Thinking About Infinitives in Terms of Formation

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Sometimes it is easier to see patterns when we think in terms of formation before categories like time and aspect. While in the case of infinitives there are some outliers that complicate any attempt to find overarching patterns across paradigms, we can note the following nonetheless.

Thematic Formation

Most verbs are thematic. When it comes to infinitives, this means that they use the theme vowel /ε/ to connect the stem of the verb to the core infinitive marker. In active verbs, that core infinitive marker is /εν:

          ἄγ/ε/εν > ἄγειν (thematic progressive active)
          ἀγ/αγ/έ/εν > ἀγαγεῖν (thematic asigmatic aorist active)
          ἄγ/σ/ε/εν > ἄξειν (thematic future active)

In the middle (and passive, except for the aorist passive), the core infinitive marker is /σθαι:

          ἄγ/ε/σθαι > ἄγεσθαι (thematic progressive middle and passive)
          ἀγ/αγ/έ/σθαι > ἀγαγέσθαι (thematic asigmatic aorist middle)
          ἄγ/σ/ε/σθαι > ἄξεσθαι (thematic future middle)
          ἀγ/θήσ/ε/σθαι > ἀχθήσεσθαι (thematic future passive)

This covers most progressive verbs (except/μι verbs and a few others), most asigmatic aorist verbs in the active and middle (except a few athematic verbs and /μι verbs), and all future verbs.

Athematic Formation

The default athematic infinitive marker is /ναι (a combination of zero-grade /εν and another active infinitive marker /αι). It is used for most athematic infinitives:

          δι/δό/ναι > διδόναι (athematic progressive active)
          βά/ναι > βῆναι (athematic asigmatic aorist active, except for /μι verbs)
          δο/θή/ναι > δοθῆναι (athematic aorist passive)*

* Because the passive voice is marked clearly by /θη/, the aorist passive infinitive uses the default infinitive marker otherwise seen in the active without confusion.

The exceptions are the perfect active infinitive and the aorist active infinitive of /μι verbs. Instead of zero-grade /ναι, they use full grade /έναι:

          δο/έναι > δοῦναι (athematic asigmatic aorist active of /μι verbs)*
          δε/δο/κ/έναι > δεδωκέναι (athematic perfect active)

* While /μι verbs proper (like δο/, θε/, and Jε/) are asigmatic in the aorist, /νυ/μι verbs (like δεικ/) are sigmatic. Thus, the aorist active infinitive of δεικ/ is δεῖξαι.

The athematic middle uses the infinitive marker /σθαι:

          δι/δό/σθαι > διδόσθαι (athematic progressive middle and passive)
          δό/σθαι > δόσθαι (athematic aorist middle)
          δε/δό/σθαι > δεδόσθαι (athematic perfect middle and passive)

Alpha Formation

The sigmatic aorist regularly uses the connecting vowel /α/. Although this technically makes the formation athematic, the active infinitive marker is /αι, not /ναι or /έναι:

          λέγ/σ/αι > λέξαι (sigmatic aorist active)

In the middle, it forms as expected:

          λέγ/σ/α/σθαι > λεξασθαι (sigmatic aorist middle)

Synopsis

The following charts plot infinitive markers as they correspond to aspects and voices. We see that it is only in the aorist active that infinitive markers vary notably:

Progressive (usually thematic, sometimes athematic)

thematic /ειν athematic /ναι

thematic /εσθαι athematic /σθαι

⬅︎ same as middle

Future (always thematic)

/ειν

/εσθαι

/εσθαι

Aorist

sigmatic /αι asigmatic /εῖν athematic /ναι /μι verb /έναι

thematic /εσθαι athematic /σθαι

/ναι

Perfect (always athematic)

/έναι

/σθαι

⬅︎ same as middle