Reasoning and Critical Thinking

Reasoning and Critical Thinking

Argument and their Elements 2 PHI 1101 Arguments in standard form • It can be useful to make the structure of an argument perfectly clear by writing its various claims in a numbered list, where: • the premises supporting a given conclusion (intermediate or final) precede it in the list; and • inferences are indicated by drawing a line and writing the numbers of the lines where the premises used in the inference may be found. Examples: (1) a simple argument • Argument: You should take the apartment: it isn’t too expensive, it’s clean and safe, and it’s close to your work. • In standard form: 1. The rent for the apartment is not too expensive (Pr). 2. The apartment is clean and safe (Pr). 3. The apartment is close to your work (Pr). 4. You should take the apartment. (FC, from 1, 2, 3) Examples (2): a complex argument • • Argument: It is clear that Smedley committed the murder. We know that only Smedley and Murgatroid could have committed the crime. But it couldn’t have been Murgatroid, because, as a reliable witness has told us, he was nowhere near the scene of the crime that day. In standard form: 1. A reliable witness informs us that M. was nowhere near the crime scene on the day of the murder (Pr). 2. M. was nowhere near the crime scene on the day of the murder. (IC, from 1) 3. M. did not commit the crime (IC, from 2) 4. Only S. or M. could have committed the murder (Pr). 5. Smedley committed the murder. (FC, from 3, 4) Principles or forms of inference • When reading or listening to arguments, we can often see that a conclusion has been drawn, but it is not always obvious how it has been drawn. • Usually, if not always, inferences exemplify repeatable patterns or forms. We can also say that they are governed by general principles. Examples • Argument: Either Smedley or Murgatroid committed the murder. It wasn’t Smedley. So it was Murgatroid. • Form: Either S or M. Not S. So M. • Principle: if there are only two possibilities and one of them is excluded, the other must be the case. Another example • Argument: Linda had a baby in January. So she must have been pregnant in December. • Form: X had a baby in January. So X was pregnant in December (of the previous year). • Principle: someone who has a baby in January had to have been pregnant in December of the previous year. Some cases are tricky • • Argument: Minou is a cat. So Minou is a mammal. Possible forms: (1) X is a P. So X is a Q. (2) X is a cat. So X is a mammal. • The principle of charity: when the goal is to promote reasonable belief, always adopt the interpretation that makes for the strongest possible argument that is compatible with the text. Unstated premises and conclusions • Some forms of inference are so well-known that authors and speakers sometimes leave parts of arguments in those forms unstated (tacit), with the expectation that their audience will supply them on their own. • Example: modus tollens is the form: If P then Q. Not Q. Not P. • Example: If the NDP had won the last federal election, Jagmeet Singh would be PM. Mr. Singh is not PM. So the NDP didn’t win the last federal election. Examples: • The NDP didn’t win the last federal election—if they had won, Singh would be PM (unstated premise: he isn’t). • If Hemingway is a great writer, then I’m William Shakespeare. (Unstated premise: I’m not Shakespeare; unstated conclusion: Hemingway is not a great writer.) • Figure it out for yourself: only Smedley or Murgatroid could have done it, and it sure wasn’t Smedley. (what’s the form in this case; and what’s missing?) Minou returns! • Recall the argument: Minou is a cat. So Minou is a mammal. • We identified two possible forms of inference: (1) X is a P. So X is a Q. (2) X is a cat. So X is a mammal. • We might add as a third possibility: (3) X is a P. All P are Q. so X is Q. • In this case we would say that there is a tacit premise, i.e., All cats are mammals. • Both (2) and (3) are compatible with the principle of charity; notice, too, that the premise declared missing on interpretation (3) is the principle of inference used according to interpretation (2). Diagramming arguments • It can be a useful exercise to draw a diagram of an argument’s structure, one that shows which premises support which conclusion(s). • We’ll present a common way of constructing such diagrams. Simple arguments (1) • In the simplest case, we have one premise (P1) supporting one conclusion (C). • Here, we simply draw an arrow from P1 to C, placing the conclusion at the bottom: P1 C Simple arguments (2) • Premises provide independent support for the conclusion: (P1) We’ve got rice. (P2) We’ve got beans. So (C) We’ve got some food. P1 P2 C Simple arguments (3) • Premises provide linked support to the conclusion: • (P1) Smith or Jones won the race. (P2) Smith didn’t. (C) So Jones did. P1 P2 C Complex arguments 1. Fred was in Kingston on Monday. (Pr) 2. He wasn’t in Ottawa. (IC, 1) 3. The crime was committed in Ottawa on Monday. (Pr) 4. Fred is innocent. (FC, 2,3) P1 IC2 FC4 P3 Example • Re-write the following argument in standard form, then draw a diagram of its structure: Archy didn’t leave the house that day. If he had, the police would have found his footprints in the snow. But they didn’t find any. And if he never left home, there’s no way he could have been in town to rob the convenience store. So he didn’t do it. Archy didn’t leave the house that day. If Archy had left home had, the police would have found his footprints in the snow. The police didn’t find any footprints. If Archy never left home, there’s no way he could have been in town to rob the convenience store. (So) Archy didn’t rob the convenience store. (1) If Archy had left home, the police would have found his footprints in the snow. (Pr) (2) The police didn’t find any footprints.

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