Chapter 6

In chapter 6, I learned other ways of how to identify or make an argument good or bad based on the different types of compound claims: “or” claims and conditionals.

This whole chapter was about looking at claims and seeing if we can reason with them based on their truth-values. It is important to understand the rules of both compound “or” claims and conditionals as we use them in everyday life and understanding their concepts will help us make stronger arguments in the future.

Today I will be talking about the contradictory of a compound claim and conditionals and their contradictories, which were two concepts presented in chapter 6.

1) Firstly, compound claims are two claims seen as one that can be connected by words such as or, and, or but. The two parts of the claim that are stated within the one claim have to be related to each other in order to have any type of truth-value.

For example: Either I won’t eat breakfast before class or I will eat breakfast before class.

These are two claims within one and have truth-value.

Determining the Contradictory of a claim: “The contradictory of a claim is one that has the opposite truth-value in all possible circumstances.”

This same rule applies to a Contradictory of an or claim and the contradictory of an and claim. When understanding contradictory of these compound claims, it is useful to identify each claim by using A, B, C, or D.

For example: The Contradictory of an or claim states that:

Claim A or Claim B’s contradictory is not claim A and not claim B.

 Or an easier way to put it is: A or B = not A and not B

So…

Claim:            (a) I will eat breakfast before class or (b) I won’t eat lunch at school.

Contradictory:  (not a) I won’t eat breakfast before class and (not b) I will eat lunch at school.

This is contradictory because it has the opposite truth-value than the initial claim. As you can see, sentence A said, will then won't. Sentence B said, won't then will.

The Contradictory of an and claim is: A and B = not A or not B.

In addition: These two contradictory concepts will help us to state claims as being false. The concept of using A, B, C, or D to identify claims will also help in future scenarios of reasoning with the other claims.

2) Conditionals and their contradictories: Conditional claims are similar to compound claims by the fact that they are considered one claim made up of two. However, they are different than compound claims because they are not connected by words such as or, and, or but, but rather they can be connected by the words: if, then.

For example: a) If don’t watch t.v right now, b) then I will get my homework done.

It is important to remember that in conditional claims, the sentence that follows if, is referred to as the antecedent and the sentence that follows then, is the consequent regardless of the order claims in the statement.

In the example above, claim A would be identified as the antecedent since it follows if and B would be the consequent since it follows then.

The Contradictory of a Conditional: “If A, then B has contradictory A but not B.”

In simpler English this would be: If A, then B = A but not B.

For example:

Claim: If I didn’t finish my homework, then I will fail my class for sure. (if A, then B)

Contradictory: I didn’t finish my homework but I won’t fail my class. (A but not B)

One final rule: “The contradictory of a conditional is not another conditional”

For example: I am a good student, even if I failed my test.

                        I am a good student, although I just failed my test.

I hope that I showed you all my understanding of the difference between compound claims and conditional claims and their contradictories. Compound claims use: or, and, but. Conditional: if, then. Understanding these types of claims will benefit to understanding whether or not an argument is good or bad. Whether its false, weak, valid, etc.