When Does a Bird become a Fish?

Many have long enjoyed those imaginative images of M. C. Escher, such as "Sky and Water I" and "Reptiles". I accept that birds do not morph into fish in "Sky and Water I", but tessellated shapes do 'turn into' reptiles in "Reptiles". What I was looking for was an image that would illustrate some of the problems of classifying things into categories. Some of the problems arise because of ambiguity, either visual or verbal. Examples of visual ambiguity include optical illusions such as Joseph Jastrow's "Duck-Rabbit" or the "Old Hag-Young Lady". Examples of verbal ambiguity include homonyms and polysemes. Even sounds can be ambiguous or illusory, such as the "missing fundamental".

When we try to classify, when is appropriate to say that something is in "either a or b" or that it is in "both a and b"? What do we do when it's really neither "either/or" or "both/and", but simply the "same thing in a different state" (or time)? As a dual-national, am I either American or British, or both American and British, ... or am I the same thing in a different state? [No pun intended; honest] As I sometimes explain when people ask, I am 100% American and 100% British. In fact (I believe), it depends on where I am. In the States, I'm American; in the UK, I'm British. As a British national, when I'm in any member state of the European Union, I'm a European citizen; this is a generalisation of being a British citizen. British citizen is a hyponym for European citizen, and European citizen is a hypernym for British citizen.

Either/Or:
'Phosphorus is either a morning star or a planet.' (The Greeks regarded the planet Venus as two separate celestial objects. Phosphorus was the morning star, and Hesperus was the evening star.) Either/Or may imply 'siblings' in a hierarchical scheme; see next.

Both/And:
'Venus is both a morning star and a planet.' What about Jastrow's 'Duck-Rabbit'? Is the one shape both a 'duck' and a 'rabbit', or is it either a 'duck' or a 'rabbit'? Both/And may imply a hierarchy, where common characteristics are attributes of the hypernym, so both a duck and a rabbit are hyponyms for animal. Both the morning star and a planet are celestial objects. (See also Wittgenstein's discussion in Philosophical Investigations.)

Same Thing, Different State/Time:
Then, there is the classic question in logic of 'are (or would it be "is") the morning star and the evening star the same star?', which is mentioned in discussions of sense and reference.

The butterfly goes through four states in its lifecycle. But when it's a caterpillar, is it a butterfly? This 'same thing, different states' can become very problematic in ordinary life, especially when there are ethical issues involved. When, for example, does the joining of two human gametes become a human being? (morula? -> blastula -> gastrula? -> organogenesis? -> ...)

Laws of Gestalt Psychology
Perhaps the laws of gestalt psychology can help us classify things into categories. These mostly have to do with visual perception, but I'd like to try to push them further into 'verbal perception'.

• "Law of Prägnanz. This law says that we try to experience things in as good a gestalt way as possible. In this sense, "good" can mean several things, such as regular, orderly, simplistic, symmetrical, etc. [Prägnanz {f} translates as pithiness, sententiousness, or conciseness. I interpret this as being very similar to Occam's Razor or the KISS principle. David Upton disagrees with this interpretation in an interesting way in an entry on his simulation blog. (This somewhat circular reference reminds me of Escher's Drawing Hands.)]
• "Law of Closure. Our mind adds missing elements to complete a figure. [This might be extended to the observation generalises from just a few examples.]
• "Law of Similarity. Our mind groups similar elements to an entity. The similarity depends on form, colour, size and brightness of the elements. [This might be extended to non-visual attributes, such as date of birth, family name, and so on.]
• "Law of Proximity. Regional or chronological closeness of elements are grouped by our mind and seen as belonging together. [Here, the opposite may be true as mentioned above, namely, 'Same sort of Thing, Different State' may fail to be seen as belonging together ... as with the morning star and the evening star.]
• "Law of Symmetry. Symmetrical images are seen as belonging together regardless of their distance.
• "Law of Continuity. The mind continues a pattern, even after it stops.
• "Law of Common Fate. Elements with the same moving direction are seen as a unit."