Inherent Inference Recognition Drill #5

[askuwheteau@protonmail.com]

Thank you Jeff...I appreciate your advice. I'll focus upon finishing the chapter.

[askuwheteau@protonmail.com]

Jeff,

I'm currently completing the Some Train diagramming mini-drill (LRB 2023 Edition, Chapter 13, pg. 435) and ran into a challenge. Below's my reasoning below:

Legend:

• ^s means a lowercase letter s is present over the conditional diagram which begins the some train.
  <> means double arrow
  <means single arrow
  > means single arrow
  <|> means double not arrow

Problem #4: J<K<^s>L yields the following inference according to the answer key: L<^s>J . However, my answer is J<^s>L.. Is my answer correct given that the some diagram goes in both directions?

Problem #7: S<|>T<^s>U yields the following inference according to the answer key: U<^s> S (negated...struckthrough). However, my answer is a negated S<^s>U . Is my answer correct given that the some diagram goes in both directions?

I ask because the textbook seems to give two different interpretations of how to form inference diagrams that go from right to left (pg. 433, paras. 1 & 2 juxtaposed against pg. 434, paras. 1-3)

Thanks,

Jonathan

[Jeff Wren]

Hi Jonathan,

The short answer to both questions is that your inferences were correct and were identical in meaning to what was written in the answer key.

As you correctly mentioned, "some" is reversible, so the statement "Some doctors are lawyers" is identical in meaning to the statement "Some lawyers are doctors." Both of these statements mean that there is at least one (i.e. some) person who is both a doctor and a lawyer.

[askuwheteau@protonmail.com]

Hi Jeff,

Thank you for explaining this. I appreciate it.

Best,

Jonathan

[askuwheteau@protonmail.com]

When doing the Most train drill, a seemingly similar situation arises as with my previous inquiry re the Some train drill.

Re the Most train drill:

#4: I have as my answer J<^m L whereas the answer key has: L > ^m J. In either case, the conditional statements are saying that Most L's are J's. Is my answer incorrect?

#7: I have as my answer Negated S < ^m U whereas the answer key has: U>^m S (negated letter S). In either case, the conditional statements are saying that Most U's are not S's. Is my answer incorrect?

[Jeff Wren]

Hi Jonathan,

The short answer to both questions is that your inferences were correct and are identical in meaning to what was written in the answer key.

The "direction" of your arrows (meaning whether they point up, down, left, right, diagonal, etc.) does not matter in diagramming. All that matters is what term is at the "beginning" of an arrow and what term is at the "end" of an arrow.

Having said that, we usually diagram left to right most of the time as that is often easier to follow since that is how we read English.

For example, if I were to diagram the statement "All As are Bs," I would diagram it

A -> B

Of course, I could diagram this statement:

B <- A

Only the physical direction (left to right) has changed, but in each diagram the arrow points from the "A" to the "B." These two diagrams are identical.

Note that these diagrams are not reversible. So diagramming the statement,

B -> A would be a Mistaken Reversal.

As for why we would ever diagram in a different direction than left to right, when you start linking multiple formal logic statements, you need to "branch out" in different directions so that you can read them all and make the appropriate inferences.

I realize that your questions were about "Most" statements, but they follow the same rules.