Here are my ideological Turing test results of your comment:
People usually use the word intuition to refer to vague impressions that are not amenable to the same sort of justification as deliberative judgments, so these are different from the example that you provided of quickly inventing a deliberative rule and making errors in the process. This makes the purported counterexample less persuasive to me than you seem to expect it to be. Evaluate this comment in the context that we both still anticipate the same experiences, so this is likely a disagreement over word usage, and not likely to be highly significant.
I think this is a very productive criticism. I feel emphasis in italics makes it easier for me to write because it makes it more similar to the way that I speak, so please don't interpret them as aggressive. The way my mind goes down this path is thus:
I have to make the qualification that I don't believe that intuitions are vague feelings that cannot be justified, but vague feelings that have not been justified. There is always some fact of the matter as to whether or not it is, in some sense. But once again, probably something we would consider as disagreeing about word usage. But I think it's an important boundary to draw. From Evans (2006):
If intuition means based on feelings without access to explicit reasoning, then that sounds like a type 1 process. But in some applications it seems to mean naïve judgement, which could be based on explicit rules or heuristics that occur to an untrained judge, in which case they would be type 2.
People often use the phrase 'intuition' to refer to confident beliefs retrieved from cached memory, and the idea is that when you go wrong, it's because intuitions are unreliable. I'm getting at the possibility that that's what people say, but it's not the whole picture.
Say that you're a judge on Pop Idol or something like that, and you have no experience doing it, and you want to quickly come up with a rule, and you retrieved the reliable intuition that pop idols are usually very physically attractive, and then invented a deliberative rule that used your subjective rating of each candidate's physical attractiveness as a measure for evaluating their general Pop Idol factor, and suppose that physical attractiveness actually does not correlate perfectly with the true general Pop Idol factor. Then you would have begun with a reliable intuition and put it into an unreliable deliberative process and obtained an 'unreliable' result in the sense that it does not optimize for the purported normative criterion of Pop Idol judgment panels, which is the selection of the best Pop Idol; you would have picked the most attractive candidate instead, and you would have made a mistake on a higher level than using an unreliable intuition: you would have combined reliable intuitions in a deliberative but unreliable way. This is closely related to the 'System 1 is fast, System 2 is slow' distinction. Reasoning that looks like fast, unreliable intuitive reasoning can really just be fast, unreliable deliberative reasoning. So the main point is not about saying that there are a lot of counterexamples to 'intuitive' reasoning being System 1, but that if you want to do real work the category 'intuitive' won't cut it, because it's still a leaky generalization, even if it isn't that leaky. Does that all make sense?
I liked your rephrasing of my comment. :) I felt that it was an accurate summary of what I meant.
I believe that we're in agreement about everything.
(This is mostly a summary of Evans (2012); the fifth misconception mentioned is original research, although I have high confidence in it.)
It seems that dual process theories of reasoning are often underspecified, so I will review some common misconceptions about these theories in order to ensure that everyone's beliefs about them are compatible. Briefly, the key distinction (and it seems, the distinction that implies the fewest assumptions) is the amount of demand that a given process places on working memory.
(And if you imagine what you actually use working memory for, then a consequence of this is that Type 2 processing always has a quality of 'cognitive decoupling' or 'counterfactual reasoning' or 'imagining of ways that things could be different', dynamically changing representations that remain static in Type 1 processing; the difference between a cached and non-cached thought, if you will. When you are transforming a Rubik's cube in working memory so that you don't have to transform it physically, this is an example of the kind of thing that I'm talking about from the outside.)
The first common confusion is that Type 1 and Type 2 refer to specific algorithms or systems within the human brain. It is a much stronger proposition, and not a widely accepted one, to assert that the two types of cognition refer to particular systems or algorithms within the human brain, as opposed to particular properties of information processing that we may identify with many different algorithms in the brain, characterized by the degree to which they place a demand on working memory.
The second and third common confusions, and perhaps the most widespread, are the assumptions that Type 1 processes and Type 2 processes can be reliably distinguished, if not defined, by their speed and/or accuracy. The easiest way to reject this is to say that the mistake of entering a quickly retrieved, unreliable input into a deliberative, reliable algorithm is not the same mistake as entering a quickly retrieved, reliable input into a deliberative, unreliable algorithm. To make a deliberative judgment based on a mere unreliable feeling is a different mistake from experiencing a reliable feeling and arriving at an incorrect conclusion through an error in deliberative judgment. It also seems easier to argue about the semantics of the 'inputs', 'outputs', and 'accuracy' of algorithms running on wetware, than it is to argue about the semantics of their demand on working memory and the life outcomes of the brains that execute them.
The fourth common confusion is that Type 1 processes involve 'intuitions' or 'naivety' and Type 2 processes involve thought about abstract concepts. You might describe a fast-and-loose rule that you made up as a 'heuristic' and naively think that it is thus a 'System 1 process', but it would still be the case that you invented that rule by deliberative means, and thus by means of a Type 2 process. When you applied the rule in the future it would be by means of a deliberative process that placed a demand on working memory, not by some behavior that is based on association or procedural memory, as if by habit. (Which is also not the same as making an association or performing a procedure that entails you choosing to use the deliberative rule, or finding a way to produce the same behavior that the deliberative rule originally produced by developing some sort of habit or procedural skill.) When facing novel situations, it is often the case that one must forego association and procedure and thus use Type 2 processes, and this can make it appear as though the key distinction is abstractness, but this is only because there are often no clear associations to be made or procedures to be performed in novel situations. Abstractness is not a necessary condition for Type 2 processes.
The fifth common confusion is that, although language is often involved in Type 2 processing, this is likely a mere correlate of the processes by which we store and manipulate information in working memory, and not the defining characteristic per se. To elaborate, we are widely believed to store and manipulate auditory information in working memory by means of a 'phonological store' and an 'articulatory loop', and to store and manipulate visual information by means of a 'visuospatial sketchpad', so we may also consider the storage and processing in working memory of non-linguistic information in auditory or visuospatial form, such as musical tones, or mathematical symbols, or the possible transformations of a Rubik's cube, for example. The linguistic quality of much of the information that we store and manipulate in working memory is probably noncentral to a general account of the nature of Type 2 processes. Conversely, it is obvious that the production and comprehension of language is often an associative or procedural process, not a deliberative one. Otherwise you still might be parsing the first sentence of this article.