#existential quantifier

[radicalhelmet]

"it" "its" "one" "this one" ok, good for a start, but consider: existential pronouns. now you too can refer to yourself using statements of the form:

(∃x)(property of x)

examples:

(∃x)(x is up late again, as usual) (∃x)(x likes cheesecake and long walks on the beach) (∃x)(x is calling for help. please send help. help)

behold. become. benew.

[omegaphilosophia]

The Philosophy of Universal and Existential Quantifiers

The philosophy of universal quantifiers and existential quantifiers deals with how these logical tools are used to express general and particular statements, respectively, and the implications of their use in formal logic, mathematics, and philosophy. These quantifiers are fundamental in the study of logic, helping to clarify the structure of arguments, the nature of truth, and the meaning of propositions.

Key Concepts in the Philosophy of Quantifiers:

Universal Quantifier (∀):

Definition: The universal quantifier, denoted by ∀, is used to express that a statement is true for all members of a particular domain. For example, the statement "∀x (P(x))" means "For all x, P(x) is true."

Example: In a mathematical context, "∀x (x > 0 → x² > 0)" means "For all x, if x is greater than 0, then x squared is greater than 0."

Philosophical Implications: The use of the universal quantifier is central to discussions about generality and the nature of universal truths. Philosophers debate whether statements involving universal quantifiers reflect objective truths about the world or are simply linguistic conventions.

Existential Quantifier (∃):

Definition: The existential quantifier, denoted by ∃, is used to express that there is at least one member of a particular domain for which a statement is true. For example, "∃x (P(x))" means "There exists at least one x such that P(x) is true."

Example: In mathematics, "∃x (x² = 4)" means "There exists an x such that x squared equals 4," which would be true for x = 2 and x = -2.

Philosophical Implications: The existential quantifier raises questions about existence and the ontological commitments of statements. When we say "There exists," what kind of existence are we affirming? This leads to discussions about the nature of existence in various domains (e.g., mathematical, physical, abstract).

Scope and Binding:

Scope: The scope of a quantifier is the part of the statement to which the quantifier applies. Understanding the scope is crucial in determining the meaning of logical expressions.

Binding Variables: Quantifiers bind variables, meaning they specify the domain over which the variable ranges. A variable within the scope of a quantifier is considered bound by that quantifier, whereas a variable outside its scope is free.

Quantifiers in Formal Logic:

Predicate Logic: Universal and existential quantifiers are central to first-order predicate logic, where they allow for the formulation of complex statements about properties and relations. Predicate logic extends propositional logic by including quantifiers and variables that can represent objects in a domain.

Truth Conditions: The truth conditions of statements involving quantifiers depend on the domain of discourse. A universally quantified statement is true if the predicate holds for every element in the domain, while an existentially quantified statement is true if the predicate holds for at least one element.

Philosophical Debates:

Quantifier Variance: Some philosophers, like Hilary Putnam, have argued for "quantifier variance," the idea that the meaning of quantifiers can vary depending on the context, and that different ontological commitments can lead to different interpretations of what exists.

Ontological Commitment: The use of quantifiers in logical expressions often implies certain ontological commitments. For example, stating "∃x (P(x))" suggests a commitment to the existence of at least one object in the domain that satisfies P(x). Philosophers debate whether such commitments are necessary or merely linguistic conventions.

Free Logic: In response to issues of ontological commitment, some logicians have developed "free logic," which allows for the use of quantifiers without assuming the existence of the objects they quantify over. This is particularly relevant in discussions about non-existent or hypothetical entities.

Applications in Philosophy:

Philosophy of Language: In the philosophy of language, quantifiers play a crucial role in understanding meaning, reference, and truth. Debates about the semantics of natural language often involve how universal and existential quantifiers are used in everyday speech.

Metaphysics: Quantifiers are central to metaphysical debates about universals, particulars, and the nature of existence. For instance, discussions about whether universal statements (like "All humans are mortal") are necessarily true, and what that says about the nature of humanity and mortality.

Epistemology: In epistemology, quantifiers are involved in formulating theories of knowledge. For example, when discussing the extent of human knowledge, philosophers might use universal quantifiers to express general knowledge claims or existential quantifiers to assert the existence of specific knowledge.

The philosophy of universal and existential quantifiers is foundational to logic, mathematics, and philosophical inquiry. These quantifiers allow us to express general and particular statements, clarify the structure of arguments, and explore deep questions about existence, truth, and meaning. Their proper use and interpretation are crucial to understanding not only formal systems but also the nature of reality and our linguistic practices.

[preacherpollard]

Meaning

Gary Pollard Among the dozens of the-most-commonly-asked-questions Carl compiled for me, most fall into one of maybe three fundamental categories. Most of them also betray a sense of chaos in how people view reality. How do I know something is true/accurate/best practice? Is it always true? What about when a person stops being alive? Is it all nothingness? What is happiness? Is it quantifiable?…

[trulymightypotato]

This morning I am just. rotating vault hunters lore in my brain, how it interacts with the hunters and how it could totally feel... a little existential horror

the fact that the artifacts have images of the hunters, and how strange it must be to pick one up and see your own face staring back at you (you were not born on this world)

some of the gems being named after some of the players, but not all--the vaults (the gods?) put them there, and they could have been named anything (you were not born on this world)

your communicator tracks your damage, your favor, your greed. The fact that "greed" is a quantifiable number attached to you is treated as normally as the damage on a sword (you were not born on this world)

Sometimes the gods speak, but not often. They seem to have an agreement with each other to prevent someone from becoming too much of a favorite without consequence. They seem to know you better than they should (you were not born on this world)

and specifically for the people playing on the smp to test the new editions: the world changes often. Sometimes in little ways, sometimes in staggering ones. Both between one heartbeat and the next. Sometimes you know it's coming. Sometimes you don't. Sometimes it seems to target you directly (you were not born on this world)

[bored-storyteller]

Warning: slight angst, angst/comfort, blood mentions, Leona licks you, some may not like it so you are warned.

Author's note: It was supposed to come out on his birthday but that's okay, it's a reworking of something I've already written in the past.

Twisted Wonderland, Leona Kingscholar x Reader

Nightmare

Leona always thought that becoming king would be the greatest joy he could ever get in life. To be acclaimed by his people, loved, respected, seen for the wonder that he truly is. All his problems disappear before his merits, finally recognized.

You're proud of him, aren't you?

He looks at you next to him, he sees your smile. You know you will share his privileges with him.

You love him, you told him in many ways.

So why that sharp pain in his stomach, that death throb under his side?

You smile happily as you hold the bloody sword in your hands. His blood, dripping on the ground, on the royal robes, flowing amidst the laughter of jubilation at the deliverance from the dying king. Ruggie celebrates too, and Jack, and Epel, and even the brats of Heartslabyus cheer in victory. You didn't even bother using magic, just a sharp blade was enough.

His hand grips the wound in a vain attempt to survive.

But if he survives, what's he ever going to do with your hate on his shoulders?

Leona closes his eyes, and for a moment he asks for everything to end soon. But then he realizes from his gasp that it doesn't have the traits of death. The pain in his stomach is suddenly gone: he's awake.

He finds himself sitting between the sheets of his bed in the dark room.

All is calm, only the pale moon is watching him. His hand is wet yes, but only with the sweat of his torment.

It's just a nightmare, he tells himelf, and Leona Kingscholar is no longer a puppy afraid of nightmares. But even as he says it, his chest hurts, a primal dread scrapes the edges of his mind.

He feels so alone in that bed. It’s not the solitude that he claims, to which he is accustomed. It's a loneliness that asks him questions that he never wants to answer, it's a real loneliness, not the one he pretends to want.

Tomorrow everything will be easier with the sun, he thinks, yet he is downstairs outside his room.

He feels cold, his bare toes starting to bother him, but he's stronger than that.

His knocking on your door is insistent and arrogant, but effective.

When you open the door, a thousand emotions pass through your eyes: concern and confusion prevail.

He stands there like a grumpy tousled cat, cuddled up and nose wrinkled as your eyes alternate between him and the time on your phone's glowing screen.

“Leona…is it��quarter past three in the morning?”

“It seems.”

He sees you flutter tired eyelids: “What's going on? Did something catch fire? Is anyone sick? Hurt?”

Leona awake during the day is already a special event, but at night it is definitely a sign of misfortune.

But he snorts: “Nothing like that. Will you let me in?”

You smile at him, stepping aside: “Well, it's the practice, right?”

He doesn't moan or huff, he just walks past you looking for the first place he can sit down. Your expression saddens.

"Leona..." You call him softly, you kneel in front of him but his eyes escape you. His ears hang over his head and for some reason his general appearance of him brings you a melancholy that doesn't usually come from him. The boredom and pent-up anger that is usually your issues with him are dissolved into an existential sadness.

“What happens?” You investigate again, as gently as possible. What on earth could have hurt the prince so much as to reduce him like this? And what can you do, little creature, in front of something like that?

Leona remains immersed in silence for a period of time that you cannot quantify, but when his green eyes finally look at yours and you can hear his voice, there is no answer waiting for you: "Do you hate me?"

That question comes out to him in such a strange tone, feeble and wounded, that it scares even him. The big bad lion is not brave enough to face his inner monsters.

You're shocked, you almost think it's a joke, or you're dreaming, because such Leona is unthinkable.

“Do people hang out with those they hate at your home?” You ask with a hint of a smile that just wants to reassure him, even if you aren't sure either. Your hands slide over his, you take them meekly as if they were wet little birds: "Why on earth should I hate you, Leona?"

His mind suddenly comes up with more reasons than are actually real, and at the same time he seeks an answer within your gaze.

Then, suddenly, his eyebrows furrow in tension as he sights something that had gone unnoticed up to that moment.

“What did you do?” He asks as his thumb brushes the edges of what looks like a dry cut on your forehead near your left temple.

“What? What is it?” You ask confused at first, as your hand goes up to his.

“Oh, no, it's nothing!” Then you laugh, relaxing “A small accident during the alchemy lesson a few days ago. Nothing serious."

A few days ago. Nothing serious.

He hadn't noticed. Even though you'd been around him most of the time, he hadn't noticed at all. You had been hurt and he hadn't noticed.

He must have let you down, and he feels humiliated. Someone looked after you so well that you didn't even feel the need to tell him – or maybe he didn't listen to you?

He bites his lower lip in an unconscious punishment, while he feels his swollen heart become heavier in the new awareness of being useless to you.

“Come here.”

His dragging you into his lap feels rough, but you sense that something has changed in him, something that had remained unknown until then.

“Leona?” You call him quietly, but he silences you with a soft whisper. You're not sure what his behavior responds to, whether it's a puppy's need for affection, the care of a lover or a primordial protective instinct that resides in the animal part of him.

His tongue slowly caresses your wound with mechanical and slow movements. They are of no use now, yet they speak of his need to have you near, to be worthy of having you.

It's a prayer for forgiveness he'll never say in words, but what's the need for words?

Your palms rest patiently on his shoulders, and his hand gently holds the opposite side of your face as he continues that primal ritual.

How many hidden sides does your magical prince have?

“You should do this more often.” You tell him, while you hug more to his chest.

“Don't get your hopes up.” He answers you, but in the meantime he feels your body abandoned in his hands, all your need to receive the love of your loved one.

Your hand rests on his neck, caresses him, then goes up his cheek, up to his sensitive ear. Leona meekly bows his head to let himself be cuddled. For once, in the middle of the night, with you, he can afford it.

You still love him, it's a relief. A relief that deserves his invaluable commitment, not to make you leave.

[hollow-lime-green]

hi hana!! so i’ve been obsessed w this since string theory: can you tell us a little bit more about your interpretation of the six eyes? i know it’s said that satoru can see in thermal and infrared, is there anything else he can see?

Oh yeah! This is a fun question! I just got stuck in traffic for an hour (as a passenger), so I am going to over-explain this. And I'm bored so I'm going to highlight it with pretty colors like I'm writing in my diary or something.

Satoru's senses basically span the ✨entire energy spectrum✨, because the Six Eyes gives him the ability to work with all types of energy. He can see the EM spectrum (infrared, visible light, and ultraviolet), he can see thermal energy, he can sense (not exactly see) some other types of energy (electrical, sound, chemical), and he can see cursed energy like we do as JJK readers (plus some extra details like the taste, color, and texture of cursed energy).

I'm about to be insufferably STEM, so more under the cut:

Electromagnetic (EM) Spectrum

The EM spectrum has infrared light at low frequencies/high wavelengths, the visible light spectrum, and then UV at high frequencies/low wavelengths. Satoru is kind of like a mantis shrimp in that he sees way more colors than a human. He's got more rods and cones and stuff. (I like physics and chemistry, don't press me on the biology).

I don't really go into the UV part that much, but I like to think that would contribute to his sunlight sensitivity! He's not an outside pet.

The blindfold blocks out the EM spectrum because the fabric blocks the transmission of visible light in the form of photons, packets of light energy. (this is a secret tool that will help us later)

Electrical Energy

I haven't really gone into electrical much either, but like he can see the flow of cursed energy, he'd be able to sense the flow of electrical energy, i.e. the movement of electrons. It gives him good circuit sense.

Sound Energy

Sound energy is vibrations* (another tool that will help us later). He doesn't really see them per se, because even the thought of him actually seeing the vibrations in the air is overwhelming, and it would block his vision so much that I don't think it makes sense for the Six Eyes

I think he would feel them with the Six Eyes kind of like a gentle breeze. It makes him ultra perceptive, but it's still another form of feedback for him to deal with.

This is why I make Satoru so terrible with enclosed spaces. If you can see those forms of energy, you're seeing not only the original instance where they're emitted, but also every secondary instance when things reflect or refract. So sound bouncing around in a train, for instance, is completely overwhelming to the Six Eyes if he's not able to use jujutsu to filter it, which I think is a skill he wouldn't master until maybe his mid 20s.

Thermal Energy

Now this is the fun one.

The Six Eyes gives Satoru the ability to see and sense the energy in things in its various forms, because he can convert it all to cursed energy, or back. So, when you think of thermal energy, you probably think of thermal cameras, which represent thermal energy in the color spectrum, which kind of looks like light.

But thermal energy is very much not light - it's actually motion. Specifically, it is atomic vibrations. The more energy something has, the more it vibrates, and that is actually the basis for what we call 'heat' or 'temperature'.

If you go deep into the philosophy of temperature, it's all a sham. It's the way we choose to interpret and understand a phenomenon we can't really see (atomic vibration) translated into something we can measure (but our scales are all relative and kind of fake. I'm looking at you, Rankine!). But that's a conversation for my very Serbian thermodynamics professor. Existential doubt really flows better in a Slavic accent.

Anyway, remember photons? Okay, so, heat and sound are not light, right, they are vibration. So instead of quantifying them as light packets, we quantify them as vibration packets, which are called phonons. I reference phonons a lot in the fic, but probably not in a way where I have appreciably explained anything about them well to non-STEM girlies.

If you think about photons/photon emission as throwing a ball of magical light at something, you can think of phonons as throwing a slinky at someone. (Which I wouldn't recommend, actually. Slinkies are remarkably difficult to throw.)

Cursed Energy

Okay this one is a gimme but obviously I have to list it. In the JJK animanga, we the reader see the cursed energy auras/flames around people, but it's understood that those are not actually seen in-universe, at least for non-Six Eyes. It's kind of dumb, but it also kind of makes sense pragmatically. If all sorcerers could see cursed energy, then it really ruins surprise elements, residual coverup, and general battle mechanics. Of course, some sorcerers are known to cover up their cursed energy, but if all of the powerful baddies did that then it wouldn't look as cool. It's whatever.

Also, the whole 'training to suppress your cursed energy release' is a hard sell if we also say that literally any sorcerer can see CE. So this is why Suguru isn't aware of when he's leaking CE. He can't see it, and then he also can't really taste/smell it because people go noseblind to their own scent.

In FIYM, Satoru is the only one that can see see it. The rest of them can still sense it, but they sense it by smell, taste, and most importantly, vibes.

Thesis: Why Energy is Gay

Okay so yes I did this to answer the question "what does Satoru see through the blindfold". But I also did this to make it gay gay homosexual. (In the grand tradition of JJK)

Touch Sensitivity

Because Satoru is sensitive to kinetic energy, living things are incredibly potent to him from a sensory perspective. People are made of energy - particularly thermal energy, chemical energy (although this is potential energy which we haven't touched on but I do reference it here and there), sound, and, of course, cursed energy.

When Satoru touches people, he feels all of the vibrational energy from those kinetic energy sources as well as the cursed energy, which to him has textures on top of the vibes, colors, and smell/taste. So of course it's overwhelming. Every touch is combined with vibration, which is very gay, and would take a long time to get used to, even if he never formed the habit of using Infinity to cut himself off from the world.

In FIYM, it's not only a fear/safety/vulnerability thing, it's also a necessary filtration step that he uses for the world. Part of this is because I kept him in Kyoto/the clan setting in his backstory for a long time, so he would have had less sound and population density to deal with. Tokyo would have been super overwhelming for him.

Information Filtering

Speaking of filtering, there are two ways for Satoru to cut down on the amount of information his senses are getting.

One is to block them, which is what he does with the blindfold (blocks photons) and Infinity (blocks phonons). Gay, tsundere, and hot.

The other is to flood or mask his senses, which is what happens when Suguru infuses the blindfold with cursed energy. It's not that Satoru can't see anything, it's that all he can see is the cursed energy, and it blocks out his ability to sense anything else because of how strong and close it is. This is meant to be a direct analog to the phenomenon of detector/sensor saturation, which is to say that a detector has hit its limit of how much it can read/measure/detect, and so everything else is lost.

When Suguru flares his cursed energy, he's doing a baby version of that. He's flooding Satoru's detector (The Six Eyes) with his cursed energy (which is easy on the eyes, for Satoru) and that inhibits his ability to sense the other pesky things. And it makes him feel better.

Physics is gay, physics can be so gay. Greg's biggest sin was not capitalizing on how gay the physics can be. Any day now we'll get an announcement for his next project, a gloomy isekai titled: Transported To a Dark Academia Yaoi Battle School And I Fall For My Physics Tutor?

Anyway, I hope you enjoyed the over-explanation, thank you for the ask, I love getting the chance to ramble about some of the science. :)

[ladyofkythera]

"pi divided by 4" is my conlang's word for "to see"

to explain what i mean by this let me get here step by step

1. numbers are formed by assigning phonemes to a base-10 positional system, such that 1 = p 2 = i 3 = t 4 = e 5 = c 6 = a 7 = k 8 = o 9 = q 0 = u plus some extra stuff like -mu to mark negative numbers and schwa to mark some unspecified number (though schwa can also be used as padding for uncomfortable consonant clusters)

2. operations are formed by placing the operands after a prefix for that operation, such that 9+10 = xə-q-pu [xəq.pu] 9-10 = əx-q-pu [əχq.pu] 9·10 = pi-q-pu [piq.pu] 9:10 = q-q-pu [qəq.pu] (it is also possible to prefix particularly ambiguous operations with f- to specifically say that this is an operation, like pi which can mean 12, 3.141592..., or multiplication, but fpi specifically means multiplication)

3. prepositions that indicate a movement in space and time are indicated by an angle within a spacetime diagram expressed as a radian, such that standing still is represented as 90º, or π/2 rad, or q-pi-i [q(ə).pi.ʔi], so a sentence like "qpii haa hhezb" would mean "i'm at rest relative to the planet", or "i'm at the planet" (note that i had to remove all the bullshit like existential quantifiers in that example sentence as to not bloat it so hard it strays from the point) so for indicating motion, one would have to slant that world line. if we wanted to express 45º, we could say π/4, or q-pi-e. but the issue there is that 45º in a spacetime diagram indicates traveling at the speed of light, which is impossible for an object with mass. so to express slower than light movement, we'd need some arbitrary number between π/2 and π/4... oh well, we'll figure that out some other day. what matters is that this frees q-pi-e semantically to be used for some other more nuanced meaning that relates to movement, and that is movement at lightspeed.

4. so, if i were to say "qpie hheza hab" that would mean that a planet is moving at lightspeed relative to me. but it can't do that, of course it can't! so the implication at play is that it's an image of the planet made out of photons that is moving at lightspeed. we can further specify that A is moving toward B with -zmu (meaning "negative redshift") so "qpiezmu hheza hab" means "[an image of] a planet is moving at lightspeed to me", or "a planet is illuminating me", and if the light hits me it's also probably hitting my retinas, meaning that i could also use it to mean "a planet is seen by me" note that even though this is glossed into english as a passive verb, it is a fully active verb with a fully active meaning. this comes down to a different idea between the languages of what it means to see. if you think about it, seeing is not an action you do at something, it's photons that do the action of getting in your eyes. the distinction doesn't really matter for natlangs but for a language built from scratch by a civilization with an understanding of modern physics, it makes sense

[sea-changed]

"When the tactics of the Spanish-American War showed the wisdom of some semblance of camouflage, blue gave way to khaki [in U.S. Army uniforms] and eventually to the olive-brown tones of Dwight Eisenhower’s famous short jacket. The standard-issue olive drabs, or 'O.D.s,' were openly derided. 'It was a shade that might have reminded an imaginative observer of the color of vomit or even excrement,' the cultural critic Paul Fussell wrote in his 2002 book, 'Uniforms.' After V-J Day, it became existentially necessary for the Army to address its image problem. Olive drab was a drag on morale and a handicap to recruitment, and the mass entry of army clothes to the civilian life, as worn by veterans to tend their lawns or to pump a customer’s gas, further eroded its prestige.

"In 1949, the Office of the Quartermaster General set about stabilizing the army uniform, and its search for a new color may have represented the most extensive development and market-testing process in the history of both apparel and bureaucracy. An advisory committee ruled that a neutral gray-green would be 'flattering to the greatest range of people,' according to a later technical report. A team from the Quartermaster Corps proposed army uniforms to about 15,000 troops in 24 cities [and] quantified the relative enthusiasm of recruits, veterans and officers’ wives[.]

"[...] Phased in between the mid-’50s and early ’60s, the army green field uniform projected “the confidence and readiness of an authoritative military force,” the historian Shelby Stanton wrote in 'U.S. Army Uniforms of the Cold War, 1948-1973.' 'Army green,' Stanton felt, 'complemented the U.S. desire to project the most professional soldiering image toward its Cold War adversaries.'"

Troy Patterson, "How the Army Jacket Became a Staple of Civilian Garb" (New York Times)

[verdemoun]

projecting because i'm putting off essay writing but sean would do great in modern times until he didn't. tw for existential cosmic horror

lenny and sean go on a queerplatonic date to a planetarium because lenny is determined to prove that learning can be fun and sean is actually pretty keen on the idea of laying on a couch watching the night sky on a giant dome screen because that sounds awesome

lenny is completely enthralled, beaming ear to ear as a black!! lecturer!! is explaining in how mathmatics is used in physical cosmology to explain the expansion of the universe, using infinite as a measurement when space is something real and seemingly quantifiable

sean's vibing. thinks it's really cool they've got footage of the earth rotating and you can see the city lights come on and hey look there's ireland!! except then it zooms out. there's the other planets and the sun, that's fun. we look like specks! and then the sun is a speck, in a cloud of specks. that is one of an infinite number of speck-clouds.

where was earth again

haha, we really are small!

hey where's God

afterwards lenny is visibly excited, babbling about how incredible it is that human knowledge has come so far in 100 years, how much is still unknown, the infinite possible things that could be discovered or learned about in another 100 years

and it hits sean that lenny believes all that stuff so it must be true, because lenny's always right

tries to laugh it off 'haha yeah guess we're pretty insignificant in the grand scheme of it' as he pulls a flask out of his pocket

lenny knows sean drinking is a bad sign and gently tells him not to, tries to offer some philosophical explanation about mankind only inventing understandable knowledge out of fear

sean finally snapping. because he’s not lenny, he’s not dutch or hosea. He doesn’t like having big theoretical ideas in his head, reading hurts and sometimes when life’s too much he just needs a drink. there’s nothing wrong with needing a damned drink every now and then (there’s definitely something wrong with sean’s alcohol use but now isn’t the time to bring that up)

he misses karen. karen understood all he was ever going to be was idiot sean mcguire. they drank together, and they understood that it wasn’t just about being fools when they were drunk. drinking made it easier to be who they were meant to be, their roles in the gang: a loud-mouthed clown and a beautiful woman

lenny sitting down beside him and just putting his arm around him, letting sean drink as he starts crying because he misses his beautiful woman so much

[lilith-hazel-mathematics]

Axiom of Hierarchy

Procrastinating a bunch of stuff to instead tell y'all about this obscure axiom in set theory. This axiom doesn't have a wikipedia page, but you'll occasionally find it mentioned in articles which study weak fragments of set theory. Today I'm gonna make it a little more popular.

Essentially, the Axiom of Hierarchy asserts that every set is contained by the Von Neumann Cumulative Hierarchy. More generally, the axiom is meant to formalize the idea that our universe of sets exists as a rank in the cumulative hierarchy. Since there are finite ranks very low in the hierarchy, this means that, in principle, the axiom should be consistent with a finite domain of discourse.

It's actually very difficult to state this axiom in the language of first-order logic. That difficulty is exactly what I'm interested in today. Naively, you might think that defining the hierarchy requires the powerset axiom, the union axiom, transfinite recursion, and a formalization of the ordinal numbers at least, and that's already most of ZFC. However, you can completely circumvent all those powerful assumptions. It's possible to define the cumulative hierarchy, and moreover establish its core properties, using nothing but the axioms of Specification and Extensionality, which are extremely weak assumptions.

The theorem of ZFC

Over ZFC, the technique of Transfinite Recursion allows us to recursively define the Von Neumann Cumulative Hierarchy. To summarize, for each ordinal number α, we define the rank V[α] recursively like so.

V[α] = ∪{𝓟(V[β]) : β<α}

Here, 𝓟 is the powerset function, and of course ∪ denotes union. I define 𝓗 to denote the class of all ranks in the cumulative hierarchy. We then define the Von Neumann universe 𝓥 to be the class of all subsets of these ranks. Equivalently, 𝓥 is the class union of the powersets of the ranks in 𝓗.

𝓗 = {V[α] : α is an ordinal} 𝓥 = ∪{𝓟(V) : V∈𝓗} 𝓤 = {x : x=x}

Over ZFC set theory, it is a classic theorem that 𝓤=𝓥, that is, the universe of all sets is exactly the Von Neumann universe. That assertion, 𝓤=𝓥, is precisely the axiom of hierarchy. This is a first-order assertion, since it can equivalently be phrased as ∃α, S⊆V[α], which avoids any mentions of classes. The axiom of Hierarchy is redundant over ZFC since it's a theorem of it, but it adds a lot of structure when included in weaker axiomatic systems.

In Second-Order Logic

We demonstrate that the axiom can be stated in Second-Order Logic, while avoiding excessive assumptions like transfinite recursion and the powerset axiom. To define 𝓗 without transfinite recursion, we instead treat it as a special case of a wellordered class.

Definition: A class W is "wellordered by membership" if it is strictly totally ordered by the membership relation "∈", and every subclass C⊆W contains a minimal element.

Definition: Cap(H) = {s : ∃(v∈H), s⊆v}, equivalently ∪{𝓟(v) : v∈H}

Definition: A class H is a hierarchy if it's wellordered by membership, and moreover v=Cap(v∩H) for each set v∈H.

Definition: A class 𝓗 is said to be the maximal hierarchy if it's a hierarchy and all other hierarchies are subclasses of 𝓗. This 𝓗 is unique if it exists. We also define 𝓥=Cap(𝓗).

The Axiom of Hierarchy: There exists a class 𝓗 which is the maximal hierarchy, and 𝓤=𝓥.

The reason it's difficult to state this axiom in first-order logic is due to three main roadblocks. Firstly, our definition of a "wellordered class" is second-order, since we quantify over all the subclasses. Secondly, our definition of a "maximal hierarchy" is second-order, since we quantify over all class hierarchies. Thirdly, the existence of a maximal hierarchy is a second-order assertion, since it existentially quantifies over all classes. Our definitions don't make it clear whether or not 𝓗 even exists.

First-order reformulation

It turns out that the Axiom of Hierarchy is expressible in first-order logic, using almost no assumptions whatsoever. In particular, the maximal hierarchy 𝓗 necessarily exists as a first-order definable class, and thus 𝓥 is also definable. As mentioned before, we only require the axioms of Specification and Extensionality to prove this.

Our first roadblock is resolved by giving a first-order definition of "a hierarchy". Namely, the required property of being "wellordered" can be reduced to quantification over sets. The reason this works is because every strict initial segment of a hierarchy will always be a set, and we can locate our minimums in those initial segments.

Theorem: If H is totally ordered under membership, and every nonempty subset s⊆H contains a minimum, then H is wellordered. proof: Let S⊆H be any nonempty subclass of H. Fix any v∈S, then construct the initial segment s={u∈v : u∈S} from Specification. If v is minimal in S then we are done. Otherwise s must be nonempty so we find minimal u∈s by premise, which is then minimal in S. In any case S contains a minimum, hence H is wellordered. QED

This shows that the property of a class being "wellordered by membership" is a first order property, hence the property of being a hierarchy is also first-order. Our second roadblock is to give a first-order definition of what being a "maximal hierarchy" means. This will follow from a strengthening of the previous technique, namely we show that each strict initial segment of a hierarchy is another hierarchy. Consequently, class hierarchies are very closely approximated by set hierarchies.

Theorem: If H is a hierarchy and v∈H, then v∩H is a hierarchy. proof: We immediately notice v∩H is a set due to Specification, namely it's a subset of v. It's also wellordered by membership, since it's a subclass of H. Moreover for every u∈(v∩H), any w∈H with w∈u shall also have w∈v and thus w∈(v∩H). It follows that u∩H=u∩(v∩H) for every u∈(v∩H), and since H was a hierarchy, we infer that u=Cap(u∩H)=Cap(u∩(v∩H)) and thus (v∩H) is a hierarchy. QED

Corollary: If H is a hierarchy, then H shall be maximal provided that: for every set hierarchy h admitting Cap(h) as a set, Cap(h)∈H. proof: Let R be any hierarchy, take any v∈R, and apply the above theorem to infer h:=(v∩R) is a set and a hierarchy. Since v=Cap(h), by premise v∈H, thus R is a subclass of H, thus H is maximal. QED

Lemma: If H is a hierarchy and u,v∈H, then u∈v implies u⊆v. proof: By contradiction suppose not, then let v be the minimal counter example, so whenever w∈u∈v then w⊆u. Since u∈v then 𝓟(u)⊆Cap(v∩H)=v, and since w⊆u then 𝓟(w)⊆𝓟(u), therefore 𝓟(w)⊆v. However, u=Cap(u∩H) = ∪{𝓟(w) : w∈u & w∈H} ⊆ v, therefore u⊆v. This contradicts our assumption of having a counter example, so no counter examples exist. QED

Lemma(Cantor): Every set s admits z⊆s with z∉s. Proof: Via Specification construct z={x∈s : x∉x}, then necessarily z∉s, since otherwise we'd have z∈z ⇔ z∉z which is impossible. QED

Theorem: If h is a hierarchy and Cap(h) is a set, then h∪{Cap(h)} is another hierarchy. proof: Let v:=Cap(h), and notice that every u∈h has u∈𝓟(u)⊆v and thus u∈v. Next, we cannot have v⊆u since then 𝓟(v)⊆𝓟(u)⊆v gives 𝓟(v)⊆v, contradicting Cantor's theorem. We cannot have v∈u, since otherwise there'd be w∈h with w∈u and v∈𝓟(w), but then v⊆w is another contradiction. We cannot have v∈v, since otherwise there'd be u∈h with v∈𝓟(u) and thus v⊆u, impossible. It now quickly follows that h∪{v} is wellordered by membership, namely with v=max(h∪{v}). Finally, h∪{v} is a hierarchy since v=Cap(h)=Cap(v∩H), and for u∈h likewise u=Cap(u∩h)=Cap(u∩H). QED

Corollary: If H is a hierarchy, then H is the maximal hierarchy if and only if for every set hierarchy h admitting Cap(h) as a set, we have Cap(h)∈H. proof: If H is the maximal hierarchy, then for every set hierarchy h admitting Cap(h) as a set, we can apply our theorem to infer h∪{Cap(h)} is another hierarchy, and thus Cap(h)∈H since H is the maximal hierarchy. The converse direction was proven previously. QED

This completes our second roadblock, showing that the property of being a "maximal hierarchy" is first-order. Our third roadblock is to give a first order definition of the maximal hierarchy 𝓗, or at the very least, a class which is the maximal hierarchy if and only if a maximal hierarchy exists. The weaker second task is now trivial, since we know every hierarchy is closely approximated by set hierarchies.

Definition: 𝓗={v : ∃h, v=Cap(h) & "h is a hierarchy"}

Theorem: The class 𝓗 is the union of all class hierarchies proof: Every v∈𝓗 admits a hierarchy h with v=Cap(h), and then h∪{v} is a hierarchy, so every member of 𝓗 is a member of some hierarchy. Conversely for any hierarchy H and any v∈H, we find v=Cap(v∩H) where v∩H is a set hierarchy, and thus v∈𝓗 which implies H⊆𝓗, hence every member of some hierarchy is a member of 𝓗. QED

Corollary: If 𝓗 is a hierarchy then it is the maximal hierarchy, and if a maximal hierarchy exists then it is 𝓗. proof: If 𝓗 is a hierarchy then, as the union of all hierarchies, it is maximal. Similarly if a maximal hierarchy exists, it must equal the union of all hierarchies, which is again 𝓗. QED

With this, we've overcome our main three roadblocks. The Axiom of Hierarchy may now be stated by first asserting that 𝓗 is a hierarchy, and then asserting that every set is a member of 𝓥=Cap(𝓗), which are seen to be first-order statements. To get a more satisfying result however, we can further prove that 𝓗 is necessarily a hierarchy. This is tantamount to demonstrating the validity of a very narrow version of transfinite recursion, which is interesting given how weak our axioms are.

Lemma: If H is a hierarchy and v is not maximal in H, then 𝓟(v)∈H and moreover 𝓟(v)=succ(v) is the successor in H. proof: Since v is not maximal in H, we can find u∈H to minimally satisfy v∈u, so u=succ(v). Immediately 𝓟(v)⊆Cap(u∩H)=u. Conversely, all w∈u obey either w∈v or w=v, so either way w⊆v and thus 𝓟(w)⊆𝓟(v), hence u=Cap(u∩H)⊆𝓟(v) and therefore u=𝓟(v). QED

Lemma: If H is a hierarchy and S⊆H is bounded, then ∪S∈H and moreover ∪S=sup(S) is the supremum operation in H. proof: Since S is bounded, we can select v∈H to be the least upper bound of S, v=sup(S). Consequently, every u∈S either has u∈v or u=v, and thus u⊆v in either case, hence ∪S⊆v. By the minimality of v, moreover every u∈H with u∈v shall admit some s∈S with u∈s, and consequently 𝓟(u)⊆s⊆∪S. Since we have v=∪{𝓟(u) : u∈v & u∈H}, then v⊆∪S and therefore v=∪S. QED

Lemma: If H is a hierarchy and S⊆H, either Cap(S)∈H or else Cap(S)=Cap(H) proof: Notice Cap(S)=∪{𝓟(v) : v∈S}=sup{succ(v) : v∈S} from the last two lemmas. If there exists u∈H such that all v∈S obey v∈u, then sup{succ(v) : v∈S}∈H giving our first case. If no such u exists, then all u∈H admit v∈S such that u∈𝓟(v) and thus Cap(H)⊆Cap(S), and since S⊆H then in fact Cap(H)=Cap(S). QED

Theorem: If A,B are hierarchies and ¬(B⊆A), then A=b∩B where b=min(B\A). proof: Immediately infer b∩B⊆A by minimality of b. While noting Cap(b∩B)=b, apply the previous lemma to infer that either b∈A or else b=Cap(A). The first case is impossible since b∉A, hence b=Cap(A) and thus A⊆b. If we did not have A⊆B, we could symmetrically find a=min(A\B) obeying a=Cap(B), but then b⊆Cap(B)=a and likewise a⊆Cap(A)=b so that a=b, which is impossible since b∉A. It follows that A⊆B, and since also A⊆b then A⊆(b∩B), therefore A=b∩B. QED

Lemma: the class 𝓗 is totally ordered by membership. proof: Given any three a,b,c∈𝓗, we find hierarchies A,B,C with a∈A, b∈B, c∈C. Apply the previous theorem to infer that the union A∪B∪C is a hierarchy containing all three of a,b,c, from which it easily follows that {a,b,c} is totally ordered under membership, hence so is 𝓗. QED

Lemma: Every hierarchy is an initial segment of 𝓗 proof: Let H be a hierarchy, and suppose a,b∈𝓗 obey a∈b∈H. Find a hierarchy A with a∈A, then either A is an initial segment of H so that a∈H, or else H is an intial segment of A and thus a,b∈A with a∈b∈H implies a∈H. Either way a∈H, hence H is an initial segment of 𝓗. QED

Theorem: 𝓗 is the unique maximal hierarchy. proof: We already know 𝓗 is totally ordered. Given any nonempty subclass S⊆𝓗, we can select any s∈S, find a hierarchy H with s∈H, and then find m=min(H∩S) since H is wellordered. Since H is an initial segment of 𝓗, necessarily m=min(S), hence 𝓗 is also wellordered. Finally, given any x∈𝓗, find a hierarchy H with x∈H. Since H is an initial segment of 𝓗, then x=Cap(x∩H)=Cap(x∩𝓗), therefore 𝓗 is a hierarchy. QED

If you like, you can use this to prove some interesting properties about 𝓥. For example 𝓥 must be a proper class, since otherwise we could form a strictly larger hierarchy given by 𝓗∪{𝓥}, which is impossible. Also 𝓥 internally models the axioms of Union and Foundation, in addition to being downward closed under subsets and membership. Moreover 𝓗 is closed under powersets whenever they exist, so if the axiom of powerset holds universally then it also holds inside 𝓥.

[mdhwrites]

What do you think of the Heroic Sacrifice trope? It's a trope as old as time: "no greater way to showcase the quality of one's character, the culmination of their growth, their worthiness as a hero, than laying down their life so that others might live."

I personally like it...most of the time. Other times it feels like it's executed for the sake of being executed. Take Superman's death in Batman v Superman - a noble act, but completely pointless because anyone with a brain writing this would see the context and go "just give Batman the kryptonite spear and have him kill Doomsday with it instead."

I'm also not a fan of the sacrifice being undone, either by the end of the story or the next film/chapter/whatever. For me, it takes away a lot of dramatic weight by simply undoing the character's choice to sacrifice themselves and have them come back fine and dandy. This is why I kinda like the way the Heroic Sacrifice plays out in Amphibia's finale: it's sort of undone, but elements are left ambiguous enough to leave the possibility that yeah, there is some kind of seriously existential consequence to come from that.

I sent this ask because I've been thinking about how, over the years, I've seen a lot of talk and fanfics about various works of fiction, lamenting and undoing a hero's sacrifice. And while most of this is obviously because it just feels better to see a character you love alive and well, some argue that, in this instance or that, it was more narratively fitting for the character to actually live instead of carrying out the trope. And that argument can have merit, if you ask me, provided you can prove it...was narratively fitting for the character to live.

So yeah, what do you make of the trope?

Character Death is maybe one of the hardest things to quantify for people because how each person feels about a death is going to come down to personal preference and the like. The only character deaths that are undone with no objection are the ones that are complete bullshit. These are usually shock deaths. Otherwise, the conversation gets a lot more complicated.

For me, I think your final sentence on this comes close to hitting the big question a writer should ask for which way to swing this. Can you make the resurrection feel like it fits within the reason for the sacrifice? It can't just be thematic to the whole story, it has to be thematic to the death itself.

THIS is actually what makes Anne coming back powerful. She dies as a culmination of her care for others and her maturity. First, that care for others has The Guardian offer her a job. Offer her a place amongst the gods. However, it is then her maturity that makes her turn it down and gives the Guardian the idea to give her her life back. For the same reasons she died, she comes back. It doesn't undercut her arc, it reinforces it.

I much cheesier example of this is the first Pokemon movie. Ash gets in the way of Mew and Mewtwo because they aren't battling like in Pokemon, they are waging WAR. So he does everything he can to stop it and loses his life in the process. When confronted with the cost, everyone has to stop and actually consider it. This shared pain of having gone so far is then what makes them cry and finding peace finds Ash his life. He did everything he could for peace and succeeded and rolling back his death fits with the idea that there was no need for this in the first place. To keep him dead would actually undercut the point because it would imply his death was necessary.

HOWEVER.

Why don't villains count as often for this? The redemptive sacrifice is made to atone for their sins... Which makes bringing them back kind of go against the point. The idea is that instead of the selfish or destructive ideals they have been motivated up until now, they no longer care about themselves and care for others. That they will throw away EVERYTHING to try and undo some of their damage. To give them back anything is pointless. The best thing to be done instead is to memorialize them. To agree that they in some way did make up for their mistakes and will be remembered fondly instead of hated.

As for my personal opinion... I am not a fan of character death. Unless it is the absolutely right thing for their character, I am usually against a character dying permanently. It is the end of all stories that could be told with them, done in a very brutal way, and that is far less interesting to me than having to deal with who they are going forward. As such, I would rather a heroic sacrifice lead to them being scarred in some way, usually literally not like they now have to deal with trauma, because just because you didn't die doesn't make the fact that you were ready to any less meaningful. If you are going to remove a character from a story and not send them off into the night gracefully to live their own life though, there are much worse ways to do it than a noble sacrifice. However, because I think the trope is unnecessary in the first place, I'm going to be ESPECIALLY critical of your work if you use it just for shock value.

Death means something, just as life does, and the passing between them should mean just as much. See you next tale.

======+++++======

I originally branched out to kind of how death and resurrection can be handled in general rather than just noble sacrifice but decided against it. This also kept Luz out of this since she didn't do a noble sacrifice. She didn't choose to die which is the whole fucking point of the trope. She just accidentally was killed while saving someone. There is a BIG difference.

I have a public Discord for any and all who want to join!

I also have an Amazon page for all of my original works in various forms of character focused romances from cute, teenage romance to erotica series of my past. I have an Ao3 for my fanfiction projects as well if that catches your fancy instead. If you want to hang out with me, I stream from time to time and love to chat with chat.

A Twitter you can follow too

And a Kofi if you like what I do and want to help out with the fact that disability doesn’t pay much.

[omegaphilosophia]

The Philosophy of Effective Altruism

Effective Altruism is a philosophy and social movement that emphasizes using evidence and reason to determine the most effective ways to improve the world and help others. It combines the altruistic desire to do good with a rigorous, results-oriented approach to maximize the positive impact of charitable actions.

Key Principles of Effective Altruism:

Maximizing Impact:

Effective altruism focuses on ensuring that the time, money, and effort devoted to helping others yield the greatest possible impact. This involves identifying causes, interventions, and charities that provide the most benefit per unit of resources.

Evidence-Based Approach:

Central to effective altruism is the use of evidence and data to assess which interventions and organizations are most successful. This often involves evaluating scientific research, performing cost-effectiveness analyses, and assessing the tangible results of various efforts to help.

Cause Prioritization:

Rather than spreading resources across all causes, effective altruism advocates prioritizing certain areas where the need is greatest, or where the most lives can be saved or improved. This could include global poverty, animal welfare, or existential risks such as climate change or artificial intelligence.

Long-Term Thinking:

Effective altruism often involves consideration of the long-term consequences of actions, including potential effects on future generations. Altruists might consider how present actions can help reduce future risks or improve the well-being of future individuals.

Moral Cosmopolitanism:

Effective altruism operates on the principle that all human lives (and sometimes animal lives) are of equal value, regardless of where a person is born or lives. This means that people should focus on causes that provide the most help to those in the greatest need, even if they are far removed geographically.

Personal Responsibility and Earning to Give:

Some proponents of effective altruism believe that individuals can do more good by earning a high income and donating a significant portion of it to highly effective causes, a concept known as "earning to give."

Openness to Self-Improvement:

Effective altruists constantly seek feedback and are willing to change their actions or strategies based on new evidence or better reasoning. The movement emphasizes flexibility and continuous improvement in pursuing altruistic goals.

Criticisms of Effective Altruism:

Narrow Focus: Some critics argue that the focus on measurable outcomes can lead to neglecting important, but harder-to-quantify, causes such as systemic social change or cultural initiatives.

Elitism: The emphasis on high-income individuals "earning to give" can create perceptions that effective altruism is only accessible to wealthy or highly educated people.

Overemphasis on Utilitarian Calculations: The movement's utilitarian focus on maximizing good outcomes can lead to difficult ethical decisions, such as favoring saving a large number of lives in the future over addressing pressing issues in the present.

The philosophy of effective altruism combines moral concern for the well-being of others with pragmatic reasoning to ensure that altruistic efforts are as impactful as possible. It encourages individuals and organizations to critically evaluate their charitable actions, seek evidence-based solutions, and prioritize causes that yield the greatest benefits for society.

[skinks]

I think many people have existential dread about work because so many people have jobs where you don’t achieve anything quantifiable in the physical world… maybe I’m just practically minded but I never feel more satisfaction at work that when I’m learning how to use a new tool and then I can make that tool do something physical. it satisfies my cavewoman brain to get the hang of a tractor or a forklift or a power tool or a welding machine or a lathe, y’know, you feel good because you’ve proven your own competence to yourself. if I had an emails job where my Monthly Performance Target was to File a Report on Client Satisfaction or whatever I’d wanna die too

[the-mspfa-200-favourites-project]

WOKEN VOID

Woken Void is the closest of these “future-200 favourites” fanadventures to the big hundo-deluxe (a thing people say I am sure), with 198 favourites. I guess technically they might never actually make it over that 200-favourite threshold, which also goes for literally any other Fanadventures that I’ve talked about in this strange mini-series of mine. But whatever, I’ve committed to this, and so I’m going to do it. I posted about it on an update that got people liking and commenting “Let’s Go!!!!!!!!” I can’t quit now. So I guess, existential crisis about what I’m even doing here even though I’ve pretty much exhausted the 200 Favourites Gravy Train I was riding for a while aside, it’s time to read WOKEN VOID.

Actually, hang on, let’s examine that existential crisis I was just having. What exactly was I trying to do with that original post? I think a lot of reactions were PROBABLY because I was going to, like, review the NEW hits, the most recent hits that everybody is abuzz about. And, like…

Well, a lot of my reviews have come from the assumption that a lot of these fanadventures were, by and large, popular, if not now, then probably back in their day. And I reached that conclusion by going, huh, the site emphasizes this threshold that most fanadventures will never ever come close to clearing, so any Fanadventures that do clear it must have had a significant impact or word of mouth, or enough people clicking on it and seeing something that they like. But I think…I think that’s not quite easy to quantify when you go below that threshold? Like, can I really assume this MSPFA, WOKEN VOID, was popular in it’s heyday? Can I really assume ANY of the MSPFAs beyond the MSPFAs we’re still talking about NOW were popular in their heyday? I guess it doesn’t have to be in their heyday, it’s just has to be at least crossing that threshold where atleast 200 people click on the webcomic, looked at it, and thought “yeah I want to get updated on this.” That’s all this threshold really means.

Okay I’m stalling a bit on this but I want to say, like…I’m wrestling with the possibility that…I don’t know. Something about reviewing things that I’m not personally into, that haven’t crossed that threshold of popularity, that I don’t think the authors would like, want me to talk about being lukewarm when literally the entire basis of this mini-series is literally just “these are SO CLOSE to the finish line of being labeled popular.” Because, like I said, I only started this mini-series because it was, like…me trying to get ahead of those comments on the original post when I said I ended the fanadventure! And I am very grateful to everybody who said well-wishes on those posts and suggested new fanadventures for me to review. I am very grateful that the response from the MSPFA community has been a positive one to this blog. That’s such a relief to me, personally. But like, now I’m starting to question what I set out to do, but I don’t want to delete the blogposts I’ve already made on those MSPFAs…AUGH!!!!!!!!

And now this post has basically become like. All about the Blog itself, and not about the MSPFA. Which is, you know, decent. Got good art, as always. It’s about Trolls, it’s not really clicking with me, you know the song and dance. But yeah…I guess…what I’m saying is that I don’t think I have to worry about MSPFAs like, blind-siding me? I think what I’m saying is that I don’t…really want to continue this mini-series. But I will definitely review new Fanadventures that cross that threshold, somehow. So…yeah.

[lilllithdraagon]

PART 9: Gender addressed in Thedas!!!

MASSIVE SPOILERS FOR DRAGON AGE THE VEILGUARD. READ AT OWN RISK.

Main Post Link

Omg. This is insane.

Like. I expected Bg3 levels of affirmation, but no. They went the whole nine yards.

(Lillith) I’m a cis woman. I don’t think this is my podium to stand on. So I’ll let Lunadys write this one.

(Lunadys) Hoi. For those of you that don’t know I’m Enby. She/They/He whatever idgaf. Taash made me cry. Multiple times. It was on multiple levels. That scream will live on with me.

Argue about the cheeseball script all you want, I saw myself in them. I was them. 42 years of shoveling shit in a world that only saw me as a servant to patriarchy and what I could provide my family for free. I finally got a power fantasy where a character is going through the same thing. I got to talk it out with them. I got to have that weird coming out to family. I saw ME.

There are characters you meet and they just...are. It isn’t glossed over if you dig. They talk about it and move on without making it their entire personality. Tarquin flew under the radar for Lillith despite her literally having the conversation with him (Lillith here to say I’m just a dumbass) and I find that both amazing and hilarious.

Ivenci is a badguy and they/them pronouns are used regardless of whether or not they’re a shitbag. Which is important! Gender doesn’t make you good or bad! That’s on your own choices and personality. Yeah the bit with Isabella and ‘pulling a barv’ falls a little flat but so what? “Frogtime” I say. “Lick a lampost in winter,” if you don’t like it. Dragon Age has always been cornball along with the heavy dose of existential dread and horror.

It didn’t feel like pandering. It felt like it was coming from a genuine place. That if you wanted to learn more about it you had that option. If not, then walk the fuck away. Choose something else. But I got to look in a mirror in my favorite franchise and recognize the person smiling back and that is worth something more than I can quantify.

Could some things have been handled better? Maybe. I’m sure people will argue about it forever. It doesn’t matter. It happened. They did it. And I will be grateful to Bioware for sticking to their guns for the rest of my life.

[mathsuggestions]

Interleave universal and existential quantifiers.