Standard metres
1889: platinum-iridium bar @ 0°C. (an exemplar—an individual object that posseses the target property in the same way that other measured objects posses it; both are of the same ontological kind)
1960: 1,650,763.73 wavelengths in vacuo of orange-red light of Krypton-86 (a pattern—not an individual object, but rather a type-repeatable object/phenomenon that is present in nature and significant in virtue of its relation to ordinary, individual objects)
1983: distance traveled by light in vacuo during 1/299,792,458 sec. (another pattern)
(Compare the 1960 and 1983 definitions to one of the proposed definitions for the kilogram as 2.15 x 10^25 atoms of Si28.)
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Perhaps Plato’s forms are patterns, rather than exemplars. This is strongly suggested by the language at 129a in the Parmenides: “… there is a form, itself by itself, of likeness, and another form, opposite to this, which is just what it is to be unlike.” And, incidentally, our translators render paradeigmata as ‘patterns’ at 132d: “… these forms are like patterns set in nature, and other things resemble them and are likenesses.”
If the pattern interpretation is correct, we might be able to break the Third Man Argument as follows:
Forms are genuine, mind-independent entities; so the form of Largeness is in fact a thing.
Forms are patterns; so the form of Largeness is just what it is to be large. ‘Largeness is large’ is thus understood not to be an instance of ordinary predication; rather, the ‘is’ is what we might call “the essential ‘is’,” such that the form of Largeness is the essence of what it is to be large, and therefore the essence of the largeness present in large things.
Now, recall one of the key inferences in the Third Man:
- There is a thing, the form of largeness, that a, b, and c all share in. [One-Over-Many]
- Largeness is large. [Self-Predication]
- Largeness is a large thing. [1, 2]
This inference will be blocked, because on this interpretation [2] isn’t a predicative statement at all. If we unpack the ‘is’ in the way specified above, we can see that the inference fails:
- There is a thing, the form of largeness, that a, b, and c all share in. [One-Over-Many]
- Largeness is the essence of what it is to be large. [Forms as Patterns]
Largeness is a large thing. [1, 2? No!]
If this inference fails for the reason specified, the vicious, infinite regress never even begins. Socrates/Plato can assert that a single form of Largeness exists, and that it can do its theoretical/explanatory work without invoking a numerically-distinct form of Largeness*.