This lead me to reflect on the idea that Buddhist doctrines describe a theory of cause and effect. I've spilt a lot of printer ink debunking the idea that paṭicca-samuppāda is a theory of causation. But the idea is particularly tenacious, and I'm unlikely to be the one that shifts it, partly because Buddhists themselves came to understand it this way. From its beginnings as a way of explaining how the experience of suffering arises, the theory became a general theory of how everything happens - a Theory of Everything. But I've tried to point out that it's not a very good TOE.
Pāli employs a number of synonyms which roughly mean cause or condition (in alphabetical order): upanisā, kāraṇa, ṭhāna, nidāna, nissaya, paccaya, hetu. Let's examine each of these in turn, and then consider them as a whole.
Upanisā (Skt upaniṣad). The dhātu is √sad 'to sit' with the preverbs upa 'near' and ni 'down' (the s is changed to retroflex ṣ by the preceding i); hence the folksy translation 'to sit down near to'. This ignores the way that preverbs work but it conveys certain religious ideas. For example upa-√sad means to 'sit upon, to approach'; while ni√sad means to 'sit down'. A number of other verbs take the upa-ni preverb combination: upa-ni-√gam 'to meet with, fall upon'; upa-ni-√dhā 'to deposit', and later 'to produce, to cause'; upa-ni-√pad 'to lie down beside'; upa-ni-√bandh 'to write, compose; to explain' (from bandh to 'bind'); upa-ni-√yuj 'to tie or join'; upa-ni-√viś 'to lay a foundation' (viś 'to enter). Thus the etymology of the verb suggests that it probably means 'to sit with', or 'to sit on'. This term is mainly used in connection with the so-called Spiral Path, the sequence of progressive conditionality that leads through ethics and meditation to wisdom. The locus classicus is the first five suttas of the chapters of 10 and 11 in the Aṅguttara Nikāya.
Kāraṇa. This word comes from the ubiquitous dhātu √kṛ 'to do, to make'. It derives from the causative form, and thus most closely resembles the English word 'cause'. It broadly takes in all kinds of agency. However it is not frequently used in relation to paṭicca-samuppāda.
Ṭhāna (Skt sthāna) comes from the dhātu √sthā 'to stand, to remain'. This word is used in a variety of literal and figurative senses. One of this is 'grounds for' as in the reason for something, the grounds on which a supposition is based. This term is not really used in outlines of the doctrine of conditionality.
Nidāna comes from the dhātu √dā 'to bind'; with the preverb ni 'down' The word dāna is a past participle thus nidāna is literally 'bound down'. Figuratively the word is used in the sense of basis, foundation.
Nissāya (we expect Skt niśrāya, but in practice this is unknown, and we find niśraya in Buddhist Sanskrit texts) is from the dhātu √śri 'to lean, to resort' and it again adds the preverb ni 'down'. The grammatical form is a gerund (a type of non-finite verb used to indicate actions preceding a main verb) which has become lexicalised, i.e. become a word in its own right. Literally it means 'leaning on; nearby'; and figurative 'by reason of, because of, by means of. A form upanissāya is also mentioned, meaning 'basis, support, foundation'.
Paccaya (Skt pratyaya) like nissāya is a gerund from a verb √i 'to go' with the preverb paṭi (Skt prati) 'towards, back'. The literal meaning is 'going back to' or 'resting on'. We get the word paṭicca (Skt pratītya) meaning 'grounded on, on account of' from the causative form of the same verb.
Finally hetu comes from the dhātu √hi 'to impell' and means 'cause, reason'. Hetu is used in relation to paṭicca-samuppāda in the famous lines spoken by Assaji to Sāriputta which resulted in Sāriputta's awakening:
ye dhammā hetuppabhavā tesaṃ hetuṃ tathāgato āha,
tesañca yo nirodho evaṃ vādī mahāsamaṇo.
Here hetu-ppabhava means 'arising or coming into being (pabhava) with a reason or from a cause (hetu).' Hetu is clearly a synonym of paccaya in Pāli as the two are often used to reinforce each other: "A reason exists, a basis exists for the purification of beings" (atthi hetu, atthi paccayo sattānaṃ visuddhiyā. M i.407). However the question here is whether or not we have free will - whether or not our efforts will bare fruit, or we are at the mercy of fate.
Now interestingly enough the word 'cause' itself is of unknown origin. It is used in Latin, but the etymology stops there. This may mean that the word is not of Indo-European origin. The Classical Latin causari meant "to plead, to debate a question." (OEtD)
I've gone into the etymology of paṭicca-samuppāda at some length. Briefly the word is a complex compound meaning 'arising from a foundation' or 'arisen based on a dependence' - hence dependent arising, conditioned co-production and so on. The choice of words here does not imply causation. On the contrary the metaphor is quite different from that of causation. Here the image evoked is of building up from a base.
We know that another form of the doctrine uses the locative absolute formulation: while x then y; when not-x, then not-y. Now Sanskrit and Pāli are very sensitive to the temporal separation of actions. One of the main uses of the gerund is to tell the reader the sequence of actions separated in time, but connected. We do this with word sequence and implication in English. In Pāli we find constructions like: sa bhagavantaṃ upasamkammati, upasamkamitvā, abhivadeti, abhivadetvā ekamantam nisidati, "He approach the Bhagavan, having approach he greeted him, having greeted him he sat to one side." The gerund form tells us that each action is completed in sequence before the main finite verb 'he sat'. Thus when the Pāli uses the locative absolute indicating simultaneity of being and non-being, this is really quite significant. If this is causation then it only works when the cause is constantly present. This is not like the impulse we give and object when we pust it. Bhikkhu Ñāṇavīra used the image of a house being built: first the foundations, then the walls then the roof. The sequence is necessary - no walls, the roof can't stay up; no foundations and the walls can't stand. The foundations enable the walls to stand, and support them while standing, but we would not ordinarily say that the foundations cause the walls to stand.
The same metaphors apply in the case of the terms nidāna, nissaya, and upanisā. All of these tell us that x is the basis or foundation for y. None of these central terms imply causation. The idea being expressed is that x is a specific condition (idapaccaya) for y; x is a necessary condition for y, and perhaps even a sufficient condition; but x does not cause y. Indeed the aspect of causation is a mystery - how the eye and form give rise to eye-discernment, and how eye-discernment is never discussed. Although the process of craving leading to grasping seems obvious, there is no explanation offer - the theory relies on our experience to make the idea seem plausible. The mechanisms are transparent to the early Buddhists - they see only effects, and necesssary conditions and not see, or at least do not comment on causes. Indeed it is not until the advent of neuroscience in the latter half of the 20th century that any plausible explanation for how desire becomes additction was put forth. A recent (2011), useful description of the state of our knowledge can be found in David J Linden's book Pleasure.
We know that one of the most popular ways of stating the idea of paṭicca-samuppāda is the verses spoken by Assaji to Sāriputta when he suggests that the Tathāgata has spoken of the causes of things that arise from a cause (hetuprabhāva). Now here hetu does mean cause in our sense - as I pointed out it comes from a verb meaing 'to impell'. But I think we have to view this in the broader context outlined above. Just because the word is used here, does not change the bulk of the technical vocabulary. Thus we might be better to translate hetu here as 'reason'.