Self-study
Hi everyone, I’m working through the Foundations module and I’m hitting a wall with chaining conditionals. I understand how to diagram individual sentences (using the G1, G2, G3 rules), but I’m confused on the "glue" that connects them.
Specifically, I’m struggling with:
How do I know which brick goes "first" in the chain if the stimulus doesn't present them in order?
If I have one brick that is positive (A -> B) and another that is negative (/A -> C), I know I need to flip one to make them match, but I’m struggling to see why or how to pick which one to flip.
For example, with the Wizard/9th-level spell drill, I could diagram the parts, but I couldn't figure out how to bridge the "Not 9th-level" sentence into the main chain.
Does anyone have a specific "checklist" or a different technique they use to decide when to take a contrapositive to force a chain to connect? Below is how I worked through the question if it helps with my question!
Wizards that cast ninth-level spells command a great deal of magical energy. Only wizards who possess extensive training in the arcane can control such magical energy. Spellcasters who can’t cast ninth-level spells still have more to learn.
heres my work: I don’t see an indicator word here, im tempted to put great deal of energy on the left but im gonna take the wizards part to be ALL and use that as a sufficient for G1 SO: FIRST BRICK: W Cast 9 level spells -> great deal of energy
Only is g2 necessary so SECOND BRICK: Can control such energy -> Wizards who posses extensive training in arcane.
It says that if they cant cast ninth level spells so that cant makes it a / so
Conclusion: /Ninth level spells - > Still have more to learn
So all together: W Cast 9 level spells -> great deal of energy, Can control such energy -> Wizards who posses extensive training in arcane. /Ninth level spells - > Still have more to learn
Chained its: W Cast 9 level spells -> great deal of energy -> wizards who possess extensive training -> /still have more to learn.
I know its wrong but im so confused...
2
3 comments
You're almost there...
You had the chain:
9th Lvl -> command/control -> extensive training
Then you have an additional piece of info:
/9th Lvl -> more to learn
But, we can flip this (flip and negate):
/more to learn -> 9th Lvl
What do we know about people on the 9th Lvl? (Refer to the chain above):
/more to learn -> 9th Lvl -> command/control -> extensive training
Developing your intuition takes time, at the start a bit of trial and error is no problem as long as you are correctly flipping (flip and negate). See how I tackle your first example:
If you have A -> B and /A -> C, the connecting idea is A. That is the only way to make a chain. If you flip and negate the first conditional you get /B ->/A and you can make the chain /B -> /A -> C (Great!). Or you can flip and negate the second conditional, getting /C -> A, making the chain /C -> A -> B (also great!). The chains say the same thing, one just might be in the correct order for a specific question. e.g. What must be the case if A happens? The answer is B must happen. The second chain is easier for quickly recalling the ideas we've written down.
My advice would be to get used to trial and error. Also, flipping and negating correctly. The rest is intuition you build over time as you map out more conditionals and answer more questions.
Hope this helps. Let me know if you have any follow ups.
@JosephCronin Thank you for the advice I really appreciate it and it definitely was helpful to see how you worked through it. My brain is wired to ask the why a lot and I guess im a bit confused as to why we would negate /9th lvl -> more to learn to /more to learn -> 9th level? After thats negated I assume we do the contrapositive of G1 which is to flip the two bricks and negate correct? Apologies if its confusing, Im getting lost in the sauce.
@JeffreyRamirez (fyi: when I say negate, or negate and flip, I mean take the contrapositive). If we don't take the contrapositive of /9th Lvl -> more to learn, then we can't add it to our chain. We need a common link, which comes from "9th Lvl". Chains are normally the best for answering questions and quickly seeing how one things leads to another.
/9th Lvl -> more to learn
vs
/more to learn -> 9th Lvl
(This is the same principle. But expressed in different ways—see lessons on contrapositive).
Then we have our chain from before:
9th Lvl -> command/control -> extensive training
Which format from above allows us to slot that conditional (more to learn etc.) right into this chain of conditionals? That's what you need to be asking.
What if we were given another bit of information..."Unless a wizard has spent 5 years at Hogwarts, they cannot be considered to have had extensive training." ...or, /5 years->/extensive training vs extensive training -> 5 years. Which format is better for our chain above?