Anonymous at Tue, 17 Sep 2024 00:09:08 UTC No. 16383970

>>16383940
Is a vacuous truth decided by convention?
I can see using implication to yield a similar result
>if there are marbles in the bag, then they are blue
This can be true even with no marbles in the bag, by definition. But an implication is different than some assertion about empty sets.

Anonymous at Tue, 17 Sep 2024 04:18:49 UTC No. 16384188

>>16383940
>>16383970
This is sort of a case of formal logic influencing informal logic, but it's also the only reasonable way for things to work. In logic, P->Q is true when P is false (because otherwise logic does not work). Formalizing your example gives something like: \forall x \in Marbles Green(x) but this is actually just syntactic sugar for \forall x (x \in Marbles -> Green(x)) which is clearly true when Marbles is empty.
Informally speaking, it just comes down to what you interpret an English sentence to actually mean. Anyone trained in mathematics will not require "all" to be more than zero, but maybe some people would interpret the sentence as also saying |Marbles| > 0. One thing to consider is that negating the sentence twice should give the same result. I would negate "All the marbles are green" as "There is a marble that is not green" and negate that again as "There is not a marble that is not green" which should be equivalent to the first sentence. Do you agree?

Anonymous at Tue, 17 Sep 2024 04:29:32 UTC No. 16384200

>>16383940
>Even though it is equally as true that all the marbles are blue, which would result in a contradiction where only one could be true.
what's the contradiction?

Anonymous at Wed, 18 Sep 2024 00:17:44 UTC No. 16385409

>>16384200
all of the marbles in the bag are green
none of the marbles in the bag are not green
blue is not green
none of the marbles in the bag are blue
contradicts with
all of the marbles in the bag are blue

in reality, given that no marbles are in the bag, the initial statement is nonsensical. it's like trying to evaluate the truth of the statement that unicorns are green. It's not false or true, unicorns do not exist.

Anonymous at Wed, 18 Sep 2024 00:31:15 UTC No. 16385418

>>16383940
>given an empty bag, all the marbles in the bag are green
This is just an ESL mistake and should be moved to >>>/lit/

Anonymous at Wed, 18 Sep 2024 01:09:06 UTC No. 16385452

>>16384188
>there is not a marble that is not green
>there is not a marble that is not blue
Seems possible, but then you can get to
>there is not a marble that is not entirely green
>there is not a marble that is not entirely red
Or I suppose the real problem is equivalencies between things just because they share a single member
>I have a bag of apples and bananas
>I have a bag of apples and no other fruit that is not bananas
>I have nothing in my bag that is not apples and bananas
Reducing some M:P(x) to an empty set doesn't imply M:P(y)

Anonymous at Wed, 18 Sep 2024 01:12:47 UTC No. 16385460

>>16385409
if "none of the marbles in the bag are [x]" means "there is not one of the marbles in the bag which is x" then
>none of the marbles in the bag are blue
and
>all of the marbles in the bag are blue
are not contradictions

Anonymous at Wed, 18 Sep 2024 01:38:04 UTC No. 16385495

>>16384188
>P->Q is true when P is false
No, you're mistranslating how English works. Consider the wikipedia vacuous truth example of "all cell phones in a room turned off" being satisfied by a room containing no cell phones. The reason this makes sense is that we understand it to mean "no cell phones in the room are on." It implicitly reverses the conditional.

Anonymous at Wed, 18 Sep 2024 02:12:28 UTC No. 16385532

>>16385495
Material implication does not line up exactly with natural language, yes.

🗑️ Anonymous at Wed, 18 Sep 2024 02:35:56 UTC No. 16385571

>>16385532
Yeah. Also a positive color identification implies fuzzy logic, not true or false. If OP were rewritten as something like "please make sure that all the bits in your string are 0," it would make more sense.

Anonymous at Wed, 18 Sep 2024 02:37:52 UTC No. 16385573

>>16385532
Yeah. Also a positive color identification implies fuzzy logic, not true or false. If OP were rewritten as something like "please make sure that all the bits in your string are flipped to 0," it would make more sense.

Anonymous at Wed, 18 Sep 2024 05:00:10 UTC No. 16385699

>>16384200
A self contradiction is when something is its own opposite and anytime you make vacuous statements, you are citing a number that is its own opposite number since 0=-0, so you are able to craft contradicting sentences that are equally "true" such that all 0 marbles in the bag are blue and all 0 marbles in the bag are not blue.

Anonymous at Wed, 18 Sep 2024 08:03:19 UTC No. 16385804

>>16385460
NTA..
I think previous anon was trying to distinguish the difference between practical logic and meaning psychoses prattle.

Anonymous at Wed, 18 Sep 2024 08:03:47 UTC No. 16385805

>>16383940
Master class in logic. You sir are beyond retarded

Anonymous at Wed, 18 Sep 2024 10:31:01 UTC No. 16385903

>>16384188
>In logic, P->Q is true when P is false (because otherwise logic does not work).
>because otherwise logic does not work
Logic doesn't work with that bullshit anyway, so best to abandon that faggotry and utilize a different system of logic. And don't even get me started on the law of excluded middle.
>He doesn't not hate you
>He hates you
Even a toddler recognizes these are different statements with different meanings yet formal logic forces them to be equivalent. So you're right that formal logic doesn't work without vacuous truths.. which would be fine if it actually fucked worked with them but it doesn't. Fuck you

Anonymous at Thu, 19 Sep 2024 20:32:05 UTC No. 16388196

>>16385903
Isn't this just misreading a cover?
Not hate could be any number of sentiments, but not not hate could only be one.

Anonymous at Thu, 19 Sep 2024 20:50:32 UTC No. 16388212

>>16385903
Just because they aren't the same statement doesn't make them different statements anon

Anonymous at Thu, 19 Sep 2024 20:53:22 UTC No. 16388215

>>16388212