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Is there some theory that explains this. When I reflect on how I reason through to an understanding of something (the Eureka moment), it appears that to me that the steps are never sufficient and that something irreducible is being missed.

That irreducible bit where actually new understanding happens seems to me important - has anyone theorised about it? Would it be tied to a theory of consciousness? To epistemology? That is how we gain actually new knowledge.

That difference is explained - once we have learned to read a map, looking at a new map has new knowledge but not the actually new knowledge of what a map is, how to read it, and what it represents and is useful for.

If anyone has I expect it to be in the continental tradition...

3

The closest thing I can think of is what is sometimes called an "epistemically transformative experience". In Frank Jackson's "Knowledge Argument" against physicalism Mary is sometimes described as having an "epistemically transformative experience" when she leaves her room and experiences redness for the first time--- even though she knew all of the physical facts about redness.

Recently, Laurie Paul has written a paper on how having a child is a similarly "epistemically transformative experience" called "What Mary Can't Expect When She's Expecting". This call for papers from Res Philosophica gives a brief description of the topic. From the CFP:

When Mary sees color for the first time, her experience is transformed in a way that she could not have predicted: she could not know what it would be like for her to see red for the first time. Such experiences are transformative for an agent in the sense that they are radically unlike the agent’s previous experiences with regard to their phenomenal character, intensity, and overall cognitive significance.

I could see your "eureka moments" as a sort of epistemically transformative experience. Despite knowing all sorts of facts, these facts don't have as much cognitive significance as they do after things "click". Just like although Mary knows a whole lot about the color red, these facts don't mean much until she experiences "what it's like" to see red.

I'm not sure how much has been written on the subject of epistemically transformative experiences. Following that CFP from Res Philosophica might be worthwhile if this is the phenomenon you're interested in.

EDIT:

It just occurred to me that there is a research trend in epistemology and theories of epistemic value that distinguishes "knowledge" from "understanding". I don't know much about the area, but you can find some discussion of the topic in this SEP article. I take it that whether there even is a significant such distinction is controversial.

  • Nice answer. This is definitely along the lines I was thinking of. Its not only big eureka moments but small ones too. But I'm also interested in ideas of poetic inspiration and epiphany (as in Joyces Portrait of a Young artist) and divine madness; but these I think are tend towards the literary - but I'd be interested to know if they have philosophical antecedents. I'm interested in them because they're unwilled although I see the force of them as an argument for experience and against physicalism. – Mozibur Ullah May 29 '13 at 2:26
  • Of course, in this example it is willed, as Mary crosses the doorway - whereas these experiences take people unawares – Mozibur Ullah May 29 '13 at 2:26
  • @MoziburUllah I'm not sure how big of a difference the "willed" part is. It is part of the situation that she has no idea what to expect, so she certainly doesn't willfully choose the experience she has. You could imagine that instead she was blindfolded and taken outside against her will and I think the experience she has when the blindfold was removed would not be substantially different. – Dennis May 29 '13 at 3:21
  • Yes, I see what you mean. One could of course tell her that she will experience something new when she crosses that doorway, so its her choice when she experiences Redness. But, as you say, and I agree - its not an important part of the scenario. – Mozibur Ullah May 30 '13 at 19:02

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