If we include base-extenders (stem-extenders_ as some kind of near-morph or submorph, then a root is that part of a word from which all affixes and stem-extenders have been removed. A root differs partially from a stem in that a stem must have lexical meaning. A root has no lexical meaning and the semantic range of the root is vague if there is any at all. A stem may contain derivational affixes.
Consider the verb defer. There is no verb stem *fer. Fer is a verbal root. It is found in refer, infer, prefer, differ, prefer, offer. The forms to the left of -fer are prefixes which cannot occur in isolation. Even these prefixes do not have a fixed lexical meaning. In a tree structured form, these verbs are composed of a prefix and a root. Together this forms a stem; the category is inherent in the stem:
The structure for See stup-id, stup-our, stup-end-ous, stup-if-y.a), for example, is the following:
We have named the new structure an `A-stem' for adjective stem. In the more common practice of creating new structures from the bottom up, the category of the head is usually copied upward. If that were the case here, we would have to call the root an A-root. It is not clear that the root has any features that imply a category. The root easily feeds the seven adjectives in See stup-id, stup-our, stup-end-ous, stup-if-y.) with the common suffix `-id' forming an adjective. It is the suffix that has the adjective forming property. Note that `-our' forms nouns, and `-ify' and `-ate' form verbs. It is simpler and less messy to assume that the root has no categorical property, though this assumption could be wrong.
We look for bases from bottom up. Start with the root; to do so removed what you think are the affixes. If you ripped off re-, -er-, +at, and +or, you did well. The root is `frig'. We find this root in frigid, But *frig-er is not a word. It has no lexical meaning; therefore, it cannot be a stem. It must be a base. Note that whereas `frig' is a root and a base, `frig-er' is a base, but it is not a root. It is not a stem since it has no lexical meaning.
See two dogs.b) could be wrong for two reasons. The first is dog is not marked for number (singular vs. plural). The second is that dog is interpreted as singular, in which case grammatical agreement does not apply.
See John plays everyday..b) needs a suffix--either `s' to mark the present tense or `ed' to mark the past tense. See John plays everyday..c) has a suffix but it is the wrong one. The time adverbial `now' requires the present, not the past tense. It is the grammar of English that required this. Sometime a particular form is phonetically missing. This could mark a construction where the form is not required. However, we don't find this in simple verbs. An example would be the following:
All three sentences are nearly synonymous. The lion in See The lioness challenged her mate..c) can only be interpreted as female when the pronominal `her' refers to the lion. Otherwise, it does not. The adjective female in See The lioness challenged her mate..b) ensures that the lion must be female, as is the case n See The lioness challenged her mate..a). The grammar does not require the use of a female form in See The lioness challenged her mate..). It is inserted if the speaker wants to include this information that is to be transmitted to the hearer.
There is some reason to believe that agreement might mark the end of a word, but this is far too speculative to discuss here. Clitics are adjoined to the end of a word, and they appear to be adjoined to words whose final morpheme is agreement.
Because of forms such as "sip-id", we see that derivational affixes are added to bases. Derivational affixes may change the lexical meaning associated with the lexical stem = base which underlies derived base=stem: hand ¯ hand+y. The latter means useful now, it doesn't refer directly to a hand, but it is derived from `hand.' Derivational affixes often change the category of the base=stem to which they are adjoined: move = verb, move+ment = noun. Sometimes they can do both: heal = verb, heal+th = noun. Here, `health' no longer refers to `healing (something)' but to one's physical or mental well-being. Sometimes it appears that a derivational suffix is added directly to a stem (lexeme): warm, warm+ly. We find it desirable to keep the pattern of derivation simple, that is, derivational affixes are added to bases, The lexical meaning is obtained from the lexicon, the vocabulary of the speaker. In words such as adverbs derived adjectives, it is best to say the warm+ly is derived from the stem "warm," The adverb is then said to inherit the lexical meaning of the stem equivalent to the base:
In See swift: root = base = stem "quick".b) the brackets enclose the underlying root=base=stem "quick"; then `ly' is adjoined to the underlying base, which makes a new stem, inheriting its meaning from the underlying stem. I will now put See swift: root = base = stem "quick".b) into a tree structure: