Where did prefix exceptions originate?

Consider the following words:

• inflammable
• invaluable

Each of these has the unusual property that its meaning is identical to its counterpart lacking the prefix. In almost all other cases, the prefix in- means "not".

Where did such exceptions originate and what are some other examples of such exceptions?

Solution 1:

"Inflammable" is derived from the verb inflame, which comes from in- and flame. The OED identifies the prefix as in-², indicating the second definition of the prefix, rather than the third, which is the negation which is what you believed it to be from. I quote the right definition below:

used in combination with verbs or their derivatives, [...] with the senses ‘into, in, within; on, upon; towards, against’, sometimes expressing onward motion or continuance, [...] . (emphasis mine)

To inflame something is to set it on fire–i.e. to use motion to cause something to be in flames.

"Invaluable" does come from in- expressing negation, and thus it means not able to be valued. However, this can be interpreted two different ways—one, it is so worthless that it has no value, or two, it is so valuable that we can not put a value on it—like the concept of there being no finite number that is larger than the rest—you can always add one. The common meaning is #2, but the OED recognizes both definitions.

Neither of these examples are exceptions—the first is misleading because the two prefixes look identical, the second can be understood in two separate ways. The best way to figure these out—have a good dictionary at hand.

Solution 2:

The word 'value' has multiple meanings. One is a sense of the goodness or quality or worth or cost of the item; the other is the description of that goodness or quality or cost or worth. So when something is valuable that means it has value, but when something is invaluable it means you can't describe its value.

Generally, when people say invaluable, they mean that it is of such high value (worth) that they cannot assign a value (price or description of worth) to it, because there is no way to describe such an extreme level of value (worth). Of course, it can also mean something is so worthless that its value (description of worth) is indescribably low.

Which brings to mind other related words: priceless and worthless. They look like synonyms, but priceless means invaluable, whereas worthless means not valuable.