Do numbers exist independently of our thought?

I dont think so. First to counter tuesdaygreen's point on trees. He says if noone existed, there would still be trees - i disagree with this. The trees WOULD cease to exist because there no longer is a mind to quantify them, the only reason we see and feel the brown-green objects in fixed positions and shapes is because our brains have the capability of translating them into "trees" for us. Without anything able to pick out all these frequencies and vibrations - what we mean to be a tree, ceases to exist completely.

Likewise for a colour - green for example, the way it appears to us, the translation of a certain range of frequencies by our brain gives us our green but thats all it is - a sort of figment of our brain's "imagination".

So numbers would not exist independantly because in the same sense, they are figments of our braimagination (ha). The number 1 would not exist, nor would what it represents exist simply because it exists as a translation of our world by our brains.

I have a hard time imagining a world without the senses. Maybe this is because all we can rely on IS our senses. But that doesn't necessarily mean that what our senses show us is in fact the correct or only translation of a muddled world there is.

This really depends on what you mean by 'exist' and what you think numbers are. Even when we think about numbers, numbers themselves are not material things, but abstract objects. If you want to say that the only things that exist are material things, then numbers don't exist period.

If you have a looser definition of existence that includes non-material objects (which I would agree with to account for holes if nothing else, see below entry) then you have to decide which kinds of non-material objects are mind-independent.

If you think that numbers are mind-dependent abstract objects, then that would mean they cannot exist without minds. However, then you run into difficulties of determining how mathematical truths are mind independent.

The way that numbers are most often defined is in terms of set-theory. For example, the number three is defined as the set of all three-membered sets. The set of all three-membered sets exists whether anyone bothers to notice them or not, and if that's what the number three is, then it exists independently of any mind.

What you want to avoid is the idea that because there isn't anyone to use the word 'three' or the numeral '3' that the referent for the word and numeral doesn't exist. If people disappeared tomorrow, there would be nobody to use the word 'tree', but there would still be trees.

"Quantities" exist independent of our thoughts; but numbers (per se) are an invention. The reason we have a base-ten number system is that humans are born with ten fingers and toes.

Yes. One of something is only and ever one of something. 2+2=4 always, whether there is someone to be there to think of it or not.

Even if we could all fly like Superman, gravity still exists.

Numbers do not, no. But what they represent does exist metaphysically despite what we think.

no, everything exists if thought by someone.

would anything exist if we didn't think about them?

who would be able to establish existence if they didn't think?

Good question. And excellent answer by tuesdaysgreen. I really can't top it. So I just ditto.

No.

Numbers are constructions of mind.

Without mind there cannot be numbers.