In turning from the considerations with consequentialism in the last posting to intuitionism in this I am not sure that we are making a move that at all parallels that supposed to hold between deontological and teleological theories of ethics. If consequentialism is broadly something one can define as holding that criteria of the rightness or goodness of an action consists in the consequences it produces then, for intuitionism to be a counter to this, it would have to be premised on some other criteria than consequences. However, intuitionism does not start out, in any variant of its claim, in this way. Rather, intuitionism is set out in the first instance as a kind of claim concerning the nature of our understanding of moral principles, not, first of all, as a view concerning the way in which such principles should be understood as determining our sense of what it is that is "right" or "good". So intuitionism is motivated by quite a different type of concern to consequentialism.
However, this first point should not obscure the kind of way that the understanding of moral principles connects to a description of what kinds of principles are justifiable so this second point does link to an account of what kinds of principles we should adopt. Both these points are joined into relationship with each other by reference to what are termed "intuitions". Intuitions, in the basic normative sense, are, apparently, what underpin our normal convictions concerning what is right or what should be done. Whilst there are arguments for holding that the notion of intuitionism was held widely amongst Scottish philosophers in the 18th century the formulation and understanding of it that seems to have first put it on the map of contemporary moral theory is the one that was set out by Henry Sidgwick in his major work The Methods of Ethics. This work is one that has received a considerable revival of interest in recent years, perhaps partly because of its importance for John Rawls (although Rawls has a very peculiar relation to Sidgwick since Sidgwick's book is intended as a sophisticated argument for utilitarianism).
Sidgwick here presents intuitionism (along with hedonistic utilitarianism and egoism) as one of the three main methods for arriving at a systematic view of morality and he presents intuitionism as integral to comprehending the morality of "common sense" (in this implying a connection to Scottish common sense philosophy although he does not draw this connection out). Sidgwick characterizes intuitionism in different ways. Initially he describes this as a view of ethics that "regards as the practically ultimate end of moral actions their conformity to certain rules or dictates of Duty unconditionally prescribed" (96) which appears to align it with the view Broad later termed "deontological". However, alongside this normative conception of it Sidgwick also puts a general conception of the claim to possess "intuitions" as some kind of moral knowledge which is related by him to the possession of certain kinds of immediate judgment (in alignment with the notion of "intuition" elaborated by Descartes).
This epistemic sense of intuition is related in the first instance to an emphasis on particulars (as in the notion of act-deontology that Broad mentions) and can thus, in a sense, converge with a form of situation ethics as a normative theory. However, least that be thought to be sufficient to describe the relation between the normative and the epistemic items Sidgwick goes on to characterize intuitionism as inclusive of a second method that brings in general rules (like rule-deontology). On this conception the general rules are held in implicit form in the reasonings of ordinary men and the task of the moral philosopher is to bring them to light and state them with precision. This kind of conception of intuitionism might be thought also to have some relationship with the emphasis on common morality that Kant sets out in the first part of the Groundwork. This point is not made by Sidgwick but has been suggested by some contemporary Kantians.
However there is added to these first two forms of intuitionism a third kind in which the task of the moral philosopher is expanded so that s/he does not just uncover the moral principles of common sense and state them in a newly precise form but also arrives at some general underlying basis to these principles that common sense itself would not have suspected (a bit like the move then from the first to the second parts of the Groundwork).
However to all these points there is subsequently added a further point by Sidgwick who suggests that intuitionism is committed to pluralism concerning value since it recognises intrinsically different and not necessarily compatible notions of the "good" and hence requires some procedure for offering lexical ordering of them (as in Rawls' discussion of the priority of the right over the good and his many other lexical orderings like that of liberty over equality). When we bring all these features together it becomes clearer that what has been discussed as "deontology" by contemporary moral philosophers has quite a background in intuitionism. Given this surprising congruence I propose to examine in more depth in further postings the position(s) that have been proclaimed as intuitionist in 20th and 21st century moral theory in order to see whether the developments in its understanding can be of further help in clarifying the status of the claims made by those who assert that there is some sense to describing Kantian ethics as deontological.