Is there an infinite amount of things that are not present?

Question

Sitting here at my desk, there is not a bottle of meth. There is not an elephant. There is not a car. There is not a unicorn. There is not a salad. There is not a cat. There is not a dog. There is not a bag of chips. There is not a kryptonian. There is not a antimatter rifle. There is not... etc.

The idea is that for any situation, whether you are sitting at a desk, whether you are eating at a restaurant, whether you are in the middle of a war, There is an infinite amount of things that are no present.

The best way to visualize this is with the internet. There is a finite but very large amount of urls. But there are an infinite amount of urls that do not work. Try going to 8dbr8ebr8ebdisnuddbdkfv.com, or ifbsifnkkvlkjbskdhdn.com, or jdndidndksn85484288.com and you will see that they are not working. They don't exist. But there is an unlimited amount of characters that could be typed into the address bar, there is an infinite amount of combinations. So it is impossible to make a functional web page for all of them.

The point is that for every working url (something present) there are 100 more non working urls (the things that are absent).

Another way to visualize this is by going to a working web page. This web page, for example. And you will see there are no pictures of buzz lightyear on it. There are no pictures of superman, no pictures of cars, no music files, etc. So for every present thing, there are many more absent things.

Is my logic valid? Does this make sense/is it correct?

Answer 1

I suspect that anyone with real training in philosophy, especially analytical, will not find this question meaningful or will be able to readily swat it aside with a closing argument.

It is badly defined, but as a pure hobbyist, I find it somewhat interesting. It concerns the relations of presence and the infinite, possibly the two most abstract and vexed terms in philosophy. The scenario "at your desk" seems to restrict "presence" to an old-fashioned perceptual or empirical definition, which does not account for memory or ideas or, indeed, very much of what we call consciousness, let alone the ancient problem of "being," what exists.

The various notions of the infinite are at least as problematic, since almost by definition (Cantor aside) one cannot "de-fine" the negation of finitude. But your "desk scenario" also seems to imply that these things "not present" are not only imaginable but expressible, this and that, hence theoretically "possible."

Possibility may be limited or rendered "finite" by logic. What is logically contradictory is logically impossible. It may be further limited, some would say, within the context of what is possible under the best and most complete implications of the laws of physics, which do change, but presumably under spacetime constraints and not willy nilly.

So it may be that a neat definition of "the infinite" is all that is "not present" and not reducible to any possible present. The negation of what can be de-fined, possibly even "nothing" in a Hegelian or existential sense. At this point, I barely know what I'm talking about.

So I can't dispute Marco Ocram's pragmatic perspective above. But sometimes a bit of mud wrestling with such terms does have useful outcomes and can help one spot overly quick assumptions in the midst of "common sense" or even science. In any case, if you are interested in formulating the relation between presence and infinitude you have a lot of reading to do. Basically, all of philosophy.

Answer 2

Yes, there is an infinite number of things that are not present at any point. Do please let us know if you find a useful or interesting application of that insight.

Answer 3

Neither the desk nor internet examples have an infinite ratio of existing to potential set elements.

The set of all physical things which are at your desk is also infinite, since both the boundaries and set elements of physical things are arbitrary. Therefore the ratio of present to absent things is infinity to infinity, which is undefined.

The set of all existing domain names is finite, however, the set of possible domain names is also finite, because the boundaries and set elements of a domain name are absolute. A domain name can have 253 characters, each of which must be representable by an octet (a set of 8 1s and 0s). An octet can have 255 values. Therefore there are 255^253 possible domain names, a large but finite number.

Answer 4

"Is there an infinite amount of things that are not present?".

"So for every present thing, there are many more absent things.
Is my logic valid? Does this make sense/is it correct?".

These are two very different amounts.

See, for example, "What is Infinity".

Infinity is more than all that is known, it is also all that is unknown, and more. Infinity doesn't have a limit.

Our galaxy is finite, and if there are many more galaxies they are finite too; and there is a finite number of them. Thus, each galaxy has a limit to how much it can hold; and so it follows that there is a finite number of things that are not present.

It is true that for every present thing that there are many more absent things, almost ∞-x, with x being a small number; much closer to 0 than infinity, almost infinity close.

Rather than so large a number as infinity perhaps it's easier to think about the smallest distance, the Planck length.

A Planck length is: 1.616255(18)×10−35 m, or 10^−20 times the diameter of a proton,

A Planck length is far closer to your size than infinity is, and yet the distance is also much smaller than the spacing between your atoms.

Answer 5

Your proposal is true if with "infinite" you mean "ridiculously, unfathomably, ginormously uber-large". I.e., infinite in a casual, human sense.

Mathematically or rigorously speaking, there is nothing infinite in the universe, as far as we know (which doesn't say much, we're not really sure). If the physicists are correct, the extent of the universe is very large, growing, but still finite at every given moment. Also, as far as we know, while atoms are not all they used to be (i.e., they're not atomar), there is a small set of "final" constituents of matter, i.e. there is no infinite recursion into the realm of the tiny, either. Certainly not if you restrict yourself to energy levels which would not pulverize your desk.

Hence, while there are very many subatomar particles in the very very huge universe, it's still finite.

Another way for infinity to creep in would be if some attribute of matter is completely continuous, or whether all of it (especially the location in space) is discrete. The jury is still out on this - we don't know if things are like "pixels" or not. Physicists are talking about the Plank Scale (of length or time) which is kind of a lower limit on these things - i.e. it is assumed that it's utterly impossible to measure anything less than "1 planck length" because doing so would require massive amounts of energy, which would create black holes via the measuring apparatus. But nobody knows if the universe is actually "pixelated" in planck lengths, or whether this is kind of an artifact of our maths.

So while we don't know if this is ultimately the nature of the universe, for everything that is measurable (so in a sense, for everything that exists), there is a kind of pixelating, discretisation effect; which in turn means that every aspect of any particle in the vincinity of your desk there are only so many possibilities, no matter how large your desk is. Even if it is as large as the whole universe.

So no, while the set of physical things that could theoretically exist on your desk is very much larger than the set of physical things that do exist there right now, it is not infinite.

For physically impossible but still imaginable concepts (like your "kryptonian" - assuming they are physically impossible), I'd prefer to ignore those anyways, but if you absolutely wish to discuss them, then I'd argue that by the previous argument, and assuming that the set of possible concepts (which are physically representable) we can come up with has a finite upper limit as well, based on the volume of brain and the assumption that the mind is purely rooted in physics, without anything beyond that.

We can ignore concepts not physically representable (i.e., purely abstract things like the "set of all sets" and so on) because that would be too meaningless a category (it makes no sense to think about a "set of all sets" sitting on your desk unless you just like to play with words).