Getting either/or from LG and two options from LR confused

Ashley2018-1

If an individual only has two choices available, for example green and purple, that could be diagrammed as /G—-> P but is that the same as the “either or rule” from logic games? The idea that at least one of these options had to be in the game? Or am I getting the two conflated?

Lime Green Dot

"... is that the same as the “either or rule” from logic games? The idea that at least one of these options had to be in the game?"

Yes! If we're talking specifically about this verbiage on LG, we should be given all the clues in the rules to determine whether we're in the ~G → P world or the ~G ↔ P ("this or that, but not both") world.

If on LR, yeah we'd have to take a careful look at how it's being presented. It's heavily context-dependent, unless reasonable, common-sense constraints would have us believe you can literally choose just one and not the other (e.g., either being alive or being dead). If all the info we have from your example are just the two colors before us and that's it, yes, we must choose at least one of G or P, and we might be able to choose both as well.

Do you have a particular game or question in mind?

Ashley2018-1

Yeah. The LR question is literal cancer. I think I shed a few tears attempting to solve it lol. It’s from prep test 62 section 4, 18. But there’s no game. I was just wondering whether /A——> B and it’s meaning (A or B or A+B) still applied to the conditional that shows up in that LR question or if it’s two separate things

Ashley2018-1

Because in that LR question there are only two options: Sending a spacecraft or relying on them to communicate so it was /SS——> C s is that an either or rule or not

canihazJD

Most of the conditional logic in this question is a red herring IMO.

We can't send spacecraft
so if there are sentient beings out there we won't know

Assumption: the only way to detect them is spacecraft.

Lime Green Dot

Well dayum.

That was possibly the hardest SA question I've ever seen. Ever. It really pulled all the bells and whistles. My intuition might have led me to the A/C that "felt" like it had the right stuff w/o really being 100% or anywhere close, but this is further living proof I need more work on lawgic.

I think in terms of the "either/or" exclusive/inclusive confusion, you're specifically referring to the actual correct A/C (D), and how it connects up with the conclusion, right? Based on the explanation video, it doesn't seem like we even need to take it into account here. I'm not sure how far you got with the diagramming, so I'm just going to break down how we can get to it w/o thinking about exclusivity/inclusivity.

--

Starting with (D), we'd have an embedded conditional:

~COMM → (DET → SSP)

But from the conclusion, we know we are trying to get to ~DET.

So before we dis-embed (a word?) the embedded conditional, it's better to get our elements lined up inside, so we take contrapositive and get:

~COMM → (~SSP → ~DET)

Now we dis-embed to get: ~COMM and ~SSP → ~DET

--

Now back to the STIM.

We've got another embedded to deal w/ in the conclusion: SB → (~INT → ~DET)

We can dis-embed to yield: SB and ~INT → ~DET

From premise 1, we know ~SSP.

From premise 2, we get: COMM → INT

We want to get it in line with the conclusion, so we take the contrapositive,
~INT → ~COMM

Combining P1, P2, and CON together, we have:

[P1] ~SSP

[P2] ~INT → ~COMM
——————————————
[CON] SB and ~INT → ~DET

It's redundant to say "SB" (there are sentient beings...), because every condition that follows is based on the existence of SB. So we may simplify the conclusion further to:

[CON] ~INT → ~DET

This is where I kind of got lost, lost, lost.

In JY's explanation, he says we at least know we need to connect up ~COMM and ~SSP from the premises with ~INT in the conclusion.

I knew this, but I really couldn't figure out how until I hit (D) and mapped it out as above. If we bring all our elements together, we'd get:

[P1] ~SSP

[P2] ~INT → ~COMM

(D) ~COMM and ~SSP → ~DET
————————————————
[CON] ~INT → ~DET

We can see that "~SSP" already jives with (D). Check. So now it really just becomes a simple connect-up b/w [P2] and ~COMM:

~INT → ~COMM and ~SSP → ~DET

--

Good heavens. 🤯 Sorry for the length, but hope this makes it clear! Let me know if there's still any confusion about why we don't need to consider either/or here.

Ashley2018-1

The entire 1st sentence is the main conclusion but I see it represented in explanations as just (Determine if there are sentient beings----> at least as intelligent as humans). Is that equivalent to the whole "If there are sentient beings outside our solar system....intelligent as humans" since the "this" next to determine is referential phrasing and points to that prior phrase?

Lime Green Dot

Yep, like I mentioned, it turns out that this whole conclusion essentially does boil down to ~INT → ~DET (contrapos. of yours). At a mechanical level, one might be given to auto-translate into an embedded b/c of the indicators that seem to separate this sentence lawgically.

But as you pointed out, when we expand the "this," we do realize that everything is conditioned on there even existing these "sentient beings" (e.g., determining there are SB, knowing whether SB are "at least as INT" as us, etc.). That's why it's unnecessary to have to translate it on its own.

Was your question about either/or | inclusive/exclusive answered?