Fallaceous Division... not as sexy as it sounds

Ahem... "The whole is different from the sum of its parts."

This little writing is to highlight the problem of the Division Fallacy: taking a generalised statement, and then projecting the properties onto every constituent that falls under the generalisation. For instance: when we're talking about traits of nations, I could say that "the Greek are lazy". If you then get all upset and prissy because you think I said all Greeks are lazy, and you "know plenty of Greeks who aren't, where do you get off", you are committing this fallacy.

So why did you? Surely individual Greeks make up "the Greek"?

Actually, they don't. Because "the Greek" do not exist at the individual level - they are simply individuals with each different personal traits - you cannot consider "The Greek" to be "the collection of all individual Greeks". It's tempting too, certainly, and almost everyone will do this (if not with the Greek then with a million other things) but it does not hold.

So let's do a little comparison:

- Apple pies are delicious, but that doesn't mean every apple pie is delicious.
- Cats are mammals, but that doesn't mean every cat is a mammal.

Hang on a second... somehow the logic seems to have broken down. Why? Same kind of words, same logical structure, but the first is true while the second is false. What's different? Crucially, the difference is a judgement call. In the first phrase, we call apple pies something that we believe to be true in the first place.

- Apple pies are delicious.

This is open to debate - there might be people who simple do not like apple pie, no matter the particular incarnation. However, in the second sentence this is not the case:

- Cats are mammals.

this is factual data. Anything that you want to call a cat has to first be a mammal (in fact, it has to be a backboned animal of the carnivorous mammal inclination, more specifcally of felidea family, and preferably even be of the genus felis).

The real fun part starts here: what say we claim that we "wish that Los Aangeles was wiped off the face of the earth, because it is a cess pool", which honestly it is and I wish it were. Does this mean I want everyone in LA dead? Not really, there isn't even the slightest logical connection between the two because "the people in Los Angeles" do not stand equal to "Los Angeles". If we removed the people for a moment from L.A., there is still a hell of a lot of stuff left, and it will still be a cess pool, just without people for a moment. In fact, removing the people still leaves "L.A." in place. If we remove everything that's left after the people leave, and then put the people back, we just have a whole bunch of people standing on an empty plot of land - clearly the people of L.A. in fact don't really matter than much in what makes L.A. at all

(critical thinking is a nasty thing - you can use it to prove yourself silly)

Let's look at it from a mathematical perspective. The Division Fallacy amounts to saying that 10 is the same as 1 plus 2 plus 3 plus 4. You might wonder where the problem lies in this, but keep in mind what natural language does. This statements tells us that some number is the sum of four other numbers.

I'll give you a moment.

Okay, moment's up - 10 is not the sum of the numbers 1, 2, 3 and 4. In fact, "10" is just a number, while "1+2+3+4" is a compound addition. If you work out the addition, you come up with a number that happens to be "10", but who said I am thinking of that particular "10" when I ask "I am thinking of the number 10. What's its decomposition?". Here, the number "10" is like the Greek: lazy. It has not told us anything about what it really is. Is it just the number 10? Then it has no decomposition at all. Is it the result of some function I was thinking of, instantiated with some specific parameters? Then it's just being lazy not revealing this function, or the parameters, so that we can guess at the missing bit. Is it actually "10"? Maybe it's just "1" and "0" stuck together as a string, in which case it's not even a number. What the hell is "10"?

And there's the question you should be asking instead: The Greek are lazy, but what do I mean with 'the Greek'?

But then, most people don't like asking questions because the answers might require them to think something over, and that's not what got us ahead in the evolutionary game, where making a snap judgement and sticking to it meant you survived. Oh no, wait. That evolutionary game ceased to matter when the human race organised itself into cooperative societies, now we're only internally competing.

"The human race doesn't suffer from the evolutionary game anymore."



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