#excluded middle

[dsudis]

are you more of an angst or fluff reader? what would you more likely find eager to read: something tagged as 'tooth-rotting fluff' or 'it's like you are chewing glass kind of angst'? i'm asking because i love angst with all my heart and detest everything that is 'cute' or 'fluffy' and have never met anyone on the internet who would be of the same opinion. despite the big community it seems everyone don't mind the constant happiness and uwus in the fics

Hello and welcome to the Logical Fallacy of the False Dilemma! 

Look, friend, I just binged 473,000 words of fic in four days. It’s a series about a character losing his hearing and coping with a worsening and complicated chronic illness--and it’s also a story about a loving, devoted, unshakeable romantic relationship at the center of an ever-growing network of friendships and found family. It made me cry repeatedly; it is a story about real losses and suffering and grief. It is also a story about partners snuggling up together at night and cooking for each other and embarrassing each other with affection and compliments. There are BABIES. 

So do I like angst or do I like fluff?

No. I like both, I like them mixed liberally together. I don’t like angst that ends in tragedy and despair--but, hey, if you do, go find you some fic! It’s out there, and the fact that it exists means you’re not the only person who likes it, by definition. 

If you want to find like-minded people, maybe go talk to the people who write fic you like, or your fellow commenters on that fic. They’re out there! Sometimes you need the darkfic and that’s fine! Sometimes you want to talk to other people who also are in that place, and they exist! I have no earthly idea why you think I am one of them, but they’re out there! Go find your people!

But for the love of God, in the fucking endless coal seam fire hellscape that is 2018--in a world that is always difficult in ways you don’t see for people you don’t know--let people enjoy their fucking fluffy happy fic along with their pumpkin spice lattes. Lots of people need a bright spot sometimes, and fic is where a lot of people find that bright spot, every bit as much as it’s where you go for safely packaged misery. Leave people the fuck alone to love what they love.

[transhermetic-witchery]

How find we this cult of Ain't. Proof by contradi'tion only works past purlee gait, 'bout around, the golden walls, not these, these seething halls. Negation pushed without it's mates, does rend, does ship, does peel the nape.

[eka-mark]

shlevy asked:

OK, can you explain the difference between what “no proposition is neither true nor false” and “all propositions are either true or false” means for an intuitionist?

I originally wrote a long & rambling post in response to this, which I might rewrite and post later. For now, I’ll try to make this shorter and more to-the-point.

For an intuitionist, a universally quantified statement like ‘∀x, R(x)’ does not mean that 'R(x)' “is the case” for each 'x'; it actually means that there's a (constructible total) function which accepts any 'x' as input and returns a proof of 'R(x)'. From this perspective, to validate “all propositions are either true or false” is to construct a function which decides every proposition. I assume I don’t need to explain why this is not possible.

Intuitionists also don’t mean the same thing as classical mathematicians when they assert the negation of a proposition. Instead of ‘~P’ asserting that ‘P’ “is not the case”, it means that we can derive a contradiction from ‘P’. So double-negation doesn’t cancel out in general, and ‘~~P’ means that ‘P’ is consistent (we can’t get a contradiction by assuming it, assuming our formal system is itself consistent).

Any proposition ‘P’ which is intuitionistically true (i.e. has a proof) is necessarily also consistent, so ‘P -> ~~P’, but some propositions are consistent without being provable, in which case the converse does not hold. LEM is one of those propositions - since classical logic is consistent iff intuitionistic logic is, it must be that ‘~~LEM’, but as per the above we cannot actually validate ‘LEM’ itself.

So we can’t have a proposition be "neither true nor false” (or equivalently “both not-true and not-false”) in the sense of having both ‘~P’ and ‘~~P’ as theorems, since the former asserts that ‘P’ implies a contradiction and the latter implies that ‘P’ does not imply a contradiction.

[spetharrific]

The title [The God Particle] ended up offending two groups: 1) those who believe in God, and 2) those who do not. We were warmly received by those in the middle.

Leon Lederman on the Higgs Boson

[execrablefrippery]

The Indeterminate/Excluded Middle

Human life, like a poetical figure, is an indeterminate middle between overspecified poles always threatening to collapse it. The poles may be birth and death, father and mother, mother and wife, love and judgment, heaven and earth, first things and last things. Art narrates that middle region and charts it like a purgatory, for only if it exists can life exist; only if the imagination presses against the poles are error and life and illusion—all those things which Shelley called "generous superstitions"—possible. The excluded middle is a tragedy also for the imagination. —Geoffrey Hartman, "The Voice of the Shuttle: Language From the Point of View of Literature," Beyond Formalism (1970)