Logic 101
Lesson 1
Induction and Deduction
Inductive arguments are those whose conclusion is probable with true premisses. They frequently start with specifics and move to generalities. For example, you may observe a series of data points, such as:
I sat beside Tony Hawk on my flight to New York.
I sat beside Michael Jordan on my flight to Atlanta.
I sat beside Alex Rodriguez on my flight to Los Angeles.
I sat beside Kobe Bryant on my flight to Miami.
You may conclude from this series of data points, “therefore, I will probably sit by another sports celebrity on my next flight.” The conclusion that I will sit by a sports celebrity on my next flight would not be supported by the data.
Deductive arguments are those that yield a true conclusion if the premisses of the argument are true and if the logical structure is valid. They often start with general premisses and move to a specific conclusion. For example, you may say:
As a sports agent, I never fly unless I am accompanied by one of my clients.
All of my clients are sports celebrities.
I always sit beside my client when I fly.
I am going to fly this Thursday.
Therefore, I am going to sit beside a sports celebrity on my flight this Thursday.
If the premisses of this argument are true, then so must be the conclusion.
I like this kid. There are a few problems with the logic, but he is directionally correct.
This one is a little weird but entertaining.
This is well done.
A valid argument is one which, if the premisses are true, then the conclusion is true. A sound argument is a valid argument with true premisses.
More on Validity and Soundness
Validity is only concerned about the structure of the argument. It is not concerned about the truth of the argument. The deductive argument above is valid because, if the premisses of the argument were true, then the conclusion would be true. The argument is not sound if I am the one speaking because I am not a sports agent. People frequently misuse the term, ‘valid’ when they use it to mean that something is true. ‘Valid’ only means that the argument inquestion is well structured.
Top Ten Words Logicians Use That You Should Know
1. Syllogsm. An argument with two premisses.
Example: All Chocolate is yummy
what I am hoding in my hand is chocolate,
Therefore, what I am holding in my hand is yummy.
This argument is not necessarily sound, but it is valid. You may take issue with either premiss.
2. Cogent. A cogent argument is an argument such that if the premisses are true, then the conlcusion is more likely to be true than false.
3. Conjunct. Either of the two parts of a conjunction. In the sentence, “Jeff got caught selling illegal fireworks, and Jeff went to jail.” Both, “Jeff got caught with fireworks” and “Jeff went to jail” are conjuncts.
The video is inacurate from a logic standpoint. The conjunction or signals a disjunct in logic.
4. Contrary versus Contradictory. A contrary condition occurs when not all of the propositions in an argument can be true. Example: “Labron James is tall and Labron James is short.” A contradictory condition occurs when when propositions have opposite truth values (one must be true and the other false). Example: “Pedro is a great baseball player” and “Pedro is not a great baseball player.” If you have two contradictory propositions, at least one will be true. If you have two contrary propositions, only one can be true, but they can both be false. From the example above, Labron James could be said to be of medium height by NBA standards making both propositions false. But Pedro is either great or he is not great. You may say that he is kind of great, but that is not great. I would vote for Pedro anyway.
5. Disjunct. Either of the two parts of a disjunction. In the propostition, “Either your mother is blind or you don’t know how to dress yourself,” “Either your mother is blind,” is a disjunct and “you don’t know how to dress yourself,” is a disjunct.
6. Sufficient Condition. A sufficient condition is one that, if true, then the propostion that it is a condition for is true. The structure is, if X is true, then Y is true. X then becomes the sufficient condition for Y. Example: “If your fish never get fed, they will die.” The fish not getting fed is a sufficient condition for your fish to die. Said another way, to say that A is sufficient for B is to say that in and of itself, knowing A to be true is adequate grounds to know that B is true.
7. Necessary Condition. A necessary condition is one must be true in order for the thing that it is a condition for to be true. Said another way, saying that X is necessary for Y is the same as saying, “Y cannot be true unless X is true.” Example: Being born in the United States of America is by law necessary for you to be the Presidient of the United States of America. In other words, if you are the President of the United States, then you were born in the United States of America. It would be impossible for you to be the president if you wre not born in the USA.
The difference between necessary and sufficient
Examples: Sufficient but not necessary
In the song Takin’ care of business by BTO, a line says, “If your train’s on time, you can get to work by nine.” Having your train be on time is sufficient for you to get to work by nine, but it is not necessary. If you were Lance Armstrong, you could get to work by nine by riding your bike.
If your playing card has a single heart in the center of the card, that condition is sufficient for you to conclude that your card is an ace, but it is not necessary.
You can also conclude that you are holding an ace if you are holding a card with a single diamond in the center or a single spade or club.
Example: Necessary but not sufficient
Being a mammal is necessary but not sufficient to being a human. You cannot be human without being a mammal, but it takes more than being a mammal to be a human.
8. Vague. if something is vague, it is unclear whether or not the thing applies to the situation being considered.
9. Self-Contradictory.
“My parents are abnormally normal.” (From “Zits” by Jerry Scott & Jim Borgman – February 25, 2004)
A proposition is self-contradictory when it must be false. Example: “I’m going on a date this weekend, but I’m not going on a date this weekend.”
Other examples:
“I always lie”
“The first rule is that there are no rules.”
“Do me a favor: don’t do me any favors.”
“Expect the unexpected.”
“My goal is to have no goals.” (From “Dodgeball: A True Underdog Story)
And finally, one of my favorite riddles…”When you say my name, I am no longer there. What am I? Answer
More self-contradiction in the comics
10. Conditional Proposition. A proposition which indicates the condition for another propostion. Example: “If the Pirates get a new manager, they will score more runs.” The condition is, “If the Pirates get a new manager.”