Between One and All

There were many interesting topics discussed throughout chapter 8. A topic discussed was “Between One and All”. There are precise generalities and vague generalities. There are a lot of similarities between one and all, which refers back to precise generalities. A vague generality focuses on different ways people talk about parts of collections without stating a certain number. There are also direct ways of reasoning with almost all and ways to argue backwards with almost all as well.

One can tell if an argument is valid if they have enough precision. An example of a vague generality is:

           

            Very few cats do not meow.

            Fluffy is a cat.

            So fluffy meows.

 This premise gives very good cause to believe the conclusion. You can also reasoning a chain with almost all. But, this argument is usually weak. All of this information focuses on what makes a general claim and is very useful for arguments. 

Chapter 8 Concept

One concept in Chapter 8 that I found useful was general claims and their contradictories. General claims declare things in a universal way about just a part of group or all of it. The contradictories of the general claims focus on words such as  “all”, “some”, and “no”. The word “all” is meant for everything or can relate to every single one.  The term “some” focuses on only at least one and “no” means not even one. A personal example from my life when I used contradictories of a general claim was when my best friend and I were growing up and we said, “no boys are allowed in our tree house”.  This also is interpreted as “nothing that is a boy is allowed in our tree house”. There are different ways of saying that nothing or no part of a collection suits some condition. There are different ways to determine whether or not information is valid and general claims and their contradictories determine this information. 

Valid and weak forms of arguments using conditionals

After reading Chapter 6, I found the information on valid and weak forms of arguments using conditionals useful and interesting. There are many arguments where it is impossible for the basis to be true and the conclusion to be false.

-If the train leaves at 2:15 and you show up at 2:25, the train will leave without you.

-The car crashed going over 70 mile per hour and now it is totaled.

Both of these examples are similar because they have valid premises and it proves that there is no way that the conclusion can be false.

Modus Ponens is another way of reasoning. For example:

If the train leaves at 2:15 and you arrive at 2:10, then the train will not leave without you.

-If you do not drive over the speed limit and pay attention to the road, you will not total your car.

These examples are valid and show another way of reasoning.

Using conditionals are very useful because it supports your argument and makes it stronger. There is no way to disprove your conclusion if you have a strong and valid premise.

Chapter 7 Discussion

Chapter 7 focuses on Raising Objections and Refuting an Argument. After reading this chapter I learned how to refute an argument directly and indirectly.

There are three main ways to refute an argument directly. One has to prove that at least one of the arguments are uncertain. Also, it is important to prove that the premises aren’t valid or strong. Lastly, one has to show that the conclusion is false.

When refuting an argument indirectly, you can’t always prove that the premises are uncertain or false. The conclusion may be argued, but the argument seems inconsistent and illogical. When I was reading about how to refute an argument indirectly, I also learned about the term “reducing to the absurd”. When one reduces to the absurd, one proves that at least one of the claims is not true and doubtful. Therefore, one is proving that the argument has an unwanted conclusion.

Chapter 6 Discussion

Chapter 6 focused primarily on Considering the Alternatives of claims and the Conditionals.  Two things that I learned from this chapter is information on the contradictory of a claim and the conditionals and their contradictories.

The contradictory of a claim focuses on the opposite of the truth that is stated. It is known as the negotiation of a claim.

In the book they gave the following example:

Contradictory of an or claim: A or B has contradictory not A and not B.

For example, a claim could be that Tim McGraw is a country singer. The contradictory of that claim would be, Tim McGraw is NOT a country singer. This proves the opposite truth-value of the circumstance.

A conditional claim can be rewritten as an “if” or “then” claim that must be truthful.

An example of a conditional claim is:

            I will go to college and get a degree and then I will become a doctor.

This claim does not contradict itself because there is no certainty about the claim because “then” was used and the claim still makes sense. 

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