Logic, All You Need To Know for Everyday, MBA, GRE, or LSAT
Read these tricks, and better than the other 94% of candidates secretly
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If you want to be more logical, you are in the right place!
If you need to take the MBA, GRE, or LSAT tests, these are the knowledge all you need to know!
I learned from the book — Logic Made Easy How to Know When Language Deceives You. The rules of logic and the history of logic. I want to share with you everything you need to know about logic.
When You Not Sure A Logic is Valid
Humans are reasoning animals, perhaps the only animals capable of reason.
A psychologist must reason from the symptoms at hand. Automobile mechanics use reason to do auto repairs. Computers are full of logic rules in order to function well. Businesses need decisions based on logical analysis to work well with the majority of employees.
The great mathematician, Leonhard Euler said that logic “is the foundation of the certainty of all the knowledge we acquire.”
Usually, you are not a logic expert. You didn’t have a habit of self-reflecting if your logic is correct. And for most cases, logic is a new word to your brain.
However, we still need to make sound logic. And we still need to make valid and wonderful arguments.
You may ask: “ Is there a quick way to self-check your logic validity?”
Yes, we have.
You don’t have to drench yourself with tons of logic terminology and the saying of Aristotle. When you are not sure whether a logic is correct, you should make a dopey example.
For example, question:
“If p (is true) then q (is true), q (is true).”
Conclusion?
Things more clear, “If flight 409 is canceled, then the manager cannot arrive in time.” Does this sentence make sense “If the manager did not arrive in time then flight 409 was canceled.”
The best way to act is not to self-check the flight information and make a decision according to the example. Since all logic is patterned, you can create another simple example to get it right.
Make a dopey example like these.
“If there is traffic, then you stop the car. You have stopped the car.” If you say “There is traffic” you would be wrong. There are many reasons that you might stop the car.
“If I am unhappy, then I will play computer games.” Right now I am playing computer games, am I unhappy? No way. There are many reasons that I might play computer games.
Make a dopey example and see if it abides by logic is a trick to have. You don’t need to have decades of experience in logical reasoning. Try to organize an example in the same format as the questions, but it is easy for you to distinguish. The logic is clear.
Top-Line Principles
Even ancient Greeks knew that reasoning is a patterned process, and deductive thought had patterns.
The vocabulary we used within the realm of logic is directly from Latin translations Aristotle used when he determined the rules of logic deduction.
The top-line principle of rational behaviors is consistency. Yesterday you told me you love climbing the mountains and I see you one day claim you rather go jogging. You are lying to me. Your behaviors are contradictory to your claims.
These words of mathematical proof were imprinted in the early days and never stopped emphasizing the importance of logic’s core principles — consistency and noncontradiction.
Premise, Excluded Middle, Universal Statement…
Proving a statement by showcasing valid, known, and accepted truths is called premises. We begin with true statements, called premises.
When we arrive at the final statement — conclusion, and since all of our premises are correct, we must be sure that the conclusion is correct.
Men cannot be both boys and girls. A statement cannot be both true and not true. Always one or the other, but never be both. True and not true, there is no middle, and we call it excluded middle.
Furthermore, if a statement about all persons, such as “Every man in this world has been taken good care of”, is a universal statement.
“Not every person has taken good care of”. “Some people have been treated badly”. Not a universal statement, but a particular statement.
A proposition is any statement that is whether right or wrong. True or false. “All Taxicabs are yellow.” (It is a false claim)
Disproof is often easier than proof. If you can find one counterexample, you will defeat the proposition. “All men are equal”. If you can find one counter, you disprove the claim.
Quantifiers are every, some, none, all…
For example, “All men are equal,” the class of men here is called subject, and the class of equal is called predicate.
Converse Statement
“All students take Math I”. Even though it is correct, the converse statement may be false. It is “All students take Math I is a student”.
Statements and converse statements are not usually both right.
Let’s take a dopey example: “All men are humans”, but it doesn’t mean “All humans are men”.
The Trouble with No
When you say negation to somebody, they will associate this with falsehood, and this makes people uncomfortable. He will be slower in evaluating the truth of the negation, more than about the falsity of an affirmation. But clearly, negation is a more difficult concept to grasp.
Professional writers use smart tricks to deal with this. They never use “no accept”, but “reject”. They never use “no right”, but “wrong”. They will avoid “no”.
Translate negatives to affirmations and more easily process information. Professional writers take extra care to make their writing more readable.
Some
In everyday life, “some” means “some but not all”. At other times, it means “some but possibly all”. But to a logician, it means “at least one and possibly all”.
Should “some” mean “some at most”, “some at least” or “some but not the rest”? English mathematician Augustus De Morgan had the answer. “Some” should be vague and remain so. Some, in common life, often means at least one and non-all. But in logic, only non-none.
Syllogisms
Two premises, both true, can lead to a conclusion, which is also true. The conclusion follows the premises. This is a three-line argument. It is named syllogism.
All A are B.
All B are C.
Therefore, all A are C.
There are three other valid syllogisms. EAE, AII, and EIO.
They are:
No B are A.
All C are B.
Therefore, no C are A.
All B are A.
Some C are B.
Therefore, some C are A.
No B are A.
Some C are B.
Therefore, some C are not A.
However, you don’t need to memorize this. It has an easy way to distinguish. If either of the premises is negative, the conclusion is negative. If one of the premises is particular, the conclusion too must be particular. (particular means “some”). When both of the premises are affirmative, the conclusion is similar.
Put Your Knowledge Away
Please don’t put your own knowledge into logic decision-making, and you will have better results.
For example, your computer is black. “All Dell computers are gray. Your computer is not Dell.” Is it logically clear that your computer is not grey?
You might think of your computer in your house (put knowledge) and say, “Yes, it follows because my computer is black.” If I give you less knowledge, your decision-making will be more logical.
“All Dell computers are gray, and my computer is not Dell.” Is it gray? Since you don’t know my computer color, the right answer is “Maybe or maybe not.”
If, AND, OR
The heart of logic is the conditional proposition. Formed by if… then….
Compare: Tea or Soda? (Not both.)
Cream or Sugar? (Both are OK.)
In logic, or means and/or.
If the first (is true), then the second (is true).
And the first (is true).
So, the second (is true).
If p then q.
p is true.
Therefore q.
What about the other class of proposition?
Proposition 1:
If p then q.
q is true.
Therefore p?
The answer is maybe or maybe not.
Let’s make a dopey example. “If it is 1 o’clock, then I will go to sleep. I will go to sleep now.” Is it 1 o’clock?
The answer is maybe.
Proposition 2:
If p then q.
p is not true.
Therefore q?
The answer is maybe or maybe not.
Let’s also take a dopey example. “If it is 1 o’clock, then I will go to sleep. Now is 10 o’clock.” Am I going to sleep?
The answer is maybe.
Fallacies
In this book Henle, Mary Henle summarizes all the common fallacies that she met in logic.
The failure to accept the logical task. The restatement of a premise or conclusion so that the intended meaning is changed. The omission of a promise. And the introduction of outside knowledge as a new premise.
Errors to failure accepting the logical task mean that one cannot distinguish whether the conclusion is logically valid or a true story. Individuals are not thinking they are tested by logical questions.
Can’t Tell are Positive Words
In logic, saying I don’t know is a virtue.
People are eager to drive a conclusion. They are averse to adopting the mindset that “no conclusion is possible”. We love bossy men. They know everything’s the answer.
And they are ashamed to commit that maybe or maybe not.
But only when they accept “maybe or maybe not”, research and study produce useful results.
All oak trees have acorns.
This tree has acorns.
Is it an oak?
The correct answer is “maybe or maybe not”.
Let’s take a dopey example:
All the cars I met today are yellow.
I met a yellow thing.
Is it a car?
Logic of Everyday Conversation
Logic is rooted in truth, but Rhetoric is planted in popular opinions and manners.
H. Paul Grice wrote a book in 1967 and the book named The Logic of Everyday Conversation. He gives more principles: Be as informative as is required; don’t give more information than is required; be truthful; be relevant; be clear; do not say what you believe to be false or which you lack adequate information; avoid obscurity of expression and ambiguity; be brief; and be orderly.
The cooperation principles require that both speakers and listeners try to be as informative, relevant, concise, clear, orderly, and truthful as possible.
Antoine Arnauld and Pierre Nicole expressed the cooperation principles that if we make our meaning understood, we don’t add more words.
Final Words
Logic and Rhetoric are withered industries today.
It is hard to recite every piece of information and the patterns in logical expression are various to memory. However, it is important if we want to make everyday business clear. And we have MBA, GRE, and LSAT tests that need to do.
However, there are ways to make a hard logical expression as simple as drinking a cup of water.
By making a dopey example. Try to rephrase the hard logical expressions with dummy examples, and I have already discussed this under “When You Not Sure A Logic is Valid” section.
Also, even though what I talk about today is simple and easy logic, they are all you need to know for an LSAT test.
After reading this, you should have clear mindsets about logic. The hard things still lie in reading comprehension and knowing clearly what the author talks about between the lines.
When I wrote this article, I was amazed at how limited logic has been used in everyday life. I thought I would learn more about logic in everyday use. But logic only exists in research papers.
Exercises in MBA, GRE, and LSAT tests make you a logic guru. And you shouldn’t pay too much attention to the knowledge. However, as far as all the knowledge you need to know about logic, I have documented it.
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