Translating sentences into lawgic

apublicdisplay

This question is taken from the Group 1 Group 2 Translation exercise but I'm finding recurring instances of odd translations into conditional lawgic. For example, how come for sentences like “Bravery is essential to overcome adversity” (Translated in the video explanation as: If Overcome Adversity then Brave) “is essential” points back to “bravery” as the necessary condition but for sentences like “Beauty is always in the eyes of the beholder” (Translated as: If Beauty then In Eyes of the Beholder) “is always” doesn’t point back to “beauty” as the necessary condition?

I would think that translating any statement that says "X is necessary for Y" would be "If Y then X" because it plainly says that so I don't understand why there's an exception for "is always."

Alex Short

Okay so these are the kind of sentences you want to have a firm grasp on before moving on - and it will be easier than you think.

I found that relying on my intuition became reliable when I began to read and truly think about what the statement in front of me meant.

For example, “Bravery is essential to overcome adversity”

think about what this is saying. Try to not think explicitly in terms of necessary and sufficient conditions unless you also understand the nature of what it means to be necessary or sufficient.

For bravery to be essential (that's a strong word) for something else, it means for that something else, you'll need bravery.

In other words, to overcome adversity, it is essential (necessary) one has bravery. If Overcome Adversity then

Something being essential for something else is the same, or close to it, as being necessary.

“Beauty is always in the eyes of the beholder”

Instead of overthinking, see that this sentence just says C is D. The word always is likely included to be potentially confusing, but to apply indicator rules to think 'beauty' is necessary is incorrect and is overthinking things. If a sentence says X is Y, it will always translate to if X then Y.

My advice is to keep practicing, memorize indicators but also memorize when you're looking at an indicator word that shows us necessity or sufficiency, as well as when it just appears as part of the necessary condition (like above).

apublicdisplay

Hey, thanks a lot. That made me see that omitting the word "always" from "Beauty is always in the eyes of the beholder" makes little difference whereas omitting the word "essential" from "Bravery is essential to overcome adversity" makes a huge difference. Focusing on the context of the whole sentence I now see that "always" is more of an irrelevant extra touch to the sentence rather than a relationship indicator.

Alex Short

Exactly - the test will throw words at you to try to fool those test takers who might overthink things, but I found it essential to learn about necessary and sufficient conditions so then I could later, while reading, not have to devote my mind to that stuff (except for a logic heavy stimulus here and there.)

While you prep, just make sure to incorporate (with whatever you're studying at the time), a macro-level understanding of what the sentences mean, how they support (or receive support) from one another, and how the argument is intended to be understood. Those things in general are often overlooked, but keep on track, learn the basics and don't give up.

And always ask questions on here if you're having any issues. Good luck!

dcdcdcdcdc

I am skeptical as to whether "always" is really a logical indicator, at least for Group 2 necessary conditions. Grammatically, English usage has the adverb "always" following the verb "to BE" and generally coming directly before any other verb. It is a temporal adverb that describes the action. In almost all cases you will see "always" before the verb that indicates the predicate and the mechanical translation of logic/lawgic will give you the correct result because we typically have A is B written out as A-->B.

Take a simple subject predicate sentence. Elephants (E) eat trees (T)

E-->T

Elephants (E) always eat trees (T)

E-->T

We still got the correct ordering of the necessary and sufficient conditions, regardless of always. It's almost like it isn't there. Because it is a temporal adverb it is describing the relationship of the two ideas to time, in this case that this is a relationship that holds "at all times." When we are reading for conditional logic, we are inclined to assume the strong "at all times" case when we translate things like A-->B, all A's are B's. It would be more significant for us to get information about times when the rule may not hold.

For example, All A's are B's. How about All A's are always B's? Did that add anything we didn't already capture in the first statement?

Now if I told you All A's are usually B's, All A's are often B's or All A's are sometimes B's, we have really weakened the meaning of "is/are." We have qualified the predicate verb so that there is now an opportunity for the relationship not to hold at some point. Before we just assumed by definition "at all times."

Basically, I think the subject-predicate relationship is really what guides us in determining the necessary sufficient conditions in sentences with "always." Maybe a rough guide would be, when in doubt, identify the idea following "always" as the necessary condition, but then again, that is usually going to begin with a verb, which should be your clue that the predicate is the necessary condition anyways.

As for the "is essential" example, that is a predicate adjective. "Is essential" is the predicate and "essential" is an adjective. The meaning of the sentence would change if we used "sufficient" as the predicate adjective. So, agreeing with the comments above, this is the reason the macro-level view can be useful. Mechanically applying a "what follows" the indicator approach can be dangerous when we ignore the meaning of the words. They have told you that the subject "bravery" has the quality of being essential. Keep that in mind. Essential for what? "To overcoming adversity." If I told you "bravery is sufficient" or moreover, "bravery is irrelevant" would we be trying to assign it as the necessary condition? I hope not.

So, overall it looks like we have some guideposts in grammar and language that flag possible necessary/sufficient conditions, but some words have meanings so clearly associated with one condition or the other that we should not ignore them, even if they are in the subject when we expect them in the predicate, or vice versa.

MrSamIam

I can see how that might be confusing. For a minute, forget about this whole "pointing back" and "pointing forward" stuff. Just use your intuition:

"Beauty is always in the eye of the beholder" = B --> EOB
If beauty is present, then we must have something that is in the eye of the beholder. Why? Because it (beauty) is ALWAYS (no matter what, whenever, however, etc.) in the eye of the beholder.

"Bravery is essential to overcome adversity" = OA --> B
This one is easy to see if you use your intuition. We are being told that bravery is an essential (pretty much "necessary") element of overcoming adversity. So, if I tell you that Jim overcame adversity, what do you know? Well you know that Jim is brave, since being brave is required to overcome adversity.

You may be getting confused due to the usage of "necessary." Often, sentences will outright tell you that something is necessary. They will literally tell you that X is necessary for Y. In other words, X is the necessary condition for Y ("pointing back") - this is what we see in the first example you posted.

Try this:
When Sarah decides to do something, she always does it right.
What can you tell me if I were to tell you that Sarah decided to do something? She did it right (since she ALWAYS does it right, when she decides to do it).
What if I told you that Sarah did something right? No clue...just because she did it right, doesn't mean she is the one who decided that she would do it.