What theory was that organisms can modify their bodies through the use or disuse of parts and that these modifications can be passed on to their offspring?

Answer 1

Epigenetics

Answer

While epigenetics explains the alternations of phenotypes due to environmental factors or epigenetic inheritance, I believe the answer needed here has to do with evolution, specifically Lamarck's ideas.

Lamarck devised the hypothesis of "use and disuse" which postulates that the extreme use of a trait or characteristic will result in it getting longer, stronger, more numerous, etc (depending on the characteristic). It also says that characteristics that are not used (disused) will get smaller, weaker, less numerous, etc and eventually disappear. While Lamarck was correct when he linked the phenotype of an organism to its environment, his proposed mechanisms of evolution (use and disuse & inheritance of acquired characteristics) are not accepted today.

Answer 2

This theory is known as Lamarckism, proposed by Jean-Baptiste Lamarck. It suggests that organisms can acquire traits during their lifetime through use or disuse of certain parts, and pass on these acquired traits to their offspring. However, this concept has been largely discredited in modern Biology, as traits acquired during an individual's lifetime are not inherited by offspring according to the principles of classical genetics.