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Implication dogma

Anonymous Mon 21 Sep 10:21:29 2020 No.12145253 View Reply Original Report

How does this even make sense?

1)I hypothesis that a bag of chips DOES NOT cost $5, however, after I visit a shop it is found to be $5 and my hypothesis is wrong. How come it is said to be TRUE in the nigger truth table?

Anonymous

Anonymous Mon 21 Sep 2020 10:32:01 No.12145277 Report

Quoted By:

>>12145253
If I'm not sure that bag of chips doesn't cost $5 then it's equally likely that it costs $5(1st entry) or it doesn't cost $5(2nd entry). Cherry picking values in a truth table because you are a retard doesn't count.

Anonymous

Anonymous Mon 21 Sep 2020 10:35:43 No.12145284 Report

Quoted By:

>>12145253
If I'm not sure that bag of chips doesn't cost $5 then it's equally likely that it doesn't cost $5(1st entry) or it does cost $5(2nd entry). Cherry picking values in a truth table because you are a retard doesn't count.

Anonymous

Anonymous Mon 21 Sep 2020 11:03:48 No.12145331 Report

Quoted By: >>12145436

>>12145253
>if a bag of chips costs $5, then i do thing
>a bag of chips does not costs $5
>still do thing anyway

Anonymous

Anonymous Mon 21 Sep 2020 11:54:49 No.12145381 Report

Quoted By:

>>12145253
once evidence doesn't matter, anything goes

Anonymous

Anonymous Mon 21 Sep 2020 12:06:23 No.12145398 Report

Quoted By: >>12145408

>>12145253
It's not a hypothetical statement. It's essentially saying that if p is true and false at the same time then anything follows.

Anonymous

Anonymous Mon 21 Sep 2020 12:14:10 No.12145408 Report

Quoted By: >>12145432

>>12145398
>What does P is true and false at the same time mean? That's neither T nor F, that's M for maybe.

Anonymous

Anonymous Mon 21 Sep 2020 12:24:35 No.12145432 Report

Quoted By: >>12145441 >>12151551

>>12145408
p->q, means p follows from q
so p = F, q = T, means that "q follows from p" is valid

for ex: "if that elephant has 9 legs, then I'm Elon Musk." is a valid statement since p is False.

Anonymous

Anonymous Mon 21 Sep 2020 12:25:10 No.12145434 Report

Quoted By:

>>12145253
I have the same doubt. Only T, F, F can be said with any certainty. All the rest is the outcome of formalizing bullshit.

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

Anonymous

Anonymous Mon 21 Sep 2020 12:26:05 No.12145436 Report

Quoted By:

>>12145331
>if a bag of chips costs $5, then i do thing
>a bag of chips does not costs $5
>dont do it
You are disproved by the 2nd column of the truth table

Anonymous

Anonymous Mon 21 Sep 2020 12:26:34 No.12145438 Report

Quoted By:

>>12145253
>Unlike the English construction "if … then …", the material conditional statement p q does not conventionally specify a causal relationship between p and q; "p is the cause and q is the consequence from it" is not a generally valid interpretation of p q. It merely means "if p is true then q is also true", such that the statement p q is false only when p is true and q is false

wikipedia

Anonymous

Anonymous Mon 21 Sep 2020 12:27:42 No.12145441 Report

Quoted By: >>12145444 >>12148560

>>12145432
Brotip: you can make a with alt + 26

Anonymous

Anonymous Mon 21 Sep 2020 12:28:43 No.12145444 Report

Quoted By: >>12148560

>>12145441
And of course it doesn't work on 4chin

Anonymous

Anonymous Mon 21 Sep 2020 12:30:51 No.12145447 Report

Quoted By: >>12145453

>>12145253
This makes perfect sense. False implies anything.

Anonymous

Anonymous Mon 21 Sep 2020 12:37:54 No.12145453 Report

Quoted By: >>12145459 >>12145953

>>12145447
Could you explain with this example?

P= "Things fall to the ground"
Q= "Gravity exists"

Anonymous

Anonymous Mon 21 Sep 2020 12:43:29 No.12145459 Report

Quoted By: >>12145462 >>12145489

>>12145453
If things fall to the ground, then gravity exists. That statement is correct.

Anonymous

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Anonymous Mon 21 Sep 2020 12:46:15 No.12145462 Report

Quoted By: >>12145471

>>12145459
Analyze it with the truth table.

Anonymous

Anonymous Mon 21 Sep 2020 12:54:49 No.12145469 Report

Quoted By:

If it bothers you stop calling it 'if.. then..'. Think of it as 'the falsehood of q is incompatible with the truth of p' and the truth table follows naturally.

Anonymous

Anonymous Mon 21 Sep 2020 12:57:29 No.12145471 Report

Quoted By:

>>12145462
t -> t

Anonymous

Anonymous Mon 21 Sep 2020 13:06:48 No.12145484 Report

Quoted By:

>>12145253
Classical logic defines implication as "not A or B", ~A?B. Given an interpretation that A is false (and not-A is true), then B could be either true or false and the interpretation would still hold.
If you want to preserve a difference between logical-or and implication, you can reject the true/false dichotomy and become an intuitionist.
I would understand A->B as "given a construction of A, a construction of B can be produced". If A is false, which means it proves a contradiction (A->?), then nothing can be constructed about B, since intuitionists reject the law of excluded middle.
In such a scenario, A->B would be proven (aka "true"), and A->? would be proven (aka A is "false"), but A itself would not be proven.
https://plato.stanford.edu/entries/logic-intuitionistic/
https://en.m.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation

Anonymous

Anonymous Mon 21 Sep 2020 13:09:23 No.12145489 Report

Quoted By:

>>12145459
f -> f :
2>5
2+1>5+1

f -> t :
-3 = 3
(-3)^2 = 3^2

Anonymous

Anonymous Mon 21 Sep 2020 14:00:07 No.12145581 Report

Quoted By:

If you'll give me a house for $10 then I'll buy it.

If it costs $20 then I won't

Anonymous

Anonymous Mon 21 Sep 2020 16:04:37 No.12145855 Report

Quoted By: >>12145866

>>12145253
It's not really a pure math derivation. It's just a tool invented for problems that require similar logic. All we did was say: NOT (P AND NOT Q) <=> P -> Q as a shorthand.

Anonymous

Anonymous Mon 21 Sep 2020 16:06:49 No.12145859 Report

Quoted By:

Imagine being as retarded as OP and make a thread about this

Anonymous

Anonymous Mon 21 Sep 2020 16:10:20 No.12145866 Report

Quoted By: >>12145891

>>12145855
~P v Q would be simpler.

Anonymous

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Anonymous Mon 21 Sep 2020 16:12:03 No.12145870 Report

Quoted By:

Logical implication isn't a good model for entailment, but the principle of explosion is verified in the theory of arithmetic (from 0=1 everything follows) and so mathematicians generally don't run into problems using it.

For alternatives, see
https://en.wikipedia.org/wiki/Relevance_logic

but the formal semantics of such logics are much harder than Boolean algebra

Anonymous

Anonymous Mon 21 Sep 2020 16:21:16 No.12145889 Report

Quoted By:

The implication truth table is intended for phrases like this:

rain -> clouds

The only condition for which this does not make sense is: rain & no clouds.

All other conditions are acceptable: rain & clouds, no rain & clouds, no rain & no clouds.

Hence, only T -> F yields F.

In other words, p -> q reads: if p is true, then q must also be true. The expression p -> q is only false when this is violated.

Anonymous

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Anonymous Mon 21 Sep 2020 16:22:28 No.12145891 Report

Quoted By: >>12145898 >>12146040

>>12145866
God I fucking hate logic notation of Boolean algebra so god damn much.
1. The symbols look to similar v, and ? look too similar and makes the equation take 10 times longer to understand
2. Because AND comes before OR in order of operations, the circuit notation is far more intuitive for someone who already learned regular algebra
Why does seem the notation purposely makes it harder to understand than it really is? Is it so discrete mathematicians and logicians can feel more intelligent by making their work look indecipherable to laypeople?

Anonymous

Anonymous Mon 21 Sep 2020 16:23:36 No.12145893 Report

Quoted By:

can use repl instead

https://www.youtube.com/watch?v=oRgYkdNpiFM

Anonymous

Anonymous Mon 21 Sep 2020 16:25:25 No.12145898 Report

Quoted By:

>>12145891
its just a fucking \/ and a /\

Anonymous

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Anonymous Mon 21 Sep 2020 16:48:14 No.12145953 Report

Quoted By: >>12145987

>>12145453
No one is explaining this basic concept using my example. Someone please explain this to me using

p= "Things fall to the ground"
q= "Gravity exists"

Anonymous

Anonymous Mon 21 Sep 2020 17:04:14 No.12145987 Report

Quoted By:

>>12145953
If things fall to the ground but nothing falls to the ground then gravity exists ,(and doesn't exist).

Anonymous

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Anonymous Mon 21 Sep 2020 17:23:16 No.12146040 Report

Quoted By: >>12146056

>>12145891
It seems pretty simple to me. If you want to see retarded logic notation, read Principia Mathematica, where the same symbol used for 'and' is also used instead of brackets to denote scope. Pic related. Some of those dots are conjuctions, some aren't. Because staring at propositions carefully to figure out what the fuck they're asserting is presumably valuable in ensuing you've paying attention.

Anonymous

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Anonymous Mon 21 Sep 2020 17:27:25 No.12146056 Report

Quoted By:

>>12146040
Fuck, actually none of those were conjunctions. Here's some.

Anonymous

Anonymous Mon 21 Sep 2020 17:38:28 No.12146097 Report

Quoted By: >>12146128

>>12145253
>T -> T
This one is evident enough. It is raining, therefore it is wet outside.
>T -> F
If you have true assumptions, you cannot get a false conclusion without having invalid logic. It is raining outside, therefore it is dry outside. This does not follow.
>F -> T
You can have a false assumption but reach true conclusions with it. All dogs are ferocious, therefore there are dogs that are ferocious. False assumption, true conclusion.
>F -> F
Garbage in garbage out. If your assumptions are false, you can also generate false conclusions. There is a big red dragon, therefore dragons exist.

Anonymous

Anonymous Mon 21 Sep 2020 17:38:58 No.12146101 Report

Quoted By:

>>12145253
You should think about logical implication as a relationship between two things. A=>B means whenever I have A, I also have B. But I could have situations where I have B but not A. In those cases, the relationship still holds. That's why they say (F=>T) = T.

Anonymous

Anonymous Mon 21 Sep 2020 17:47:28 No.12146128 Report

Quoted By:

>>12145253
To follow up on >>12146097

Your post is confusing validity with soundness. All the structures in your chart except (T -> F) are logically valid, you can get them without having any errors in logic. However, the only one that is sound is (T -> T), as soundness is based on what is actually correct not what is structurally correct. The truth table addresses validity, not soundness.

Anonymous

Anonymous Mon 21 Sep 2020 21:10:22 No.12146732 Report

Quoted By:

>>12145253

The way you formulate the 'problem', both p and q have the same meaning:

a bag of chips costs $5

If p and q are the same predicate, you cannot set p to F and q to T.

Zoomer

Zoomer Mon 21 Sep 2020 21:17:11 No.12146747 Report

Quoted By:

No convincing answers. Relevance logic ftw

Anonymous

Anonymous Tue 22 Sep 2020 12:35:50 No.12148560 Report

Quoted By:

>>12145441
>>12145444
Nice tripps
> $a \rightarrow b$
Feel mogged yet?

Anonymous

Anonymous Tue 22 Sep 2020 12:55:42 No.12148587 Report

Quoted By:

>>12145253
I always thought of it this way, though I'm sure it's not quite right. "If the moon is made of cheese, then California is in the U.S." Though the antecedent is false, the consequent is true in any case.

Anonymous

Anonymous Tue 22 Sep 2020 15:56:59 No.12148971 Report

Quoted By:

>>12145253
>the nigger truth table?
imagine being dumber than a nigger

Anonymous

Anonymous Tue 22 Sep 2020 19:29:56 No.12149576 Report

Quoted By:

Because you are confusing if with iff (if and only if).
"The sky is blue, if the grass is red" is a true statement. The color of the sky doesn't depend on the color of the grass.
"The sky is blue, if and only if the grass is red" is false because the grass is not red but the sky is blue.

With the material conditional (if P, then Q), you might think the truth of P is a necessary condition for the truth of Q. But this is not the case. The opposite is true. Q is necessary for P. P is sufficient for Q, but not necessary.

Anonymous

Anonymous Tue 22 Sep 2020 21:23:09 No.12149882 Report

Quoted By:

>>12145253
p := OP is not a fag
q := (0 = 1)
p -> q

if p is false, you can prove anything

Anonymous

Anonymous Tue 22 Sep 2020 21:27:06 No.12149891 Report

Quoted By:

>>12145253
>1)I hypothesis that a bag of chips DOES NOT cost $5, however, after I visit a shop it is found to be $5 and my hypothesis is wrong.
thats not even an implication you retard

If a bag of chips costs $5, THEN ill buy it
>go to store
>find chip
>cost $4
>still buy chip
>thank you chip

what the fuck dont you understand

Anonymous

Anonymous Tue 22 Sep 2020 21:45:27 No.12149944 Report

Quoted By:

>>12145253
Imagine someone says
"If I come to your house, make sure you get a pizza."
Then if they don't visit your house, it doesn't matter whether you have pizza or not. Either way you you are still complying with their request, because their request only stated specific conditions for when they visit. The statement doesn't say any about what to do if they aren't visiting.

Anonymous

Anonymous Wed 23 Sep 2020 05:17:05 No.12151273 Report

Quoted By:

>>12145253
Are you literally retarded?

Anonymous

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Anonymous Wed 23 Sep 2020 05:20:29 No.12151281 Report

Quoted By:

>>12145253

Anonymous

Anonymous Wed 23 Sep 2020 06:16:53 No.12151364 Report

Quoted By:

"If I'm president of USA, then I'm not president of USA" is false only if I am Trump. Otherwise it is true.

Anonymous

Anonymous Wed 23 Sep 2020 06:24:01 No.12151378 Report

Quoted By: >>12151551

>>12145253

This is a limitation of propositional logic
when you only have two truth values (true and false), you don’t have a value for soundness.

If you did have a value for soundness, then the table would be:

T T T
T F F
F T S
F F S

Anonymous

Anonymous Wed 23 Sep 2020 06:42:36 No.12151435 Report

Quoted By:

>>12145253
>If OP is not a faggot than I have a PhD
>OP is a faggot
>I still have PhD
lol

Anonymous

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Anonymous Wed 23 Sep 2020 07:20:20 No.12151526 Report

Quoted By:

>>12145253
This is baby teir logic, if you don’t get it your teacher must really suck.

Anonymous

Anonymous Wed 23 Sep 2020 07:28:06 No.12151551 Report

Quoted By:

>>12145432
>>12151378
>>12145253
To stop being snarky. A lot of people are Messi g the point.
All the highlighted line is really saying is
1.Q.
Therefore
Q.
....
Remember you already declared Q true.

Anonymous

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Anonymous Wed 23 Sep 2020 07:32:46 No.12151567 Report

Quoted By:

>>12145253
It is not the case that given P true, Q won't be true.
Hope that helps

Anonymous

Anonymous Wed 23 Sep 2020 07:43:24 No.12151588 Report

Quoted By: >>12151608

>>12145253
>hypothesis that a bag of chips DOES NOT cost $5, however, after I visit a shop it is found to be $5 and my hypothesis is wrong.
So you are saying
P is true if chips do not cost $5,
What is your Q?
P and q are simple statements that are EACH true or FALSE. You really have only said one statement. Going to the store the way you said it is unrelated.

Anonymous

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Anonymous Wed 23 Sep 2020 07:53:59 No.12151608 Report

Quoted By:

>>12151588
So you need something like
P: it is Tuesday.
Q: chips are $5
......
Is it Tuesday?
p->q
Chips are $5
.....
Is it not Tuesday?
Chips are (still) 5$.
....
It is not the case that given P true, Q won't be true.
Hope that helps. Try these p and q in the rest of your lines, Your problem is your oj hypothesis doesn’t make any sense here, it didn’t have a q

SAGE

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SAGE Wed 23 Sep 2020 08:02:11 No.12151628 Report

Quoted By:

>>12145253
Think of it more like this

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