I agree with the second viewpoint pangtongshu listed. Numbers are words and symbols representing amounts, and are the basics of mathematics (which is why for me -1^(1/2) is not a number, it is a formula, so no problem with that). Much in a similar way, though not completely so, as letters.
Thank you for explaining while I was away, pangtonshu, although it's not as simple as numbers just existing like normal objects in some distant galaxy. To really understand this, you have ask a lot of existensial questions. Take speech for example: Speech is sound. Sound is vibrations in the air that are picked up by your ears. These vibrations are translated into electrical and chemical signals that are transmitted to your brain. But, speech also starts in your brain as an electrochemical signal that is transmitted to the muscles in your throat, tongue, jaw and diaphram. You could say that speech exists in your mind. Or you could say that speech is just a simpler term for saying that the neurons are firing off in your brain so that you can communicate with fellow members of your species. Or you could say that speech doesn't exist, there are only the vibrations in the air and the nerve signals going through your brain and forcing your muscles to contract and relax.
There are problems with all 3 of these standpoints. The first one, for example, is if numbers exist, where do they exist? We use numbers in our brains, so could they exist like speech? But, numbers would still exist even if we did not, they have so much to do with the universe. So, numbers do exist in space and time, but they dont?
There are also problems with the adjective view of numbers. 1 means 1 of something. 2+3 means you had 2 something, and you get 3. -2 means you owe someone 2 objects. But then, what do numbers like pi and the square root of -1 do? You can't have 1/0 something.
Then there's fictionalism's problems, the main one being "if it doesn't exist how do we use them?" I honestly have no idea how to answer this question, like I said I belive in the platonic philosophy where it exists at least as neurons firing in your brain.
Or you could say that speech doesn't exist, there are only the vibrations in the air and the nerve signals going through your brain and forcing your muscles to contract and relax.
Speech IS muscle activity, vibrations and neural signals. Although this is a very simplistic way to put it. The act of speaking was there before the concept and definition of 'speech', so you are kinda looking at it the wrong way imo. Same way with numbers, as already evidenced by Mage even many animals can count up to a certain number, or have an understanding of amounts, but they don't know what a number is, because WE defined 'one' as 'one'.
I personally have a platonic view of numbers, where they do exist, just not in space and time.
If you want to maintain that there is this Platonic heaven, then you're more than welcome to. You're going to vulnerable to 'third man' arguments, but it is what it is. However Plato was not aware of set theory, which is a fairly reasonable and (mostly) straightforward way of defining numbers. So say that numbers themselves exist depends on your definition of a number. But you're not going to make that claim by itself without some sort of substantiation. So you might back off and just claim that sets exist, which is at least a more tenable approach. Better still is to define numbers in terms of mathematical logic. This gets you out of a number of ontological difficulties and provides a very clean and efficient way of defining what a number is. But if you go that route, you're not going to be able to claim that numbers exist - at least, in any metaphysically significant (or recognized) sense of the word.
So maybe ask yourself 2 questions: 1) What is a number? 2) What is entailed by your notion of 'existence'?
You are right ! Numbers do not exist. All those things with math, Litters, pounds and other things, are not real, they are made by us only because we cant live without naming things.
But everything that has a name exist. We give the name of the numbers and even if they don't exist now they do, so deal with it 1cat+1cat=2cats :3
This is a neat topic, I'm surprised not many people have posted. First off, there are some questions that I think are worth answering in my previous post. But in any case:
You could say that speech exists in your mind. Or you could say that speech is just a simpler term for saying that the neurons are firing off in your brain so that you can communicate with fellow members of your species. Or you could say that speech doesn't exist, there are only the vibrations in the air and the nerve signals going through your brain and forcing your muscles to contract and relax.
This seems to conflate the notions of sound, speech, and thought in a way that undermines the analogy. It's also worth noting that numbers don't have any of the salient features characterised by the analogy. So maybe find a different way to think about it - especially the sufficient conditions for something to qualify as existing.
You are right ! Numbers do not exist. All those things with math, Litters, pounds and other things, are not real, they are made by us only because we cant live without naming things.
But everything that has a name exist. We give the name of the numbers and even if they don't exist now they do, so deal with it 1cat+1cat=2cats :3
Not sure what you're on about here. Certainly not presenting a contradiction as an argument. So what are you trying to show?
I think he means that we arbitrarily define many mathematical concepts, as in units of measurement (feet, meters, pounds, etc.). Numbers, however, aren't arbitrary. They are abstract representations of physical quantities, such as 1 cat. This implies that numbers don't exist in a physical sense in the same way that dog (the abstract notion of a living creature) doesn't exist but Dog (the aptly albeit uncreatively named fuzzy thing slobbering on the floor) does. In this case, numbers exist in the physical world as the quantities they represent
...Maybe
Of course, this all depends on your definition of existence. Does an abstraction actually exist (they're certainly apparent in our minds) or does something have to be physical to stake that claim? To take it a step further, if abstractions exist, do abstractions of abstractions (such as i) exist, or does the possibility of abstracting the abstract prove the non-existence of abstractions?
I think numbers do exist, just not in a real state. I think they are something that we now of and that exists, they just don't hold mass. They are ideas that all people can share. I also no people used numbers (in a way) before numbers even existed. People have clocks inside them and can tell the difference between to things quickly and even when these differences are small. This has been true since before the human race invented the idea of "numbers". I guess I am not fully convinced they exist, but I am pretty sure.here is the video about time perception
