Important FORMAL LOGIC realization

chosun1
Posts: 5
Joined: Mon Mar 29, 2010 11:47 pm

Important FORMAL LOGIC realization

Postby chosun1 » Fri Apr 02, 2010 9:54 pm

I just realized after looking at a binary game that there is a conditional linkage that can't be made.

Let's say rules were
#1: A-> BvC
#2: B->D
You can't make the inference A->D b/c C-> ~D possibility

On the otherhand,
#1: A-> B
#2: BvC ->D
You can make the inference A->D b/c it'll be D regardless whether B or C chosen

skip james
Posts: 264
Joined: Sat Sep 19, 2009 2:53 am

Re: Important FORMAL LOGIC realization

Postby skip james » Sat Apr 03, 2010 12:17 am

chosun1 wrote:I just realized after looking at a binary game that there is a conditional linkage that can't be made.

Let's say rules were
#1: A-> BvC
#2: B->D
You can't make the inference A->D b/c C-> ~D possibility

On the otherhand,
#1: A-> B
#2: BvC ->D
You can make the inference A->D b/c it'll be D regardless whether B or C chosen


Yeah that's pretty important to realize.

Another way to think of this:
chosun1 wrote:#2: BvC ->D


is to think of it as two separate conditionals.

B --> D

C --> D

and then you can more clearly see the logic behind your inference here:

chosun1 wrote:the inference A->D b/c it'll be D regardless whether B or C chosen



On the flip side, you can also think of conditionals that do this:

A ---> B & C

as being two separate conditionals:

A ---> B

A ---> C

This makes it easier to understand, I think.

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Gemini
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Joined: Thu Mar 11, 2010 9:23 pm

Re: Important FORMAL LOGIC realization

Postby Gemini » Sun Apr 04, 2010 3:05 pm

This is all assuming that A, B, C, and D are the only players... which is often not the case for LG, lol, as there are usually at least 6. :)

CMDantes
Posts: 420
Joined: Thu Feb 04, 2010 2:37 pm

Re: Important FORMAL LOGIC realization

Postby CMDantes » Sun Apr 04, 2010 4:35 pm

Excuse my ignorance, but what does the v signify in BvC?

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FreeGuy
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Re: Important FORMAL LOGIC realization

Postby FreeGuy » Sun Apr 04, 2010 4:44 pm

CMDantes wrote:Excuse my ignorance, but what does the v signify in BvC?


it means "or"

CMDantes
Posts: 420
Joined: Thu Feb 04, 2010 2:37 pm

Re: Important FORMAL LOGIC realization

Postby CMDantes » Sun Apr 04, 2010 4:59 pm

FreeGuy wrote:
CMDantes wrote:Excuse my ignorance, but what does the v signify in BvC?


it means "or"


Thanks.

chosun1
Posts: 5
Joined: Mon Mar 29, 2010 11:47 pm

Re: Important FORMAL LOGIC realization

Postby chosun1 » Tue Apr 20, 2010 12:06 pm

Here's another formal logic tidbit

Some ppl debate whether they should take a formal logic class. Besides the obvious pointlessness of such a class to ppl wh are not taking comp sci or linguistics, there are rlly only a few elements that truly help on the LSAT. I'll save you the money and give you just the two most important things I learned from taking the class.

1. DeMorgan's Laws

DeMorgan's Law basically tells you how to convert a statement when a negative is attached. So for say an example that states " it is not the case that both A and B are used," you would write...

~ (A&B)

which according to DeMorgan's Laws is equivalent to...

~Av~B

this law actually helped me on one of the logic games in the Superprep Book.

2. Sufficient and Necessary

Now, most ppl don't get what is inherently the nature of the sufficient and necessary.

There are two ways I look at this:

a. sufficient leads to the necessary, but something else can lead to the necessary

ex. President signs a bill -> Becomes law

But something else can lead to a bill becoming a law, say "congress overrides the President's veto," thus this shows that there are other sufficient grounds for the necessary condition.

b. Premise and Conclusion
the most important thing I learned from a formal logic class is this and without this, I wouldn't have begun to solve many of the logical reasoning questions.
Sufficient and necessary is also parallel to premise and conclusion, that’s why ppl say in court lingo “There are sufficient grounds for this necessary conclusion”
Premise: A
Conclusion: B
Inference: A->B
This helps a lot of assumption, justify, strengthen, and conform principle questions.
Most ppl look at an assumption, justify, strengthen question and try to look for the new premise, new conclusion elements per the POWERSCORE method of Supporter answer choices. But sometimes these elements are not so recognizable. Take for example, a question like this…

Ex. Bob is very tired after he comes back home.
Therefore, Bob took a nap.
What most strengthens this statement?

There 1st sentence is the only premise to prove the conclusion in the 2nd sentence.
The answer choice would be not in similar words, but something to the equivalent of “ If is exhausted after work, he must go to sleep”

On Conform Principle questions, this Premise, Conclusion dichotomy is even more important.
Let’s say there was a principle…
Ex. If an action if not popular, then it must lack majority consensus or news media negatively reports on it.
Writing this out in FORMAL LOGIC abbreviation, it would be…
~ AP -> ~ MC v ~NMPR
( AP = action popular, MC = majority consensus, NMPR = news media positively reports on action)
You will never see a conclusion that states something “lacks majority consensus or news media negatively reports on something.” Why? Because these are simply the CRITERIA/GUIDING PRINCIPLES to judge whether the OUTCOME/JUDGMENT (action) is indeed correct
The OUTCOME/JUDGMENT must be the conclusion, so we take the contrapositive of the statement and match the answer choices to it.
So…
MC & NMPR -> AP
If an answer choices has ~AP, then it is not a correct answer choice.




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