/sci/ - Science & Math » Thread #13423298

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Anonymous Thu 22 Jul 14:20:33 2021 No.13423298 View Reply Original Report

Quoted By: >>13423304 >>13423309 >>13423315 >>13423319 >>13423593 >>13425489 >>13426255 >>13426332 >>13427665 >>13427670 >>13427773 >>13429894 >>13429901 >>13429903

>all integers are even or not even (odd)
>all animals are either mammals or not mammals
>all (valid) statements are either true or false

Why is it that we can express any concept in terms of being either x or not x? Why is it that there is no 3rd option? What is this principle called?

Anonymous

Anonymous Thu 22 Jul 2021 14:22:12 No.13423304 Report

Quoted By: >>13423342 >>13423604

>>13423298
>either true or false...Why is it that there is no 3rd option?
Maybe

Anonymous

Anonymous Thu 22 Jul 2021 14:23:49 No.13423309 Report

Quoted By: >>13423325

>>13423298
You will never be a woman.

Anonymous

Anonymous Thu 22 Jul 2021 14:25:13 No.13423315 Report

Quoted By: >>13423325

>>13423298
> Why is it that there is no 3rd option? What is this principle called?
Law of the excluded middle.

Anonymous

Anonymous Thu 22 Jul 2021 14:26:46 No.13423319 Report

Quoted By: >>13423346

>>13423298
It's the "law of the excluded middle". It's intuitively obvious, but so-called "intuitionists" take issue with it.

Anonymous

Anonymous Thu 22 Jul 2021 14:27:46 No.13423325 Report

Quoted By: >>13423344 >>13423346 >>13423906

>>13423309
What does that have to do with my thread? Are you an actual anon or a shitposting bot?
>>13423315
What happens if we try working with a framework that doesn't have any equivalent to the law of excluded middle? Does this lead to any interesting results? I imagine it would lead to all sorts of contradictions.

Anonymous

Anonymous Thu 22 Jul 2021 14:28:56 No.13423330 Report

Quoted By: >>13423349 >>13423599

it is the principle of excluded middle, it is a metaphysical law of thought

There is no third option because everything that exists, whether it be a physical thing, sensation, thought, idea etc. must be the object of consciousness. This includes predicates of subjects. For example an apple is simply all predicates of intelligibility that can be apprehended by reflection on that object.

The essence of an object is simply identical to its apprehended intelligible character through consciousness. And this is the unique nature of consciousness: You are immediately aware of intelligibility through its obvious presence, or you are not.

Anonymous

Anonymous Thu 22 Jul 2021 14:32:39 No.13423342 Report

Quoted By:

>>13423304
But "maybe" is in meaning simply saying that we haven't determined the truth value of a statement, it does not imply that the statement is neither true or false. Or both true and not true simultaneously.

Anonymous

Anonymous Thu 22 Jul 2021 14:32:51 No.13423344 Report

Quoted By:

>>13423325
>What happens if we try working with a framework that doesn't have any equivalent to the law of excluded middle? Does this lead to any interesting results? I imagine it would lead to all sorts of contradictions.
it just becomes weaker, it would be interesting to measure degrees of uncertainty of exclusion of values, but it would all ultimatley be reducuble to the 2 value system

Anonymous

Anonymous Thu 22 Jul 2021 14:33:43 No.13423346 Report

Quoted By:

>>13423325
>What happens if we try working with a framework that doesn't have any equivalent to the law of excluded middle?
As >>13423319 noted, such frameworks exist. One of the practical consequences is that some of the forms of proof lumped together under the name "proof by contradiction" become invalid.

Anonymous

Anonymous Thu 22 Jul 2021 14:34:37 No.13423349 Report

Quoted By: >>13423365

>>13423330
Where can I read more about the metaphysics of logic? What is the term for this line of discussion/topic?

Anonymous

Anonymous Thu 22 Jul 2021 14:41:34 No.13423365 Report

Quoted By:

>>13423349
>metaphysics of logic
Hegel would say that pure logic (NOT formal systems like computer programs, finite axiom systems, etc) is actually identical to metaphysical reality, and this is how we reason about God, etc.

But if you want to know about the laws of thought, Plato and Leibniz are probably the best

https://en.wikipedia.org/wiki/Law_of_thought

Anonymous

Anonymous Thu 22 Jul 2021 15:46:12 No.13423593 Report

Quoted By:

>>13423298
base 2

Anonymous

Anonymous Thu 22 Jul 2021 15:48:38 No.13423599 Report

Quoted By:

>>13423330
>There is no third option because everything that exists, whether it be a physical thing, sensation, thought, idea etc. must be the object of consciousness
Stopped reading there.

Anonymous

Anonymous Thu 22 Jul 2021 15:51:02 No.13423604 Report

Quoted By: >>13426364

>>13423304
https://en.wikipedia.org/wiki/T-norm_fuzzy_logics

Anonymous

Anonymous Thu 22 Jul 2021 16:25:30 No.13423688 Report

Quoted By: >>13423967

>every number is either 1 or 2, there is no third option
lmao what a fucking idiot you are OP

Anonymous

Anonymous Thu 22 Jul 2021 17:25:03 No.13423906 Report

Quoted By:

>>13423325
>What happens if we try working with a framework that doesn't have any equivalent to the law of excluded middle? Does this lead to any interesting results? I imagine it would lead to all sorts of contradictions.
the system doesn't work. The reason we can do logic and use it to derive conclusions is because we have both the law of the excluded middle and the law of non-contradiction. If you remove the law of the excluded middle, now the law of non-contradiction doesn't make sense because there are cases where a third option can be given. You also lose the concept of the opposite of a statement.

Anonymous

Anonymous Thu 22 Jul 2021 17:41:30 No.13423967 Report

Quoted By:

>>13423688
I'm fuck you're mom

Anonymous

Anonymous Fri 23 Jul 2021 01:11:58 No.13425489 Report

Quoted By:

>>13423298
I would coin it binary existence
Though don't superpositions not inhibit this trait?

Anonymous

Anonymous Fri 23 Jul 2021 05:53:08 No.13426238 Report

Quoted By: >>13426300

>every fruit is either a plum or not a plum
>graft a plum branch on an apricot tree
>obtain a pluot
>"Ahhrgh everything is pure chaos!"
It's not about reality, it's about thought and categories. You mean something when you say "mammal" or "true" or "plum". Whether a particular event, object, other phenomenon, or concept fits your meaning or not is somewhat subjective. You can think less categorically, and say that a pluot is both a plum and not a plum, and the world will not collapse on itself. Or you can say a pluot is a kind of plum. Or you can say a pluot is not a plum. No one gives a fuck.

Anonymous

Anonymous Fri 23 Jul 2021 06:03:32 No.13426249 Report

Quoted By:

triadic logic

Anonymous

Anonymous Fri 23 Jul 2021 06:05:26 No.13426255 Report

Quoted By: >>13426321

>>13423298
Look up Hume.

Anonymous

Anonymous Fri 23 Jul 2021 06:28:31 No.13426300 Report

Quoted By:

>>13426238
>>13426238
It could be more general to think of everything as a continuum than a binary category

a pluot could be a 0.5 plum

it's the best way to describe color, in terms of a few different continous numeric properties

Anonymous

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Anonymous Fri 23 Jul 2021 06:39:24 No.13426321 Report

Quoted By: >>13426323 >>13427762

>>13426255
>Hume
Refuted by Kant.

Anonymous

Anonymous Fri 23 Jul 2021 06:42:05 No.13426323 Report

Quoted By:

>>13426321
In whose classic tome the first paragraph is a single sentence.
And who everyone interprets in any way they want.
I believe Kant can refute God if one tries.

Anonymous

Anonymous Fri 23 Jul 2021 06:50:21 No.13426332 Report

Quoted By: >>13426338

>>13423298
>construct the category of mammals
>define "not mammals" as any animal that isn't a mammal
>"hurr why isn't there a third option???"
anyone who pretends that there should be something that isn't true or false should be thrown in the mental asylum

Anonymous

Anonymous Fri 23 Jul 2021 06:52:30 No.13426338 Report

Quoted By: >>13426350

>>13426332
maybe

Anonymous

Anonymous Fri 23 Jul 2021 07:01:22 No.13426350 Report

Quoted By: >>13426364

>>13426338
not sure if you're trolling so if you are congratulations you baited me

maybe is not a third option. all statements are true or false. "maybe" is something that we humans say when we don't know the truth or falsehood of a statement, because all statements being true or false does not mean that they are immediately obvious to us humans.

Anonymous

Anonymous Fri 23 Jul 2021 07:08:33 No.13426364 Report

Quoted By: >>13427458 >>13427609

>>13426350
see: >>13423604

>all statements are true or false
Response: This sentence is false.

Anonymous

Anonymous Fri 23 Jul 2021 15:51:51 No.13427458 Report

Quoted By: >>13427636

>>13426364
>This statement is false.
False.

Anonymous

Anonymous Fri 23 Jul 2021 15:59:03 No.13427487 Report

Quoted By:

there are non-binary logical systems but you still use binary logic to reason about them :^)

Anonymous

Anonymous Fri 23 Jul 2021 16:56:25 No.13427609 Report

Quoted By:

>>13426364
>define new logic where things can be neither true or false
yes, if you define a system with more than true and false then you can have more than true or false. in classic logic, however, this is not the case, and people like you are dunning kruger retards who don't know what you are talking about.

Anonymous

Anonymous Fri 23 Jul 2021 17:04:51 No.13427636 Report

Quoted By:

>>13427458
Which means its true

Anonymous

Anonymous Fri 23 Jul 2021 17:14:09 No.13427665 Report

Quoted By:

>>13423298
>>all (valid) statements are either true or false
What is a "valid" statement?
Look into the liars paradox. You will find statements that are "true" and "false" and "true and false" and "not true and not false"

But then you might just post hoc say those statements aren't "valid". In which case you are just defining validity so that you reach the conclusion you want

Anonymous

Anonymous Fri 23 Jul 2021 17:15:24 No.13427670 Report

Quoted By:

>>13423298
>Why is it that there is no 3rd option? What is this principle called?
its called projecting retard effect, its what happens when someone thinks they understand something but in reality are mistaken and instead wind up projecting their line of thinking onto their observation.

first off your second example isnt based in reality as its not actually mammals and not mammals. See, there definitely are binary concepts like even and odd. And yes 'it's possible to turn any concept into a binary one', its not actually the same thing as 'every concept has to be binary'. its a good question though as to why anything can be binary and also why or how things aren't binary

youre on a decent path with your philosophy but you haven't figured out the right questions to ask yet.

Anonymous

Anonymous Fri 23 Jul 2021 17:24:46 No.13427693 Report

Quoted By:

inb4 paraconsistent logic

Anonymous

Anonymous Fri 23 Jul 2021 17:57:16 No.13427762 Report

Quoted By:

>>13426321
more like denied

Anonymous

Anonymous Fri 23 Jul 2021 18:03:32 No.13427773 Report

Quoted By:

>>13423298
>>all (valid) statements are either true or false

I suppose this could be captured in what you call valid, but there are propositions which are undecidable.

Anonymous

Anonymous Sat 24 Jul 2021 06:33:25 No.13429894 Report

Quoted By:

>>13423298
>all (valid) statements are either true or false
refuted by Gödel

Anonymous

Anonymous Sat 24 Jul 2021 06:37:28 No.13429901 Report

Quoted By:

>>13423298
Before, I've used the four states states:
>x
>not x
>either/both x and not x
>neither x nor not x

Anonymous

Anonymous Sat 24 Jul 2021 06:38:37 No.13429903 Report

Quoted By:

>>13423298
For the same reason there are only 2 genders. I kid, but that's also the truth.

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