Math Problem, Arguement with the teacher. Easy Logic.

[Xojins]

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.

Perhaps, but the rules of logic are different than those of math. Those statements are not undefined, the third statement is a fallacy while the fourth is a truth. Your teacher wasn't completely right but neither were you.
[sub]I've taken a logic class btw.[/sub]

 

[FarleShadow]

I'm going to agree with your teacher, in the sense that you should just accept it and get on with something else.

That's the worst thing that could possibly be done. If you don't understand it you'll have a hell of a time when you see it in-depth in a future time (like college or whatever it is you Americans call it ). I know that after me not understanding a good 50% of Mechanics 1, when Mechanics 2 referenced M1 I struggled an awful lot. Its easier to be understood now, while its fresh than to have incorrect things for future problems.

Imagine if you didn't understand why 2+2=4, and why it didn't equal 5. Then when you met multiplication you'd have difficulties. I know I've chosen something basic that most people do, but you get my drift

Ehem, UK.
Moving on.

Well, yes. But one would hope that if someone sucked at 'Mechanics 1' they wouldn't then go "OH BOY, I CAN'T WAIT FOR MECHANICS 2: REVENGE OF THE STUPID!", to follow your example.
I say 'You should just accept it and move on' in a sense that 'Yes, its stupid, now learn it, LEARN IT HARD' Accept the fact you're having problems with it and try harder to understand it, because it ain't changing or getting less obtuse.

 

[Drug Crazed]

I'm taking that as a joke, because that won't fly in college, even in writing things for Computer Science and Math classes.

Its called flippancy. I write weekly for the fun of it, and make typos. I usually spell check. I thought not to bother on a forum. But hey, its alright because english graduates who only have 5 contact hours have all that time to point out my flaws!

You'll find that Computer Science can be much harder on typos because computers don't understand them, so when you do make them you tend to notice and fix them. Seriously, you knew what I meant by usely, why bother bringing it up?

incorrect logic

GARGH!!!!!!!!!!!!!!! 0.3 != 1/3! Its 0.3 recurring, which when you multiply by 3 equals 0.9 recurring, which you can easily prove is 1.

 

[Plurralbles]

the example was kind of stupid

 

[Drug Crazed]

Well, yes. But one would hope that if someone sucked at 'Mechanics 1' they wouldn't then go "OH BOY, I CAN'T WAIT FOR MECHANICS 2: REVENGE OF THE STUPID!", to follow your example.
I say 'You should just accept it and move on' in a sense that 'Yes, its stupid, now learn it, LEARN IT HARD' Accept the fact you're having problems with it and try harder to understand it, because it ain't changing or getting less obtuse.

One would also hope they weren't doing Further Maths and thus needed to do both modules.

The issue wasn't that M1 wasn't understandable. I resat it and got the extra marks because my M2 teacher went over it again with me. The teaching was bad, not me. Especially since after M1 made sense, all of M2 did.

In other news: I HATE UNREADABLE CAPTCHA

 

[Dastardly]

snip

When you evaluate the "truth" of a statement, you aren't evaluating whether it's useful. You're evaluating whether the logic is sound.

If A, then B. In this case, A is "medicine," and B is "feel better." And you have four possible permutations of truth/falsehood here:

The information we are given tells us that medicine will make you feel better. Knowing this, if:

1. A and B are both true, the statement is "Take medicine, feel better." This is true.

2. A is true, B is false, so the statement is "Take medicine, don't feel better." This doesn't line up with the information we are originally given, so it's false.

3. A is false, B is true, so the statement is "Don't take medicine, feel better." Since the information doesn't tell us medicine is the ONLY way to feel better (it only tells us that taking the medicine will definitely do the job), we can't call this statement "false." It's true, if only on a technicality--it's logically sound.

4. Both A and B are false, so the statement is "Don't take medicine, don't feel better." Also lines up with the information we're given, so it is logically sound, and therefore true.

Your teacher is using a useful technique when teaching students about logic--the usefulness of a statement, or whether or not you agree with the statement, is separate from whether or not the logic behind the statement is internally consistent with the information upon which it is based.

For a better understanding of If/Then, and the logic behind why certain statements are true (sound) or false (unsound), consider this example:

"If the animal is a dog, it is a mammal." - This is the information we are given, which is therefore assumed to be true for the purposes of these operations. Assumptions are useful, just as you assume a chair will support your weight without extensive testing each time you sit. Conveniently, we also know this to be scientifically true (dogs are, in fact, mammals), but that isn't important except to help you understand how if/then statements work.

So, knowing this, let's assume each of the following:

1. A and B are both true: "The animal is a dog, therefore it is a mammal." Makes sense. Dogs are mammals.

2. A is true, B is false: "The animal is a dog, and it is not a mammal." This conflicts with the information we are given, so it is false. There are no such things as non-mammal dogs.

3. A is false, B is true: "The animal is not a dog, and it is a mammal." This doesn't conflict with our information--we aren't told that ONLY dogs can be mammals, just that dogs themselves must be mammals. This statement is consistent with our information, so it is true. It could be a cat, after all.

4. A is false, B is false: "The animal is not a dog, and it is not a mammal." This also does not conflict with the information we are given. It could be a lizard--not a dog, not a mammal. This statement isn't useful, but it is logically sound.

THE ONLY way for an 'if/then' statement to be false is if we satisfy the "IF," and the "THEN" result does not occur. This would mean that the original statement would be false. Since you cannot falsify the GIVEN, it is instead the CONCLUSION that is false.

 

[Singletap]

So why did they choose to use the word truth in stead of "Not false"

 

[Jaime_Wolf]

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"

You're talking about material implications, colloquially refered to as "if" statements. They're a formal construct with particular truth conditions (true if and only if both the antecedent and the consequent are true or if the antecedent is false). They are not the definition of "if", though many bad teachers often equate the two. An astounding amount of metaphorical blood has been shed in both philosophy and linguistics trying to figure out how to describe what "if" actually means formally (spoiler alert: this is still a very open, very difficult question, which is why so many posts here are arguing about it with no real conclusion), so there is actually no such thing as an actual "if statement" in the overwhelming majority of logics.

For more on material implications, you could take a look at this: http://en.wikipedia.org/wiki/Material_implication

Especially the "Philosophical problems with material conditional", which is badly named (there aren't any real problems with it, there are just problems with how people keep misapplying it).

 

[hopeneverdies]

When we learned "If, Then" statements, we were given the options of Always, Sometimes, or Never. Things work like that in all branches of math (Algebra, Geometry, Calculus, etc). To say that there are only two absolutes (True/False, Always/Never) is a failure on the teacher's part. There are almost always exceptions to the rule.

 

[Dastardly]

the example was kind of stupid

Actually, it's a great example to use, because it gets to the heart of the matter--the truth of a statement, in the sense that we use "truth" in logic, isn't based on whether the statement is useful or whether we agree with it. In the logic realm, "true" and "false" are really just based on whether or not the logic is sound.

GIVEN: All turtles have wings, and Speedy is a turtle.

The statment "Speedy the turtle has wings" is TRUE. Not because turtles have wings in the real world, but because the conclusion follows from the premises. The statement is logically sound.

Getting students to separate normal ideas of true/false, and to become aware of their assumptions about logic, is the most important thing a teacher can do when covering logic problems like this. You may only assume the information that is given. Everything else must be arrived at through logical operations on the given, regardless of what you think about the information.

 

[zfactor]

-snip-

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.

-snip-

So you were taking "If you take your medicine then you will feel better" as the true statement, correct? Then you needed to determine if "case 3 and 4" were true or false, based on the first true statement. Am I right in this explanation of the problems?

If I am right (hopefully, otehrwise this post is meaningless...) case 3 and 4 ("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") are indeterminable as true or false. The teacher wanted you to say 3 is false (which it is) and 4 is true, but given the first statement, you cannot tell with case 4.

It's actually a common logical fallacy. I forgot what the name was but it goes like this:

If A implies B; (If you take your medicine then you will feel better)

Then not A does not neccessarily imply not B. (If you don't take your medicine then you won't feel better)

So your "case 4" is inteterminable as true or false, given the premise. Hope my explanation helps...

 

[Zero-Vash]

Basic if then says "if A, then B". Which, unless proven otherwise, you are to generally to assume is a true statement. The trick with if then is it doesn't work backwards.

In your case, I'm guessing each question is stand alone, not related to each other. Which would make both true by default. If the 4 cases are related then one has to be false.

 

[Danny Ocean]

So why did they choose to use the word truth in stead of "Not false"

Because in common parlance 'Truth' is the opposite of 'False'. It's quicker to say. Simple really. I'd have thought that you'd have been taught what it really means in your classes. Perhaps that's coming later after challenging you with this or something.

 

[Danpascooch]

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"

Saying you'll feel better if you take your medicine does NOT prove that you won't coincidentally feel better if you don't, or that you will feel like shit if you don't. Meaning those cannot be declared false, but they also cannot be declared true.

Your teacher is wrong, you are not allowed to assume ANYTHING. That's the most important part of logic, I just did a unit on boolean algebra in a Discrete Math course, she's full of shit, find a reputable link on line showing an example that is different than what she said, print it and bring it to class.

 

[Danpascooch]

So why did they choose to use the word truth in stead of "Not false"

Because in common parlance 'Truth' is the opposite of 'False'. It's quicker to say. Simple really. I'd have thought that you'd have been taught what it really means in your classes. Perhaps that's coming later after challenging you with this or something.

There is no information placing them into one category of the other, you don't just say something is true because you can't prove it false, I just did an extensive unit on boolean algebra and logic in a Discrete Mathematics course, she's full of shit, the whole point is to PROVE these things.

 

[Singletap]

I'm just making my new views on this clear, it in itself is undefined, you don't know if the medicine will make the person better but you awesome it is true to continue the work because it has a point to?

 

[WanderingFool]

Im going to have nightmares tonight, thanks to this thread. Instead of give my view (since it is the same as atleast half of the comments in this thread), ill just say I agree with your teacher.

 

[akibawall95]

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.

I am no math teacher so I may be wrong but, math almost always has to be true unless you do it wrong. With math you should never have to guess, there is always a formula or way to do a something. Also if you do not have enough info to complete a problem you can almost never do it. Even with variables you are not guessing you have enough information to solve it. With conditional statements A has to lead to B (if it rains we do not play the game) sorry that is just how it goes. The only thing I do not understand is "if you do not take the medicine then you will get better" maybe eventually you will get better. Correct me if I am wrong please.

 

[marcus905]

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"

The way I see it is this:

Let's rephrase the problem trying to use a less ambiguous choice of words:

1. You are ill (Cpt. Obvious)
2. Your illness has no cure except for the above mentioned medicine
3. The aforementioned medicine certainly cures the illness (in other words it cannot fail in curing you)
4. You have the choice of either taking or not taking the medicine.

If #2 is true, then:

a.If you take the medicine, you'll feel better. (true, as per #3)
b.If you take the medicine, you won't feel better. (false, as per #3)
c.If you don't take the medicine, you will feel better. (false, as per #2)
d.If you don't take the medicine, you won't feel better. (true, as per #2)

If #2 is not true:

a'.If you take the medicine, you'll feel better. (true, as per #3)
b'.If you take the medicine, you won't feel better. (false, as per #3)
c'.If you don't take the medicine, you'll feel better. (undefined, but true, per missing #2)
d'.If you don't take the medicine, you won't feel better. (same as above)

To try to define the 2 undefined cases you must rephrase them in more mathematically-precise derivatives:

Assuming a set S containing an infinite number of cases (think of it as parallel universes) on whether you take this medicine (or not) causing your being well (or not):
c'^. Each and every case in the set S has the effect of curing the illness without taking the medicine.
d'^. Each and every case in the set S has the effect of not curing the illness without taking the medicine.
Using this wording, then they're both false or undefined respectively whether you can demonstrate even a single event that doesn't match those statements or not.

Instead, rephrasing differently:
c'*. There exists a case in the set S that has the effect of curing the illness without taking the medicine.
d'*. There exists a case in the set S that has the effect of not curing the illness without taking the medicine.
In this case, to prove these statements true, you only have to demonstrate that there is a single case in which the course of events matches the statement, else the cases are undefined.

Now, you have narrowed and stated the undefined cases.
If you want to put this in binary logic instead of ternary logic, you'd have to have a postulate saying that
5. All cases that aren't definitely provable and therefore undefined are to be considered as false.
(a postulate saying
5'. All cases that aren't definitely provable and therefore undefined are to be considered as true.
works equally well)

By taking then any of the aforementioned alternative rephrasings you'd have a certain true/false statement.

Now, if you look at the (34)'* rephrasings, with the ternary-binary narrowing condition (also called defaulting condition) 5', then the cases are always both true therefore explaining what your teacher had intended to say.

I hope this was not too long and please excuse my mathematical/logical fallacies (should there be any) as I'm just a computer engineering student and not a mathematician.