Followup to:  Words as Hidden Inferences

"What is red?"
"Red is a color."
"What's a color?"
"A color is a property of a thing."

But what is a thing?  And what's a property?  Soon the two are lost in a maze of words defined in other words, the problem that Steven Harnad once described as trying to learn Chinese from a Chinese/Chinese dictionary.

Alternatively, if you asked me "What is red?" I could point to a stop sign, then to someone wearing a red shirt, and a traffic light that happens to be red, and blood from where I accidentally cut myself, and a red business card, and then I could call up a color wheel on my computer and move the cursor to the red area.  This would probably be sufficient, though if you know what the word "No" means, the truly strict would insist that I point to the sky and say "No."

I think I stole this example from S. I. Hayakawa—though I'm really not sure, because I heard this way back in the indistinct blur of my childhood.  (When I was 12, my father accidentally deleted all my computer files.  I have no memory of anything before that.)

But that's how I remember first learning about the difference between intensional and extensional definition.  To give an "intensional definition" is to define a word or phrase in terms of other words, as a dictionary does.  To give an "extensional definition" is to point to examples, as adults do when teaching children.  The preceding sentence gives an intensional definition of "extensional definition", which makes it an extensional example of "intensional definition".

Followup to:  The Parable of Hemlock

Suppose I find a barrel, sealed at the top, but with a hole large enough for a hand.  I reach in, and feel a small, curved object.  I pull the object out, and it's blue—a bluish egg.  Next I reach in and feel something hard and flat, with edges—which, when I extract it, proves to be a red cube.  I pull out 11 eggs and 8 cubes, and every egg is blue, and every cube is red.

Now I reach in and I feel another egg-shaped object.  Before I pull it out and look, I have to guess:  What will it look like?

The evidence doesn't prove that every egg in the barrel is blue, and every cube is red.  The evidence doesn't even argue this all that strongly: 19 is not a large sample size.  Nonetheless, I'll guess that this egg-shaped object is blue—or as a runner-up guess, red.  If I guess anything else, there's as many possibilities as distinguishable colors—and for that matter, who says the egg has to be a single shade?  Maybe it has a picture of a horse painted on.

So I say "blue", with a dutiful patina of humility.  For I am a sophisticated rationalist-type person, and I keep track of my assumptions and dependencies—I guess, but I'm aware that I'm guessing... right?

But when a large yellow striped feline-shaped object leaps out at me from the shadows, I think, "Yikes!  A tiger!"  Not, "Hm... objects with the properties of largeness, yellowness, stripedness, and feline shape, have previously often possessed the properties 'hungry' and 'dangerous', and thus, although it is not logically necessary, it may be an empirically good guess that aaauuughhhh CRUNCH CRUNCH GULP."

The human brain, for some odd reason, seems to have been adapted to make this inference quickly, automatically, and without keeping explicit track of its assumptions.

And if I name the egg-shaped objects "bleggs" (for blue eggs) and the red cubes "rubes", then, when I reach in and feel another egg-shaped object, I may think:  Oh, it's a blegg, rather than considering all that problem-of-induction stuff.

Followup to:  The Parable of the Dagger

"All men are mortal.  Socrates is a man.  Therefore Socrates is mortal."
        — Aristotle(?)

    Socrates raised the glass of hemlock to his lips...
    "Do you suppose," asked one of the onlookers, "that even hemlock will not be enough to kill so wise and good a man?"
    "No," replied another bystander, a student of philosophy; "all men are mortal, and Socrates is a man; and if a mortal drink hemlock, surely he dies."
    "Well," said the onlooker, "what if it happens that Socrates isn't mortal?"
    "Nonsense," replied the student, a little sharply; "all men are mortal by definition; it is part of what we mean by the word 'man'. All men are mortal, Socrates is a man, therefore Socrates is mortal.  It is not merely a guess, but a logical certainty."
    "I suppose that's right..." said the onlooker. "Oh, look, Socrates already drank the hemlock while we were talking."
    "Yes, he should be keeling over any minute now," said the student.
    And they waited, and they waited, and they waited...
    "Socrates appears not to be mortal," said the onlooker.
    "Then Socrates must not be a man," replied the student.  "All men are mortal, Socrates is not mortal, therefore Socrates is not a man.  And that is not merely a guess, but a logical certainty."

Once upon a time, there was a court jester who dabbled in logic.

The jester presented the king with two boxes.  Upon the first box was inscribed:

"Either this box contains an angry frog, or the box with a false inscription contains an angry frog, but not both."

On the second box was inscribed:

"Either this box contains gold and the box with a false inscription contains an angry frog, or this box contains an angry frog and the box with a true inscription contains gold."

And the jester said to the king:  "One box contains an angry frog, the other box gold; and one, and only one, of the inscriptions is true."