Notes on Logical Arguments

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1 Notes on Logical Arguments CSci 1001 January 19, Introduction Logic can mean different things to computer scientists. For example, computer architects often deal with bit-level logic. A specific example of this is doing logical operations like AND and OR on a bit-by-bit basis to two bytes of data. Computer programmers must deal with program logic such as the different branches a program can take depending on the conditions in the program. Theoretical computer scientists must prove results using logically rigourous arguments. The resulting proofs are often quite similar to the types of proofs you may have seen in a math class. Finally, computer scientists, and all people, use logic when using natural language to communicate. It s this last type of logic that we ll look at in this note. One (of the many) ways we judge if information is reliable is whether the information presented is logically convincing. There are different ways that an argument can fail to be convincing. One problem occurs if the facts used as a basis for the argument are incorrect. For example, the claim Since the Internet was invented in France, countries other than the U.S. should have a larger role in Internet governance is not very convincing. The reason for this is that the premise the Internet was invented in France is not true (French researchers contributed to the creation of the Internet, but the bulk of the work was done in the United States). So even if you believe that countries other than the U.S. should have a larger role in Internet governance you would not find the given argument convincing because the premise is false. Another way arguments can fail to be convincing is when the premises and conclusion are all true, but the line of reasoning to get from the premises to the conclusion is not rigorous. For example, support someone says The CSci 1001 lab room is in the EE/CSci Building. Room is a computer lab in the EE/CSci Building. Therefore the CSci 1001 lab is in EE/CSci Each of the three statements here is true, but you can t logically conclude the third from the first two for example, replace with Then you have the same argument, with the first two statements being true, but the conclusion being false. Still another type of problem can occur when people draw invalid conclusions from correct facts. For example, the argument In 1997 a computer beat the world chess 1

2 champion; therefore computers are smarter than humans. is invalid. The first statement, In 1997 a computer beat the world chess champion, is indeed correct. However, the conclusion, computers are smarter than humans, does not follow logically from this since smartness means more than one party defeating another in a single chess match. Logicians have identified a number of fallacies that commonly occur and result in invalid arguments. It is important to remember that an invalid argument does not necessarily mean the premises or conclusion are untrue it just means that the argument for going from the premises to the conclusion does not follow logically in some way. In the remainder of this note we ll look at some of the many logical fallacies, as well as a few biases that often appear in arguments. 2 Ad hominem fallacy An ad hominem argument attacks a person or organization making an claim rather than examining the claim itself. The general form is A says X. A is not reputable. Therefore X is not true. For example, consider the argument Microsoft says Vista is the best operating system. However, Microsoft is a company that has been accused of some questionable business practices. Therefore Vista is not a good operating system. Notice that the argument here is invalid; it tries to imply that Microsoft is not reputable rather than analyzing the merits and/or shortcomings of Vista. Remember again that the argument being invalid does not imply the conclusion is true; neither does it imply it is false. Vista may or may not be a good operating system the point here is that the argument being made isn t made in such a way that we can use it to determine whether Vista is a good operating system. 3 Appeal to authority fallacy An appeal to authority argument claims that because an authoritative person or organization says something, it must be true. While it is true that people or organizations often have special expertise that makes their claims more likely to be true, the appeal to authority fallacy takes the claims at face value without any further scrutiny. For example, the argument The NFL (National Football League) claims that any reuse of a football telecast is illegal, unless it is authorized by the NFL. Therefore any non-authorized Internet posting of any part of a NFL football telecast is illegal. is an appeal to authority based on the expertise of the NFL. However, is the claim really correct? For example, what do the relevant copyright laws say? Is it possible that there are some reuses of football telecasts that wouldn t violate copyright laws? 2

3 4 Appeal to the people fallacy An appeal to the people argument claims that because everyone (or the majority, or at least a significant number) believes something, then that something is true. Notice the connection of this argument to the ethical system of cultural relativism. A common type of argument based on this fallacy is the everyone s doing it or many people are doing it argument; for example: Because many people download copyrighted music for free, it s legal for me to do it. 5 Begging the question Begging the question occurs when an argument s premise contains the desired conclusion. For example: Microsoft s Windows operating system is more popular than Linux is. Therefore more PCs have been sold with Windows on them than with Linux. 6 Confirmation bias Confirmation bias is tendency to be seek and interpret information so as to confirm what one already believes. For example, if I am a partisan member of political party A, then positive information about parts A s members or actions might more easily catch my eye, but I might be less likely to read or believe negative information. 7 Eyewitness fallacy The fallacy of believing that eyewitnesses are always 100% accurate in the recall of events. There are be a number of reasons why eyewitnesses may not be totally accurate. These include a biased viewpoint, a faulty memory, and an imperfect understanding of what transpired. 8 False cause fallacy The false cause fallacy is the contention that because one event preceded a second event, it caused the second event. As an example, take the argument World War II required massive computations, for example, for ballistics. The first computers appeared shortly after World War II. Therefore World War II was the cause of the first computers. While the computational requirements of World War II were certainly a factor in the rise of computers, this argument neglects the many other contributing factors, such as pre-wwii office machinery. Additional note: the example in the above paragraph is also an example of the single cause fallacy, the fallacy that events have only one cause. There are a number of fallacies, 3

4 some of which can overlap at times. The ones listed here not only give you an idea of some of the types of fallacies, but are the more important ones for this class. 9 Hindsight bias Hindsight bias is the tendency to overestimate what we knew in the past, or what could have been foreseen. For example, as we ll see in class, computer representation of numbers is done using the binary number system. We take the advantages of this for granted nowadays, to the point where it s easy to assume that using binary numbers must have been an obvious choice in early computers. It wasn t. Hindsight bias is one reason why doing a consequentialist ethical analysis of past events can be difficult: since we often know some of the consequences, we assume that the people involved in making the decision either knew of the consequences, or could have easily foreseen them. 10 Many-any fallacy The many-any fallacy is the fallacy that because many items in a group have a certain characteristic, all items in that group do. As an example of this, consider the argument Many Apple products have been major successes in terms of their impact on popular culture. The Newton personal digital assistant was an Apple product. Therefore the Newton had a major impact on popular culture. 11 Nirvana fallacy The Nirvana fallacy is the contention that a solution must be perfect in order to be useful. One common example of this relates to Internet regulation: the argument goes that because the Internet is decentralized, crosses international boundaries, etc. it is impossible for any Internet regulations to be 100% effective, and therefore the Internet should not be regulated. This disregards the fact that even if a regulation is not 100% effective, it may nonetheless promote desired behavior and reduce unwanted behavior. 12 Slippery slope fallacy A slippery slope argument is the contention that if one event is allowed it will inevitably lead to a larger undesirable event. This type of argument can be fallacious if the consequent event is taken as inevitable without any further justification. For example, If we allow the government to regulate the Internet, then the government will start collecting all sorts of data from the Internet, and then the government will use this data in all sorts of ways that will undermine people s privacy. There may (or may not) be reasons to 4

5 limit Internet regulation, and having more Internet regulation may (or may not) lead to a decrease in privacy. But the argument here that more Internet regulation will inevitably lead to a major loss of privacy is not valid it does not establish why more Internet regulation will necessarily lead to a loss of privacy. 13 Virtuality fallacy The virtuality fallacy claims that because something happens in virtual space (e.g., on a computer or on a communication network) it is not real. For example, some malicious hackers will claim that because they are not physically trepassing when they hack into a computer system, their actions are acceptable and no harm is done. The virtuality argument fails to take into account that cyberspace costs are real (so, for example, even if a hacker did not steal or damage any information in a computer system, but only viewed it, there are still costs, for example to the system administrator who must investigate whether the hacker did any harm). Moreover, actions in cyberspace can have very real effects on people. For example, slander in cyberspace can be as hurtful to people as slander in speech or hardcopy written communications. 5

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