In the physical sense, it has a clear external boundary. A collection of worker ants can be counted; they do not blur into each other like drops of paint on a surface.Azathoth wrote:Is a worker ant discrete? It is useless unless it is part of a colony
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In a functional sense, it partakes of some of the properties possessed by cells in a multicellular organism...
Firstly, when considering a fish at the macroscopic level, one does not have to envisage the quantum fields of its sub-atomic components; one acknowledges they exist, but a good reductionist uses the appropriate level of physical reality to deal with the matter at hand, which for us, is fish qua fish...FBM wrote:
...Even aside from divisibility into components which eventually become wave functions and fields, in what way is an apparently singular fish discrete, other than just as a convenient fiction? It seems to me that it could be just as accurately described as a local, ongoing set of phenomena within a larger continuum. There's a constant flow of stuff going in and out, and the external boundaries are far less clear-cut than a casual look would suggest, I think....
Individual organisms may not have the "perfect discreteness" that one would expect of a platonic object. They are indeed dynamic, and over time, most their atoms will undergo replacement as they feed and excrete, and their size and other aspects of their nature will change. For some purposes, it may be useful to consider them as a "local, ongoing set of phenomena within a larger continuum". Again, none of this changes the fact that it is absurdly easy to count them, name them, scoop them up individually etc. Their discreteness is not down to human consciousness "chopping up" reality into bits, it exists inherently in the nature of at least some objects in the universe we inhabit.
Of course, there are situations where humans do grab discreteness where none really exists; the classic example would be the names we give to the colours of the rainbow; quantum effects aside, the spectrum of light is a true continuum, and our "chunking" of it is a process of our consciousness. The fact that the human mind does this (for quite practical reasons) in some circumstances is not evidence that the whole of reality is non-discrete.
The whole point of my excursion into the way that our physical reality contains objects that are discrete is to back up my assertion that numbers (at least counting numbers) exist in nature. In any defined region of space time, a set of countable objects exists, and the number of those objects is not imposed by an intelligent observer, but an inherent property of that set. Not only that, but the property of "seven" is transferrable - it is a property of any other set containing the same number of discrete objects, even in a universe where intelligent observers had never evolved.
And yes, Jim is pretty annoying. I'm wary of him too. 
