Wednesday, December 29, 2021

Raven's Paradox Real Bad

I have to make fun. This is a ludicrous amount of incompetence.
The point of paradoxes is to find a hole in human reason and fix it. (Ref: Xeno's paradoxes.) The point of the raven paradox is to show how there's a hole in a particular person's brain and they need to shut up and sit down.

My search pattern actually started with this, by the way: "If this apple is red, then ravens are black." Modus tollens: "If this raven is not-black, apples are not-red." This is somewhat wrong, but it's close enough to find the right one with [algorithmic][non-reasoning][non-conscious] error-checking.

First, how are ravens defined? As always, a good definition makes questions of identity trivial; anything else makes them impossible.


How are you supposed to tell something is a raven if it's not black? (Mutatis mutandis for any defining feature of a raven)? Don't do the thing backwards: you make a definition and then count the number of entities that go in the category, rather than counting a bunch of entities and then hoping a category fits around them. 

At best you're trying to verbalize a nonverbal category, which will always suffer from measurement error. However it is defined, you will find non-black ravens, non-bird ravens, and also non-ravens who are a child of two ravens. (More on this tomorrow morning.) 

Once you've defined ravens as black, then you don't need any evidence for the proposition that non-black things are non-ravens; it's true by, uh, definition. "This non-black raven isn't a raven." Formal fallacy: equivocation.

If we don't define ravens as black, then we've contradicted the premise. "If something doesn't have three sides, it isn't a triangle. Now, try to find the non-three-sided triangle." If ravens aren't inherently black or inherently have a set of properties that imply black, then the problem is already over. The other properties are undefined and can vary. You paint a raven; ta dah!
We'll have the opposite problem: finding non-ravens are ravens, because they're close enough. "Flying carrion eater," catches crows. If the child of two ravens is a raven, then we're all especially funny-looking archeobacteria. Also fish. And lizards. And...

Pick your poison: equivocation or self-contradiction? Which flabbergastingly bad error would you like to ascribe to this alleged paradox?
Intuition does not contradict inductive logic.


Totally a coincidence: Carl Gustav Hempel was kind of funny-looking across at least three axes. It is often particularly the less-capable scholars, the midwits, who feel the need to browbeat the plebs out of their intuitive understandings.


Other errors: "Via contraposition, this statement is equivalent to:

(2) If something is not black, then it is not a raven."

Wrong contrapositive if you intend to do induction. "All ravens are black" ~> "Not all non-ravens are non-black." Vacuous, not useful. Every statement of the form, "Not-all non-X entities are Z," is true. (There is an apparent exception, but it's merely bad grammar.)

Check, contradiction: "If something is not white, it is not a raven." By mass, there's more evidentiary support for this statement than the statement, "Ravens are black." You find lots of evidence because, if ravens really were white, the apple would still be red. The method cannot distinguish between a true statement and a false one.
This epistemic method allows you to prove 0=1. "If something is non-one, it is non-zero." Inductive statements only need to be usually true...right? Right?
This is easy to predict if you analyze induction by converting it to deduction. The latter is possible because induction was always a variety of deduction; essentially approximate or statistical deduction. Or possibly vice-versa. Either way there's no genuine distinction. 


Imagine the actual experiment: SELECT ALL non-black FROM universe.
Err, but you already know what a raven is, or you wouldn't be able to tell if the non-black thing is a raven or not. SELECT ALL non-black FROM raven. A tad faster. Don't look at all things and check if they're ravens, look at all ravens and check if they're black. I mean, duh. 

Practical considerations do in fact reflect on how you ought to construct pure logic. Do it the easy way or you'll make yourself stupid. 

Imagine the actual experiment, again: SELECT ALL non-black FROM universe. This apparently proves ravens are black. Okay, now kill and eat every raven. Yummy bird pies. SELECT ALL non-black FROM universe. The state of ravens has varied maximally, yet our body of evidence tells us it hasn't changed at all. Every element in the empty set is also white and blue and yellow, so...

ProTip: don't use irrelevant non-evidence as evidence. Amazingly, it turns out independent variables are independent.


Check, contradiction, again: let's imagine that instead of ravens, we're talking about some future object. What colour will Apple's next product be? 

Look at all these things that aren't Apple's next product and are black! It won't be black. Hey, there's a whole lot of things which aren't Apple's next product and are white. It won't be white. Why, it seems it won't be any colour at all... "If something has a colour, then it is not Apple's future product release." 

Indeed I can prove that Apple's next product will be absolutely anything, as long as it has not actually released. "If something is not [something which does not yet exist], then it is not God." Did I just prove that God will be the next release!?!

When you find an epistemic method during a rep of set 1, always plug in a false statement and see if it appears to prove that statement. Then bash your head against your desk, because it probably can. If instead you write it down and it gets in Wikipedia, then bash your whole civilization's head against its desk, because it's too stupid to live. 

No comments: