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Logic is the study of the principles of correct reasoning associated with the formation and analysis of arguments. An argument consists of two or more claims, one of which is called the conclusion. The conclusion is the claim in the argument that is supposed to be supported by, shown to be the case by, demonstrated by, justified by, warranted by, or proved to be the case by the premise or premises. A premise is a claim in the argument that is supposed to support, show, demonstrate, justify, warrant, or prove the conclusion. The fundamental purpose of an argument is to persuade or convince someone of the truth of one's concluding claim. In other words, when we put forward an argument, we want others to be persuaded or convinced of the conclusion we arrived at and believe to be true, and we use another claim, or other claims, as supposed support for the truth of that conclusion.

My fallacious argument about Goths can be rephrased, simply, like this: “Because every Goth I've ever met and know of has been saturnine, shady, surly, and, of course, suspect (the premise of my argument), therefore all Goths I meet will in fact be saturnine, shady, surly, and, of course, suspect (the conclusion of my argument).” A complete argument has at least one premise and only one conclusion, but arguments usually have two or more premises. So, for example, I was watching a South Park rerun one night called “Ike's Wee,” and Cartman put forward an argument for why we should be convinced drugs are bad that could be paraphrased like this: “If you do drugs, then you're a hippie; if you're a hippie, then you suck; if you suck, then that's bad (all premises); so, if you do drugs, then that's bad (conclusion).”

Arguments are composed of claims, a concluding claim (the conclusion) and at least one supporting claim (the premise). A claim is a statement, proposition, judgment, declarative sentence, or part of a declarative sentence, resulting from a person's beliefs or opinions, which communicates that something is or is not the case about the self, the world, states of affairs, or reality in general. Claims are either true or false, and again, are the results of beliefs or opinions that people have concerning any part of what they perceive to be reality. We make our beliefs and opinions known through claims. For example, the claims “I am typing this chapter on a laptop” and “Chewbacca is a Wookie” are true, whereas the claims “I was the 40th president of the United States” and “The Sun revolves around the Earth” are false. A claim is shown to be true or false as a result of evidence, which can take the forms of either direct or indirect testimony of your senses, explanations, the testimony of others, appeal to well‐established theories, appeal to appropriate authority, appeal to definitions, and good arguments, among others. So, that I am typing on a laptop is shown to be true by the direct testimony of my own senses, that Chewbacca is a Wookie is true by definition of “Chewbacca,” that I was president of the United States is false because of the testimony of the senses of others and authorities, and that the Sun revolves around the Earth is false because of indirect sensory evidence as well as the well‐established heliocentric theory. Some claims are difficult, or impossible, to show true or false with evidence. Claims like “God exists,” “Abortion is always immoral,” and “I have an immortal soul” would fall into this ambiguous category. That is probably why ideas, issues, and arguments surrounding these claims are considered to be “philosophical.”

As rational, adult critical thinkers, we have beliefs or opinions that we think are true about reality as we perceive it, and we express those beliefs or opinions in written or spoken claims. But we can't stop there. We must convince or persuade others as to why we hold these beliefs, and when we do so, we must give a reason or set of reasons (the premises of our argument) for why we hold to a particular belief (the conclusion of our argument). So, for example, in “The Passion of the Jew” Kyle believes strongly that the Jewish community in his hometown should apologize for Jesus's death. If asked why the Jewish community in his hometown, or anyone, should be convinced or persuaded to apologize, Kyle's argument might look like the following:

 Premise 1: Since Jews are known to have been partly responsible for the death of Jesus

 Premise 2: And, since an action like this requires that one should apologize

 Premise 3: And, since the Jews in South Park are part of the Jewish community

 Conclusion: Therefore, the Jews in South Park should apologize for Jesus' death

Let's note a few things about this argument. First, it has been placed into standard form. Putting an argument in standard form means placing the premises of the argument first, the conclusion last, and clearly dividing the premise(s) and conclusion with a horizontal line. This is a handy tool because it helps make the logical form and parts of the argument clear. And, as we will see later, standard form makes the argument easier to analyze in terms of whether the conclusion follows from the premises as well as whether all the premises are true.

Notice the word since at the beginning of the premises and the word therefore at the beginning of the conclusion. The word since is an example of a premise‐indicating word, along with words like because, for, for the reason that, and as, among others. The word therefore is an example of a conclusion‐indicating word, along with words like hence, so, thus, this shows us that, we can conclude that, and we can reason/deduce/infer that, among others. Premise‐indicating and conclusion‐indicating words are important because they usually let us know that premises and a conclusion are coming in an argument. At times, it can be incredibly difficult to tell if someone is putting forward an argument, so you can look for these indicating words to see if there is an argument in front of you and, further, you can identify what the conclusion and the premise(s) of the argument are. Unfortunately, these indicating words are not always present, and people sometimes place the conclusion anywhere in their argument (sometimes it will be the first claim, sometimes the second, sometimes the last). In such cases you must supply these words to make the structure and parts of the argument apparent.