FORMAL / LOGICAL SYSTEMS
An analogy takes the form of an informal comparison of
opposites, in which opposites are compared directly.
For example, "Cat: Mouse :: Dog : Cat"
Reads: "Cat is to mouse just as dog is to cat".
Cat and mouse are informal opposites, and so are dog and cat.
Furthermore, each opposite pair must have a certain express
relationship, and the relationship must be of the same character
for the overall comparison to qualify as an analogy.
So, for example, although we might assume this works:
"Mouse : Dog :: Large cat : Small cat" in fact this doesn't work,
because the cats might be friends, or the dog might not attack
mice like cats do.
In general, analogies are limited by what I call 'modal'
relationships. That is, they 'just happen to be the case' therefore,
they do not have universal significance.
We cannot say, for example, that a hateful dog loves cats, even
though we can say that hate is the opposite of love, and dog is the
MODAL opposite of cats. This terminology was developed later
by Nathan Coppedge to explain the difference between analogies
and categorical deductions. Categorical deductions, by contrast,
DO CLAIM universality.
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