If mathematical entities exist independent of minds then surely that solves the argument of whether maths is invented or discovered.
Yes but that does that mean the converse is true?
Even if we assert that mathematical entities do NOT exist apart from mind, what does that really entail? Does that settle everything? We still have a universe that appears to obey mathematical laws -- mind or no mind, observer or no observer.
"Does one really have the right to ask "what form would these objects take", etc., if one accepts platonism? One can argue that where, how, and form are also independent of the mind as well so I am not sure if such questions can be solved on such a simple level."
you'll have to explain that to me for it seems you are making your mathematical entities epistemically unknowable.
"I maintain that numbers are not just as good as their representations. I was trying to make a point of that, that life would be quite hard if we accepted this view."
Perhaps we are talking cross purposes, I am claiming that numbers are a mind dependent concept we invented to describe fundemental laws of the universe. We both agree these laws would not change if every mind disapeared tommorow and yet you still seek to take these representations into your ontology.
Math_Magician- you go from saying that numbers are human inventions that represnt quantities which are independent of our minds to saying that numbers exist without minds, surely you mean to say the quantities exist without minds, ie what numbers represent.
I do not think I have the issue clear in my head but it is an interesting debate none-the-less
Directly mind dependent? Symbol dependent of the mind, would perhaps be an important distinction.
We are only really arguing about what these symbols represent, you say thay represent mathematical entities of some sort and I say they do not. I say that out of my, admittedly limited, knowledge of philosophical arguments against the Platonist position rather positive arguments for my own position. I believe there are fundemental laws that govern what goes on in the universe and and there are nominal quantities of matter and energy (or just energy if that's what matter boils down to) which conform to these laws, and maths is a description of these laws and how they affect the matter and/or energy. Whether that is a good and potentially coherent account I can't really say myself without further study, so let the debate rage on and I may learn something.
I am not so sure that we can say there will be a 1-1 correspondence between mathematics and physics if one says it is just a language. Mathematics is usually a few steps above physics.
I think mathematics and numbers in general are a continually evolving idea made up by the mind as part of process to order complex (human) thought patterns, and to apply some kind consistancy to the natural world and the relationships of all things in existance to one-another.
In the short span of human history, numbers have evolved many times; Mayans used a base of 20 (i think) instead of 10, Roman numerals???, Arabs figured out that they needed a number zero...
I don't think this is a very good argument at all. It really doesn't matter which culture used what type of system of number. Of course there will be variation, but that doesn't touch the concepts themselves. I also don't think that the word "evolved" should be used here.
I'm just trying to say that i think people "discover or invent mathematics".
-i have never been able to properly explain myself in earth's atmosphere...
Yes, I would say that people discovered mathematics, but not invented it.
..
" ~ in Vegas, i got into a long argument with the man at the roulette wheel over what i considered 2b an odd number. "
tx for the input, from 1. much appreciated #
If you are interested in this sort of thing you should read "Number: The Language of Science" .. Einstein recommended it as one of the best popular science books ever.. =) .. I never finished it because my friend who had lend it to me wanted it back... But it was quite an interesting read; e.g. about the ability of primitive people to know if all their oxen are there even though they don't have a number system...
Math_Magician- you go from saying that numbers are human inventions that represnt quantities which are independent of our minds to saying that numbers exist without minds, surely you mean to say the quantities exist without minds, ie what numbers represent.
I said that we invented the symbols...
Reading back you are quite right Math_magician, not sure what tree I was barking up there. From what you said though we have our human invented symbols and our mind independent quantites out there in the universe so do we need to add these mathematical entities to this? We can say these quantites are of a nominal nature and avoid any need to have mathematical entities existing. I don't know if you're a Platonist, Im just asking in general.
"We can say these quantities are of nominal nature and avoid any need to have mathematical entities existing"
What exactly do you mean here? My fault at not getting your agrument....
It may well be you're not getting it because it doesn't work but I'll try and explain what I mean. My understanding of the word nominal is from the arguments regarding whether universals exist. Here's a link that will be much more useful than my ramblings http://plato.stanford.edu/entries/nominalism-metaphysics/
My point was can't we just have individual instantiations of quantities without the mathematical entities in the same way we can have properties without universals. This is in no way a fully thought out theory, just a thought.
I'll take a look at it soon and report back.
So I did a little bit of research. I was mildly surprised that the arguments I found for nominalism are just based off of Occam's Razor. Now, I do respect this principle of course, so I would not like to directly pick a fight there. However, it appears somewhat silly for the nominalist to say that abstract entities are redundant and therefore meaningless after Occam's Razor, as one may ask if Occam's Razor is an abstract concept itself (which I think it is). The nominalist can't use what he "proved" to answer this, so it sounds a little circular to me.
An abstact entity and an abstract concept are not the same thing. The nomanalist can hold as many abstract concepts as he likes, indeed it would be hard to function without abstract concepts, as long as he does not hold an abstact concept on the basis of the existence of a abstact entity. Or at least that is my understanding, been a while since I looked at any of the arguments.
The point I think that is important that you bring up, Math magician, is that cognitively, I think we have a great ability for generating symbols, which is entirely distinct from the concept itself.