Traditional logic II Chapter 12

[KF2000]

My daughter is doing TL II, Chapter 12, and is struggling to extrapolate the epicheirema for #'s 20 and 26. She can't figure them out on her own, and even looking at the answers do not help, as she cannot see how those were formulated. The most problematic ones are the first one of #20; and the right to bear arms and the environment ones from #26.

Suggestions? Explanation?
TIA,
AMDG,
Sarah

[trob]

Re: Traditional logic II Chapter 12

My daughter is doing TL II, Chapter 12, and is struggling to extrapolate the epicheirema for #'s 20 and 26. She can't figure them out on her own, and even looking at the answers do not help, as she cannot see how those were formulated. The most problematic ones are the first one of #20; and the right to bear arms and the environment ones from #26.

Suggestions? Explanation?
TIA,
AMDG,
Sarah

My son is taking this class right now. I will ask him tomorrow and see if he can help.

[martin]

Re: Traditional logic II Chapter 12

Sarah,

Is she able to do any of it? Could you post what she has so I can see where she might be going wrong? Thanks.

Mr. Cothran

My daughter is doing TL II, Chapter 12, and is struggling to extrapolate the epicheirema for #'s 20 and 26. She can't figure them out on her own, and even looking at the answers do not help, as she cannot see how those were formulated. The most problematic ones are the first one of #20; and the right to bear arms and the environment ones from #26.

Suggestions? Explanation?
TIA,
AMDG,
Sarah

[KF2000]

Re: Traditional logic II Chapter 12

I can, but she is at work right now. So when she gets home tonight I will have her post.

Thanks!
Sarah

[KF2000]

Re: Traditional logic II Chapter 12

Mr. Cothran,

For the first syllogism of question #20, I tried to put the first premise into logical form as 'All men are mortal because no men are gods', then extrapolate it. From what the book said about extrapolating I thought men would be the minor term, mortals would be the major term, and gods would be the middle term. The only way I could figure it out was to say 'No gods are mortal, No men are gods, Therefore all men are mortal.' But that's not a valid syllogism. I looked in the answer key, but it put 'All things that are subject to death are mortal, All men are subject to death, Therefore all men are mortal.' It didn't use the term gods at all, which I thought was how you did extrapolating...using the terms in the premise. It also added the term 'all things that are subject to death,' and I don't know where that came from.

The second one I had trouble with was the one concerning the Constitution in question #26. I put the first premise into logical form as 'All situations in which the Constitution protects the right to keep and bear arms are situations in which gun control laws should be rejected, since no law is a thing which can violate the Constitution.' I thought 'situations in which the Constitution protects the right to keep and bear arms' would be the minor term and 'situations in which gun control laws should be rejected' would be the major term in the extrapolated syllogism. But 'since no law is a thing which can violate the Constitution' doesn't have either of those terms, it has two new ones. I got stuck right there. The answer key didn't help, because it didn't seem to use the causal statement's terms. I couldn't even skip over the causal statement and figure out what the main syllogism's terms were and how they fit together.

My last problem was the syllogism concerning the environment in question #26. I put the first premise into logical form as 'The destruction of the environment is a thing which will ultimately be the undoing of the human race, since no people are people who can live on an unlivable planet.' I thought 'destruction of the environment' would be the minor term and 'a thing which will ultimately be the undoing of the human race' would be the major term. But again the terms in the causal statement are completely different. When I tried to figure out the enthymeme in the main syllogism I had a little trouble, but I finally figured out with the help of the answer key that I had to replace 'destruction of the environment' with 'polluters' and it would work.

Thank you for your time and your help.
Elizabeth

[martin]

Re: Traditional logic II Chapter 12

Elizabeth,

In regard to the first one, I think the answer key gives a very liberal version of the answer. But I thought of a better one.

Here is what you know based on what the epicheireme gives you:

Proof: __________________
No men are gods
All men are mortal

Now the first problem you see here is that you have a universal affirmative in the conclusion and one of your premises ("men are not gods," which I converted to the equivalent "No men are gods") is a universal negative. But we know that cannot be because if either premise is negative, it cannot yield an affirmative conclusion. Likewise, we know that if there is an affirmative conclusion, all the premises must be affirmative. So we've got a problem. How do we solve it?

The only way we can solve it is by somehow making the conclusion negative or the minor premise affirmative. Let's try the first way.

In order to do this, we must employ the rules of equivalence. On p. 82 of Book I, we used obversion to show that "All S is P" can be converted to the equivalent "No S is not-P." So let's see if we can use obversion in the conclusion to make it negative. When we do that, we get "No men are not mortal."

Proof: __________________
No men are gods
No men are not mortal

At this point, we should probably go back to our mnemonic verse to see if there is a valid syllogism form that has an E minor premise and an E conclusion to give us a clue to what the missing major premise should be. If I do that, I discover that this could be either a CAMESTRES or a CAMENES. Let's try the CAMESTRES route.

If it is a CAMESTRES. then we know 1) that the major premise must be an A statement:

Proof: All ____are ________
No men are gods
No men are not mortal

And we know 2) that the middle term ("gods") must be the predicate, since it is 2nd figure and therefore a prae-prae. So we get:

Proof: All ____are gods
No men are gods
No men are not mortal

Now we just fill in the major term (not mortal):

Proof: All non-mortals are gods
No men are gods
No men are not mortal

Again, the conclusion here ("No men are not mortal"), a universal negative, is not exactly what is in the book ("All men are mortal") a universal affirmative, but it is logically equivalent to it. As long as it is logically equivalent, it is, for our purposes, the same.

Does that make sense? So this is the one I would use here.

And by the way, it would have worked to work towards the 4th figure CAMENES too, getting

All non-mortal are gods
No gods are men
No men are not mortal

[martin]

Re: Traditional logic II Chapter 12

On exercise 26, you have two components given to you. And, again, I always start by identifying the conclusion and then filling in the premise I am given:

Proof: No law can violate the Constitution
______________________________
Gun control laws should be rejected

We have the same problem as in exercise 20: An affirmative conclusion with a negative premise. Also, we don't see either the major or minor term in the given premise. It can't possibly be valid stated this way. So let's see if we can state it another way.

The conclusion is a nice compact A statement, so let's leave it and is and see what we can do about the premise. Is there a way we can restate it so that it means the same thing but includes either the major or minor term?

It seems rather hard to put it in any form that would include the minor term ("gun control laws"), so let's try the major term. Isn't the statement "No law can violate the Constitution" just shorthand for saying "All laws that violate the Constitution should be rejected" (partly since there actually are laws that violate the Constitution, making the way this is formulated clearly false)?

So we get:

Proof: All laws that violate the Constitution should be rejected
______________________________
Gun control laws should be rejected

Now all we have to do is to figure out the minor premise. Furthermore, we have A statements in both the major premise and the conclusion, so we know that we have a BARBARA here. So we know to put the middle term as the predicate, and the minor term in the subject:

Proof: All laws that violate the Constitution should be rejected
Gun control laws violate the Constitution
Gun control laws should be rejected

[KF2000]

Re: Traditional logic II Chapter 12

Mr. Cothran,
Thank you so much for your help. These answers are a lot easier to understand. I do have one follow up question:

In the gun control question, why didn't you use the first half of the major premise - "If the Constitution protects the right to keep and bear arms..."?

Also, if you had time to help with the environment question, I would like to see that too.

Thanks,
Elizabeth

[martin]

Re: Traditional logic II Chapter 12

Ellizabeth,

Sometimes you just have to cut words that are not essential to the reasoning. Again, every time you are trying to complete an enthymeme or sort out a syllogism, you start with the conclusion, getting your minor and major terms, and then the only other term is the middle term. If the words used in the stated argument are not one of these, then they should not be a part of the argument. They may be saying something, but not something that is a part of the argument itself.

Does that make sense?

And sorry for not answering the environment question, I was thinking you were saying you had resolved that, and looking back at your question, it looks like maybe you did. Your original terms were different from the terms in the key on the surface, but that is only because I am giving you sloppy arguments as you will see them in real life that you have to tame (logically speaking) and put into some coherent form. That means that you have to put it in terms of what the argument really means rather than the way someone may have actually said it. So when you replaced 'destruction of the environment' with 'polluters', you were just taking vague language ("destruction of the environment" is a vague abstraction), and putting into concrete terms (WHO is doing the destruction, polluters).

Again, the examples I'm giving you are intentionally sloppy in their language, so you have to separate the wheat from the chaff. It appears to me that that's what you did.

_______________________
_______________________
Polluters should pay a heavy price

[KF2000]

Re: Traditional logic II Chapter 12

Mr. Cothran,
That makes a lot of sense, and it will help me a lot in the chapters l have left. Thank you so much for all your help! I really appreciate it.
Sincerely,
Elizabeth