Why is everything translated into conditionals?

vorrath.johanna

Hello Everybody,

I am currently working my way through the Logic Games section. I've taken multiple symbolic logic courses in University and learned all about logical operators, such as ampersand (conjunctions), wedge (disjunction), horseshoe/arrow (conditional) and triple bar (biconditional).

I keep trying to translate the given sentences with the common logical operators used in symbolic logic, but the 7Sage program seems to only use conditionals to translate every sentence...

One example that stood out to me is: "Neither ... nor". In symbolic logic that normally translates to either (~A & ~B ) or into ~(A v B ), according to the DeMorgan's laws. However, 7Sage suggests the translation: A -> ~B C -> ~B
Can someone explain to why we aren't using the other logical operators? It is distinctly possible that I am missing something or misunderstood something, so I would appreciate any help!

Johanna

clear227

If other logical operators make more sense, you should use them. I also took logic in college and do "~A & ~B".

WinningHere

I may be terribly wrong, but I think the course translates to what is most efficient for the LSAT. I do not think the LSAT requires that deep a knowledge of symbolic logic, but rather, especially in games, more deductive logic (which is what I took in college). But agree with above, use what works for you.

phosita_phoeatah

I also took propositional logic in undergrad and am more familiar with the conventions that @"vorrath.johanna" mentioned.

As such, when I started the CC section on logic games, I was also a bit perplexed at first when 7Sage has "or" written out as /P --> Q. I think one of the key reasons for doing this is that it forces one to get into the mindset of noticing the triggering conditions, and certainly, writing P or Q as "/P --> Q" or "/Q --> P" encourages that type of response. And this practice is particularly conducive for chaining conditionals, which are often expressly the main theme of In & Out games.

That said, it isn't perfect, as the example of "neither nor" above shows. Even worse is when one needs to translate P or Q but not both. I personally write it as P xor Q, and it has the benefit of appearing in a clear, uncluttered manner. 7Sage uses conditionals to represent this, and that alone tends to make things confusing (not to mention the fact that xor rarely occurs, which makes it even more stress-inducing to write in terms of conditionals). I actually skipped JY's explanation of a particular game where the xor operator played an important role.

But overall, the former approach works for the vast majority of scenarios I've come across (at least in PT 1-35), where the latter is advantageous for only a few instances. In which case, the 80:20 rules prevails: adopt the notation that is helpful for 80% (actually higher than that) of situations, but be prepared to use the alternative notation in the other 20% of situations.

As a trained chemist, perhaps this scenario above (specifically, inability of a particular representation to fully capture an idea) was a bit easier to accept. It isn't all that different from utilizing Lewis Dot Structures to represent certain aspect of chemical structures, while utilizing other representations to illustrate aspects that Lewis Dot Structures cannot represent well.

vorrath.johanna

@phosita_phoeatah Thank you for your thorough response! I really enjoyed your explanation and the suggestion of the 80:20 rule. I will be applying that approach to my future studies.