As an aside, Is there not also equally social agreement as to what the traffic laws **are**? (the scope of applicability of a law seems to me to be be the same category of thing as the statement of the law, independent of domain of control, and without the statement of the scope, the law itself seems to me to be incomplete.)
MW: Yes of course. We have parliaments or the like to establish and agree them.
More to the point, for me, what are the practical implications of limiting existential quantifiers to a particular category of the things we talk about?
MW: I make no attempt to do so. You may be confusing my remarks with those of JS. If you allow a category, then you can quantify over it as far as I am concerned. I don’t allow a category called abstract individual. Under 4D I find it unnecessary. So in my scheme of things you cannot quantify over abstract individuals, but that is only because there are not any to quantify over.
In other words, how does it *help* to not let people say, 'there exists a rule, there exists a color, there exists a category of binary relations, called symetric relations? (Or, am I mistaken, and this is all OK -- but if it IS OK, then what is not OK?).
MW: Yes that is OK, just as long as those things do exist, and it is reasonable to argue that they exist (for you) if you wish to quantify over them (this is I believe essentially Quine’s definition of what it is to exist).
I believe that some people seem to think that if a computer cannot decide if a statement is true or false, then it should be disallowed, so they do not like anything but restricted kinds of first order logic, so I think I understand the nature of their view, as a practical matter, (even though I think that this view is pernicious). But you seem to have a theory about ontological languages that I just can't see what it will do.
MW: I do not have a theory about logical languages, but of the sorts of things that exist that you might wish to speak about in a logical language, however restricted or expressive it may be.
( I am not sure whether you choose to identify 'individuals' based on a relationship between those things and phenominological experience or between them and physics (which do seem to me to be miles apart, even though both are hard to grasp), but however you pick out the individuals from the non-individuals, how does it make people's understanding and description of the world easier and different from what it would be otherwise?
MW: Two key and related considerations in developing a coherent and comprehensive ontology are the fundamental kinds of thing that exist, and how you know if two of them are the same or different (identity). In general, the smaller number of categories the better, providing, of course, that they are sufficient to describe everything that could be of interest.
So, we might admit sets as a fundamental category, and we might have as the identity criterion that two sets are the same if they have the same members.
Now what can we come up with for things that exist in space-time? My choice is the spatio-temporal extent, quite literally any piece of space-time that might or might not be contiguous.
It is quite easy to see that you and I are pieces of space-time, and that because you and I are not coincident, that we a different objects. But what about say Barak Obama and The President of the United States. We can see that at the moment these two objects are coincident, but we probably want to say that they are not identical. One approach is to introduce abstract individuals and to say that the President of the United States is an abstract individual, and that Barak Obama is acting as the President of the United States. However, by adopting 4D with identity based on coincident spatio-temporal extents I can avoid this. This is because although Barak Obama now is coincident with the President of the United States now, it is not true that Barak Obama for the whole of his life is coincident with the President of the United States from the declaration of independence to the present day and beyond. But then what is the spatio-temporal extent of the President of the United States? Well we already said that today Barak Obama was coincident with the President of the United States (so if today I have shaken the hand of Barak Obama, I have also shaken the hand of the President of the United States). We can therefore go back in time and see that the President of the United states consists of the states of the various persons holding the office whilst they held that office. The only thing you have to get over is that you can construct one object out of temporal parts of other objects. Once you have done that though, you can do away with abstract individuals. This in my view is a useful simplification, since I am not at all sure what abstract individuals really are, whilst I am quite sure what spatio-temporal extents are.
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