Reply to tim wood Is this going to be another endless thread where loose terms like "absolute" are introduced but never explained, and then people proceed to talk past each other ad nauseum?
Terrapin StationMarch 17, 2019 at 20:15#2658550 likes
I think the "No" is the most errant nonsense. Weigh in. Someone's an idiot (imho). If it's me I might as well find out now - sometimes the price of an education.
Not sure exactly what you're asking. In math, we always called 2+2=4 a given number fact. It's not something that has to be proved or verified.
Is this going to be another endless thread where loose terms like "absolute" are introduced but never explained, and then people proceed to talk past each other ad nauseum?
Good point. Obviously I can't speak for Tim, but this discussion came out of a discussion about morality, where moral absolutism was contrasted with moral relativism. So maybe that's what he has in mind. That the truth of mathematical statements aren't relative to or dependent on anyone or anything, like how some people think that the truth of moral statements is best explained as relative to subjects and their subjective qualities or acts, like feelings and judgements. It would simply be the case that 2 + 2 = 4, absolutely, objectively, independently, not relative to anyone or anything, not requiring of any explanation in subjective terms.
Try reading the OP, S. Someone not you denies that 2+2=4 is demonstrably true. Nothing to do with morality. That's why this is the math forum.
Wow. I read your opening post, and in it, you didn't make clear your meaning of "absolute", and that was clearly a problem for at least one respondent, so absent any clearly expressed meaning from you, I stepped in and explained what it meant in the other discussion, and applied that here, minus the moral terminology obviously. I'm not so stupid as to fail to realise that this is maths, not ethics, so don't speak to me as though I am.
But yes, it is demonstrably true. Of course it is. But whether it is true absolutely is a different question.
"
there's no reason to say that any mathematical statement is universal.
— xxxx
Do you endorse that?
I'm not sure. What would it mean to say that a mathematical statement is universal?
He followed that up by saying that no mathematical statement is universally constructed by humans. Is that what he meant? And what does [I]that[/I] mean? That every single human must make the statement that 2 + 2 = 4? That doesn't make much sense to me. Why would we even be talking about that? Why would every single human do that, or need to do that? Why would someone claim that? I don't really get the denial, because I don't get why anyone would make that affirmation to begin with.
Every single one of the respondents thus far has said that there's a problem with ambiguity, with the possible exception of Terrapin. Maybe you or Terrapin, as the instigators of this discussion, should actually take that onboard and do something about it, instead of leaving the rest of us scratching our heads.
I certainly don't think that 2 + 2 = 4 is only true on Thursdays, or depends on feeling or mood. But I think that that's an obvious straw man. Has anyone actually said that? Or did you just pluck it from thin air? Dependent on some mathematical model, if that's the right term, perhaps. Or dependent on what it means. That would make way more sense. You don't have to conjure up imaginary targets which are easy to attack. What's the point in doing that?
I am at a loss as to what to make of your thread. The topic that you coyly avoid naming is Is 2 + 2 = 4 universally true? - which, of course, poses the exact same question as you do here. What was the point of duplication?
He followed that up by saying that no mathematical statement is universally constructed by humans. Is that what he meant? And what does that mean? That every single human must make the statement that 2 + 2 = 4? That doesn't make much sense to me. Why would we even be talking about that? Why would every single human do that, or need to do that? Why would someone claim that? I don't really get the denial, because I don't get why anyone would make that affirmation to begin with.
Why I'd say that is because, on my view, "Mathematics is an abstracted way of thinking about relations," Which means that every human who engages in it must at least think "2 + 2 = 4" (or whatever alternative they think instead, and some people definitely think alternatives instead--we run into them as students in mathematics classes, at least). Not everyone has to bother with mathematics, although it's a bit more difficult to avoid basic arithmetic.
Reply to Frank Apisa You may think that you are supporting the OP by claiming that 2+2 equals 4 by definition, but you are actually doing the opposite. If it is nothing more than a definition, then it is just an arbitrary convention, like naming. 2+2 could just as soon equal 5, if we agreed to define it that way.
In a way, this is true. Of course, no one literally defines the result of 2+2 - it can be rather easily proven from the axioms of arithmetic - but the axioms of arithmetic are themselves conventional in the sense that there is no completely a priori justification for adopting them. Indeed, there are any number of alternative algebras, some of which have been found to be useful or at least interesting.
However, there must be a good reason for why conventional arithmetic is so important for us - and that could be a topic for a philosophical discussion, except that the OP doesn't seem to be interested in such a discussion.
It should be true given certain basic assumptions about symbols and logic.
Most importantly the law of identity needs to be true or "X=X". What's on the left of "=" is considered the same value as what's on the right of "=". To prove they're the same we would need to be concerned with their value and not their appearances. "2+2" and "4" may look different but if they have the same value that means they're the same.
Then there's the number symbols
1 = o
2 = oo
3 = ooo
4 = oooo
Then the "+" symbol is an operation that combines the group of objects together.
So 2+2 or "oo+oo" does the equivalent of removing the "+" and pushing the 2 groups together to get "oooo".
The "oooo" looks like what's defined to be the symbol "4". Using that law of identity again 2+2=4 for that reason.
You may think that you are supporting the OP by claiming that 2+2 equals 4 by definition, but you are actually doing the opposite. If it is nothing more than a definition, then it is just an arbitrary convention, like naming. 2+2 could just as soon equal 5, if we agreed to define it that way.
I both disagree and agree with you, Cat.
First, though...just to be precise, I did not say that 2+2 equals 4 by definition...I said that 2+2 in base ten equals 4 by definition. And it does. Obviously in base 4 it would not...2+2 would equal 10.
But these are just symbols for an idea...a shorthand of sorts.
A single unit plus another single unit will always equal "a single unit plus another single unit." We could say it that way (and continue in its extensions) ...or we could devise a system of symbols to denote the thought we are trying to convey in order to make arithmetic possible.
The Romans obviously did it in a (what we consider) cumbersome way.
The Arabic numeral method seems to work better.
It is an agreement and a convention...but it is an absolute as notion.
So I agree that I was NOT supporting the OP (I think the OP wrong because of wording) and I disagree insofar as I was not "actually doing the opposite"...which twists this replay into a pretzel.
The subject actually is not all that interesting to me. Discussions about "absolutes" often end up as verbal pretzels.
I am a new member just trying to see how the board works. Philosophy can be tricky...and end up in "going nowhere" discussions. Just want to see how this forum works...or more exactly, how some of the folk here work.
Pattern-chaserMarch 20, 2019 at 12:09#2668210 likes
Not sure exactly what you're asking. In math, we always called 2+2=4 a given number fact. It's not something that has to be proved or verified.
That's because it's presented axiomatically. It is defined to be true. There's nothing wrong with this, but we should be aware that it's being done. The truth of "2+2=4" depends on number theory and arithmetic, for a start. Maybe other stuff too. And all of this 'stuff' is human-created. That it proves useful in describing some parts of the real world is not magic. We created maths to help us think about the real world. Why would we be surprised when it proves useful for that task? :smile:
And all of this 'stuff' is human-created. That it proves useful in describing some parts of the real world is not magic. We created maths to help us think about the real world. Why would we be surprised when it proves useful for that task?
I agree with this strongly, although many on this forum do not, for example, see the "Could God not have just built a computer..." thread.
That's because it's presented axiomatically. It is defined to be true. There's nothing wrong with this, but we should be aware that it's being done. The truth of "2+2=4" depends on number theory and arithmetic, for a start. Maybe other stuff too. And all of this 'stuff' is human-created. That it proves useful in describing some parts of the real world is not magic. We created maths to help us think about the real world. Why would we be surprised when it proves useful for that task?
wonderful -
I have said quite a few times on here that all physics is, is a mathematical model of some observed reality. Redundant and maybe seems obvious when I say this - but often it seems not. The reality is real, the physics is the model. Once we have a model - than we can change the variables and see what what it predicts, and then experimentally test the predictions. If they work, we have a good model, if they don't we go back to the drawing board.
Comments (20)
Absolutely.
Not sure exactly what you're asking. In math, we always called 2+2=4 a given number fact. It's not something that has to be proved or verified.
Good point. Obviously I can't speak for Tim, but this discussion came out of a discussion about morality, where moral absolutism was contrasted with moral relativism. So maybe that's what he has in mind. That the truth of mathematical statements aren't relative to or dependent on anyone or anything, like how some people think that the truth of moral statements is best explained as relative to subjects and their subjective qualities or acts, like feelings and judgements. It would simply be the case that 2 + 2 = 4, absolutely, objectively, independently, not relative to anyone or anything, not requiring of any explanation in subjective terms.
Wow. I read your opening post, and in it, you didn't make clear your meaning of "absolute", and that was clearly a problem for at least one respondent, so absent any clearly expressed meaning from you, I stepped in and explained what it meant in the other discussion, and applied that here, minus the moral terminology obviously. I'm not so stupid as to fail to realise that this is maths, not ethics, so don't speak to me as though I am.
But yes, it is demonstrably true. Of course it is. But whether it is true absolutely is a different question.
Quoting tim wood
I'm not sure. What would it mean to say that a mathematical statement is universal?
He followed that up by saying that no mathematical statement is universally constructed by humans. Is that what he meant? And what does [I]that[/I] mean? That every single human must make the statement that 2 + 2 = 4? That doesn't make much sense to me. Why would we even be talking about that? Why would every single human do that, or need to do that? Why would someone claim that? I don't really get the denial, because I don't get why anyone would make that affirmation to begin with.
Every single one of the respondents thus far has said that there's a problem with ambiguity, with the possible exception of Terrapin. Maybe you or Terrapin, as the instigators of this discussion, should actually take that onboard and do something about it, instead of leaving the rest of us scratching our heads.
I certainly don't think that 2 + 2 = 4 is only true on Thursdays, or depends on feeling or mood. But I think that that's an obvious straw man. Has anyone actually said that? Or did you just pluck it from thin air? Dependent on some mathematical model, if that's the right term, perhaps. Or dependent on what it means. That would make way more sense. You don't have to conjure up imaginary targets which are easy to attack. What's the point in doing that?
I am at a loss as to what to make of your thread. The topic that you coyly avoid naming is Is 2 + 2 = 4 universally true? - which, of course, poses the exact same question as you do here. What was the point of duplication?
Why I'd say that is because, on my view, "Mathematics is an abstracted way of thinking about relations," Which means that every human who engages in it must at least think "2 + 2 = 4" (or whatever alternative they think instead, and some people definitely think alternatives instead--we run into them as students in mathematics classes, at least). Not everyone has to bother with mathematics, although it's a bit more difficult to avoid basic arithmetic.
Just to put my two cents into play...
...if you mean 2+2=4 in base ten...
...it seems indisputable.
It seems to reduce to a definition. We define 2+2 to equal 4 in base ten.
Sorta like we define a triangle as a plane having 3 angles. If it has more or less...it just is not a triangle.
In a way, this is true. Of course, no one literally defines the result of 2+2 - it can be rather easily proven from the axioms of arithmetic - but the axioms of arithmetic are themselves conventional in the sense that there is no completely a priori justification for adopting them. Indeed, there are any number of alternative algebras, some of which have been found to be useful or at least interesting.
However, there must be a good reason for why conventional arithmetic is so important for us - and that could be a topic for a philosophical discussion, except that the OP doesn't seem to be interested in such a discussion.
Most importantly the law of identity needs to be true or "X=X". What's on the left of "=" is considered the same value as what's on the right of "=". To prove they're the same we would need to be concerned with their value and not their appearances. "2+2" and "4" may look different but if they have the same value that means they're the same.
Then there's the number symbols
1 = o
2 = oo
3 = ooo
4 = oooo
Then the "+" symbol is an operation that combines the group of objects together.
So 2+2 or "oo+oo" does the equivalent of removing the "+" and pushing the 2 groups together to get "oooo".
The "oooo" looks like what's defined to be the symbol "4". Using that law of identity again 2+2=4 for that reason.
I both disagree and agree with you, Cat.
First, though...just to be precise, I did not say that 2+2 equals 4 by definition...I said that 2+2 in base ten equals 4 by definition. And it does. Obviously in base 4 it would not...2+2 would equal 10.
But these are just symbols for an idea...a shorthand of sorts.
A single unit plus another single unit will always equal "a single unit plus another single unit." We could say it that way (and continue in its extensions) ...or we could devise a system of symbols to denote the thought we are trying to convey in order to make arithmetic possible.
The Romans obviously did it in a (what we consider) cumbersome way.
The Arabic numeral method seems to work better.
It is an agreement and a convention...but it is an absolute as notion.
So I agree that I was NOT supporting the OP (I think the OP wrong because of wording) and I disagree insofar as I was not "actually doing the opposite"...which twists this replay into a pretzel.
The subject actually is not all that interesting to me. Discussions about "absolutes" often end up as verbal pretzels.
I am a new member just trying to see how the board works. Philosophy can be tricky...and end up in "going nowhere" discussions. Just want to see how this forum works...or more exactly, how some of the folk here work.
That's because it's presented axiomatically. It is defined to be true. There's nothing wrong with this, but we should be aware that it's being done. The truth of "2+2=4" depends on number theory and arithmetic, for a start. Maybe other stuff too. And all of this 'stuff' is human-created. That it proves useful in describing some parts of the real world is not magic. We created maths to help us think about the real world. Why would we be surprised when it proves useful for that task? :smile:
I agree with this strongly, although many on this forum do not, for example, see the "Could God not have just built a computer..." thread.
wonderful -
I have said quite a few times on here that all physics is, is a mathematical model of some observed reality. Redundant and maybe seems obvious when I say this - but often it seems not. The reality is real, the physics is the model. Once we have a model - than we can change the variables and see what what it predicts, and then experimentally test the predictions. If they work, we have a good model, if they don't we go back to the drawing board.