BITS OF LOGIC

Thomas Russell Wingate
October 2009



1


An argument is the application of reasoning to premises.

2


An argument must be either correctly reasoned (valid) or incorrectly reasoned (invalid). Which it is depends upon no one’s opinion.

An argument is a chain of statements. It does not matter how many of the statements are true, or how true they may be when taken one by one. If even one statement is not connected (in logic) to the next one, the argument is shattered.

3


Hypothesis: if A, then B.
Converse: if B, then A.
Inverse: if not A, then not B.
Contrapositive: if not B, then not A.

The hypothesis and the contrapositive are either both true or both false. To prove (or disprove) one is to prove (or disprove) the other.

There is never any link whatsoever between the hypothesis and the converse, the hypothesis and the inverse, or the converse and the inverse.

You may draw concentric circles to prove this.

                   4

 

You learned to speak and hear your language before you learned to write it. You must halfway unlearn the habit of hearing in order to acquire the habit of reading.

 

Writing is not speech on the page. Writing is something else. To be educated is to know what else.

 

Many things you have heard all your life do not make sense when you stop to think about them. Why absorb and repeat the blunders of others?

 

Although you have often heard it, you must never, as long as you live, use “all ... not.”

 

Treat yourself: look up “Venn Diagram” in Wikipedia.

 

Poor grammar may bring you embarrassment. Poor logic may get someone killed.

 

 

5


To find out what is true, you must look at the real world, not at the argument being made—even if you are the one making the argument.

People presenting an argument are in the real world, are they not? Look at them closely. They have been looking at you to find your soft spots.

6


Propagators of an argument do not (ordinarily) wish you to examine its structure. They are employing the argument to get you to see things their way. If you fail to detect invalid argument, or deceptive wording, how is that not your fault?

Caveat lector, caveat auditor.

7


American debaters speak of “the hidden premise.” British debaters speak of “the suppressed premiss.” (Notice the difference in spelling.) I prefer the British usage here, but I defer to my countrymen’s.

A hidden premise is something someone does not want to talk about, or something no one wants to talk about.

8


To prove its point—to make its case—an argument must employ major premises, minor premises, and conclusions.

Nearly all arguments are valid (coherent). Someone has spent years polishing them. If you direct your efforts to finding mistakes in reasoning, you will probably find that your approach has been anticipated and thwarted

9


It is more fruitful to spend your mental time seeking out hidden premises.

These have been hidden exactly because they will not stand up to examination, cross-examination, and exposure.

They are raw nerves. Invectives protect them. Brace yourself.

10


Intellectual tradition transmits valid arguments drawn upon premises.

A credentialed education—even a self-education—is an unreliably labeled mixture (not an alloy) of the verified, the unverified, and the unverifiable. It can stifle more than it stimulates.

11


A conclusive argument must be properly built upon premises that are clear (not blurry) and true in the factual (not an emotional) sphere.

Wishful thinking and dreadful thinking are contaminations of the factual by the emotional.

These impostors come disguised. Logic is meant to expose them.

Think of icebergs: what you don’t see is far larger (and closer) than what you do see.

12


Nearly all political divisions depend upon fallacies such as this:

It’s either A or B.
A is not true.
Therefore, B is true.

Therefore, you should believe B.
Only bad people (unlike you) believe A.


In so far as logic is concerned, it is perfectly possible that A and B are both (even if unequally) untrue.

One must ascertain the truth content of A and B by examining the real world, not by repeating familiar incantations purporting to explain or improve it.

13


Reflect, please, on the fact that Lincoln kept Euclid’s Elements in his saddlebag and studied late at night by lamplight. “You can never make a lawyer,” he said to himself, “if you do not understand what ‘demonstrate’ means.”

A writer need not be a lawyer, but if he is ineffective at exposition, what in the world is he trying to become or remain a writer for?
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