Final answer:
We specify 'dominant' or 'recessive' for homozygous organisms to indicate which type of allele they carry in two copies, unlike heterozygous organisms, which carry both and express the dominant allele's phenotype.
Step-by-step explanation:
When discussing homozygous and heterozygous organisms, specifying 'dominant' or 'recessive' is necessary for homozygous organisms to convey which allele is present in two copies. For example, when an individual is homozygous dominant (TT), it means both alleles for a particular gene are dominant. Conversely, if an individual is homozygous recessive (tt), both alleles are recessive. This specification is necessary because the phenotype depends on whether the dominant or recessive allele is present in a double dose. In contrast, a heterozygous individual (Tt) has one dominant and one recessive allele. Since the dominant trait masks the recessive one, there is no need to specify 'dominant' or 'recessive' in this case as the phenotype will be determined by the dominant allele.
The Law of Dominance helps to explain this occurrence, where dominant alleles mask the effects of recessive alleles in heterozygous pairings. As a result, heterozygous organisms will manifest the same phenotype as homozygous dominant individuals, while the recessive trait is only visible in homozygous recessive individuals.