Language is often explained as the product of generative rules and a memorized lexicon. For example, most English verbs take a regular past tense suffix (ask-asked), which is applied to new verbs (faxed, wugged), suggesting the mental rule "add -ed to a Verb." Irregular verbs (break-broke, go-went) would be listed in memory. Alternatively, a pattern associator memory (such as a connectionist network) might record all past tense forms and generalize to new ones by similarity; irregular and regular patterns would differ only because of their different numbers of verbs. We present evidence that mental rules are indispensible. A rule concatenates a suffix to a symbol for verbs, so it does not require access to memorized verbs or their sound patterns, but applies as the "default," whenever memory access fails. We find 21 such circumstances for regular past tense formation, including novel, unusual-sounding, and rootless and headless derived words; in every case, people inflect them regularly (explaining quirks like flied out, sabre-tooths, walkmans). Contrary to the connectionist account, these effects are not due to regular words constituting a large majority of vocabulary. The German participle -t applies to a much smaller percentage of verbs than its English counterpart, and the German plural -s applies to a small minority of nouns. But the affixes behave in the language like their English counterparts, as defaults. We corroborate this effect in two experiments eliciting ratings of participle and plural forms of novel German words. Thus default suffixation is not due to numerous regular words reinforcing a pattern in associative memory. Because default cases do not occupy a cohesive similarity space, but do correspond to the range of a symbol, they are evidence for a memory-independent, symbol-concatenating mental operation.