Question in Short:
Why is it that the terms valuable and invaluable mean almost the same thing while the terms famous and infamous are almost semantically opposite in meaning? That is, one is used to describe something/someone well known for their good qualities, while the other is used to describe something/someone well known for their bad qualities?
Question in Detail:
One of the answers to the question titled Difference between “valuable” and “invaluable” [closed] suggest that the term valuable is almost synonymous with invaluable, although the preferred answer points out their subtle differences as being costly and priceless, respectively. That is, something that can be bought or sold (valuable), as opposed to something that cannot be bought or sold (invaluable), yet is treasured.
Why is it that the terms famous and infamous are not semantically synonymous according to these online references?
Best Answer
The prefix does its job faithfully regardless of the ultimate result of connotation or implication. Some explanation may be in order.
in-: prefix denoting 'not'.
∴
in + famous → not famous
&
in + valuable → not valuable (Patience!)
fame: good reputation; famous: widely known for something good;
infamy bad reputation; infamous: widely known for something bad. – Naturally?
value (n): worth;
(to) value (v): to estimate the worth of;
valuable: that whose worth can be estimated;
invaluable: that whose worth can not be estimated; too valuable.
It all adds up nicely.
The prefix modifies in a mechanical way here, while the meaning on the other hand, depends on the nature of the word, its original implication, even its etymology and usage. Even not valuable can be understood in the right context to mean something that cannot be valued (not value+able).