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What is the fundamental difference between something that exists and something that doesn't exist?
What exactly are we claiming when we say that something "exists"?
Is there a distinctive property that all existing things possess that all non-existing things don't possess?
The concept of existing is certainly a human invention but I can't identify what we are trying to point out with this concept.
Any ideas?
Following Quine, a fairly popular approach to the question of what exists is to say that those things exist that are indispensable to our best scientific theories. On this view, electrons exist because our best account of fundamental physics includes them. Water exists, but phlogiston does not. Composite objects such as tables and kangaroos exist, because they are made up of fundamental parts, though it is notoriously difficult to say what constitutes the identity conditions of a composite object. There might be tricky cases where it is disputed as to whether a things exists, but on this view, the ultimate arbiter is science.
Abstract objects such as numbers can be said to have a kind of existence, according to Quine, since we need them to do science. Although that claim has been disputed by Hartry Field among others.
Quine's approach to ontology is very minimalistic, and his account still leaves many questions unanswered. Do universals exist, independently of particular instances of them? Do minds exist? In what way might we say that fictional objects exist? Is there a realm of non-existent objects or potential objects that subsist or have some second tier of being? Philosophers disagree about how to handle examples such as these.
Also, scientific theories are underdetermined by data, so it might be possible for two equally successful scientific theories to entail the existence of different kinds of objects.
As to your last question about what we are trying to do by talking about existence, the question of what exists seems to be very fundamental. We tend to think about our experiences, and attempt to make sense of them, by supposing that there are things, properties of things, and relations between things. Maybe it would be possible to create an account of our experiences in other terms, such as ideas or processes, but for most people it seems natural to accept that there are things, and these things have properties and they participate in relations. It is not an accident that our best logics work this way: we quantify over things, and use predicates to express their properties and relations. Once this basic framework is in place, the whole of our knowledge rests on the question of what things does our universe consist of.
There are several accounts of existence. The two most popular are probably the classical notion and the Frege/Russel notion.
The classical notion is that existence is something that some objects have and others don't. Horses have this something and unicorns don't. Some philosophers have noted that this something can't be a property because an object has to exist before it can have any properties; that is, a thing has to have existence before it has properties, or in order to have properties. There have been hundreds of thousands of words written about what this something is and what sorts of things have this something.
The Frege/Russel notion of existence is that existence isn't something that individuals have; it is just a higher-order predicate. According to this notion, it is not, for example, cats that have existence, but rather that the set of cats is not empty or that the concept of cats is instantiated. It is simply a logical notion.
What condition(s) must be met to claim that something exists?
The conditions for making any claim whatsoever are that you be able to make that claim. This is probably not the answer you are looking for but this is the question you asked.
Maybe we could rephrase your question?
What condition(s) must be met for something to exist?
There cannot be any condition on something that doesn't exist because it doesn't exist.
There cannot be any condition on something that exists for it to exist because it already exists.
Conditions cannot be on reality since reality already exists and exists as it is, which includes the existence of any particular thing.
Maybe we could ask a somewhat different question?
What condition(s) must be met for us to know that something exists?
This is essentially the question addressed by other answers.
We can begin by observing, à la Descartes, that being conscious involves knowing that you are conscious and so involves knowing that you exist as a conscious thing. Are there any conditions? Not any that anyone would know except obviously that you need to be conscious. We may want to say that you need to perceive the world around you but no. It is possible to be conscious without perceiving the world around you, and this seems enough to know that you exist as a conscious thing.
However, this does not solve the problem of the conditions for us to know that other things than our own consciousness exist. What are the conditions for us to know that the Moon exists? It doesn't seem that we know the answer to that because it doesn't seem that we even know that the Moon exists to begin with.
We certainly know the mental image that we naïvely take to be the Moon but we know it as part of our own consciousness, so we are going back to the initial resolution of the conditions for knowing that we are conscious. And that we should know some content of our own mind does not imply that we should also know that whatever it may seem to represent or signal also exists.
So, it seems that the condition for us to know that something exists is that it be somehow part of our own consciousness, and then we only know that it exists at the moment that we are conscious of it. If something is in our own consciousness, then we know that it exists (as such).
However, our concept of existence goes beyond existence as mental object. We believe that the Moon exists somehow outside our own mind. Perhaps thanks to philosophy and science, we also realise that the Moon we are conscious of is not the real Moon, if this one exists at all. We also realise that the real Moon is unlikely to be much like the Moon we are conscious of.
The most plausible conclusion is that we cannot possibly know that the real Moon exists. We can believe that it does, and we do, we may even be "dead certain", but, presumably, we cannot know that it really exists.
That being said, it doesn't seem to matter in any way.
It doesn't matter because we don't need to know whether the Moon really exists. What we need is essentially to survive, prosper and reproduce. Our beliefs seem on the whole good enough to help us achieve that. Humanity seems to have survived, prospered and reproduced for more than 300,000 years. Life has existed for several billion years. Animal species which have a brain and rely on their beliefs about their environment may have existed for several hundred million years. So, there is no doubt that the sort of beliefs we have work. No only that, but we broadly understand how they can be so operationally effective.
So, a better question could be:
What are the conditions for our beliefs to be operationally effective in helping us survive, prosper and reproduce in the real world?
This seems a much more tractable question and one which is essentially the subject of various sciences, including the cognitives sciences, formal logic, evolutionary biology etc., and the actual answer to this new question will emerge with every new result coming from these sciences.
However, a basic answer is that the beliefs we develop as a direct result of our perception of our environment provide an effective basis for our survival, our prosperity and our reproduction. Technological and scientific progress, and the operational effectiveness of our technology and our science also seem to prove that we need to stick to the scientific method for developing our beliefs about the real world. The scientific method is really just our ordinary, native rationality applied in a systematic way. Science is just rationality plus organisation, cooperation, professionalism, use of our technology etc., and, crucially, memory of our science beyond the life span of individual humans through successive generations. And rationality is essentially facts plus logic.
These are the conditions.
These are the conditions not to know that things exist, but certainly to be able to trust our belief that the Moon exists to the point that we can send a man to land on it and come back alive with a handful of Moon dust.
Perhaps the best definition of existence is that attributed to George Berkeley: esse est percipi (existence is perception).
If you perceive a hammer with your smashed finger, it exists. If you feel sadness, it exists. If you perceive an opportunity, it exists. If you don't perceive an irregularity on a surface, it doesn't exist... for you. If you don't perceive dark matter, either with your instruments, your reason, equations, your senses, then, it does not exist.
Notice there is a difference between empirical existence (what the senses perceive: unicorns vs. horses) and plain existence (what any form of intuition allows perceiving). Commonly, science refers to the former, but in any other case, it's about plain existence (e.g. crisis, order, poverty, beauty, respect, danger, numbers, etc. can't be perceived by the senses, but do exist for most). For example, quarks can't be perceived by the senses, but they do exist because science tells so.
Notice existence is subjective: UFOs, beauty, danger or God are perceived by some, not by all. That is, some believe they exist, some don't.
My understanding has always been that something exists if it has at least one measurable property. Hence a brick has size and mass, a photon has wavelength and energy, and my lifetime may be measured in years. That’s not a great definition since it depends on what tools you have to make measurements but it’s a start. It does allow for the intriguing possibility of having multiple frames of reference that don’t overlap at all.
I think, the question is not well posed: The word "exists" has several different meanings.
Something exists if it's part of our universe. As such, horses exist, but unicorns don't. This meaning of the word is relatively straight forward. However,
ideas and abstract things are said to exist as well. Numbers exist. Several classes of numbers exist (natural, integer, rational, irrational, transcendent, complex, etc. pp.). Other mathematical constructs exist. The ideas of wizards, vampires, unicorns, homeopathy exist in the minds of humans.
Things can exist in imaginary worlds. There is a philosoper's stone in Harry Potter. There are also magic wands. There is also a ring world somewhere far away where people walk on the inside of a mind boggling large, tremendously fast rotating ring. Ask Larry Niven about it.
As such, heated arguments about whether something exists or not are pretty mute. If you want to use the word "exists" in a negative sense, it's better to say in which context it does exist. I.e. a philosoper's stone exists in Harry Potter's world, but not in ours. Likewise, vampires exist in various forms in many different books, but luckily, they won't come to suck your blood. And mathematicians create abstract concepts simply by definition, so you cannot claim that imaginary numbers don't exist. They exist in mathematical and physical formulas, and they are dead useful. I've never talked to an imaginary number, though.
I would say anything that can be perceived from six senses " touch, sight, hearing, smell, taste or thought " can be claimed of existing.
For example :
I see a bat in front of me so I claim that the bat exists .
I smell an odor, I claim their are tiny particles of that odor in the surrounding .
I taste something so I claim there exists something in my mouth.
I hear people talking across the room so I claim there are people across the room.
I touch something soft, round and jiggly so I claim its a Balloon.
A 'x' religion person thinks that the 'x' religion god is real so he tries to prove the gods existence through thought/argument for example who created the tree, oceans etc.
