Archive for the ‘Mark Zegarelli’ Category

Word of the Day: Categorical statements

March 30, 2008

Categorical statements are statements that talk about whole categories of objects or people. Furniture, chairs, birds, trees, red things, and cities that begin with the letter T are all examples of categories.

There are two types of categorical statements:

  • Universal statements: These are statements that tell you something about an entire category. Here’s an example of a universal statement:

    All dogs are loyal

    This statement relates two categories and tells you that everything in the category of dogs is also in the category of loyal things. You can consider this a universal statement because it tells you that loyalty is a universal quality of dogs.

  • Particular statements: These are statements that tell you about the existence of at least one example within a category. Here’s an example of a particular statement:

    Some bears are dangerous

    This statement tells you that at least one item in the category of bears is also in the category of dangerous things. This statement is considered a particular statement because it tells you that at least one particular bear is dangerous.

Logic for Dummies by Mark Zegarelli

Assume it’s “easy until proven difficult”

March 4, 2008

I saw this phase in a book I am reading1: “easy until proven difficult”

It occurs to me that oftentimes I approach a task assuming that it is complex and difficult. The result is I solve the task in a complex fashion. It is only later that I see how to simplify it. Then, after removing all the complexities that I unnecessarily added, I realize that the task was actually simple. Perhaps if I go into a task assuming that it is “easy until proven difficult” I can bypass adding unnecessary complications.

[1] Logic for Dummies by Mark Zegarelli

People love simplicity

January 11, 2008

People love simplicity.

Have you ever read halfway through a movie review and then skipped to the end to find out whether the movie got a thumbs up or a thumbs down?

Have you ever paged through a car magazine checking out how many stars every car received?

Have you ever sat with a friend rating the guys or girls you both know on a scale of 1 to 10?

Movies, cars, guys, and girls are complicated.  There’s so much to understand.  But people love simplicity.  I’m sure you, like me, feel a sense of relief when you can reduce all of that complexity down to something small enough to carry in your pocket.

Logic was invented with this need in mind.  With logic you can take a complicated statement in English and write it with just a few and, or, and not symbols, and reduce the sentence to a single truth value: either True or False.

Logic for Dummies by Mark Zegarelli

How to phrase a complex sentence in a clear, unambiguous fashion

January 6, 2008

Complex sentences oftentimes contain and, or, and not. There are various ways to express anded sentences, ored sentences, and noted sentences. Depending on which way you use, a sentence can be easily understood or ambiguous.

Suppose we denote the sentence “I will go shopping today” by the letter A, i.e.

Let A = I will go shopping today.

And likewise for these sentences:

Let B = I will do cleaning today.

Let C = I will call my Mother today.

We can translate the negation of A in any of these ways:

  • It is not the case that I will go shopping today.
  • It isn’t true that I will go shopping today.
  • I will not go shopping today.
  • I won’t go shopping today.

We can translate A and B in any of these ways:

  • I will go shopping today and I will do cleaning today.
  • I will both go shopping today and do cleaning today.

We can translate A or B in any of these ways:

  • I will go shopping today or I will do cleaning today.
  • I will either go shopping today or do cleaning today.

Now suppose that we need to combine the sentences in more complex ways.  For example:

(not(A) and B) or (not(C))

For not(A) there are four ways to translate it.  Which way should we use?  Our choice can have a big impact on the understandability of the final sentence.  Likewise for anding and oring.  Here’s one way to express it:

I will not go shopping today and I will do cleaning today or I will not call my Mother today.

Although the sentence is technically correct, it’s somewhat confusing because the parentheses are gone and everything runs together.  A good way to clean it up is to express it as:

Either I will not go shopping today and I will do cleaning today or I will not call my Mother today.

The word either clarifies just how much the word or is meant to encompass.   Thus the words either and or act in combination like parentheses.

— Extracted from Logic for Dummies by Mark Zegarelli

Humans are relatively good at induction and relatively poor at deduction; computers are just the opposite

December 21, 2007

Induction is reasoning from a limited number of observations toward a general conclusion. A classic example: After observing that 2 or 10 or 1,000 ravens are black, you may decide that all ravens are black.

Another way of thinking about induction is that it is reasoning by pattern recognition – we fill in the gaps of missing information.

With deduction you start with a set of possibilities and reduce it until a smaller subset remains. For example, a murder mystery is an exercise in deduction. Typically, the detective begins with a set of possible suspects — the butler, the maid, the business partner, and the widow. By the end of the story he has reduced this set to only one person: “The victim died in the bathtub but was moved to the bed. Neither woman could have lifted the body, nor could the butler with his war wound. Therefore, the business partner must have committed the crime.”

Humans are relatively good at induction and relatively poor at deduction. Any of us is capable of instantly recognizing a face (an inductive task), yet most of us would have a tough time quickly doing the deductive calculation:

(239.46 x 0.48 + 6.03) / 120.9708

Computers are relatively poor at induction and relatively good at deduction. A simple pocket calculator can quickly and perfectly do the calculation, while it is a very hard programming challenge to get even a powerful computer to accurately recognize a face.

The Origin of Wealth by Eric D. Beinhocker and Logic for Dummies by Mark Zegarelli