Is this a valid statement?
Perhaps generally.
There are historical events that have no hard objective evidence but are assumed to have occurred because of later political climates. and diverse sources.
There is no evidence of 2+2 being equal 4, and there is no evidence for basic laws of logic, like law of excluded middle. So yeah, go ahead, dismiss math and logic.
Is it valid? Only if you agree with it.
>>349625
>there's no evidence of 2+2 being equal to 4
but there is you dumb shit.
>Theorem 1. Two plus two equals four.
Proof of Theorem 1. The set of integers is an (infinite) group with respect to addition. Since 2 is an integer, the sum of 2 and 2 must also be an integer. Suppose, for the sake of contradiction, that 2 + 2 < 4. We have 2 > 0. Adding two to both sides, we get 2+2 > 0+2. Since 0 is the identity element for addition, we have 2 + 2 > 2. Hence
2 < 2 + 2 < 4
so 2 + 2 must equal 3. Since 3 is prime, by Fermat’s Little Theorem we have the following for a ∈Z+:
a^(3−1) ≡ 1 (mod 3)
a^(3−1) ≡ 1 (mod 2 + 2)
But
a^(3−1) = a^3/a = (a×a×a)/a = a×a
and, for a = 2,
2×2 ≡ 0 (mod 2 + 2)
since, by the definition of multiplication, 2×2 = 2 + 2. So, we have
2^(3−1) ≡ 0 (mod 2 + 2)
2^(2+2−1) ≡ 0 (mod 2 + 2)
This is a contradiction to Fermat’s Little Theorem, so 2+2 must not be prime. But 3 is prime. Hence 2+2 must not equal 3, and therefore 2+2 ≥ 4.
It remains to show that 2 + 2 is not greater than 4. To prove this we need the following lemma:
>>349780
>Lemma 1.
∀a ∈Z, if a > 4, ∃b ∈Z such that b > 0 and a−2 = 2 + b.
If 'a' were a solution to the equation 2 + 2 = a, then we would have a−2 = 2+0. The lemma states that this cannot hold for any a > 4, and so a = 4, as desired. So, it only remains to prove our lemma.
Proof of Lemma 1: The proof is by induction over a. Our base case is a = 5. Let 5−2 = 2+b. Five is the 5th Fibonacci number, and 2 is the 3rd Fibonacci number. Therefore, by the definition of Fibonacci numbers, 5−2 must be the 4th Fibonacci number. Letting 'f_i' denote the ith Fibonacci number, then we have
'f_i' − 'f_i'−1 > 0
for i =/= 2, because 'f_2' − 'f_1' = 'f_0' and 'f_0' = 0, but 'f_1' = 1, and the Fibonacci sequence is nondecreasing. Hence (5−2)−2 > 0.
Now, suppose that ∃b ∈ Z such that b > 0 and (k−1)−2 = 2 + b. We need to prove that, for some b' > 0, k−2 = 2+b'. Our inductive hypothesis is equivalent to:
k−1−2 = 2 + b
k−1−2 + 1 = 2 + b + 1
k−2 = 2 + (b + 1)
Since 1 > 0 and b > 0, we have (b + 1) > 0. Thus, letting b0 = b + 1, we have a nonnegative solution to k−2 = 2 + b0, as desired.
By Lemma 1, it is not the case that 2+2 > 4. Hence 2+2 ≤ 4. We also have 2 + 2 ≥ 4. Therefore,
2 + 2 = 4
>>349588
That is an absolutely valid statement. Just be careful when you apply it. Your friend tells you he ate chicken for dinner? There is no evidence, but eating chicken isn't that extraordinary or important. A preacher says that unless you stop masturbating that you will burn for all eternity in another dimension? Might want to ask for some evidence
>>349625
There is plenty of evidence that math and logic work. Take for example space ships and computers
>>349625
You're right insofar as certain words like "and", "if", "or", "either", etc. have a certain prelogical understanding that is necessary for logic.
Insert Kant, etc.
But to even consider objects discretely, math follows. You can't take two blocks and two blocks and not have four blocks. If you construct math based on this intuitive approach you can't deny its validity.
>>349822
prove the following statement:
This statement is false.
>>349843
logic systems being provable does not in any way imply that every sentence you can come up with is logical
it's a nifty little logic experiment but I don't see what you're trying to prove with babby's first paradox
>>349780
>he thinks a proof is an evidence of something
Proof only good as evidence if its axioms has evidence, and there is no evidence of integral numbers existing, especially with properties you ascribe to them. I mean, of course you can postulate anything you want and then produce sound proofs out of it, but it isn't any differ from theologists arguing about angels and stuff.
>>349822
This isn't an evidence though, whatever you believe "works" isn't a proof of something - ask Christians, they'll tell you prayer do work, the only difference is observational error margin.
>>349862
>This isn't an evidence though, whatever you believe "works" isn't a proof of something
I didn't say it was proof, just evidence. If we can use math to calculate a rocket's trajectory to land on Mars and it works out, that is evidence that math works
>>349862
>Proof only good as evidence if its axioms has evidence, and there is no evidence of integral numbers existing, especially with properties you ascribe to them. I mean, of course you can postulate anything you want and then produce sound proofs out of it, but it isn't any differ from theologists arguing about angels and stuff.
Do you deny your car works? All mechanical devices you use were created using mathematical reasoning. It survives application to a huge degree.
It's not like prayer at all.
>>349838
> You can't take two blocks and two blocks and not have four blocks
Why? Just because it didn't happen before doesn't mean it will never happen.
>>349874
>I didn't say it was proof, just evidence. If we can use math to calculate a rocket's trajectory to land on Mars and it works out, that is evidence that math works
That doesn't solve Hume's problem of induction. But mathematics is still the best system we have to apply onto reality, so whatever.
>>349883
You're right, but if I took two and two blocks, put them together and had only three, then human knowledge would instantly be reduced to nothing and we wouldn't be able to have a conversation anymore.
>>349862
mathematics is based only on what is undeniably provable, and no advances can be made without scrutinizing new theorems to ensure that they do not assume information that is not concretely proven
Pardon me for not including footnotes to explain how the multiplication function works and how it can be proven that the Fibbonacci series isn't arbitrary numbers
You're looking at mathematics from the point of view of philosophy, and seem to have no knowledge at all of what math even is beyond what you must have learned in algebra class. The base ideas and axioms of mathematics are not only omnipresent in nature, but self-evident and have been tested with success millions of times.
>>349879
>All mechanical devices you use were created using mathematical reasoning
Wrong. Many foundations of the mechanical device we use today were created before the application of mathematical models. It doesn't matter if the math doesn't exist. The mechanical device would continue to operate with or without mathematical proofs.
>>349874
>>349879
Just because some theory produces useful results doesn't mean it's true or reflect the things as they actually are, there is no logical link here, you can produce useful results with absolutely wrong theories. For example Newton's physics is quite useful in everyday use, but we know its axioms are actually incomplete (i.e. false) because of relativity. Same with math and logic - surely 2+2=4 is useful thing to know, but there is no logical evidence this is a complete truth and all truth. We don't even know if there is such thing as "truth about abstract numbers".
>>349843
All statements contain implicit assertions about their own truth. Thus:
This statement is false.
This statement is true and this statement is false.
are not contradictory statements.
The latter is a simple contradiction of the form "A and not A", and hence is false.
>>349901
So what? Just because not A would be inconvenient to us doesn't mean A is true.
>>349903
>The base ideas and axioms of mathematics are not only omnipresent in nature, but self-evident and have been tested with success millions of times.
I was okay with what you said until here. WTF? Go in nature and find me a number.
Also, if math is self-evident then why has it taken us thousands of years to develop basic notions such as the countability of infinite sets?
>>349903
> but self-evident and have been tested with success millions of times.
> self-evident
> tested with success millions of times
Oh boy, just like idea of God is self-evident and have been tested with success millions of times. Are we talking about logic or your wishful thinking?
>>349950
where the fuck did you come up with that? Religion has nothing at all to do with what i posted
>>349921
>Wrong.
Wrong. Every part in your car was built using math. You're misunderstanding me.
>>349927
Yes, you're right, I agree, math is not an absolute structure of True™ knowledge. But if you think that means you can just handwave it, then you're a fucking moron.
>>349936
Because I want to have a constructive talk about philosophical ideas, not listen to some cunt try to be the next Sextus Empiricus. I take the truths of mathematics in a pragmatic light, I don't appeal to absolutes anyway.
>all these suckas who haven't read big papa hume
>>349955
"Self-evidence" is on the same level as religion though, it's an unprovable personal opinion and has no place in logic. You can't base evidence for math on "well I kinda feel it's true".
>>349967
religion is untestable, mathematics is testable. You can use theorems and equations to predict the natural world with success
>>349960
Hume is great for being so pragmatic, even though people ignore that side of him and flip out about the arguments against things like induction and causation.
Hume says that the problem of induction doesn't change your odds of winning a pool game, so in reality it's not worth worrying about too much.
>>349980
>mathematics is testable.
Only to itself, which then mathematics is an infinite set of tautological statements. You have to apply it to reality, and how exactly you correlate numbers with sensation is a big problem.
>>349588
it is asserted without evidence.
>>349958
You see, I'm not arguing just for the sake of arguing and I have to intention to be edgy disprover of all the math. Yet the question was about Hitchens Razor, and my point is, to really accept it you have to dismiss math and logic because, strictly speaking, there is no evidence for them.
>>349996
Only if you ignore the entire history of scams and conspiracies that didn't have evidence
>>349980
> mathematics is testable
Yeah, by math itself.
>You can use theorems and equations to predict the natural world with success
It doesn't make them true. As I've said, you can use Newton's laws with great success, even though they are false.
ITT people confuse the words "logical proof" with "evidence"
>>350005
>Yet the question was about Hitchens Razor, and my point is, to really accept it you have to dismiss math and logic because, strictly speaking, there is no evidence for them.
But there's plenty of evidence for mathematics, and good reason to believe that evidence. Maybe you should just read books on its history.
I mean, to even apply Hitchen's Razor to logic, you're using logic in the process. You can't assume the consistency of logic to prove logic's own inconsistency.
>>350030
>mfw people think there's some higher form of evidence that's necessary for practical belief
Look, in the end, what always matters is how much you can apply what you've reasoned in your day to day life. Math and logic you can apply consistently to reality, so that's why we use them. You can be skeptical about it all day, it really doesn't matter.
>>350005
https://en.wikipedia.org/wiki/Proof_by_contradiction
I'd suggest you read that carefully, the biggest problem with using Hitchen's razor as a tool to prove logic inconsistent doesn't follow.
>>350028
>It doesn't make them true. As I've said, you can use Newton's laws with great success, even though they are false.
There is no truth outside of being able to use something with great success.
We can describe things much better than before but that's all.
>>350081
Yeah but that's a non-constructive proof though.
>>350016
I'm not even arguing against it you fuckface
the whole point is that the only argument against it applies equally to everything it is against. everything you would call evidence is also not evidence.
how can a person be as stupid as you? i hope it hurts to live.
>>349940
>Also, if math is self-evident then why has it taken us thousands of years to develop basic notions such as the countability of infinite sets?
>>350458
>everything you would call evidence is also not evidence
Yes, your ability to speak nonsense is unparalleled
Even hard facts and evidence can be dismissed easily.
>>349588
which means up until the 70s or 90s
a+b=c
a^n+b^n=/=c^n
was not a valid theory
As a rule of thumb, yes.
If someone is asserting something with nothing backing it, then yes you can just ignore it.
IIRC the point Christopher Hitchens was making when he said this was that if you're making a claim, the burden of proof is on YOU to produce evidence, not the person with the counter-point.
>>349625
This doesn't count. Basic laws of logic and mathematics are human constructs. They are axioms because they are useful. It is absurd to suggest that a philosophical proposition should satisfy its own criteria.
>>349588
Who gives a fuck, nigga? The new season of South Park is on and I need to play Fallout 4.
>>349625
>doesn't understand the term "self-evident"
This is why trust came into being.
>>349782
I notice that you had to define that over Z+, let's make the problem a little harder and start with the following statements;
You have an open non-finite semigroup containing a series of objects related by some homomorphism '+' (that is to say, you get associativity for free and that your group is abellian I'm being generous. If you want to make it harder prove it for an automorphism)
Demonstrate that two instances of the object '2'. To make it a little easier, I'll let you start with the object '0' already defined such that when '0' is an argument in '+' then the result of this morphism is that for +(a,b) where if either a or b is the object '0', then the result of this morphism is the object b or a respectively.
I cannot promise that the morphism is invertable, or that the semigroup is abellian.
>>349780
shut the fuck up you STEM nerd.
>>351235
If that's your only response to him, then I think it reflects more poorly on you than it does on him. His argument has a few obvious flaws as shown >>351205, but rather than address those notions you instead decided to silence what you considered to be an opposition.
I dont think this is the place for you; pure mathematics is a branch of logic which is a branch of philosophy which is a humanity. If you want to use mathematical or scientific arguments in philosophy that is entirely reasonable, so long as you accept the limitations those arguments entail.
>>349625
Every time I have combined two groups of two objects I have discovered that I have one group of four objects, and there is an extensive written record of other people discovering the same. There is evidence in practice even if not in theory.
>>351295
While in practice you are correct, mathematically you require the following assumptions.
Your groups are abellian, non finite, with a defined ordering, an additive basis and a multiplicative basis, and the assumption of strictly non negative integer values.
>>351275
>the limitations those arguments entail
they don't
you goddamn nerd
>>349588
>Is this a valid statement?
No. I dismiss Hichens Razor without evidence since it was asserted to me without evidence.
