Additive Inference Drill

[zwglanz]

So I'm understanding all the concepts of this chapter, but in action i'm having trouble.

When I hit a <--/-->, does the some train stop there? For instances, #1 of the drill is Some As are Bs, No Bs are Cs, and All Cs are Ds. I diagram it all correctly, but I would've thought that you could conclude that some A->D. #2 All Xs are Ys, Some Ys are Zs, and Most Xs are Ws. I wanted to make X -> Y into a some and make it a <--->, which I thought would lead me to be able to conclude that some w->Z. But then you get to #3, No Es are Fs, All Fs are Gs, and All Gs are Hs. Why is it on this one that I can turn it all into somes and work my way back up to the /E? Can someone help me identify where i'm going wrong?

[Dave Killoran]

Hi Z,

You are actually running into multiple problems here, which is why this probably seems quite confusing. A few thoughts:

The doesn't stop the inferences in the Some Train. It just turns the relationship into a negative one. Compare the following two relationships:

• 1. A B C
  
  Inference: A C
  
  2. A B C
  
  Inference: A C

Same inference, one just has a negative on C.

Second, you should go back and review the Rules of Reversibility. They play a role in some of your confusion as far as I'm seeing.

Third, go use the book site code in the front cover of the 2023 versions, or see Chapter 1 for the book site in other versions. I wrote an expanded set of explanations for each of the items in this drill that takes the inferences step-by-step There are also some additional discussions of each drill in this forum.

Thanks!

[HarmonRabb]

Hi, I have some of the some confusions as OP. From the drill on page 463 (2024 edition) we come up with the diagram:

Code: Select all

 A <--s--> B <--|--> C --> D

I don't understand why we can't make the inference:

Code: Select all

A <---s--> D

We ride the some train from A to B
We ride the double not arrow from B to C
We ride the arrow from C to D

Where have I gone wrong?

[Dana D]

Hey Harmon,

Your last inference is where you're making the mistake - looking back at Dave's example, the last inference is A C - that's a negated C. The inference is that some (at least one) A does not meet the criteria of C, and we know that has to be true because some A B, and B C - which means absolutely no B are ever C.

If absolutely no B C, but we know at least one (some) A are B, then we can be sure there is at least one A C - or at least one A that does not fit the criteria for whatever C is, because it is a B.

In your example, we don't actually know that A D. We know some A are definitely not C, or A C, but what about the rest of A? We have no idea about the relationship between A and D, so we can't say for sure A D.

Hope that helps!

[HarmonRabb]

Thanks for your reply Dana, I really appreciate the level of detail!

The logic in your explanation makes sense to me but I'm still struggling with trying to match it to the rules in the chapter.'

I thought when a double not arrow is followed by an (all) arrow we can always make an inference. Is it a case of the combination of a some arrow follow by a double not arrow cannot produce any further inferences after the double not?

[HarmonRabb]

Thinking about this further, it is because the first inference gives us "Not C" and thus we cannot recycle the inference because the relationship is C--->D ?

[Jeff Wren]

Hi Harmon,

That's exactly right.

The Double-not Arrow can be tricky, especially when combining it in longer chains.

Remember that what it represents is two conditional statements in one.

Here B <-|-> C

Means

B -> Not C

And its contrapositive

C -> Not B

If you were to diagram this problem using:

A some B -> Not C

Then you'd more easily spot that "All Cs are D, diagrammed C -> D" doesn't connect to make an inference.

[HarmonRabb]

Thanks, I appreciate the detail

[jilliank]

Third, go use the book site code in the front cover of the 2023 versions, or see Chapter 1 for the book site in other versions. I wrote an expanded set of explanations for each of the items in this drill that takes the inferences step-by-step There are also some additional discussions of each drill in this forum.

Thanks!

Where night these explanations have moved to? The QR code on the inside cover of my book takes me to a link that no longer exists. I’d love to find more info on the this topic and the other free lessons mentioned throughout the text but most of the QR codes open this error page:

IMG_0741.jpeg

[Stephanie Oswalt]

Third, go use the book site code in the front cover of the 2023 versions, or see Chapter 1 for the book site in other versions. I wrote an expanded set of explanations for each of the items in this drill that takes the inferences step-by-step There are also some additional discussions of each drill in this forum.

Thanks!

Where night these explanations have moved to? The QR code on the inside cover of my book takes me to a link that no longer exists. I’d love to find more info on the this topic and the other free lessons mentioned throughout the text but most of the QR codes open this error page:

IMG_0741.jpeg

Hi jilliank,

Which edition (year) of the Bibles do you have? Once I have that I can point you to the right resources. Thanks!