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Eugine_Nier comments on A wild theist platonist appears, to ask about the path - Less Wrong
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Yes, but I don't think this uses the word 'exist' in the same way. There's a particular set of formal steps I can go through to convince myself that two numbers are twin primes, and a different set of steps which will convince me that some particular pair is the largest such pair, or that there isn't a largest pair. But this seems different from what is meant by saying that the number two exists.
I'd say not. I tend to use two independent terms when discussing the nature of a thing's existence; I will discuss first whether or not something is real; and then whether or not that real thing exists.
To be real; a thing must be an accurate description of some pattern of behavior that things which exist conform to. (I realize this is dense/inscrutable, more in a bit.) To exist; a thing must directly interact in some fashion with other things which exist; it must be 'instantiable'.
So numbers, mathematical constructs, words; these things are real but they do not exist. We can recognize them in how the things which do exist behave. The concepts are not themselves instantiated -- ever -- but we can handle them symbolically. If I hold three pebbles in my hand, that means there is a precise arrangement of pebbles; it has a precise relationship with two the arrangement we'd call "two pebbles" and the arrangement we'd call "four pebbles" and so on. But you'll never see/hear/touch/smell/taste the number 3. It's physically impossible for that to occur; because the number, 'three', does not exist. Pebbles on the other hand do exist; you can take a pebble and throw it into a lake.
I find that this differentiation between different meanings of the term "to be" makes the discussion vastly simpler. It eliminates whole swaths of silliness (like TAG for example); I am perfectly free to say "I can prove using the Laws of Logic that the Laws of Logic do not exist."
I'm not convinced this distinction holds up all that well. For example, would you say that software "exists"? How about supply functions? Nations? Boeing 747s? People? Force fields?
Edit: yes, what gRR said.
No. But it is real. Software is a pattern by which electrons, magnetic fields, or photochemically-active media are constrained. The software itself is never a thing you can touch, hold, see, or smell, or taste; it never at any point is ever capable of directly interacting with anything. Just like you and me; we are not our bodies; nor our brains; nor the electrons or chemicals that flow through the brains. We are patterns those things are constrained by. I am the unique pattern that, in times past, created the password to the LW account, Logos01; and you the pattern that (I presume) created Eugine_Nier. But neither of us, physically, exist. This is important to notions of substrate-independence; where goes your pattern, is you. (Remember your Ship of Theseus problem.)
Right now I am downloading onto a VM on my workstation the 12.04 release of Lubuntu. This software is being pulled over ethernet to be delivered to a virtual harddrive image where it will be configured and installed. If I say I have LibreOffice installed too, it is clear I am talking about a specific release/instance/copy. We talk about identity in terms of software "Have you tried the latest Halo? It's awesome! ^_^" -- and two people can apparently own exactly the same game. But of course these are multiple copies of the pattern. It's even possible to talk about backups and restores. This is because the only thing that matters about defining whether something is or is not the software is that pattern.
Real but do not exist. If every last person of the US packed their bags and got onto a rocket and shot themselves to Mars, it'd still be the United States of America. Even if every last person died while on that rocket and their kids were the ones who took over for them. Substrate independence once again demonstrates this.
Exist. It is possible to see/hear/touch/smell/taste a Boeing 747 (I hear they taste like burnt chocolate and chicken.) It is possible for two Boeing 747's to be run into one another; or for a comet to strike one. It is not possible for a factory to churn out political constructs or minds. (Though it is possible for them to assemble all the pieces that would, when activated, allow for the presence of a mind.)
While you CAN take all the individual components of a Boeing 747 apart and put them back together again to make the same object; or over time transfer pieces into / from it (Theseus's Grandfather's Axe) -- what you can't do is just "declare" a different physical object to BE that original Boeing 747. You can't have five of the same Boeing 747. That is because it is a thing which directly interacts with other things.
See the above. If some temporal accident causes me to split into two, both of those people would still be ME. (Though their cohabitating the same space would cause divergence of identity over time.) Again, this is because what I physically am is irrelevant to determining my identity (and identity is the conformance to a specific pattern).
"In physics a force field is a vector field that describes a non-contact force acting on a particle at various positions in space." You see that word, "acting"? To "act upon" something is quite literally definitional to being said to "interact with" a thing. By the definition I have provided of 'exists', and the definition of 'force field' as found on Wikipedia, force fields definitionally exist.