Maths & Order

[Speakpigeon]

What would you say is the necessary condition for:

(a < b) → (c < d)​

EB

 

[Malintent]

a False Dichotomy would be the required condition.

 

[beero1000]

What would you say is the necessary condition for:

(a < b) → (c < d)​

EB

There will be many necessary conditions for any given statement. What exactly are you asking for?

 

[Speakpigeon]

What would you say is the necessary condition for:

(a < b) → (c < d)​

EB

There will be many necessary conditions for any given statement. What exactly are you asking for?

Just one necessary condition and nothing else.

I can't make it more explicit without giving it away and spoiling the exercise for my purpose.

I thought the answer was easy. I hoped to establish the answer as reasonably obvious to the practiced brain, i.e. most people with a training in maths or science.

I may have to admit my own answer might be wrong despite its obviousness to me.

I can at least say that the answer is uncomplicated and not difficult.

It also has a certain elegance and beauty to it if that can motivate candidates.

and isn't there a way of checking this on the Internet?
EB

 

[beero1000]

There will be many necessary conditions for any given statement. What exactly are you asking for?

Just one necessary condition and nothing else.

I can't make it more explicit without giving it away and spoiling the exercise for my purpose.

I thought the answer was easy. I hoped to establish the answer as reasonably obvious to the practiced brain, i.e. most people with a training in maths or science.

I may have to admit my own answer might be wrong despite its obviousness to me.

I can at least say that the answer is uncomplicated and not difficult.

It also has a certain elegance and beauty to it if that can motivate candidates.

and isn't there a way of checking this on the Internet?
EB

I am saying that there is no such thing as "the" necessary condition, and I have training in math and science.

A necessary condition for a statement P is a statement Q satisfying "If P then Q". For any statement P there will be infinitely many statements Q that satisfy that implication.

So, ((a ≥ b) or (c < d)) is a necessary condition for (a < b) → (c < d), and so is a ≤ a, or "Speakpigeon is not a married bachelor", or any of a number of others.

It might be clear and obvious to you, but it's a nonsensical question to me.

 

[Speakpigeon]

Just one necessary condition and nothing else.

I can't make it more explicit without giving it away and spoiling the exercise for my purpose.

I thought the answer was easy. I hoped to establish the answer as reasonably obvious to the practiced brain, i.e. most people with a training in maths or science.

I may have to admit my own answer might be wrong despite its obviousness to me.

I can at least say that the answer is uncomplicated and not difficult.

It also has a certain elegance and beauty to it if that can motivate candidates.

and isn't there a way of checking this on the Internet?
EB

I am saying that there is no such thing as "the" necessary condition,

I think there is but that shouldn't stop you.

and I have training in math and science.

That's why I posted in here, to have answers from people with a training in maths and/or science.

A necessary condition for a statement P is a statement Q satisfying "If P then Q". For any statement P there will be infinitely many statements Q that satisfy that implication.

Right. The thing is, I can't possibly explain it to you but let me say I understand fully your response.

Now, either you think you know everything and we can leave it at that or you grow up and take what other people say at face value.

So, ((a ≥ b) or (c < d)) is a necessary condition for (a < b) → (c < d), and so is a ≤ a, or "Speakpigeon is not a married bachelor", or any of a number of others.

So, if you want to grow up, assume for a start that all the answers you provided are irrelevant (again I understand them) and assume there's just one necessary condition (not of the kind you provided). And then you can try again to find it.

It might be clear and obvious to you, but it's a nonsensical question to me.

I can't promise you'll find the answer I have in mind of course and I accept I might be wrong but it's an interesting problem to solve. So do you want to try and solve it or do you think you can't possibly ever learn something new?
EB

 

[beero1000]

I am saying that there is no such thing as "the" necessary condition,

I think there is but that shouldn't stop you.

and I have training in math and science.

That's why I posted in here, to have answers from people with a training in maths and/or science.

A necessary condition for a statement P is a statement Q satisfying "If P then Q". For any statement P there will be infinitely many statements Q that satisfy that implication.

Right. The thing is, I can't possibly explain it to you but let me say I understand fully your response.

Now, either you think you know everything and we can leave it at that or you grow up and take what other people say at face value.

So, ((a ≥ b) or (c < d)) is a necessary condition for (a < b) → (c < d), and so is a ≤ a, or "Speakpigeon is not a married bachelor", or any of a number of others.

So, if you want to grow up, assume for a start that all the answers you provided are irrelevant (again I understand them) and assume there's just one necessary condition (not of the kind you provided). And then you can try again to find it.

It might be clear and obvious to you, but it's a nonsensical question to me.

I can't promise you'll find the answer I have in mind of course and I accept I might be wrong but it's an interesting problem to solve. So do you want to try and solve it or do you think you can't possibly ever learn something new?
EB

So, you're the one playing games by asking vague questions, using nonstandard meanings of standard terms, and smugly refusing to clarify, and I'm the one who thinks I know everything and needs to grow up? This has got to be the shittiest attempt at Socratic questioning that I've ever come across, you might want to work on that.

 

[Kharakov]

What would you say is the necessary condition for:

(a < b) → (c < d)
​

EB

The necessary condition is if (a < b) then (c < d).

 

[Speakpigeon]

So, you're the one playing games by asking vague questions, using nonstandard meanings of standard terms, and smugly refusing to clarify, and I'm the one who thinks I know everything and needs to grow up? This has got to be the shittiest attempt at Socratic questioning that I've ever come across, you might want to work on that.

It was nothing Socratic in intent or form. I asked a simple question. The answers you diligently provided (thanks) are notoriously uninteresting, as you should know, so there's no need for you to take it from on high. I'm also impressed at your lack of interest in the idea that there might be more interesting answers, but there you go.

Still, I guess I do have my answer now. I really was interested to see if my own answer would come as obvious to other people and the answer is clearly "not at all", which is a disappointment.

Your problem, though, is that you think you can claim that you use terms in a standard way. Let me remind you that modern logic only exists since the turn of the 20th century but that the systematic study of logic exists since at least Aristotle some 2500 years ago. Also, there's a significant minority of logicians who simply disagree with the idea that what you call 'standard logic' is standard logic. Rather, yours is just the majority view and there is a strong opposition to it. This means there's no consensus among experts. This means there's effectively no standard (and I'm knowlegeable about rules for international standards). So I guess you're using the word 'standard' in a non-standard way. Clever trick.




Still, since it seems you see yourself as knowledgeable about logic, and in a talkative mood, perhaps you could tell us what is logic according to the view you think is 'standard'. Is it completely arbitrary? If not, what would be the justifications for it's fundamental principles? Is it simply a branch of mathematics or something else altogether? How can we know that a particular description of logic would be correct? If you can't answer that confidently then you should turn down the rethoric.
EB

 

[Speakpigeon]

What would you say is the necessary condition for:

(a < b) → (c < d)
​

EB

The necessary condition is if (a < b) then (c < d).

Ok, that's clever and funny enough but it's not too interesting.

I thought you guys would be game for that kind of Maths & Order riddle but it may be less irrisistible than I thought.

And it seems I am running out of potential gamers. How many lives do you have?
EB

 

[beero1000]

So, you're the one playing games by asking vague questions, using nonstandard meanings of standard terms, and smugly refusing to clarify, and I'm the one who thinks I know everything and needs to grow up? This has got to be the shittiest attempt at Socratic questioning that I've ever come across, you might want to work on that.

It was nothing Socratic in intent or form. I asked a simple question. The answers you diligently provided (thanks) are notoriously uninteresting, as you should know, so there's no need for you to take it from on high. I'm also impressed at your lack of interest in the idea that there might be more interesting answers, but there you go.

Still, I guess I do have my answer now. I really was interested to see if my own answer would come as obvious to other people and the answer is clearly "not at all", which is a disappointment.

Your problem, though, is that you think you can claim that you use terms in a standard way. Let me remind you that modern logic only exists since the turn of the 20th century but that the systematic study of logic exists since at least Aristotle some 2500 years ago. Also, there's a significant minority of logicians who simply disagree with the idea that what you call 'standard logic' is standard logic. Rather, yours is just the majority view and there is a strong opposition to it. This means there's no consensus among experts. This means there's effectively no standard (and I'm knowlegeable about rules for international standards). So I guess you're using the word 'standard' in a non-standard way. Clever trick.

Still, since it seems you see yourself as knowledgeable about logic, and in a talkative mood, perhaps you could tell us what is logic according to the view you think is 'standard'. Is it completely arbitrary? If not, what would be the justifications for it's fundamental principles? Is it simply a branch of mathematics or something else altogether? How can we know that a particular description of logic would be correct? If you can't answer that confidently then you should turn down the rethoric.
EB

Uh huh. Maybe you're just not very good at posing riddles. I've told you why your question doesn't make sense and asked what you meant. Then, instead of clarifying or specifying an alternate convention, you decide I'm not open-minded enough to try to find answers to your nonsensical question and you try to redefine the word standard . Hint, it doesn't mean ancient or unanimous.

Why don't you explain your answer and then we can all see for ourselves?

 

[Kharakov]

I'm grasping at straws here, but does the answer have something to do with throwing popcorn at zombies?

 

[Speakpigeon]

I'm grasping at straws here, but does the answer have something to do with throwing popcorn at zombies?

I'm French, so I wouldn't know about the kind of New World magic you'd use over there when in disarray. Be careful with the popcorn, though.

Maybe we can try with baby steps, like this:

What would you say is the necessary condition for x ≡ 30?

where '≡' stands for 'divisible by').

EB

 

[Speakpigeon]

Uh huh. Maybe you're just not very good at posing riddles. I've told you why your question doesn't make sense and asked what you meant. Then, instead of clarifying or specifying an alternate convention, you decide I'm not open-minded enough to try to find answers to your nonsensical question and you try to redefine the word standard . Hint, it doesn't mean ancient or unanimous.

Why don't you explain your answer and then we can all see for ourselves?

Just give me a necessary condition that's not trivial even according to what you think is logic.
EB

 

[Kharakov]

What would you say is the necessary condition for x ≡ 30?

where '≡' stands for 'divisible by').

What is the necessary condition for x%30 ≡ 0?? That x is a multiple of 30. It's the same thing as saying x%30 = 0 though, so if you're going for something deeper, you'll have to name what you want.


The only absolutely necessary condition for your first if a<b then c<d statement is trivial as well- c<d. There are no other requirements.

 

[Malintent]

f(a) = c

A relationship between a and c must exist, or you are expressing a false dichotomy (like I originally said).

 

[Kharakov]

Isn't the relationship between c and d the only important one?

It's not:

if and only if (a<b) then (c<d)

 

[Speakpigeon]

where '≡' stands for 'divisible by').

What is the necessary condition for x%30 ≡ 0?? That x is a multiple of 30. It's the same thing as saying x%30 = 0 though, so if you're going for something deeper, you'll have to name what you want.

I want necessary conditions, nothing more profound than that. It's a maths problem, not some kind of philosophical puzzle. And if you can't find any, it's also a legitimate answer.

The only absolutely necessary condition for your first if a<b then c<d statement is trivial as well- c<d.

Ok...

Oops! No!!! For gawdsake, ((a < b) → (c < d)) could be true and (c < d) still false. You write that down one hundred times before you can come back, you hear?!

There are no other requirements.

Ok.
EB

 

[DrZoidberg]

What would you say is the necessary condition for:

(a < b) → (c < d)​

EB

a is less than b. If it's an equation you can give a and b any value you like.

 

[Speakpigeon]

f(a) = c

A relationship between a and c must exist,

That's a start. The 'must' is. Inasmuch as it conveys the idea of necessity.

"f(a) = c" too is an idea.

or you are expressing a false dichotomy (like I originally said).

I have to say I don't see the relevance of a false dichotomy in here.
EB