Logic is all about argument and persuasion. Consider the following conversation between two students:
Student A: Hey there! I just realized something really cool.
Student B: Let’s hear it.
A: I realized that color isn’t real.
B: Ok, I’m confused. Why do you think that?
A: Well, we see with our eyes, right? And seeing is just what happens when light hits our eyes and our brain processes it in a certain way. The reason something looks ‘blue’ is just because the light that bounces off of it is a different frequency than the light from something that looks ‘red’. So, different colors don’t have anything to do with the objects we are seeing, they’re just different kinds of light waves!
B: Well, what you say may be true, but I’m not sure you’ve proven that ‘color isn’t real’.
A: What do you mean?? I just told you that color is just our brain’s response to light waves, so color is just something ‘in our brains’, or at least something that we think we see after our brain processes light in a certain way — the stuff we think has different colors might all in fact just be the same shade of gray. The only thing that matters is how our brain processes different light waves!
B: You still haven’t convinced me. I accept that our brains react differently to different light waves when we see color, but you haven’t given me a reason to think that this directly means that color isn’t real. Couldn’t we use our brains to get the sensation of different colors from light waves with different frequencies AND for it to be true that the objects are actually colored? Maybe the light waves just transfer the color from the object to our brains. If you want me to believe your conclusion, you are going to have to give me a better argument than that!
What’s happening here? Well, Students A and B are arguing about a conclusion: “color is not real”. To try to convince Student B, Student A presents an argument with premises (i.e. assumptions): “seeing is light hitting our eyes”, “the frequency of the light determines the color we see”, (and other premises). Student B isn’t convinced, because they don’t think that the conclusion follows from the premises. That is, Student B thinks you can’t infer “color isn’t real” from the premises Student A offers.
[Activity]: Can you think of any discussions in your experience that are similar to the one between Students A and B? Share with the class/with a partner, explaining what the argument was about, explaining why you had a disagreement and what it was about. Could learning concepts like the bolded ones above help you in future discussions? If so, how?
[Activity]: What do you think is the point of logic? What do you think we study in logic and why? Share with a partner!
Logic can be understood as the formal study of correct reasoning patterns. In general, we make decisions, pass judgments, and express opinions in a fairly patterned fashion. Whether explicitly or implicitly, we start from a set of assumptions which we use to arrive at some further belief. Our starting assumptions are called premises, while our belief resulting from our starting assumptions is called a conclusion. The process of moving from premises to conclusions is commonly called an inference or argument.
Logic can also be understood as the formal and precise study of reasoning in order to make it clear and unambiguous. Sometimes when we informally reason and make arguments, it is difficult to understand what exactly our conclusions are and on what basis we reached those conclusions. Logic helps to bring clarity to the answers to these questions.
It is useful here to observe that, for our purposes in logic, we care mainly about declarative sentences. Declarative sentences are sentences that assert something which can be true or false. For instance, the sentence “The sky is blue.” asserts something (true) about the sky, and the sentence “Fire is cold.” asserts something (false) about fire. For this reason, both are examples of a declarative sentence. To see the difference, consider questions like, “Are you hungry?”, or commands like, “Close the door!”. By themselves, these sentences do not state anything about the world. On their own, they cannot be true or false in the way that the declarative sentences “You are hungry” and “The door is closed” can.
Inferences are fundamental to virtually every kind of decision-making practice we engage in. As such, we certainly have some intuitive notion of what counts as a good inference and what does not. For example, you probably have an intuition that something goes wrong in the following exchange:
Premise 1 (P1): Aristotle is a person.
Premise 2 (P2): All people are mortal.
Conclusion (C): Therefore, Aristotle is not mortal.
To what went wrong, we introduce the notion of logical form. Every inference is reducible to a structural pattern or form. We can study these forms to establish which arguments lead to good conclusions and which don’t. In future lessons, we will develop a vocabulary to describe logical forms. We will see that the example above is called a syllogism, and we will discuss properties of syllogism such as validity and soundness.
[Activity]: In your own words, describe what you think is wrong with the argument above!
[Activity]: With a partner, come up with your own examples of arguments like the one above. Try replacing ‘All’ with ‘Some’, putting ‘not’ in front of ‘mortal’, replacing the words with others you like better – get creative! Discuss how each argument you come up with works (or doesn’t). Try to find patterns!