Monthly Archives: January 2016

Analyzing a real argument

Mr. Nance,

I lead a group of young men in Intermediate Logic and they wanted to put their skills to use. They used an argument they pulled from chapter 1 of the book Defeating Darwinism. We tried several different ways of representing the propositions but always came up with an invalid argument. We really want it to be valid! What do we need to do? The original argument is: “If God created space and time, then He is outside of time. Therefore, He is not affected by time.” Any helpful hints will be very appreciated. Continue reading Analyzing a real argument →

10 Ways to Thwart Copiousness

Rhetoric
  1.  Be too cool to ask questions or learn anything new.
  2.  Try not to think hard, but if you must think, compartmentalize your thoughts.
  3.  Spend your free time indoors staring at a screen.
  4.  Fear ideas that differ from your own, and never read anything you disagree with.
  5.  Only be friends with people your own age who think like you.
  6.  Avoid people who know more than you.
  7.  Have no heroes.
  8.  Never travel far from home, but if you must, stay only in comfortable places.
  9.  Never think through what the Bible says about anything.
  10.  Never pray.

HT: Brian Daigle.

If you are interested in 10 ways to increase copiousness, you might be interested in Fitting Words. Continue reading 10 Ways to Thwart Copiousness →

More Notes on Shorter Truth Tables

Shorter truth tables take some time to learn. Do not rush through them. Students need lots of examples to see how they work.

Make sure you and they understand the concept behind them. You are assuming that the argument is invalid (by making the premises true and the conclusion false). If this assumption leads invariably to a contradiction, then the argument cannot be invalid, so it must be valid. But if you can assume the argument is invalid and fill out all the truth values without any contradiction, you have shown that the premises can be true and the conclusion false, i.e. you have shown it to be invalid.

Keep this in mind also: You must place the truth values under the main logical operator. The main logical operator is the operator in the column that would be the last to be filled out in the larger truth table. For example, consider this compound proposition:

~(p • q) ⊃ r

If this were a premise of an argument, the T would be placed under the conditional. But for the proposition

~[(p • q) ⊃ r]

the T would be placed under the negation. Working the truth values all the way out would result in the following:

~[(p • q) ⊃ r]
T   T T T  F  F

Must we do every unit?

Intermediate Logic,

Over my 25 years of teaching logic, I have often been asked this question:

“Intermediate Logic is a challenging course, especially trying to complete it all in one semester. Is each unit equally important, or can I skip something if I can’t fit it all in?”

The short answer is “You don’t have to do it all.” Unit 1 on Truth Tables is foundational to propositional logic, as is Unit 2 on Formal Proofs. Both of these are essential and must be completed by every student. Unit 3 teaches the Truth Tree method. A truth tree is another tool that does the same job as a truth table: determining consistency, equivalence, validity, etc. Some people like truth trees more than truth tables, since they are more visual. But Unit 3 could be considered an optional unit. Unit 4 covers Applying the Tools to Arguments. This is where the rubber meets the road for propositional logic, showing how to apply what has been learned up to this point to real-life reasoning. Consequently, Unit 4 should be completed by every student. Note that if you skip Unit 3, one question in Unit 4 will have to be skipped (namely, Exercise 28c #1). Unit 5 on Digital Logic – the logic of electronic devices – is entirely optional. Like Unit 4, this unit covers a real-life application of the tools of propositional logic, but one that is more scientific (though ubiquitous in this age of computers and smart phones). Though optional, many students find that they really enjoy digital logic.

As a teacher I have sometimes skipped either truth trees or digital logic. In fact, only with my best classes have I taught both Unit 3 and Unit 5. The Teacher Edition of the Intermediate Logic text includes two different schedules, one for completing every unit, and another for skipping Unit 5.

For answers to more FAQs, take a look HERE.

The Pattern of T & F in Truth Tables

Mr. Nance,

I was doing the exercises for Intermediate Logic Lesson 6 and got stumped by #2. In the part of the proposition that is ~q ⊃ ~p, when I was doing the defining truth table for the variables, I assumed the first variable, though out of order alphabetically, would get the TTFF pattern. But in the answer key, the letter that comes first in the alphabet (p), though the consequent, got the TTFF pattern. Why is that? Continue reading The Pattern of T & F in Truth Tables →

#20 – Failure and Success

Commonplaces

“If at first you don’t succeed then skydiving definitely isn’t for you.” – Steven Wright

“We are never defeated unless we give up on God” – Ronald Reagan

“The greatest danger for most of us is not that our aim is too high and we miss it, but that it is too low and we reach it.” – Michelangelo Buonarroti

“By failing to prepare you are preparing to fail.” – Ben Franklin

“Strive not to be a success, but rather to be of value” – Albert Einstein

Quick negation rules

Uncategorized

Here are some quick rules to help you symbolize propositions that use negation:

Not both p and q  =  ~(p ⋅ q)
Either not p or not q  =  ~p v ~q
Both not p and not q  =  ~p ⋅ ~q
Neither p nor q  =  ~(p v q)

Truth tables can be used to show that the first two proposition forms are equivalent, and the last two forms are equivalent. The meaning of the sentences also help to show this.