1.6: Footnotes

1. Psychologists have determined, for example, that most people are subject to what is called “confirmation bias”—a tendency to seek out information to confirm one’s pre-existing beliefs, and ignore contradictory evidence. There are lots of studies on this effect, including even brain-scans of people engaged in evaluating evidence. All of this is very interesting, but it’s psychology, not logic; it’s a mere descriptive study of reasoning. From a logical, prescriptive point of view, we simply say that people should try to avoid confirmation bias, because it can lead to bad reasoning. ↵
2. We distinguish propositions from the sentences that express them because a single proposition can be expressed by different sentences. ‘It’s raining’ and ‘Es regnet’ both express the proposition that it’s raining; one sentence does it in English, the other in German. Also, ‘John loves Mary’ and ‘Mary is loved by John’ both express the same proposition. ↵
3. Reasoning in the sense of drawing inferences from a set of statements is a special case of this persuasive activity. When we draw out reasonable conclusions from given information, we’re convincing ourselves that we have good reasons to believe them. ↵
4. I know, I know. But it’s almost certainly true. Consumer Reports conducted a study in 2015, in which they tested 458 pounds of ground beef, purchased from 103 different stores in 26 different cities; all of the 458 pounds were contaminated with fecal matter. This is because most commercial ground beef is produced at facilities that process thousands of animals, and do it very quickly. The quickness ensures that sometimes—rarely, but sometimes—a knife-cut goes astray and the gastrointestinal tract is nicked, releasing poop. It gets cleaned up, but again, things are moving fast, so they don’t quite get all the poop. Now you’ve got one carcass—again, out of hundreds or thousands—contaminated with feces. But they make ground beef in a huge vat, with meat from all those carcasses mixed together. So even one accident like this contaminates the whole batch. So yeah, those burgers—basically all burgers, unless you’re grinding your own meat or sourcing your beef from a local farm—have poop in them. Not much, but it’s there. Of course, it won’t make you sick as long as you cook it right: 160° F is enough to kill the poop-bacteria (E-coli, etc.), so, you know, no big deal. Except for the knowledge that you’re eating poop. Sorry. ↵
5. John Teehan, 12/24/2006, “A Holiday Season for Atheists, Too,” The New York Times. Excerpted in Copi and Cohen, 2009, Introduction to Logic 13e, p. 25. ↵
6. Definitions, actually. We’ll study two different deductive logics, each with its own definition of form. ↵
7. What counts as a “logical term”, you’re wondering? Unhelpful answer: it depends on the logic; different logics count different terms as logical. Again, this is just a rough gloss. We don’t need precision just yet, but we’ll get it eventually. ↵
8. What about the conclusion? Does it have to be true? Yes: remember, for valid arguments, if the premises are true, the conclusion has to be. Sound arguments are valid, so it goes without saying that the conclusion is true, provided that the premises are. ↵
9. Possibly helpful hint: universal generalizations (All ___ are ____) are rarely true, so if you have to make one true, as in this example, it might be good to start there; likewise, particular claims (Some ___ are ___) are rarely false, so if you have to make one false—you don’t in this particular example, but if you had one as a conclusion, you would—that would be a good place to start. ↵
10. Also excerpted in Copi and Cohen, 2009, Introduction to Logic 13e, pp. 58 - 59.