Thank you Andrew for a very considerate reply. What you say

But what Paul is talking about, surely, is the nature of God: the ‘visible’ things that have been made reveal something of, help us to understand or grasp, the ‘unseen things’ of God, namely his ‘everlasting power and deity’ - in other words, that he cannot be adequately represented by manufactured objects. Those who worship idols are without excuse because ‘although they knew God, they did not honor him as God or give thanks to him’ (1:21 ESV). 

 does raise another issue which I also thought about whilst considering this passage, namely that of the universal applicability of Paul’s argument. I first thought of it in the homosexuality context: the principal argument of the pro-homosexuals is that the context is culturally limited. I would not argue that there are no valid points in favour of the homosexual camp here but I would argue that this at least is not one of them. Because if it is, then it is not possible (for either Paul or the modern orthodox theologian) to make a case that all men have fallen short of God’s glory on the basis that they all knew he existed and were aware of his attributes.

The same applies here: if Paul’s message is that those who knew god existed but refused to recognise his divine attributes are without excuse, then this says nothing about those who had no belief in god at all. It almost even exonerates them. But I also think that Paul would hardly have done the same, that he would be thoughtless enough to believe that the world only consisted of those in his personal cultural experience. That is why I think he is not making a generalisation at all. He is giving his own experiences of what the preaching of the Gospel does. 

The other thing I would say in reply is that the same cautions arise whether we talk of God’s existence or his attributes. I just don’t see how you can look at creation and even if you already believe God exists, be able to have some knowledge of his character merely by looking at what you see around you. It is simply too subjective. I certainly wouldn’t blame you for thinking that God was ephemeral given how many things appear to naturally decay (taking a Platonist perspective) and I wouldn’t blame you for thinking he was a merely a principle of randomness (taking a moden evolutionary perspective) as examples.

This does raise other questions and I am sure you or another will think of some obvious ones! 

But I am not troubled by the fact that I may not understand the point Paul was trying to make.

I agree. As would the apostle Peter. However I am troubled by the fact that so many understandings (as recorded in translations and commentaries) are plainly nonsensical. Calvin was one fo the worst at this in my view, even making black white and white black, for example in his commentary on Rom 9:10-18. Unfortunately his interpretation has become standard fare for Christians the world over and they believe it in the main unquestioningly because a) it is ingrained in the culture anyway such that there is no alternative available, b) because it gives them a sense of self-righteousness, as I explained before and c) because it arouses mystery due to its plain nonsensical nature.

I would point out, though, that Calvin was only developing Catholic theology inherited from Augustine, which in turn was inherited from Plato (and the neo-Platonists). I would argue that the so called emergent church needs to emerge not only from evangelicalism but from many other forms of orthodoxy too. The reason I guess why the issue of evangelicalism is to the fore now in terms of the emerging church being specifically a reaction against it, is that much of the credal positions adopted by modern evangelicals were the response (in my view) to liberal currents in theology and these credal stances became much too dogmatic and authoritarian; and in polarising themselves, they have both lost important aspects of Christian character. One of the tasks of an emerging church should surely be to allay the fears amongst evangelicals of liberalism and that there are indeed some good points to be drawn out of that.

Thanks Sam, that was an interesting comment on the thread you linked.

 One slight technical issue:

 The word ποίησις is not the same as ποίημα. The former is a more abstract noun whereas the latter, as used here in Romans, is quite concrete.

Upon reflection, and after considering some of the comments to my original post, I think rather than be specific about ποίημα referring to the Gospel, I would translate it as "special works" hence ‘what are invisible in his nature from the creation of the world become visible when considered through his special works.’ That leaves open whether this is a specifically Israel related thing or not.

I did briefly consider if Paul was quoting someone else but you will perhaps agree that this is unnecessary a position to adopt (given that it is rather lacking in evidence) when taken with 2:14, would give a similar result. Let me then explain what I mean in reference to 2:14f;

The KJV has this as the translation:

14For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves: 15Which shew the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another;)

Now even Cranfield thinks that this is wrong. In the Greek text, the ‘by nature’ appears directly between "which have not the law" and "do the things of the law". thus

14οταν γαρ εθνη τα μη νομον εχοντα φυσει τα του νομου ποιωσιν ουτοι νομον μη εχοντες εαυτοις εισιν νομος

    15οιτινες ενδεικνυνται το εργον του νομου γραπτον εν ταις καρδιαις αυτων συμμαρτυρουσης αυτων της συνειδησεως και μεταξυ αλληλων των λογισμων κατηγορουντων η και απολογουμενων 

(I’ve underlined the two arms of the phrase and you can see φυσει (by nature) directly in between the two)

 hence could apply to either of those ideas. However, the KJV and many other translations leave no room for ambiguity here. See how it places the ‘by nature’ after the word ‘do’, which makes it impossible for the English reader to read the other side of the ambiguity:

"For when the Gentiles which by nature have not the law, do the things of the law…"

You need to think carefully about what this could mean. The KJV version (which is the version taught in most orthodox and evangelical churches) argues that Gentiles do not need the law because they have the law written on their hearts, whereas the Jews (somehow!) didn’t have the law written on their hearts and needed a written law to keep them in decent moral order.

Aside from the obvious and indeed grotesque anti-semitic implication here, the KJV translation also relies on what I think is a serious translation / cultural error that frequently appears elsewhere and particularly in Calvin. It is this: "written on the heart" does not mean  "there by instinct" but rather "wilfully and knowledgeably committed to". Thus the correct (in my view) translation of this passage is

For when Gentiles, who are born without the law of Moses, do the things which the law requires, even though without the law, they are their own law, i.e. those who show that they have committed themselves willingly to the law and so their consciences bear witness of their various intentions, whether to render them culpable or to exonerate them…

Paul is obviously speaking of proselytes here and this lays open to question who the epistle is addressed to in the first place: Jew first and also Greek. But the letter is surely addressed to the entire Christian community in Rome, therefore it makes sense to suppose that Paul is distinguishing between the Jewish Christians and the Gentile (proselyte) Christians. The criticism is therefore either against the Jewish sector of the believers or against the implied Jewish community as a whole. This is made completely explicit in 2:17ff. The meaning of the latter part of ch. 1 is therefore more logically:

"We know" (referring to the identity of Jews as being teachers of the world and advocates of God’s true wisdom - see 2:18f) that God’s justice is visited on all forms of unrighteousness, etc., etc, but be careful because you Jews in particular are equally guilty and you won’t get away with it just for being Jews.

And then, coming back to ποίημα, this would relate, assuming the validity of the above reasoning, only to those who were aware of God’s special works, in this case the Jews.