>>16279608
>why logic hard? :(
Grug never needed logic, for all these winters, to survive. Neither did his parents, nor the parents parents, for all these winters back to when this land was young. Why Grug brain evolve to handle logic when it not necessary?

>>16279608
This just means that the two statements on the left and right mean the same thing

It reads:
(Left:)
It is false that there exists an X such that X is a member of group D where P applies to X

(Middle:)
if, and only if,

(Right:)
For all X which are a member of group D, P does not apply to X

I don't remember the technical significance of P(x) but that's the jist of what it's saying

>>16279619
But Grug exapted his cognitive abilities for other pursuits now that don't necessarily involve hunting strategizing, but these other tasks still hard :(

>>16279608
because it's so different to how we think in daily life you have to get used to it. eventually you parse quantifier expressions like this fluently.

>>16279630
It is interesting how things like the pic in OP start off looking like the language of FTL alien megaminds but once you get the hang of it your reaction to what's in OP would just be "Yeah o_o Obviously?"

fags

>>16279608
Logical equivalence and propositional logic. Why are you posting this here and not in >>>/g/ where all the comp sci fags are?

I disapprove of the triple equals usage, which should be reserved for definition.

>>16279659
Computer Science belong on /sci/

>>16279666
What OP really means is Philosophy belong on /sci/

>>16279671
>>16279669
Well yeah, physics is just natural philosophy. Fucking retards.

>>16279690
And philosophy of science, and philosophy of math, yes we get it, there's a philosophy for everything.

>>16279608
De Morgan's laws are the only thing that aren't immediately obvious about propositional logic. Even then, just draw up a Venn Diagram and stare at some pretty pictures, I'm sure you'll get it eventually.

>>16279851
>that aren't immediately obvious about propositional logic
But they are.
>>16279608
It's not.

>>16279608
meme field

>>16279608
The logical sentence in picrel is trivial yet I fail to see how can one EMPIRICALLY prove it without sounding like "obviously, duh". It doesn't seem to be an arbitrary axiom since any other alternative form leads to unnaturally illogical statements.
Could there be a universe where the statement:
~(-]X € D, P(X) ) (The negation of P(X) to be true for some X in D) implies that -]X € D, ~P(X) (There is an element in D such as P(X) is false)

>>16279627
>10,000 years later
>Grug realises that none of these surrogate activities will ever give him the fulfillment his ancestors have been seeking for hundreds of generations
>They live 'till 90 and never have to worry about disease and starvation, but life is just as unfair and unfulfilling as it was in the stone age
>Everything we do and believe in today is hyperreal
>"Civilised" beliefs are just primal beliefs that have been sublimated into a more refined and elegant form
>"Civilised" behaviours are just primal behaviours that have been sublimated into a more refined and elegant form
>Grug no enjoy living in a world where everyone LARPs as a gentleman whilst hiding a brutal caveman under a thin veneer of pseudointellectualism
>Grug want to return to monke because monke is simple and honest

False encoding leads to false equivalence. Just because some students don't like homework doesn't mean the negation of that proposition means to switch quantifiers. To encode the first statement, you need to use set theory more carefully. Instead of using D--the container of all students, you need to use a subset of D so that when you negate the statement, it implies that those students that don't like homework are in that particular subset.

>>16279661
>which should be reserved for definition
Those are logically equivalent and have the same implications. For all intents and purposes either could be the definition of the other.

>>16279608
You are doing an affirmation by saying liking homework is not the case

>>16280382
>Just because some students don't like homework
That wasn't the proposition. The proposition was that it's not true that some students like homework.

>>16280407
That's the same thing

>>16280432
>That's the same thing
It isn't. If some students don't like homework, there may still be a subset of students that like homework. If it is not true that some students like homework, then no such subset can exist.

>>16280440
>Some students not liking and some liking it are not mutually exclusive.
Right. And I'm telling you that some students not liking it wasn't the fucking claim.

>>16280436
That's what i am saying retard lmao. Some students not liking and some liking it are disjoint sets within the set D.

>>16280443
And i am saying it doesn't matter, whats so hard to understand here? As long the word some is used, liking or not liking becomes irrelevant if you have not been asked to identify such a set.

>>16280444
See
>>16280443
The claim is there is no students that like homework within the set of students. If the set of students that like and dislike homework are disjoint, what does that say about the set of students that dislike homework and the set of students overall?

>>16280455
No, the claim is that SOME students don't like homework, that automatically becomes a subset of its own, the rest like homework by definition.

>>16280446
>As long the word some is used
That's not how this works. That's not how any of this works.

That'd mean "there are not some green suits in a deck of cards" and "there are some green suits in a deck of cards" are logically equivalent.

Pay attention to where the fucking negative is within a logical construction.

>>16280461
>No, the claim is that SOME students don't like homework
>It is not the case that some students like homework.
Learn2read

>>16280463
This is not the same as a deck of cards which has more than two colours, the negation works because liking and disliking are negatives of each other.

>>16280464
Which is the same thing lmao, where did you retards learn your logic?

>>16280465
>the negation works because liking and disliking are negatives of each other.
The negation is of some, not of liking.

I ask you, what is the negation of some?

As I said, learn2read.

>>16280466
I took logic in college. Sounds like you should take a course.

>>16280468
the negation of some is some like i keep telling your retarded ass that it doesn't matter when some is used.

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>>16280474
>the negation of some is some

>>16280480
the negation of some people liking something is some people not liking something, my god you must be a high school student if i have to explain such basic statements to you

>>16280482
It is not true that you have made some points.

>>16280485
fuckoff faggot, show me where i am wrong if it is the case that you can, or do you need me to explain the meaning of can?

>>16280482
>the negation of some people liking something is some people not liking something
NTA but the negation of some people liking something is nobody liking something. It's not equivalent to the claim that some people dislike it. In the case where the number of people is greater than 1, "nobody likes it" is a strictly stronger claim that "someone dislikes it". In the case where there's exactly 1 person, the claims are logically equivalent. When there's 0 people, "some people dislike it" is strictly stronger.

>>16280494
the negation of nobody liking something is everyone liking something and we have not been given any numbers so your retarded assumption about greater than one is irrelevant here

>>16280496
Oh my god you are insufferable. By that logic, suppose 1 person likes something and another person dislikes it. Is it true that everyone likes it? No. Therefore its negation is true. According to you, that means that everyone dislikes it. That's wrong.

>>16280503
You have a set with one person liking it and another disliking it which proves my point about some liking and some disliking. We are talking about people in specific sets here not the whole world. You are trying to sneak in some retarded assumption about everyone when it is clear that the context is specific sets.

>>16280496
(Some or none) is the opposite of all. None is the opposite of some. This isn't difficult.

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>>16280511
You are beyond help.

>>16280516
what is difficult for you is thinking we are talking about pure quantifiers instead of propositions

>>16280542
He's mentally challenged or trolling. Stop feeding him.

>>16280544
lmao are you still seething, afraid to refute me aren't you

>>16280530
>https://en.wikipedia.org/wiki/Quantifier_(logic)
>to disprove a "there exists an x" proposition, one needs to show that the predicate is false for all x

>>16280553
one also needs to show that this is the case for a specific set/subset, again the problem here is not about predicate logic, its about the poor encoding into set theory, how many posts do i have to make for you undergraduate retards to understand this?

>>16280561
>one also needs to show that this is the case for a specific set/subset
Which is trivial by moving to second order logic where the same logical relationships hold fucking true and can be applied to sets.

Not that you even need to fucking bring sets into this discussion, but I digress.

>>16280573
We could even do it by defining P(x) well enough, but have you seen any such definitions? All we have is an assumption of liking/disliking homework and retards itt keep arguing that 'no student likes homework' is justifiable because they are making implicit assumptions about those students liking something else like sports or video games, things that have not even been mentioned.

>>16280600
>because they are making implicit assumptions about those students liking something else like sports or video games
Can you show anywhere where anything like that is brought up ITT?

Why did these retards write, statement then negation. It is confusing because you don't know whether you are supposed to negate the original statement or whether the negation is the implication of the original statement? I think this is where the confusion is.

>>16279608
that's just worded autistically

"It is not the case that ANY students like homework," sounds better because people sometimes actually say "not any"

>Not any of the students like doing their homework
>All of the students don't like doing their homework
Yup. It tracks. No students like homework. You just have to convert it into rune language and then back to English.

>>16280482
>some people like something
>not(some people like something)
>not any people like something
vs
>Some people don't like something
See the issue. Some people not liking something is different from not any people liking something.
>>16280496
>The negation of nobody liking something is everyone liking something
>Not nobody likes you
>at least somebody likes you
Nah.
>Nobody doesn't like you
>everybody likes you
Sure, why not, but that isn't how a negation is applied in logic.

It seems you're just getting caught up on what is being negated. This is how a negation works. First you take your statement and test out every possibility(some, all, and none):

"nobody likes something"
>Say only some people like it, is the statement still true? no
>Say everybody likes it, is the statement still true? no
>Say nobody likes it, is the statement still true? yes

Now, you just invert the results to get the negation. Change each yes into no and vice versa

Not(nobody likes something)
>only some people like it. yes
>everybody likes it. yes
>nobody likes it. no

Now we can test it against your theory that the negation is everybody likes something
Everybody likes something
>an amount of people like it. no.
>everybody likes it. yes
>nobody likes it. no

That's a yes yes no, to a no yes no. In other words, the inversion of (nobody likes something) is (some people like something) and it's not (everybody likes something) because to negate at statement is to make the opposite results.

>>16280869
typo
>an amount of people like it
should be
>only some amount of people like it

>>16279608
this is just saying students don't like hw, simple enough. definition of a limit is harder, too many abstract variables and relationships for my brain to keep track of all in one sentence

This is retardedly poorly worded. Are they saying that
>it is not the case that 'some students like homework'
or that
> it is not the case that 'some' students like homework
If it's the first why color code 'some' and leave the sentence that should be in quotes in tact and if its the second, why negate the whole statement?
There's simply too little information here and let's not even talk about the statement to negation implication. Whoever is teaching this should think about what their retarded teaching methods, which they carried over from highschool-- like color coding-- are doing to students.

>>16281116
>If it's the first why color code 'some' and leave the sentence that should be in quotes in tact and if its the second, why negate the whole statement?
Because the color coding corresponds to the components of the logical formula beneath the sentences and the "∃" means "some".

>>16279608
It is not the case that some threads OP makes aren’t stupid. All threads that OP makes are stupid.

>>16281149
This gives the wrong impression that only some is being negated. You have big bright colors emphasizing the wrong thing.

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>>16279608
You are saying there are people in this board who can't comprehend it? And I am sharing the same board with them?
Fine! Read this!
https://archive.org/details/logic00hodg or https://library.lol/main/013e87f91e6943d44cdadbbdcbde0edc

>>16279608
Because language is shit. Literally shit. Even those sentences are garbagely constructed. It should be something like:

Some Students liking homework is a falsity. Which is equivalent to No student likes homework.

We don't put the false in front, but we do in logical notations because it makes sense. We also just don't construct sentences in this formal way ever.

>>16279719
there's a philosophy for everything yet none of them achieve shit.

>>16281181
Again, they aren't for emphasis. They're to highlight the important terms in the sentence and tie them into the underlying logic.

Also, only some is being negated, lmao.

>>16280085
"Proving" it empirically would mean just showing a bunch of examples. Why not just prove it logically?

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>>16280085
Instead of an empirical "proof" here's a natural deduction style proof. So we know it's correct so long as the rules of natural deduction are sound. Pic made using
https://proofs.openlogicproject.org/

>>16279608
autists demanding you learn there autism.

>>16279608
What subject of logic? The only thing I find it difficult was forcing, I really don't consider logic as hard

>>16279608
first sentence better:

"there exists no student that likes homework"

>>16282063
how do i read this?

>>16279608
Because trying to convert natural language into a cute equation never works because they're fundamentally opposed.

>>16279608
This is interesting.
Any good books for beginners on logic?

>>16280335
>>"Civilised" beliefs are just primal beliefs that have been sublimated into a more refined and elegant form
>>"Civilised" behaviours are just primal behaviours that have been sublimated into a more refined and elegant form
What a retarded statement to make. Consciousness has only existed for ~3000 years. Do you really believe ancient cavemen were *anything* like us?

>>16284096
This is the real truth. But I wouldn't say they always have to be opposed, just that the concepts used in formal logic currently are not always the same as the concepts in natural language that underlie the words that they co-opt to use in the formal logic.

>>16283667
It's Fitch notation. The statement above each horizontal line is an assumption, and the statements below the line but still to the right of the attached horizontal line are things proven true under that assumption.

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>give me ~(-]X € D, P(X) ) X € D, ~P(X) apples please

>>16284453
>>16284453
Math beyond arithmetic is useless.

>>16283667
Given there is not something, assuming there is some thing would mean there is not some thing which means there is not anything. Given there is not anything, assuming there is something and there is some thing would mean there is nothing which means there is not something. Therefore there not being something is necessary and sufficient for there to be not anything.

Basically.

>>16279608
Really just practice