How to Classify Varieties of Consequence

Göran Sundholm is well-known for his insistence that logic, to be pursued properly, requires a rich conceptual framework that in current logical theories is often, unfortunately, encountered in an essentially impoverished form. One of the conceptual distinctions he has been constantly urging is that between the various senses of consequence. I agree that logic needs a rich conceptual framework, and that especially with respect to consequence many crucial distinctions must be maintained. However, these for me are not quite the same as those urged by Göran (at least not obviously so), and in this paper I explain which I think the distinctions should be and why they are crucial. This, I hope, may lead to comparing notes with Göran; which, I believe, may yield some interesting results.