# Amateur Topologist

#### Everything but topology.

Tag: optimality theory

# Opti-Fucking-Mality Theory, Part 2

In my previous post, I gave a basic explanation of optimality theory as it relates to the phenomenon of expletive infixation. At the end, I mentioned that the word laser is not infixable; I know of no speakers who would accept *la-fucking-ser. While we can state that ‘there are these rules that must be satisfied in order for infixation to be possible’, it’s better to continue to work within the optimality theory-based framework. So to do this, we introduce another rule, Infix, which corresponds to ‘there is an actual infix presented in the word.’ Right away, we see that the existence of pre-fucking-view implies that Infix is more important than Clash; in the notation of optimality theory, this is written as Infix >> Clash. Further, since we cannot have *pre-fucking-view, IP >> Clash.

But this doesn’t address the central problem: *la-fucking-ser, despite not violating any of these rules, is unattested. This, as it turns out, is because Clash is fundamentally the wrong rule. An even better illustration, that Clash cannot be the rule we’re looking for, lies in the word-pair unbelievable and irresponsible. They both have identical stress patters (a trochee followed by a dactyl). However, they don’t have the same infix patterns: un-fucking-believable, but not *ir-fucking-responsible. No rule based only on stress patterns can account for this difference. It helps to gather a table of prefixed words:

unbelievable irresponsible
antebellum irreconcilable
cryogenics florist
overdrive malodour

The fundamental common characteristic is that in the infixable words, the syllable boundary between the prefix and the root word is ‘strong’ in some sense; it’s easy to state that the boundary in unbe- is between the /n/ and the /b/. On the other hand, in irre-, there’s confusion: is the boundary between the two /r/s? Is it between the second /r/ and the /e/? In more formal terms, the /ən.bə/ syllable juncture is considered strong, whereas the /ɪr.rə/ juncture is weak. This same pattern extends to all the other words, and so we delete Clash and create a new rule, Strong, which states that the infix must fall at a strong syllable juncture. So we see that the table for irreducible predicts infixation between /rə/ and /’duː/:

IP RP Strong irre-fucking-sponsible irresponsible *! ir-fucking-responsible *!

By contrast, for unbelievable, we have:

IP RP un-fucking-believable unbe-fucking-lievable unbelievable *

Much like the intuitive explanations for IP and RP, we can come up with an intuitive explanation for Strong: an infix inside a weak syllable boundary would be more like an infix inside a syllable, which is invalid; we can even see that Clash falls out as a special case when dominated by RP; a stressed-unstressed syllable juncture (as in /leɪ.sər/ vs. /leɪs.ər/) is typically a weak juncture; an infixation into stressed-stressed syllable junctures would violate Clash, but unstressing the former syllable would violate RP.

There is, however, one phenomenon we can’t account for: despite the fact that I pronounce undo undo, I only have un-fucking-do, not *un-fucking-do. There are two explanations for this, but one of them also predicts extraneous forms; giving the two explanations, as well as showing why one is wrong, will be the subject of the final part.

# Opti-Fucking-Mality Theory, Part 1

Expletive infixation (meaning the process by which you get words like ‘un-fucking-believable’, ‘irre-fucking-futable’, and yes, ‘opti-fucking-mality’) is traditionally explained based on a rule which involves the prosody (i.e., the lyrical structure) of the word. But the usual theory, which was first given by John McCarthy in his “Prosodic Structure and Expletive Infixation” is rather inadequate. It’s consistent with all of the data it provides, but it fails to give an explanation of one key phenomenon: when the word ‘destroy’ is infixed as ‘de-fucking-stroy’, the ‘de-’ becomes stressed, and the vowel lengthens from ‘deh’ into ‘dee’. Since the prosodic hypothesis states that the structure, so to speak, of the root word isn’t modified by the infix, this is hard to explain, especially since the change from ‘ih’ to ‘ee’, or [ɪ] to [iː] (see here for a chart of IPA tables) isn’t necessarily produced by stress. So another alternative is desirable.

Enter optimality theory. According to optimality theory (or OT), we can come up with a certain set of rules and a ranking for them; the valid infixation (or infixations) whose first rule violation is lower-ranked than any other infixed forms. Since some words, such as laser,cannot be infixed, the statement that ‘there must be an infixed word’ must also be a rule in and of itself, which can be violated. So let’s set up a few base rules:

• IP: The pronunciation of the infix word is preserved.
• RP: The pronunciation of the root word is preserved.
• Clash: There are no two adjacent stressed syllables.

I left out the Infix rule; we’ll come back to it later. Let’s take a look at a sample word, kindergarten (using bold for stress).

IP RP Clash kinder-fucking-garten kin-fucking-dergarten *! kin-fucking-dergarten *!

What this means is that only the first form, kinder-fucking-garten has no violatins of any rules. The other two violate one rule each; the ! indicates that each violation is the ‘first’, or highest-priority one. The two light-gray cells in the bottom row indicate that, for purposes of comparing fitness, those cells are irrelevant; in optimality theory, only the first violation is relevant.

Of course, this isn’t terribly useful for figuring out the actual rankings of constraints, and rankings are relevant; moreover, there are a few rules that haven’t been introduced yet that cannot be violated: as an example, *la-fucking-ser, despite not violating any of these rules, is not considered acceptable by the majority of English speakers. So what do we do?