Another is to simply say that that the domain is the universe, or that it's everything, or that it's unrestricted. All of those can be expressed without speaking in terms of existence.

Any domain which is not constrained to iterate/refer only to things which themselves exist would lead to wrong conclusions such as "flying unicorns exist".

What is it you want, exactly?

To show that the definition you referred to, in all its variants, isn't useful. I did not forget that you didn't claim it was useful, just that it was common, but I also noticed you did not explicitly agree that it was not useful. If you do agree on that, there is no need to further dwell on useless rephrasings.

I agree that since the body of human knowledge is limited, any definition must eventually contain circles of some size. However, not all circles are created equal: To be useful, a definition must refer to some different part of your knowledge base, just because without introducing new information, there is nothing which could be useful.

"2 is defined as something with the property of being 2" isn't useful because there is nothing new introduced. "That which exists, exists" isn't useful for the same reason. Because all the definitions you referred to still contain "exist", the additional information ("things in a set") is superfluously added, the "exist" on the right part of the definition still isn't unpacked. Hence, no additional information is introduced, and the definition useless, being equivalent to "2 is defined as 2".

"Pain is when something which is in the set of 'being able to experience pain' experiences pain" just reduces to "pain is when pain", which must be useless since it contains no additional concepts.

If the additional "identity" aspects etcetera helped any in explaining the concept of "exist", then the definition would not need to refer again to just the same "exist" which the "identity" supposedly helped explain.

Seems like a pattern with other philosophical types here. Maybe they don't teach philosophers to listen, I don't know. For comparison, TheOtherDave manages to carry a thoughtful, polite and insightful discussion even when he disagrees. More regulars here could learn rational discourse from him.

Agree on both counts. I'll second your advocacy of a TheOtherDave as a posting style role model. In particular he conveys the impression that he is far better than the average lesswrong participant at understanding what people are saying to him. (Rather than the all to common practice of pattern matching a few keywords to the nearest possible stupid thing that can be refuted.)

Maybe they don't teach philosophers to listen, I don't know.

I can tell you from experience that 'they' don't. Do you know who does teach this?

I'm a mathematical fictionalist, so I'm happy to grant that there's a good sense in which mathematical discourse isn't strictly true, and doesn't need to be.

Are you asking for a definition of an intuitionistic 'exists' predicate, or for the intuitionistic existential quantifier?

You've redefined 'x exists' to mean 'x is described by a map that has been tested and so far has seemed reliable to us', and 'x is true' correspondingly. One problem with this is that it's historical: It commits us to saying 'Newtonian physics used to be true, but these days it's false (i.e., not completely reliable as a general theory)', and to saying 'Phlogiston used to exist, but then it stopped existing because someone overturned phlogiston theory'. This is pretty strange.

Another problem is that it's not clear what it takes to be 'found reliable enough to use as a guide for further travels'. Surely there's an important sense in which math is reliable in that sense, hence 'true' in the territory-ish sense you outlined above, not just in the map-ish sense. So perhaps we'll need a more precise definition of territory-ish truth in order to clearly demonstrate why math isn't in the territory, where the territory is defined by empirical adequacy.

I think your view, or one very close to yours, is actually a lot stronger (can be more easily defended, has broader implications) than your argument for it suggests. You can simply note that things like Abstract Numbers, being causally inert, couldn't be responsible for the 'unreasonable efficacy of mathematics'; so that efficacy can't count as evidence for such Numbers. And nothing else is evidence for Numbers either. So we should conclude, on grounds of parsimony (perhaps fortified with anti-Tegmark's-MUH arguments), that there are unlikely to be such Numbers. At that point, we can make the pragmatic, merely linguistic decision of saying that mathematicians are using 'exists' in a looser, more figurative sense.

Perhaps a few mathematicians are deluded into thinking that 'exists' means exactly the same thing in both contexts, but it is more charitable to interpret mathematics in general in the less ontologically committing way, because on the above arguments a platonistic mathematics would be little more than speculative theology. Basically, we end up with a formalist or fictionalist description of math, which I think is very plausible.

You see, we aren't so different, you and I. Not once we bracket whether unexperienced cucumbers exist out there, anyway!

Re 2. First, let me adopt bounded realism here, with physics (external reality or territory) + logic (human models of reality, or maps). Let me ignore the ultraviolet divergence of decompartmentalization (hence "bounded"), where Many Words, Tegmark IV and modal realism are considered "territory". To this end, let me put the UV cutoff on logic at the Popper's boundary: only experimentally falsifiable maps are worth considering. A map is "true" means that it is an accurate representation of the piece of territory it is intended to represent. I apologize in advance if I am inventing new terms for the standard philosophical concepts -- feel free to point me to the standard terminology.

I suspect you have, in fact, reinvented something. For reference, how does this "bounded realism" evaluate this statement:

On August 1st 2008 at midnight Greenwich time, a one-foot sphere of chocolate cake spontaneously formed in the center of the Sun; and then, in the natural course of events, this Boltzmann Cake almost instantly dissolved.

It makes no predictions; this is, in a sense, epiphenomenal cake - I know of no test we could perform that would distinguish between a world where this statement is false and one where it is true. Certainly tracking it provides us with no predictive power.

Yet is it somehow invalid? Is it gibberish? Can it be rejected a priori? Is there any sense in which it might be true? Is there any sense in which it might be false?

Sorry if I'm misinterpreting you here; I doubt this has much effect on your overall point.