Exercise: Deductive & Inductive Reasoning
In Chapter 3, you have read about the two types of human reasoning, “deductive” and “inductive.” Deductive reasoning relies on logical relationships between claims and tells us, given what we know or assume to be true, what must necessarily be true. Consider the following example of a deductive argument in the form of modus ponens:
Premise 1: If it is raining outside, then I have an umbrella.
Premise 2: It is raining outside.
Conclusion: Therefore, I have an umbrella.
In this example, if the premises are both true, then the conclusion is guaranteed to be true. What this means is that premise 1 and premise 2 are logically related such that if both are true, then the truth of the conclusion is required. In other words, if it is true that “if it is raining outside, then I have an umbrella,” and it is true that “it is raining outside,” then it cannot be false that “I have an umbrella”….because that’s just what it means to say “if it is raining outside, then I have an umbrella.” You may be thinking, though, that it is quite possible that it is raining outside but I forget my umbrella. But notice that this would make the first premise false. It is false that “if it is raining outside, then I have an umbrella,” when it is raining outside, but I don’t have an umbrella. In fact, that are no conditions under which it is true that “if it is raining outside, then I have an umbrella,” and it is raining outside, but I don’t have an umbrella. This is because, again, that’s just what it means to say that “if it is raining outside, then I have an umbrella.” On pp. 45-46, you read about some of the most common deductive argument forms and you saw examples of each. These are: modus ponens, modus tollens, and the hypothetical syllogism.You may see more deductive argument forms here: Deductive Argument Forms Because moral arguments are always deductive, you read more about them than about inductive arguments. Still, inductive arguments are an important part of human reasoning so I will say a bit more about them here. Rather than relying on logical relationships between claims, inductive arguments draw conclusions on the basis of observation and experimentation. Inductive reasoning, then, is the backbone of the scientific method. While deductive reasoning is characteristic of logic and mathematics, inductive reasoning is characteristic of the applied sciences. At a very basic level, we are taking inductive reasoning for granted when we assume that the world really is the way we observe it to be. For instance, I observe a computer screen in front of me, so I assume that there really is a computer screen in front of me. But is it guaranteed that there is a computer screen in front of me simply because I observe it? You might reply, “Well, of course, and you can touch it too!” However, if you have ever had a very vivid dream, or if you have seen the 1999 movie, “The Matrix,” then you will admit that there are situations we can imagine in which I observe a computer screen, but there really isn’t one there. (A note: This question of whether, and to what extent, we can rely on our observations will become relevant again in our module on environmental and animal ethics. It will be discussed further there, along with ethical issues related to scientific claims. It is also a topic we discuss in my Introduction to Philosophy class quite a bit.) For a critical thinking class, though, our goal is to determine what is most likely true, or what is most reasonable to believe. I typically say to students at this point, “It is not most reasonable to believe that we are in the Matrix, so we will leave this problem of induction behind for now…” Then one semester, a student replied, “Yeah, I bet that’s what people in the Matrix think too.” Indeed! Yet, at some point, if we need to decide what we should do, we must make that decision about what is most reasonable to believe. Overall, there just aren’t enough things we know with the strength of deductive reasoning to rely only on what is guaranteed to be true. When we don’t know what is guaranteed, we must still decide what is most likely true. That is exactly what science helps us to do. In particular, the scientific method helps us to make good generalizations and is indispensable to causal reasoning. Read more about inductive reasoning here:
Kris Barton & Barbara G. Tucker: Inductive Reasoning ______________________________________________________
For this assignment, you will be demonstrating your understanding of deductive and inductive reasoning. First, create your own example of each of the three deductive argument forms discussed on pp. 45-46: modus pones, modus tollens, and hypothetical syllogism. I gave an example of one, modus ponens, above, about it raining outside and me having an umbrella. That’s exactly what I’m asking you to do. Don’t use my example or an example from the book or internet. Just think of your own example to show you can create the argument forms. It is only necessary to create one example of each argument. Please state the argument so that the logical form is apparent rather than discussing your argument in a passage. You may use this format:
1. premise
2. premise
3. conclusion
Your examples should look just like my example of modus ponens above, only with your own original content. To show your understanding of inductive reasoning, answer the following using the reading in the textbook and the link provided above:
1. What is inductive reasoning?
2. How does inductive reasoning differ from deductive reasoning?
3. What is a generalization?
4. What is causal reasoning?
5. What is sign reasoning?
6. What is analogical reasoning?
7. Describe a situation where you have used one of the types of inductive reasoning that you defined in questions 2-5.
To be clear, your submission to this dropobox should include:
1) one original example for each of the three deductive argument forms, and
2) your answers to the seven questions above.
