In natural sciences, the key criterion for proving the existence of an object (like a physical particle of a previously unknown kind, an atom of a previously unknown element or an organism of a previously unknown species) is its observation and/or observation of traces of the existence of this object (radiation, remains of vital activity etc.). Only objects that meet this criterion can be classified (e.g. entered in the periodic table of elements or described as a species). Single unknown organisms or species cannot enter the classification. Despite this, the current system of phylogenetic terms (holo-/monophyly, paraphyly, and polyphyly as they are currently defined) is not adapted to the separation of known and unknown organisms (as well as populations, species, etc.) including ancestral ones. There are longstanding confusion and controversy regarding these “phyletic states”. There seem only two ways in such a situation. The first way is to somehow directly include unknown ancestors in taxa, describe species for them and unavoidably to introduce at least one paraphyletic subtaxon during dividing each taxon. The second way is do not include unknown ancestors in taxa directly and amend the system of concepts and terms. Here the second way was followed and the possible definitions of the main phylogenetic concepts for the views of dealing only with known group members were proposed. Inability to provide a concise definition of holophyly using the existing terms indicates the lack of more basic concepts. These concepts were also proposed here and holophyly was defined using them near the end of the paper. The intersection of four basic “phyly” (enophyly, merophyly, kollitophyly, and schizophyly) results in the unambiguous triad of holophyly, paraphyly, and schizophyly. The definitions of the terms in this triad are believed to be unambiguous unlike the widespread definitions of holo-(mono-), para- and “polyphyly”. Here, many terms were defined using others in order not to make the definitions too cumbersome. Nevertheless, the “primary phyly” seem not less useful in phylogenetic discussions than the phyly of the triad. So also is the terms inprestor, rendestor, ancessure, drade and skade as well as the more precisely defined term clade. The first two terms seem to be necessary and important regardless of the views on the classification of unknown organisms.