I wrote an email to my potential advisor, politely declining an offer for a PhD position. And he has replied saying that he's sad to hear that, and asking if there's anything he can do to convince me otherwise. How do I reply to this?
I would just reply that you thank him for his interest but that it isn't possible to work together at this time. But suggest that you would be honored/happy to stay in contact for the future if your fields of interest intersect.
Over the long run you want to build up a set of contacts like this and you have an opportunity to start it. He might be a future source of advice on your research or your career. But such contacts need to be nurtured.
I would, however, hold off on such a reply until you have a firm and accepted position elsewhere.
First, tell no lies. Second, thank the professor for their vote of confidence in your ability. Be gracious.
If you are accepting a placement with another advisor or at another institution then say so. You need not provide any reasons justifying your decision. Simply be polite and state the bare minimum required to convey your situation.
If you have chosen not to pursue a degree at this time then say that. Again, you need not justify this decision. Just say that you are not pursuing this any further for the time being.
Brevity and courtesy are your allies here.
There is nothing out of the ordinary here - they made an offer, you declined, they inquire if there is anything they could do to change your mind (presumably you did not provide a concrete reason for declining, otherwise they would have probably made an offer that potentially changes this reasoning or, if that's not possible, wouldn't even have asked).
How to go forward is completely up to you: If you declined for a reason that can potentially be fixed (most importantly if another university made a better funded offer) you can let them know and see what happens - but you are also completely in your right to not tell them and just go forward with another option. In this case I recommend phrasing your answer politely but generically (e.g., "Other position was a better fit for my research interests.").
I would recommend the latter option particularly if your actual reason may be offending, such as because you went for a higher-status university or because you did not find the project exciting. If your reason is rather neutral but cannot realistically be changed (e.g., you would prefer to move to city / country A rather than B, your spouse likes the other place better, etc.), you can just let them know truthfully - no reasonable person should think less of you because of this.
Well, he wanted to have you and is trying to find out whether there is any condition that he may change to convince you otherwise (e.g. pay, conditions or something else).
If there isn't way to convince you, then you can simply make clear that you made up your mind to pursue some other option, and, if you wish to be more specific, you could say what you decided: to change location/take up a PhD somewhere else/go to industry/become a stay-home father or just state that you have decided not to pursue a PhD at this time, whatever of these is the case.
Of course, you should not invent a non-existing reason, but this should go without saying.
There are basically two scenario's here. The professor still has an open PhD position, and you're not going to take it. That means he'll have to find someone else. But why didn't you accept that position? Was that purely because of reasons that are particular to you? If so, tell the professor. That means he might have more luck with the next candidate.
But if the offer was structurally lacking in some respect, and the professor might be in a position to change that, then it's fair to let him know. It won't affect you, since you already declined. But you're helping both the professor and his future PhD student.
In addition to the suggestions in other answers, you might consider suggesting some collaboration without and independently of being his Ph.D. candidate. Perhaps suggest a visit. If you're super-interested in what he's doing, maybe co-advisorship might be relevant. Of course - you might not be interested and then it's not relevant. I'm just saying that interaction/affiliation with a senior researcher is not a binary "nothing" vs "I'm with him" choice.
Another point is - maybe there is something he could do to convince you:
- He might be able to offer something you don't know is possible (e.g. in terms of payment, equipment, undergrads/M.Sc. students who could assist you, or other benefits I haven't thought of).
- You might be making an assumption that's invalid about your chosen position, which he could disavow you of. Now, this is trickier, because he's obviously biased, but it's not impossible. I mean, people do sometimes choose Ph.D. positions based on such assumptions.
So if you like him / his research group enough to be open to such arguments, perhaps don't dismiss this opportunity and offer, say, an audio chat to discuss this, in which you would be more forthcoming about how you made your decision and he will make his "pitch".