thing acting in a way that provides a benefit, we infer that its function (or one of its functions) is to provide that benefit. The second premise makes this assumption explicit. When we turn to the next sentence, we have a puzzle. “Hence it is plain that not fortuitously, but designedly, do they achieve their end.” This sentence begins with “hence,” so we naturally assume that it is supposed to be a conclusion supported by what precedes it. If we pursue this interpretation, the argument will look like this: 1. Unintelligent things always or nearly always act in the same way, so as to achieve the best result. 2. If a thing always or nearly always acts in a certain way, so as to achieve the best result, then that thing performs a function. 3. Therefore, unintelligent things perform a function. Therefore, unintelligent things perform their functions by design (and not by accident). The puzzle is that nothing in the argument appears to support this new conclusion. Why shouldn’t natural beings perform their functions by accident rather than by design? Nothing in the text speaks to this question, and so it may be unclear whether Aquinas means this to be a new premise or an intermediate conclusion supported by what comes before. · Again, we can interpolate an unstated premise that will render the argument 4. valid. Aquinas apparently finds it obvious that if a thing has a function, it must have been designed to perform that function. If this is right, then the complete argument up to this point runs as follows: 5. Unintelligent things always or nearly always act in the same way, so as to achieve the best result. · [premise] 6. If a thing always or nearly always acts in a certain way, so as to achieve the best result, then that thing performs a function. · [premise] 7. Therefore, unintelligent things perform · [intermediate conclusion, · from (1) and (2)] 8. If a thing performs a function, it does so by design. · [implicit premise] 9. Therefore, unintelligent things perform their · [intermediate conclusion, · from (3) and (4)] 10. The remainder of the argument is now straightforward. The next sentence states another premise. · a function. · functions by design. [premise] [premise] [from (1) and (2)] [from ?] (6) If an unintelligent thing performs a function by design, then there exists an intelligent being that ensures that it performs this function. [premise] And from this, Aquinas moves directly to his main conclusion: (7) Therefore, there exists an intelligent being that ensures that natural objects perform their functions. [conclusion, from (5) and (6)] What just happened? We took a dense philosophical text and we turned it into an explicit argument. Along the way, we did our best to make the author’s unspoken premises explicit and to understand what they might mean. The result is a recon struction of the original argument. Step 4 We are now in a position to assess the argument as we have reconstructed it. We have two questions to ask: Is it valid, and are the premises true? Taking the second question first, we twenty-first-century philosophers will have doubts about premise (1)—Do most natural things really act so as to achieve the “best result”?—and also about premise (6). The heart of an animal performs a function. Must it have been designed by an intelligent being for that purpose? Certainly not; natural selection can do the job even if no intelligence is involved. So the premises of the argument are certainly open to question. But even if we waive this objection and suppose that the premises are true, there is a further problem. The conclusion (7) claims there is a single intelligent being that ensures that natural things perform their functions. But the premises only require that each natural thing be directed toward its end by some intelligent being or other. To see the difference, note that it is one thing to say that every clock has a designer and another to say that there is a single master-designer who is responsible for every clock. This means that we can accept Aquinas’s premises and much of his reasoning without accepting his main conclusion. Even if every natural thing was designed by an intelligent being, it does not follow that a single intelligent being designed them all. Verdict: Aquinas’s argument, as we have re constructed it, is not valid. This brings up a very important point. We have given a reasonably careful reconstruction of Aquinas’s argument, but despite our best efforts, the argument as we have reconstructed it is clearly bad. Now of course no one is perfect: good philosophers sometimes give bad arguments. But when you have produced a reconstruction of an argument by a good philosopher and the result is an argu ment that is clearly flawed, that is a sign that you may have misunderstood the original argument. The philosophers represented in this collection are all good philosophers, so you should approach their arguments with this in mind: Before you dismiss an argument on the basis of your reconstruction of it, you should be sure that your reconstruction is the most charitable interpretation you can find. A charitable reconstruction will present the argument in its best light. It may still involve mistakes, but they will not be gross and obvious mistakes. The most convincing way to object to a philosophical argument is to take the time to identify the best possible version of it, and then to show that this version of the argument is still no good. Exercise: Provide a reconstruction of Aquinas’s argument that does not commit the logical error mentioned above in the transition from (6) to (7). 5. FORMAL VALIDITY Consider: ARGUMENT I Every number is an abstract object. Abstract objects are not located in space. So numbers are not located in space. This is a concrete argument with a specific subject matter. It is about numbers, spatial location, and so on. But we can abstract from these specific features of the argument in order to focus on its form. One way to do this is to replace all of the subject-specific terms in the argument with schematic letters, leaving only the logical skeleton of the argument in place. In the case of argument h, this yields the following schematic argument. Every F is a G. Gs are not H. So Fs are not H. Once we have identified this schematic argument, it is easy to produce other arguments that exhibit the same form but concern an entirely unrelated subject matter. For example: ARGUMENT J Every whale is a mammal. Mammals do not lay eggs. So whales do not lay eggs. In this case, it is clear not just that our original argument is valid but that any argument generated from it in this way must be valid. (The second premise in argument j is false, as every platypus knows. But that does not prevent the argument from being valid. If that puzzles you, review the definition of validity.) When an argument is an instance of a scheme all of whose instances are valid, the argument is said to be formally valid. Note: An argument can be valid without being formally valid. Consider: ARGUMENT K Every crayon in the box is scarlet. So every crayon in the box is red. The underlying form of this argument is: Every F is G. So every F is H. And it is obvious that many arguments of this form will not be valid. (Exercise: Give an example.) Of course, we can make argument k formally valid by adding the premise, “If a thing is scarlet, then it is red.” As we have emphasized, this is always worth doing when you are analyzing a philosophical argument. And yet, the original argument is valid as it stands, since it is absolutely impossible for the premise to be true and the conclusion false. Formal logic is the study of formally valid arguments. It aims to catalog the vast array of formally valid arguments and to provide general principles for determining whether any given argument has this feature. Formal logic is an intricate, highly developed subject at the intersection of philosophy and mathematics, and it can be extraordinarily useful for the student of philosophy. Here we list some examples of formally valid arguments along with their traditional names. In what follows, the sche matic letters P, Q, and R stand for complete declarative sentences. For your amusement, we also include the standard symbolic representations of these forms of inference. Here “→” means “if . . . then”; “~” means “it is not the case that”; and “∨” means “or.” MODUS PONENS If P then Q P _________ Q MODUS TOLLENS If P then Q It is not the case that Q ___________________ It is not the case that P DISJUNCTIVE SYLLOGISM Either P or Q It is not the case that P ___________________ Q P → Q P _____ Q P → Q ∼Q _____ ∼P P ∨ Q ~P _____ Q HYPOTHETICAL SYLLOGISM If P then Q If Q then R _________ If P then R CONTRAPOSITION P → Q Q → R _____ P → R If P then Q ___________________________________________ If it is not the case that Q, then it is not the case that P P → Q _______ ∼Q → ~P All of this may seem obvious, but it can sometimes be quite tricky to determine whether an argument is formally valid. Consider: A person is responsible for a choice only if it is a free choice. Every human choice is either caused or uncaused. If a choice is caused, then it is caused either by prior events or by the agent himself. If a choice is caused by prior events, then it is not free. If a choice is uncaused, it is not free. So a choice is free only if it is caused by the agent himself. But no choice is caused by the agent himself. So there is no such thing as a free choice. So no one is ever responsible for his choices. Is this a valid argument? You could stare at it for a while, and you might find yourself persuaded one way or the other. Or you could take a logic class and learn enough formal logic to settle the matter conclusively once and for all. One of the great advantages of formal logic is that it permits us to prove that an argument of this sort is valid by breaking it down into steps, each of which is indisputably an instance of a valid form. 6. A PUZZLE ABOUT FORMAL LOGIC Apart from its utility as a tool, formal logic is a source of philosophical perplexity in its own right. Imagine a long row of colored squares on the wall in front of you. The left-most square (square 1) is bright red; the right-most square (square 1000) is bright yellow. The squares in between run from red on the left through orange in the middle to yellow on the right. But there are so many of them that they satisfy the following condition: (1) Square n and square n + 1 are indistinguishable by ordinary means. If you had a measuring device, you might discover that they differ slightly in color, but you can’t tell them apart just by looking, no matter how hard you try. (If you don’t think this is possible, get out your paint set and play around. It is easy to produce a sequence of colored patches running from red to yellow that satisfies this condition.) We now note what appears to be an obvious fact: (2) If two things are indistinguishable by ordinary means, then if one of them is red, so is the other. If someone shows you a red rose and tells you, “I’ve got another rose that’s indis tinguishable from this one, but it’s not red,” you would know immediately that he was lying. It’s built into our concept of red that if two objects look just alike to the naked eye in broad daylight, then either both are red or neither is. From these two premises, it follows by modus ponens that: (3) If square n is red, then so is square n + 1. But now we’re in trouble. For we can reason as follows: (4) Square 1 is red. (5) If square 1 is red, then square 2 is red. (6)  So square 2 is red. (7) If square 2 is red, then square 3 is red. (8) So square 3 is red. . . . (1002) So square 999 is red. (1003) If square 999 is red, then square 1000 is red. (1004) So square 1000 is red. But this is nuts. It was built into our description of the situation that square 1000 is not red; it is bright yellow! What’s gone wrong? If you look closely, you will see that this argument has only three premises. Two of them are stipulated as part of our description of the situation: square 1 is red, and adjacent squares are indistinguishable by ordinary means. The other premise is (2), the claim that there cannot be two indistinguishable things, one of which is red, the other not. The argument uses only one rule of inference: modus ponens. And this leaves us with only two responses to the paradox: either (2) is false and there is a sharp cutoff between red and “not red” somewhere in our [premise] [3] [4, 5, modus ponens] [3] [6, 7, modus ponens] 1000. 1001, modus ponens] [3] 1001. 1003, modus ponens] series or modus ponens is not a valid rule of inference after all. What is the best response? The problem is called the sorites paradox (pronounced saw-rye-tees), and it remains unsolved. 7. WHAT MAKES AN ARGUMENT GOOD? We have seen (see section 2 earlier) that valid arguments can be lousy arguments. The same goes for sound arguments. The question of God’s existence is the most important question in the philosophy of religion. But it is easy to produce a sound argument that settles it: ARGUMENTS L AND M L:  God exists. Therefore, God exists. M:  God does not exist. Therefore, God does not exist. These arguments are both formally valid, and one of them has true premises. That means that one of them is sound. But neither of these arguments is a contribution to philosophy, and neither could possibly provide a reason for believing its con clusion. Why not? The obvious answer is that these …