Do abstract objects exist?
For example, while we do know, for certain that there are concrete objects, like five stones, do abstract things like, say, the actual number five, exist? If so, how can one prove that abstract objects exist beyond, or is it an impossible metaphysical question?
Update:If an abstract object ('concept' as you call them) have no independent existence beyond the noetic, then, certainly, we cannot say that it really 'exist', but rather, it is a mental construction.
Comments
Abstract objects aren't objects, they're concepts that we invented them and gave meaning to them.
"we cannot say that it really 'exist', but rather, it is a mental construction."
That's correct
Good question. Abstractions do not exist although they certainly appear to exist or seem to exist. Just as an oasis appears to exist in the mind of a man dying of thirst in the desert. For example, time does not exist in nature but was invented by human in order to calculate the distance between the occurrence of events. The clock exists but time is something that cannot be touched or seen or heard. The universe is in a constant state of change which gives off the illusion of time. The fact that we think linear, one thought and the other thought, also makes it appear as if time is moving forward.
This can be taken even further. All concepts are abstractions and none of them actually exist. When you see a beautiful sunset. The word beautiful is an abstraction. It's an idea that humans invented. The sunset is not beautiful or not beautiful it just is. A bird probably doesn't see a sunset and come up with abstract concepts to explain it. Without humans none of these concepts such as beautiful, right and wrong, time, money, etc. would exist. The universe just is. No translation is needed.
We can go even further and say that the mind itself is an abstraction. The thoughts that make up your so-called mind are abstractions. You cannot touch, see, hear or taste your thoughts. You are aware of your thoughts but where are they? Are they just your imagination? Do they actually exist? How about yourself? If your thoughts are abstraction then what about the concept your 'self' or self-awareness? These are also abstractions. You cannot touch or see self-awareness. It appears or seems like there is a 'you' somewhere in your head but there isn't. It's the oasis in the desert.
Hope this helps.
The actual number 5 is not an "object". It is a concept. Many abstract concepts exist, but only in the minds of humans.
As Kant suggested, everything we believe is ultimately bound to our empirical experience. Modern-day cognitive psychology reports how we truely do that and, with reference to your question, Piaget's work is most telling: people combine easier schemes into extra complexe ones and, utlimately, the most intricate schemes are formal. They're void of empirical content, constitute generalities about characteristics or relations and we can fill them with contextual elements. So, they exist in our intellect as constructions that we will manipulate. It's the case of theories and principles. I will use the proposal of self-enjoyable prophecy which, in itself, isn't certain to the stipulations in which it arose -- it conveniently is a general description. In essence, a self-fulling prophecy is a situation wherein someone align their conduct hence to their expectations and hence expand the chances of making it happen. That's void of content material -- i can use it in any drawback. For example, a person who feels they have got little probabilities of succeeding at an examination won't learn as so much or work as tough, each of that are correlated with lower grades. For this reason, that scholar tends to "show to himself" that he's certain to fail for the reason that his negative expectations altered his conduct in a unfavourable way. If you wish to have an different illustration, here's an other one. In economics, we will measure pleasure (we name it utility) with a few one-of-a-kind equations. Any individual who couldn't recognize formal schemes would not see why i will decide on ordinarilly any function to graph utility versus the consumption of some good or carrier... But when I do, then i know the operate ought to meet unique criterion reminiscent of being at all times growing (more is constantly higher) and it needs to be concave toward the x axis as a rule (that is as a result of the perspective towards hazard). The purpose that i can work this fashion is that I do have some intellectual illustration to govern: I can't deduce from nothing, so if I make deductions, it is that I had some intellectual instance unto which I would function. That's clearly what Piaget called a "scheme" -- the operation and the representation taken together. By means of inference, they have got to exist, as a minimum as a lot as the operation I participate in or as the effect you become aware of.
Plato theorizes that ideas and physical things exist in seperate "realms".
For instance, the unicorn does not exist in our physical world. But it certainly exists in the sense that you can imagine one, draw one, describe one, etc. It exists in the world of the ideas.
A number follows the same basic guidelines, I think. When nature is constructing itself, it does not "think". It does not have any idea of the proportions and numbers that we have assigned to it. Those are not real things. Any symbol could represent the value of "5". But it is the value itself, of whatever various thing you are messuring, which gives physical meaning to the idea that represents it.
Let me show you (5).