He would simply go to a chart that listed the geologic column by ‘ages’ and find the place where the index fossil appears, and thereby the geologists could tell the paleontologist how old his fossil was.
If it sounds like circular reasoning, it is because this process in reality is based upon circular reasoning.
The question should be whether or not carbon-14 can be used to date any artifacts at all? There are a few categories of artifacts that can be dated using carbon-14; however, they cannot be more 50,000 years old.
The object's approximate age can then be figured out using the known rate of decay of the isotope.
For organic materials, the comparison is between the current ratio of a radioactive isotope to a stable isotope of the same element and the known ratio of the two isotopes in living organisms.
If one knows how much of this radioactive material was present initially in the object (by determining how much of the material has decayed), and one knows the half-life of the material, one can deduce the age of the object.
Carbon dating is used to determine the age of biological artifacts up to 50,000 years old.
Other methods scientists use include counting rock layers and tree rings.
When scientists first began to compare carbon dating data to data from tree rings, they found carbon dating provided "too-young" estimates of artifact age.
Also, many fossils are contaminated with carbon from the environment during collection or preservation procedures.
Scientists attempt to check the accuracy of carbon dating by comparing carbon dating data to data from other dating methods.
These artifacts have gone through many carbon-14 half-lives, and the amount of carbon-14 remaining in them is miniscule and very difficult to detect.
Carbon dating cannot be used on most fossils, not only because they are almost always allegedly too old, but also because they rarely contain the original carbon of the organism that has been fossilized.
All dating methods that support this theory are embraced, while any evidence to the contrary, e.g. Prior to radiometric dating, evolution scientists used index fossils a.k.a. A paleontologist would take the discovered fossil to a geologist who would ask the paleontologist what other fossils (searching for an index fossil) were found near their discovery.