Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Sequence Exercise: "Extensions and Intensions" from "A Human's Guide to Words"

12 Normal_Anomaly 17 April 2011 08:22PM

Exercise for “Extensions and Intensions

Give an intensional definition for each of the following words:

  1. Shoe
  2. Hope
  3. Wire
  4. Green
  5. Politician
  6. Apple

Now rank them from easiest to define to hardest.

Describe how you would give an extensional definition of the same words:

  1. Shoe
  2. Hope
  3. Wire
  4. Green
  5. Politician
  6. Apple

Again, rank them from easiest to hardest.

Are the two lists the same? If not, what tends to make something easier to define intensionally than extensionally and vice versa?


You can share your answers in the comments. I'm interested in seeing how similarly people think of these things. Please make suggestions as to how this could be improved or augmented and what to do the same/differently in future exercises. My current plan is to do more from the sequence "A Human's Guide to Words." This post will be edited in response to suggestions.

Sequence Exercise: first 3 posts from "A Human's Guide to Words"

27 Normal_Anomaly 16 April 2011 05:21PM

 Folktheory, RobinZ, and I are designing exercises to go with the sequences. Here’s my first one. Please make suggestions as to how this could be improved or augmented and what to do the same/differently in future exercises. My current plan is to do more from the sequence "A Human's Guide to Words." This post will be edited to in response to suggestions.

 

Exercise for “The Parable of the Dagger," "The Parable of Hemlock," and "Words as Hidden Inferences

This exercise is meant to be worked on a computer. You can fill it out either in your head or by copying the text into a word processor. Please do not read ahead of where you are working. Where applicable, answers are posted in rot13.

 

1. List several properties which are common to crows. Here’s a picture of one to help you out:

 

______________________        ______________________       

 

 ______________________        ______________________       

 

______________________        ______________________       

 

Some of the characteristics you may have put down are “black,” “bird,”  “can fly,” and “caws.”

People in the time of Aristotle believed things were logically 100% certain to have all the properties that were part of their definition. For instance, they said they could be 100% certain that Socrates was mortal because humans are mortal "by definition."

Now, thinking like an Aristotelian and using those four characteristics, is that bird in the linked picture a crow?

Answer: Lbh pna’g fnl jurgure vg vf be abg. Lbh unira’g frra vg syl be urneq vg pnj.

 

2. Now, suppose I (assume I’m completely trustworthy) were to tell you that there is a crow behind that door. If your brain worked like Aristotle thought, you would be certain that it had all the properties listed above. Think of two ways that you could be wrong.

Some possible answers:

Gur pebj pbhyq or n ungpuyvat, jvgubhg erq srnguref be gur novyvgl gb syl.

Vg pbhyq or na nyovab.

Vg pbhyq or obea zhgr.

 

If you were able to think of any of those answers, that shows you weren’t really certain. The fact that answers exist shows that it would be incorrect to be certain. If you were, and you looked behind the door and saw an albino crow, you either would have denied it was a crow, and been wrong, or you wouldn’t have been able to believe it was white. Assigning something zero probability means you can never update your beliefs no matter how much evidence you see.

Saying an object belongs in a category does not force it to conform to the attributes of the category.