I think math is not real. Of course to say that uses in a sense logic, which is a form of math (or math is a form of logic). So it may be paradoxical. However I am sure math is just an abstraction of real phenomena, and does not relate to the phenomena itself. It is a tool humans have, one of our filtering methods (a la kant) to understand the world. If so, what is the consequences of this?

You might want to read about mathematical fictionalism. That might be where you're headed, depending on how you interpret the concept of a number.

https://plato.stanford.edu/entries/f...m-mathematics/

Edit: You may also want to look at mathematical nominalism:

https://plato.stanford.edu/entries/n...m-mathematics/

What if you upload a mathematical structure, e.g. a finite group, onto a computer. That's real, isn't it?

That's not really the point; sure it's real but only as digital stuff, binary data, 1s and 0s. The question is if the meaning is real

To ascertain the meaning of something, one surely has to begin with its definition.

So are you saying the question is if the definition of e.g. a group is real?

yes

So what, then, are your criteria for a definition to be real?

(Sorry, but I am unable to figure that out entirely from the OP.)

Generally anything you can sense, but that is thrown into question also as to its true nature. The problem is the mind's filter keeps us from knowing really what is real (noumena).

If I look at three balls sitting on a table, am I properly sensing a "three-ness" of the balls or is that merely an abstraction of the configuration? Or if I physically place the three balls on the table, is that "three-ness" real or something that's all in my mind?

Well I can sense a math definition. I can see it written down, can't I?

Also, your OP seems to indicate that you think logic is real. How do empiricists explain the reality of logic?

all this talk of three-ness and balls...


well that's the question, is it real or all in your mind

Well... what's your answer? And don't take this as some sort of position that you must ultimately take and defend to the bitter end. But it's hard to really explore the ideas without assuming a position and thinking through some of the difficulties and consequences of that position.

Most mathematicians are some form of Platonists when it comes to it. We tend to see mathematical objects as existing in a mind-independent way, that the underlying structure of a group would still exist even if we weren't around to think or talk about it. Things like that.

https://plato.stanford.edu/entries/p...m-mathematics/

You can sense a math problem and you know it's a math problem because you were taught its a math problem. the question is whether math refers to something beyond human comprehension or if its just a structure of human comprehension that we've elevated to the status of object

I think empiricists explain logic as a way of parsing information that is only gained through experience. logic is just an organizing method for us to make it comprehensible. And I would argue that the world is chaos but for our logic (and other focusing tools), which makes it small enough for us to navigate.

My position is that numbers are not real. In either scenario you laid out, the three-ness is arbitrary and merely a way for us to communicate a fact about the objects, like greeness or bigness.

Let's say dogs have black and white vision. They see all balls as shades of grey. Who is right, the dogs or humans?

Let's say dogs can't do math. Let's say they organize objects by color, size, and smell. Pool balls have a smell that is unique and dogs can sense it. Let's also say there's another quality of pool balls called Y. Y is sensed by dogs and dolphins but not humans. Z is sensed by porcupines and squirrels but not dogs. I can imagine there are millions of properties of each object in the world. Given that if you break them down into atoms (which we can't see, but another being might). So by elevating math to a high position, it is like a dog elevating smells to a high position, ordering them into hierarchies and then branching off into whole sub-fields of smells. But this smell-rithmatic science is studied for years by pups but really they are only investigating the limits of their own minds (which is something).

So? Is the English language not real either? Is this conversation not real?

The question appears to keep changing.

No my first question was what are the consequences of math not being real. You've changed it by questioning the assumption.

No, I am merely trying to understand the assumption, i.e. what you mean by "real". Apparently it is an unusual and controversial meaning, since you think that definitions which appear in real books and journals in real libraries, are not real.

real = exists

Holding OPs view gets difficult once you acknowledge that relations between existing things have a sort of existence (mind-independent) similar to mathematical objects. Relations such as: 'in addition to', 'less than', 'more than', 'equal to', 'similar to', 'different than' etc.

To remain consistent you'd also need to deny the existence of relations. This is problem. Things are clearly related in the world.

Okay. So either nominalism or fictionalism.

Do you believe that the following statement is meaningfully interpreted as true: "1 + 1 = 2"?

It's meaningful in the sense that it is logically consistent. If by true you mean "refers to things in themselves in the noumenal world" then no.

Okay.

We've already established that you reject mathematical Platonism. If you want to actually think through the consequences of your belief, you need to think harder.

Is it false that "1+1=2"?

It's not at all clear to me that relationships exist "in the world."

It's not clear they exist in the world. I agree. Is it clear they exist only in the mind?

It's neither true nor false.