Math Problem, Arguement with the teacher. Easy Logic.

[Singletap]

Hello Escapist Forum

Today me and my tenth grade geometry teacher had a argument. I'm not great in math class but we recently started logic and it seems to come very easily to me, most likely through making games and such on the computer.

Here is the problem and I don't see the logic in her teachings.

We were going over the "If" "Then" statements and one of the problems was.

If you take your medicine then you will feel better

we then had to take the 4 truth or false cases and decide rather they are true or false, easy right?

Well I had a small problem with case 3 and 4, they said

"If you don't take your medicine then you'll feel better"
"If you don't take your medicine then you won't feel better"

She said they default as true, I argued that that's impossible, they must be undefined, I see no truth in these cases you can't just assume in math without a reason to.

She got very worked up thinking that I was trying to confuse the kids but I simply did not understand the logic and she didn't make a good attempt to show me what she was saying. I'm still confused and I believe she is wrong I will change my thoughts if I can see a sense of reason.

Can I get some help here.

From Jesse Bergerstock aka SingleTap "Tap"

 

[Count Igor]

The whole of maths is pretty much assumption.
As is everything.
It could be that you'll get better anyway, so that would be true.

 

[Singletap]

The whole of maths is pretty much assumption.
As is everything.
It could be that you'll get better anyway, so that would be true.

I don't understand how the hole of math is a assumption, I have decided that using mathematics is the best way to determine reality which is the nothing less than the absolute truth of things. How can you assume the truth of something when you could be wrong, this makes it non absolute and pointless to consider as fact.

Also, how can you say that it is true. What if you got worse if you did take the medicine which would make it false. There is a %50 %50 chance there.

 

[Atmos Duality]

In order to use Math as a proof for what is real and measurable, we must assume Math itself is real, which would require a proof other than Math, or it would be circular logic (which is a fallacy).

Fun stuff.

 

[Darth IB]

Thing is, there is no 'undefined' in Formal Logic. "if A then B" is considered to be true as a statement if both A and B are true, or if A is false (regardless of B's truth value). This is because as long as A is not true (e.g. medicine is not taken) it can not be inferred that A does not cause B.

 

[Singletap]

In order to use Math as a proof for what is real and measurable, we must assume Math itself is real, which would require a proof other than Math, or it would be circular logic (which is a fallacy).

Fun stuff.

I'm not posting this to debate proof of reality. To summarize my thoughts of using math as proof is that true math is perfect as is reality and it can be used to measure reality because of the equal perfection between the two, also I am 15. Haha.

 

[Mike Laserbeam]

Ever heard of Proof By Induction?
First Step:
Assume true for n=1

Maths is all about assumption

 

[Jonluw]

I see what they're getting at. You're just not supposed to go so deep as to think "I might get better even if I don't take my medicine".
It's a really bad example, to be fair.

 

[Atmos Duality]

I'm not posting this to debate proof of reality. To summarize my thoughts of using math as proof is that true math is perfect as is reality and it can be used to measure reality because of the equal perfection between the two, also I am 15. Haha.

Oh, I'm just ribbing you.

I fail to realize how being 15 years old is relevant though.

 

[Singletap]

Thing is, there is no 'undefined' in Formal Logic. "if A then B" is considered to be true as a statement if both A and B are true, or if A is false (regardless of B's truth value). This is because as long as A is not true (e.g. medicine is not taken) it can not be inferred that A does not cause B.

I'm having a hard time comprehending this, why not just say it is false, why say it's true. Couldn't that lead a extended version of the problem in the wrong direction since you are just assuming it as true. Just because A doesn't cause B doesn't mean that the statement is true.

 

[Shynobee]

If you take your medicine then you will feel better

"If you don't take your medicine then you'll feel better"
"If you don't take your medicine then you won't feel better"

From Jesse Bergerstock aka SingleTap "Tap"

Here are the givens based on the first statement:
medicine makes you feel better
no medicine means you stay sick forever

thus:
case 3 should be false
case 4 should be true

Based on reading what you said, this is how I see it. I assumed the givens based on the initial question.

In math, you make a lot of assumptions. Get used to that one.

 

[Singletap]

Ever heard of Proof By Induction?
First Step:
Assume true for n=1

Maths is all about assumption

I have not heard of Proof By Induction and until I fully comprehend Proof By Inductions I can't tell you rather I agree or not.

 

[Tallim]

Think of it as a drinking game and the true or false is dependant on if you follow the rules.

If you see a camel then take a drink. (stupid but whatever)

So if you see a camel then take a drink - you have followed the rules so true.
if you see a camel then don't take a drink - you have broken the rules so false.
if you don't see a camel then take a drink - tricky one but you haven't broken the rules: true.
if you don't see a camel then don't take a drink - you have followed the rules so true.


I don't much like the wording your teacher used. But she is correct.

 

[The_root_of_all_evil]

3 fails if the medicine is a placebo.
4 is true if it isn't.

Therefore you're both wrong. It depends on an external circumstance, which reverses the logic of the choice based on it.

Sorry.

(If the logic is taken as only reliant on those two premises, then the teacher is right. If there is no way of knowing if the medicine is a placebo, you are right)

 

[Singletap]

If you take your medicine then you will feel better

"If you don't take your medicine then you'll feel better"
"If you don't take your medicine then you won't feel better"

From Jesse Bergerstock aka SingleTap "Tap"

Here are the givens based on the first statement:
medicine makes you feel better
no medicine means you stay sick forever

thus:
case 3 should be false
case 4 should be true

Based on reading what you said, this is how I see it. I assumed the givens based on the initial question.

In math, you make a lot of assumptions. Get used to that one.

What you said can be correct but also it could also be that the medicine ends up not helping at all which could make it false which brings us back to the beginning of it being a %50 %50 shot.

Also I don't understand why you should have to make assumptions in math, they must have been proven before people just started assuming right?

 

[Darth IB]

Thing is, there is no 'undefined' in Formal Logic. "if A then B" is considered to be true as a statement if both A and B are true, or if A is false (regardless of B's truth value). This is because as long as A is not true (e.g. medicine is not taken) it can not be inferred that A does not cause B.

I'm having a hard time comprehending this, why not just say it is false, why say it's true. Couldn't that lead a extended version of the problem in the wrong direction since you are just assuming it as true. Just because A doesn't cause B doesn't mean that the statement is true.

I might have misunderstood your problem, but the way I understood it the medicine thing was just an example of If... Then... (aka conditionals).
In such a case what you were evaluating was the truth-value of the entire original claim (if you take medicine you will feel better) combined with whether or not certain variables were true.

So: If you take medicine and you feel better, then it is true that if you take medicine then you will feel better;
If you take medicine and don't feel better, then it is not true that If you take medicine then you will feel better;
If you don't take your medicine and feel better, for all you know it's true that you would also have gotten better had you taken medicine;
If you don't take medicine and don't feel better, again for all you know you would have felt better had you taken your medicine.

You could say Formal Logic generally goes with 'innocent until proven guilty'.

 

[Singletap]

Think of it as a drinking game and the true or false is dependant on if you follow the rules.

If you see a camel then take a drink. (stupid but whatever)

So if you see a camel then take a drink - you have followed the rules so true.
if you see a camel then don't take a drink - you have broken the rules so false.
if you don't see a camel then take a drink - tricky one but you haven't broken the rules: true.
if you don't see a camel then don't take a drink - you have followed the rules so true.


I don't much like the wording your teacher used. But she is correct.

I'm sorry I don't understand, If I see a camel then I take a drink right, well why would I take a drink if I didn't see the camel, what if the drink is acid I don't want, that so I choose not to take a drink because I didn't see the camel.

 

[Mike Laserbeam]

Ever heard of Proof By Induction?
First Step:
Assume true for n=1

Maths is all about assumption

I have not heard of Proof By Induction and until I fully comprehend Proof By Inductions I can't tell you rather I agree or not.

Proof's by Induction
Well I don't fully understand the concept either, but basically it's when you prove that something is true simply by assuming so to begin with. Once you've assumed it is true for one thing, you can prove it's true for everything (Sort of)
The first assumption has a reason, but no real justification, you just want it to be true so you say that it probably is. So, even though I've not really solved your problem, I hope to show you that you can assume all sorts of stuff when it comes to these things

But hey, I'm not a Maths teacher, just a student!

 

[Singletap]

Thing is, there is no 'undefined' in Formal Logic. "if A then B" is considered to be true as a statement if both A and B are true, or if A is false (regardless of B's truth value). This is because as long as A is not true (e.g. medicine is not taken) it can not be inferred that A does not cause B.

I'm having a hard time comprehending this, why not just say it is false, why say it's true. Couldn't that lead a extended version of the problem in the wrong direction since you are just assuming it as true. Just because A doesn't cause B doesn't mean that the statement is true.

I might have misunderstood your problem, but the way I understood it the medicine thing was just an example of If... Then... (aka conditionals).
In such a case what you were evaluating was the truth-value of the entire original claim (if you take medicine you will feel better) combined with whether or not certain variables were true.

So: If you take medicine and you feel better, then it is true that if you take medicine then you will feel better;
If you take medicine and don't feel better, then it is not true that If you take medicine then you will feel better;
If you don't take your medicine and feel better, for all you know it's true that you would also have gotten better had you taken medicine;
If you don't take medicine and don't feel better, again for all you know you would have felt better had you taken your medicine.

You could say Formal Logic generally goes with 'innocent until proven guilty'.

Right, the teacher said the same thing, innocent until proven guilty but I don't see why I should consider it as innocent, I don't know that why not just say I don't know. It's more correct it seems to me. If I see someone in court and he is being accused of committing a crime I don't say, that man is innocent! I say I hope that man is innocent but I don't know that.

 

[SirTankred]

Well I think the issue is as I understand it you are only given one assertion:

Medicine makes you better.

The only way to contradict this, is a case where you take medicine and you don't get better. If you don't take medicine, you have no idea what will happen because the first assertion doesn't say anything about what happens to you if you don't take medicine. Thus it could be true that not taking medicine might make you better worse, the same, or explode based on the information presented.