Sojourner's Song

“I have become a pilgrim to cure myself of being an exile.” -G. K. Chesterton


Aaron Telian

I'm a clumsy Christian on a journey of discipline and discovery with Jesus. As a recovering Pharisee, I'm learning to trust God's grace over my goodness. I love the world, and I'm excited about learning what it means to be salt and light in a Post-Christian culture. This is where I write about living the sojourn.


View My Profile

Blog Archive

  • ►  2009 (26)
    • ►  June (1)
    • ►  May (2)
    • ►  April (10)
    • ►  March (1)
    • ►  February (3)
    • ►  January (9)
  • ►  2008 (112)
    • ►  December (5)
    • ►  November (10)
    • ►  October (1)
    • ►  September (5)
    • ►  August (8)
    • ►  July (6)
    • ►  June (13)
    • ►  May (13)
    • ►  April (4)
    • ►  March (9)
    • ►  February (18)
    • ►  January (20)
  • ▼  2007 (121)
    • ►  December (8)
    • ►  November (12)
    • ►  October (10)
    • ►  September (8)
    • ►  August (8)
    • ►  July (12)
    • ▼  June (11)
      • Iron Lake
      • Reasoning With Rabbits
      • The Future Of Christian Higher Education
      • A Timeless Trail
      • Nightfall In The City
      • Writing As Language
      • Three Is Company
      • Towards A Christian Asceticism
      • Cityscapes
      • On Working Heartily
      • Behind The Scenes
    • ►  May (11)
    • ►  April (10)
    • ►  March (14)
    • ►  February (5)
    • ►  January (12)
  • ►  2006 (90)
    • ►  December (16)
    • ►  November (15)
    • ►  October (17)
    • ►  September (20)
    • ►  August (11)
    • ►  July (11)

What Susan Said

  • What Susan Said
    - Due to time limitations and lack of quote material, What Susan Said will be indefinitely discontinued. If you’ve enjoyed this blog, leave a comment and l...
    16 years ago

Blogroll

  • As The Deer
  • Bibliological Bibble-Babble
  • Cerulean Sanctum
  • Coffee Cup Apologetics
  • Free Believers Network
  • Greg Boyd
  • Internet Monk
  • Jesus Shaped Spirituality
  • Kingdom People
  • Letters From Kamp Krusty
  • MercatorNet
  • My One Thing
  • Reclaiming the Mission
  • Solomon's Porch Oakhurst
  • The God Journey
  • The Gospel-Driven Church
  • The Scribbles of a Sojourner
  • What Susan Said



Sponsor a Child in Jesus Name with Compassion
Save Children

Labels

  • Art
  • Blogging
  • Books
  • C. S. Lewis
  • Church + State
  • Church Life
  • Culture
  • Derek Webb
  • Economics
  • EduCore
  • Emerging Church
  • Family
  • Freestyle Piano
  • G. K. Chesterton
  • Happenings
  • Hiking
  • History
  • Holiness
  • Israel
  • Jesus
  • Language
  • Music
  • Nature
  • People
  • Photos
  • Poetry
  • Poverty
  • Prayer
  • Reading + Writing
  • Religion
  • Rich Mullins
  • Scraps
  • Scripture
  • Society + Government
  • Southwest Slalom
  • Spiritual Thoughts
  • Story
  • Technology
  • Travel
  • Yosemite

My Amazon.com Wish List
cash advance
Dell Computers
Free Counter
RSS Feed
Add to Technorati Favorites

Tuesday, June 26, 2007

Reasoning With Rabbits

I took very little formal logic in school, but it was enough to know that there's more to the subject than I'd guessed. I've since forgotten a lot of it, but for some reason, one bit has stuck with me: it's called the contrapositive.

When you take a logical statement and turn it inside-out, you have the contrapositive. There is, however, a specific way of doing this, in order to preserve the logical consistency.

When working with logic, sometimes it is helpful to use "nonsensical" sentences in order to be sure you're really thinking the thing through and not taking any shortcuts. That is what I am going to do to demonstrate how to derive the contrapositive.

We begin with this logical statement, describing a make-believe world of red rabbits:

If it is red, then it is a bunny.

That is our starting point, and we must treat it as fact in order to logically manipulate it. To find the contrapositive of the statement, change both terms to a negative, and reverse the order. You should wind up with a statement which looks something like this:

If it is not a bunny, then it is not red.

But, but - what about the fire hydrants and stop signs and - and - ketchup? Sorry. Not a bunny, not red.

What's enjoyable about this particular logical maneuver is that if you get confused you can easily step back and think your way through it. All red things belong to the class of bunnies: check. All non-bunnies belong to the class of non-red things: check. But not all non-red things necessarily belong to the class of non-bunnies. This fact is not deducible from our original statement, which said only that the bunnies had monopolized the color red. We do not know if they similarly hijacked other colors. You could possibly have blue bunnies, for instance.

Tidy, isn't it?

Image courtesy of ericclaridge.com
Posted by Aaron at 6:26 PM
Labels: Scraps

4 comments:

Max Parish said...

Yes, very tidy. Thanks for the mental caffeine. I like the diversity of your blog.

Question: were those really nonsensical statements, or were they meaningful propositions that simply don't obtain in the actual world? :-)

10:33 AM
Aaron said...

Ack - I knew someone would catch that! Throwing around a word like "nonsensical" when talking about logic is asking for trouble.

I'll accept your clarification, but I'm not sure about the "obtain" bit. Did you mean "pertain"?

12:05 PM
Max Parish said...

Not at all. It is just more of that esoteric philosophical jargon. You may have a given state of affairs. Quite often, you will compare that state of affairs with a larger context. If it "fits" or "matches," than that state of affairs obtains. This is usually referred to in the context of taking a given state of affairs -- say, whether red rabbits live in America-- and seeing if it "obtains" in the actual world. However, it can also be used in evaluating whether a state of affairs "obtains" in a hypothetical world.

There you have it. That and 75 cents will by you a cup of coffee.

11:12 PM
Aaron said...

Ah, very good. Thanks for the lesson!

11:35 PM

Post a Comment

Newer Post Older Post Home
Subscribe to: Post Comments (Atom)

The Fine Print...

All material on this blog remains my intellectual property. You are free to quote and disseminate any and all of it, but please use proper blogging etiquette, credit (link back to) the source, and make an effort to keep potentially controversial ideas in context. Thanks for reading.

Finally, brothers, rejoice. Aim for restoration, comfort one another, agree with one another, live in peace; and the God of love and peace will be with you. - 2 Cor. 13:11