Another Semester, Another Sh*t Show
| We can go by 100IQ standard for the average person. |
| If that doesn't suit your fancy, then how can a proof, which may require explanation from the one who proved it, be worth anything to anyone who wouldn't find something like 5X always being even if X is even obvious? |
| However, it's incorrect, because what if they also use an umbrella when it's sunny? |
In mathematics you always use axioms and theorems as premises, so you don't have to bother with "what if this premise is false?", and if you need a premise that's unproven you simply prove it.
| I can't believe you're defending proofs against basic logic that I'm putting forward. |
| If going by your standards, what would be "clear"? |
| And this doesn't even state that you needed all premises, only that the ones you have are true. |
If you have an umbrella then it's raining outside.
You have an umbrella.
It's Friday.
Therefore it must be raining outside.
This would be considered very sloppy, though.
| 1. Denial and reaction to something new, especially for callow youth, is normal and vital. It is akin to skepticism as a foundational part of the scientific method. |
So you're an old man, thanks.
| 3. Never accept words as absolutely true without questioning them. |
Alright Socrates.
| 5. Running away is intellectual cowardice but admitting defeat is honorable. |
Thanks ever NFL player ever.
| 8. Selfishly, I get nothing out of you kow-towing to the greatness you unilaterally bestow on me. |
So sarcasm doesn't get you off?
Againtry, there's great misunderstanding with my position. I'm saying proofs are overly pretentious and have standards that don't matter except for in some rare cases. In most cases, the level of mathematical proof is too formal to make sense to use it. Why is the GCD of a prime P, and another number A, 1 if P doesn't divide A? Why do you need a whole mathematical proof for this?
On my test, there was a question about proving that a line and a circle don't meet. They clearly never touch when graphed. However, to do the proof, you needed to calculate the equation of the circle, do some magic, and prove that the two equations don't share common common ground on the graph - because showing a graph where they don't touch wouldn't prove anything, would it? What's the point of a mathematical proof in this case other than to be completely retarded when the answer is so plainly obvious? Again, I'm sure there are rare cases where it may not be as obvious to someone whether or not they intersect, and they don't have a graphing calculator on hand (*SHRUG*), and then maybe it'll help them out. But at the same time, there are other ways to figure it out.
| So we're assuming that knowledge of mathematics is inherent to intelligence? |
Yes? Unless you think there's some other standard.
| the point of proving that is not to prove that, but to train you to prove more difficult conjectures |
Sure, but even more difficult things can be proven without a formal mathematical proof.
| If you don't want to accept those terms you're free to go find a class that will accomodate you, or just study by yourself. |
Since when has this been true?
| If there are instances where they have an umbrella and it's not raining outside then not all the premises are true. |
My bad, slightly misphrased:
If it's raining outside, then you have an umbrella.
You have an umbrella.
Therefore it must be raining outside.
And this is valid yet incorrect since you may also take an umbrella when it's sunny outside. The fact that you can have an umbrella under other circumstances doesn't invalidate the other premises.
| You are misunderstanding what proofs are for and you clearly don't understand what it means for a syllogism to be valid and true. |
Arguing this shows a complete lack of understanding what my position is here. I've never argued against the validity of proofs or what their point is. I argue that you don't need the extent that a mathematical proof makes you go through in order to achieve the same proven scenario. In the end, a mathematical proof won't be less fallible just because they took a harder route.
| That's never been a requirement. |
That's what I was saying with a proof being valid yet incorrect.
EDIT:
Found a funny invalid proof:
1. If an omniscient being would believe P, then P is true.
2. An omniscient being would believe that an omniscient being exists.
3. Therefore, an omniscient being exists.
Last edited on
| Yes? Unless you think there's some other standard. |
| Sure, but even more difficult things can be proven without a formal mathematical proof. |
| Since when has this been true? |
| If it's raining outside, then you have an umbrella. You have an umbrella. Therefore it must be raining outside. And this is valid |
If this is the quality of the course, I would ask for my money back. This is super basic stuff.
| I've never argued against the validity of proofs or what their point is. [...] In the end, a mathematical proof won't be less fallible just because they took a harder route. |
I recommend that you show a bit more humility and recognize that you don't know everything, and that your teachers are teaching you this way for a reason. Otherwise every mathematics course you have from now on will kick your ass so hard you'll be wearing your buttocks as a hat. Scratch that, every course, period.
| 1. If an omniscient being would believe P, then P is true. 2. An omniscient being would believe that an omniscient being exists. 3. Therefore, an omniscient being exists. |
Yeah, there are some missing statements that become more obvious if you translate it to logic:
O(x) = x is an omniscient being
B(x, P) = x believes P
1 B(x, P) ^ O(x) → P
2 O(x) → B(x, ∃y[O(y)])
---
∃y[O(y)]
As you can see, there are no assumptions about anyone believing P or an omniscient being existing at all, so it is impossible to do anything useful with the conditionals, so it is impossible to get anywhere.
We can however, prove that O(x) → ∃y[O(y)] but that is provable from first principles, nothing to do with any of our assumptions.
That shows that if we indeed assume there is an omniscient being then our propositions can be used to prove that there is an omniscient being...but of course we have already assumed that in the first place!
| That's what I was saying with a proof being valid yet incorrect. |
What does incorrect mean? I don't think including useless assumptions means anything about validity. If you mean optimal then sure, but that's a pretty useless metric to judge everything by.
Last edited on
Apparently I am working my way backwards up your post...sure hope I don't get bitten in the ass by that lol.
Oh this is a great example:
R -> P
P
---
R
A classic example of an invalid proof. It is NOT valid, since you cannot get from the premises to the conclusion.
| My bad, slightly misphrased: If it's raining outside, then you have an umbrella. You have an umbrella. Therefore it must be raining outside. And this is valid yet incorrect since you may also take an umbrella when it's sunny outside. The fact that you can have an umbrella under other circumstances doesn't invalidate the other premises. |
Oh this is a great example:
R -> P
P
---
R
A classic example of an invalid proof. It is NOT valid, since you cannot get from the premises to the conclusion.
| Since a proof is simply a argument... Proven? No. Argued for, sure, and you may convince some people and not others. |
It would be proven. The same with evolution, just because it was proven doesn't mean that people won't accept it. And evolution didn't need to create a mathematical proof in order to say with certainty that it happened 🤷♂️ There are so many ways to prove something that a mathematical proof just won't accept. A mathematical proof makes it almost impossible to prove many things without first proving it to yourself by a standard that actually makes sense to use.
| It has always been true. You don't have to go to university. |
If the goal is a degree, then it's not true.
| No, the argument is invalid. "P => Q. Q, therefore P" is the fallacy of affirming the consequent. |
Yea, I realized that immediately after, I'm a bit busy so I didn't have time to think about what a proof missing elements would be. That may have been a wrong path there.
| These two statements are in opposition |
No, they're not. The validity of a proof is known, I wasn't arguing that. Some proof are correct and some aren't - I'm saying that I'm not arguing that proofs themselves are inherently wrong or shouldn't be done.
| If you think that a proof is disputable regardless of how much rigor it has been written with, then you don't understand what it means to prove something. |
You yourself stated this was possible by going to stupid claims such as the fallibility of the human brain or computer (if one was used in the proof). Moreover, a proof is disputable if there exists the possibility of a counter-example. This is why proofs which use to be though the be true after rigorous creating were shown to be false. So no, a proof can be disputable no matter how much rigor has been put it, it all comes down to whether or not all cases have been accounted for and if anything in the proof could be invalidated.
| And I think your previous two posts clearly show that, because you can't distinguish valid, invalid, and vacuous arguments. |
I've got plenty on my plate from these classes, a few posts where I may have overlooked simple details would hardly prove this.
| I recommend that you show a bit more humility and recognize that you don't know everything |
When did I suggest that I did? Does the simple opinion that a mathematical proof is too high standard and high maintenance for practical use (outside of some rare cases, say this all the time) somehow me boasting a wealth of knowledge? Every other side argument here has been a sideshow to my main point. Either way, if I knew everything I likely wouldn't care about anything either. Not every bit of knowledge is worth knowing.
| your teachers are teaching you this way for a reason. Otherwise every mathematics course you have from now on will kick your ass so hard you'll be wearing your buttocks as a hat. Scratch that, every course, period. |
Don't make me laugh. That professor wouldn't be able to solve the proofs he shows us without the book in his hand. I've learned from plenty of teachers and professors, but that doesn't mean they all have something worth learning. And as for you, just because I gave a few simple examples of our proofs means nothing as to what proofs we're supposed to do on a regular basis for homework, quizzes, and tests. I put the simple ones simply because it made things easier to talk about.
You yourself don't seem to truly understand what these proofs are when you argued before that graph may not prove that a line and circle don't intersect because it may be a precision error. The truth is (in my class anyway), they could be miles apart on that graph, it wouldn't "prove" it mathematically. A Venn diagram wouldn't prove that two sets do/don't share common elements. Nothing direct proves anything. The simple logic class with axions and such was simple. The rules of a mathematical proof were all there, but it doesn't reflect what a mathematical proof actually is when you go about it. They're parallel in concept, not parallel in application.
Well helios, I never expected some of these flatly wrong arguments from you. Either you want to argue any side you can get a hold of, or I really misjudged.
| What does incorrect mean? |
A proof would have been valid had all the assumptions and premises used been correct. But something wasn't and so the proof is incorrect. However, the logic of the proof itself is valid given the assumptions made.
Ah, I see! You are talking about "soundness" which is to be both "valid" ( https://en.wikipedia.org/wiki/Validity_(logic) ) and also all of the premises must be true.
I think it's interesting that (at least I assume!) you like coding but don't like proofs when they are identical! Proofs are just taking a set of assumptions and transforming them into your desired conclusion, just like how programming is taking your computer's state and transforming in into your desired state (e.g. outputting text onto a console).
Your dislike of some proofs seems to be similar to someone complaining that X language doesn't support Y feature which is quite understandable ("Why can't I just assume x+y is odd when x or y is odd?") but it is just something you have to accept, just like you have to accept that there is no fibbonaci generator in C++, you'll have to find one or make one yourself, even if you know that it exists doesn't mean C++ is going to know how to do it!
I think it's interesting that (at least I assume!) you like coding but don't like proofs when they are identical! Proofs are just taking a set of assumptions and transforming them into your desired conclusion, just like how programming is taking your computer's state and transforming in into your desired state (e.g. outputting text onto a console).
Your dislike of some proofs seems to be similar to someone complaining that X language doesn't support Y feature which is quite understandable ("Why can't I just assume x+y is odd when x or y is odd?") but it is just something you have to accept, just like you have to accept that there is no fibbonaci generator in C++, you'll have to find one or make one yourself, even if you know that it exists doesn't mean C++ is going to know how to do it!
If the omniscient joke proof is true then by changing line 2 the opposite is true. Sadly it is not a joke with some people - they believe it.
It’s also noteworthy how @zapshes’s story is changing. Is this advancing after enlightenment or face-saving? I doubt we’ll ever know.
It’s also noteworthy how @zapshes’s story is changing. Is this advancing after enlightenment or face-saving? I doubt we’ll ever know.
| there's great misunderstanding with my position. |
| I'm saying proofs are overly pretentious |
| and have standards that don't matter except for in some rare cases. |
| In most cases, the level of mathematical proof is too formal to make sense to use it. |
| you like coding but don't like proofs when they are identical! |
Not quiet, proving something in terms of logic is different than doing so for a mathematical proof. I've said it before, I prove things all the time - I have to. But if I went about proving everything in terms of a mathematical proof, there would be no point.
| Your dislike of some proofs seems to be similar to someone complaining that X language doesn't support Y feature which is quite understandable |
I guess it's similar? C++ is a low level language, so you'd expect it to be the way you described. But a proof doesn't have that restriction, only that the proof must actually prove. To what standards a proof should prove something should depend on the thing, this is why a mathematical proof isn't always useless, but having such a standard for every proof doesn't make sense.
| It’s also noteworthy how @zapshes’s story is changing. |
Tell me where exactly. Maybe I was a bit more critical at the start since I was venting, but my point has always remained that a mathematical proof is pointless in 90%+ of circumstances.
| Not really, the nearest I could get to that is I don't think you have a position. That way you can change 'it' at the drop of a hat. In any case you stated it was a rant at the start so no surprises there. |
My position CAN change at the drop of a hat, give me reasoning which I agree with, and I may even say a proof is important to learn and I'll do my very best. I may have changed my tone with how I express my point, but the point has always been there.
| Well, you do in fact keep saying that but nowhere in all of this enjoyable experience have you gone beyond that assertion. |
Yea, so where exactly did I change my story? It's pretentious, the level you have to go to in order to finish a mathematical proof is pointless in most situations - occasionally I admit it may be beneficial to have.
| Despite being patently untrue no examples of an alleged rare case has ever been forthcoming from you. An assertion but no evidence. Full marks for consistency. |
One such case is the one Helios linked with doing multiplication with your fingers. A proof would be useful there to know that it works when a more intuitive deduction may be harder to get.
| A big big job indeed and one that requires a clear knowledge and understanding of "too formal" vs "formal enough". |
I think you're retarded
| I think you're retarded |
But therein lies the essence of my thesis about your worth as an air-breather (an assumption - anaerobes usually smell badly but I'll give you the benefit of my considerable but restrained doubt )
You can attack me as much as you like. I don't care.
But you need to know your (objectively assessed) denial, ignorance, reactionary uncompromising attitude, flip-flop positions, callowness, gross inexperience, impetuosity, stubbornness and inability to learn has destroyed your essentially non-existent self-admitted rant-based case entirely.
You are set on a course of a lifetime of unhappiness and un-employability.
Don't ever go near a Philosophy department - you'll be cut to pieces.
But feel free to continue - I'm not a censor and I have the absolute confidence in myself that I can pull the plug on your silly trip any time.
I had thought you might have some worthwhile insights I could learn from but sadly your type of no useful contribution to learning is a dime a truckload.
Have you thought of a career in a litter patrol and save yourself the trouble of learning anything whatsoever once you know how to squeeze the handle and drop stuff into the bag? Seriously! You're well suited - maybe jump in the bag yourself.
Last edited on
So... Getting back to that proof about an omniscient being...
If you were to show that omniscient being something new that it didn't know before, would that shatter its belief in an omniscient being, and therefore cause itself to disappear into the firmament?
Or would having something it didn't know about in the first place just in itself prove that it wasn't an omniscient being in the first place.
... Or, by showing the omniscient being that new thing, would it suddenly be an even more omniscient being than it was before?
If you were to show that omniscient being something new that it didn't know before, would that shatter its belief in an omniscient being, and therefore cause itself to disappear into the firmament?
Or would having something it didn't know about in the first place just in itself prove that it wasn't an omniscient being in the first place.
... Or, by showing the omniscient being that new thing, would it suddenly be an even more omniscient being than it was before?
Last edited on
| ... Or, by showing the omniscient being that new thing, would it suddenly be an even more omniscient being than it was before? |
If that was the only thing it didn't know, then that being has just become omniscient and wasn't before. This would mean that this being, since he was omniscient-1, would have also known that there was a bit of information that he did not know - so it wouldn't shatter his own belief.
Of course, if the information is a complete surprise, that means there's a whole situation there in which the being didn't know about and clearly wasn't omniscient at all.
Topic archived. No new replies allowed.