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Discussion – Logic and Argument

Perkins

Discussion – Logic and Argument

Logic involves evaluating arguments.  But what is an argument? An argument is a connected series of sentences or claims intended to establish (conclude) another sentence/claim.

Typically, an argument has two claims called premises and a third claim called a conclusion, as in:

  1. If today is Monday, then I have a class. Premise 1.
  2. Today is indeed Monday. Premise 2.

_______________

  1. Therefore, I have a class today.                              Conclusion.

The conclusion in a logical argument follows from the given premises.  In other words, the conclusion makes sense.

We can say that the argument is logical.

So, a good argument is a logical argument, meaning one that makes sense!

But, once again, what things make sense?

Consider, for example, the following three claims:

  1. If someone lives in New York, then this person lives in the US. Premise 1
  2. Mark does not live in New York. Premise 2
  3. Therefore, Mark does not live in the US. Conclusion

Does this argument make sense?   No.

The conclusion does not follow from the premises. The first claim is true because New York is part of the US. The second claim is also true – Mark does not live in New York. But, the third sentence does not follow from the first two claims. We cannot conclude that Mark does not live in the US just because he does not live in NY.  We will say that the conclusion does not follow from the premises. Our assignment writing help is at affordable prices to students of all academic levels and disciplines.

Now consider this:

  1. If someone (anyone, any person) lives in New York, then this person lives in the US.
  2. Ana does not live in the US.
  3. Therefore, Ana does not live in NY.

This makes sense. If Ana does not even live in the US, then how could she live in NY? So, of course the conclusion is true and if follows the previous two sentences.

Now let’s go back to the argument from Monday:

  1. If Sam gets 100 points (out of 100) on the test, she will get an A grade for that test.
  2. It turns out Sam got an A on this test.
  3. Therefore, Sam must have gotten 100 points on the test.

Is the conclusion logical?

If you answered “NO” then congratulations!

If you said yes, well- why did you?

After all, the given condition in premise 1 does not say: “Only if you get 100, you can get an A.”

Compare the logic of the argument about Sam to the logic of the argument about Ana:

  1. If someone (anyone, any person) lives in New York, then this person lives in the US.
  2. Ana lives in the US.
  3. Therefore, Ana lives in NY.

This argument makes no sense.  Explain why.

Explain here:

Ana lives in the US but that does not necessarily mean she live in New York. The US has other states other than NY and Ana lives in another state and not NY.

Notice, first we were given a condition: IF X, then Y.         Meaning:

If someone lives in NY, then that person lives in the US.        If X, then Y

Similarly:

If someone gets 100 points, then that person gets an A.           If X, then Y

Then we were told that Y is true.    Meaning:

Ana lives in the US.

Similarly:

Sam got an A on the test.

You probably wrote that concluding that Ana lives in NY was illogical, meaning concluding X from Y was illogical.

Can we say the same about Sam’s points on the test?  To conclude that Sam got 100 points would be like concluding that Ana lives in NY just because she lives in the US.

Again, the condition is: If someone (a student) gets 100 points, then that person gets an A.

The condition is not:   “Only if you get 100, you can get an A.”

Just like we are not saying: “Only if you live in NY, then you live in the US.”

Explain here in your own words the difference between these two statements:

“If you live in NY, then you live in the US.”  And:  “Only if you live in NY, then you live in the US.”

The first statement shows that NY is part of the US, and hence, if a person is living in NY, then they are in the US. The second statement implies that NY is the US; that is, another name for NY is the US. NY, in this case, represents the entire country.

Now explain the difference between:

“If you get 100 points, you will get an A.”   And:  “Only if you get 100, you will get an A.”

The first statement shows that getting 100 points guarantees one a grade A. One can get an A with less than 100 points. In the second statement, it implies that 100 points are equivalent to an A. Anything between 0-99 points is not an A.

So, just because Ana got an A, we cannot conclude that she necessarily got 100 points.  It may well be that she earned 99 or 98, and so on.  We are not told that garnering 100 points is necessary to get an A.  We are merely told that getting 100 points is sufficient, meaning it’s enough to get an A.

Now that you’ve started thinking about what makes sense check for yourself again if you can easily determine how logical the following 11 arguments are.

Argument 1.

  1. If someone is right now in Botswana or in Chad then that person is in Africa.
  2. John is not in Botswana or Chad right now.
  3. Therefore, John is not in Africa right now.

Say if the conclusion is logical:

The conclusion is not logical. Africa comprises more than two countries. John could be in another African country, which is neither Chad nor Botswana.

Argument 2.

  1. If one has a dog, then one has a pet.
  2. John has a pet.
  3. So John has a dog.

Explain in your own words why the conclusion does or does not follow from the two premises:

The conclusion does not follow the two premises. Although a dog is a type of pet, it is not the only kind that one can have. Cats, for example, are pets too. John has a pet, but it is not necessarily a dog; it may be a cat.

Remember, the first two claims in each example are called premises. The last sentence is a conclusion. The three claims (the two premises and the conclusion) constitute an argument.  When the conclusion does not follow the premises in a logical way, meaning a way that does not make sense, we will call such an argument invalid.  Conversely, when the conclusion follows the premises in a way that makes sense, we will call such an argument valid.

Argument 3.

  1. If this painting does not have any colors, then this painting is not blue. Premise 1
  2. But this painting has many colors. Premise 2
  3. Therefore, this painting definitely has a blue color in it.                                          Conclusion

Say if the argument is valid or invalid:

This argument is invalid. A painting with no colors is not a painting at all; it has neither blue nor any color for that matter. However, as it turns out, the painting has many colors, but it does not necessarily mean that one of the colors in the painting is blue. Also, many is a term that is relative. Anything more than one is many. That said, the many colors could have blue or may lack the color blue.

Argument 4.

  1. If someone is right now in Rio de Janeiro, then that person is in Brazil.
  2. Ana is in Rio de Janeiro right now.
  3. So Ana is in Brazil.

Determine if the argument is valid or invalid; explain your answer:

The argument is valid. Ana is in Brazil because de Janeiro is in Brazil

Argument 5. 

  1. If someone is not in Africa, then that person is not in Sudan or Kenya.
  2. Ana is in Africa right now.
  3. So Ana is in Sudan or Kenya.

Is the argument valid? Explain.

The argument is not valid. Africa has other countries besides Sudan and Kenya. Ana could be in any other country in Africa that is not Kenya or Sudan.

Argument 6.

  1. If roses are red, then violets are blue.
  2. Roses are red.
  3. Therefore, violets are blue.

Say if the argument is valid or invalid and why:

The argument is valid. The violets are blue only if the roe are red. Because roses are red, then the violets are blue

Argument 7.

  1. If someone is in NY, then this person is in the US.     Premise 1.
  2. Ann is not in the US.             Premise 2.
  3. Therefore, Ann is not in NY.                            Conclusion

Is the argument valid? Explain.

The argument is valid. NY is in the US, and Ann is not in the US so, there is no way she could be in NY.

Argument 8.

  1. If someone lives in NY, then this person lives in the US. Premise 1.
  2. Ann lives in the US. Premise 2.
  3. Therefore, Ann lives in NY. Conclusion

Is the argument valid? Explain.

This is not valid. The US has other states other than NY. Ann lives in the US and maybe in NY or any other state.

Argument 9.

  1. If Sam gets 100 points (out of 100) on the test, she will get an A grade for that test.
  2. It turns out Sam earned 100 points on this test.
  3. Therefore, Sam received an A.

Determine if the argument is valid or invalid:

The argument is valid. 100 points earn one an A grade. Sam earned 100 points and thus got an A grade.

Argument 10.

  1. If Sam gets 100 points (out of 100) on the test, she will get an A grade for that test.
  2. It turns out Sam got an A on this test.
  3. Therefore, Sam must have gotten 100 points on the test.

Explain in your own words if this makes sense.  Is the conclusion logical?

The conclusion is logical.  The first premise states that 100 points is what will get Sam an A grade. He got an A, which implies he must have met the criteria to earn an A, that is, 100 points.

Argument 11:

“Earth is bigger than Venus, but Venus is bigger than Mars. So Earth is bigger than Mars.”

Think about which claims in this argument are the premises and which sentence is the conclusion.  Do you think the conclusion follows the premises?

Explain:

Yes, it does. The Earth is bigger than Venus, and Mars happens to be smaller than Venus. So, in ascending order of size, the planets are as follows: Mars, Venus, and Earth. This means Earth is bigger than Mars, which makes the conclusion correct.

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Question 

Discussion – Logic and Argument

What is an Argument?

Logic involves evaluating arguments.  But what is an argument? An argument is a connected series of sentences or claims intended to establish (conclude) another sentence/claim.

Typically, an argument has two claims called premises and a third claim called a conclusion, as in:

  1. If today is Monday, then I have a class. Premise 1.
  2. Today is indeed Monday. Premise 2.

_______________

  1. Therefore, I have a class today.                              Conclusion.

The conclusion in a logical argument follows from the given premises.  In other words, the conclusion makes sense.

We can say that the argument is logical.

So, a good argument is a logical argument, meaning one that makes sense!

But, once again, what things make sense?

Consider, for example, the following three claims:

  1. If someone lives in New York, then this person lives in the US. Premise 1
  2. Mark does not live in New York. Premise 2
  3. Therefore, Mark does not live in the US. Conclusion

Does this argument make sense?   No.

The conclusion does not follow from the premises. The first claim is true because New York is part of the US. The second claim is also true – Mark does not live in New York. However, the third sentence does not follow the first two claims. We cannot conclude that Mark does not live in the US just because he does not live in NY.  We will say that the conclusion does not follow from the premises.

Now consider this:

  1. If someone (anyone, any person) lives in New York, then this person lives in the US.
  2. Ana does not live in the US.
  3. Therefore, Ana does not live in NY.

This makes sense. If Ana does not even live in the US, then how could she live in NY? So, of course, the conclusion is true and if follows the previous two sentences.

Now, let’s go back to the argument from Monday:

  1. If Sam gets 100 points (out of 100) on the test, she will get an A grade for that test.
  2. It turns out Sam got an A on this test.
  3. Therefore, Sam must have gotten 100 points on the test.

Is the conclusion logical?

If you answered “NO,” then congratulations!

If you said yes, well- why did you?

After all, the given condition in premise 1 does not say: “Only if you get 100, you can get an A.”

Compare the logic of the argument about Sam to the logic of the argument about Ana:

  1. If someone (anyone, any person) lives in New York, then this person lives in the US.
  2. Ana lives in the US.
  3. Therefore, Ana lives in NY.

This argument makes no sense.  Explain why.

Explain here:

Notice, first, we were given a condition: IF X, then Y.         Meaning:

If someone lives in NY, then that person lives in the US.        If X, then Y

Similarly:

If someone gets 100 points, then that person gets an A.           If X, then Y

Then, we were told that Y is true.    Meaning:

Ana lives in the US.

Similarly:

Sam got an A on the test.

You probably wrote that concluding that Ana lives in NY was illogical, meaning concluding X from Y was illogical.

Can we say the same about Sam’s points on the test?  To conclude that Sam got 100 points would be like concluding that Ana lives in NY just because she lives in the US.

Again, the condition is: If someone (a student) gets 100 points, then that person gets an A.

The condition is not:   “Only if you get 100, you can get an A.”

Just like we are not saying: “Only if you live in NY, then you live in the US.”

   Explain here in your own words the difference between these two statements:

“If you live in NY, then you live in the US.”  And:  “Only if you live in NY, then you live in the US.”

Now explain the difference between:

“If you get 100 points, you will get an A.”   And:  “Only if you get 100, you will get an A.”

So, just because Ana got an A, we cannot conclude that she necessarily got 100 points.  It may well be that she earned 99 or 98, and so on.  We are not told that garnering 100 points is necessary to get an A.  We are merely told that getting 100 points is sufficient, meaning it’s enough to get an A.

Now that you’ve started thinking about what makes sense, check for yourself again to see if you can easily determine how logical the following 11 arguments are.

Argument 1.

  1. If someone is right now in Botswana or in Chad then that person is in Africa.
  2. John is not in Botswana or Chad right now.
  3. Therefore, John is not in Africa right now.

Say if the conclusion is logical:

Argument 2.

  1. If one has a dog, then one has a pet.
  2. John has a pet.
  3. So John has a dog.

Explain in your own words why the conclusion does or does not follow from the two premises:

Remember, the first two claims in each example are called premises. The last sentence is a conclusion. The three claims (the two premises and the conclusion) constitute an argument.  When the conclusion does not follow the premises in a logical way, meaning a way that does not make sense, we will call such an argument invalid.  Conversely, when the conclusion follows the premises in a way that makes sense we will call such an argument valid.

Argument 3.

  1. If this painting does not have any colors, then this painting is not blue. Premise 1
  2. But this painting has many colors. Premise 2
  3. Therefore, this painting has definitely a blue color in it.                                          Conclusion

Say if the argument is valid or invalid:

Argument 4.

  1. If someone is right now in Rio de Janeiro, then that person is in Brazil.
  2. Ana is in Rio de Janeiro right now.
  3. So Ana is in Brazil.

Determine if the argument is valid or invalid; explain your answer:

Argument 5. 

  1. If someone is not in Africa, then that person is not in Sudan or Kenya.
  2. Ana is in Africa right now.
  3. So Ana is in Sudan or Kenya.

Is the argument valid? Explain.

Argument 6.

  1. If roses are red, then violets are blue.
  2. Roses are red.
  3. Therefore, violets are blue.

Say if the argument is valid or invalid and why:

Argument 7.

  1. If someone is in NY, then this person is in the US.     Premise 1.
  2. Ann is not in the US.             Premise 2.
  3. Therefore, Ann is not in NY.                            Conclusion

Is the argument valid? Explain.

Argument 8.

  1. If someone lives in NY, then this person lives in the US. Premise 1.
  2. Ann lives in the US. Premise 2.
  3. Therefore, Ann lives in NY. Conclusion

Is the argument valid? Explain.

Argument 9.

  1. If Sam gets 100 points (out of 100) on the test, she will get an A grade for that test.
  2. It turns out Sam earned 100 points on this test.
  3. Therefore, Sam received an A.

Determine if the argument is valid or invalid:

Argument 10.

  1. If Sam gets 100 points (out of 100) on the test, she will get an A grade for that test.
  2. It turns out Sam got an A on this test.
  3. Therefore, Sam must have gotten 100 points on the test.

Explain in your own words if this makes sense.  Is the conclusion logical?

Argument 11:

“Earth is bigger than Venus, but Venus is bigger than Mars. So Earth is bigger than Mars.”

Think about which claims in this argument are the premises and which sentence is the conclusion.  Do you think the conclusion follows the premises?

Explain:

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