What is the difference between a conception of something and a theory of something? Is the conception more extensive in content or less?
Example: iterative conception of sets and ZFC
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1This is a great question. The difference, I think, is between constructive vs axiomatic approaches to explication. With regards to sets, for example: you can either assume some primitive objects (urelements) and construct the rest of the universe out of them by some recursive procedure (this is the constructive/iterative-conception approach) or you can assume primitive theorems (axioms) and reduce the rest of the truths about sets to those axioms (this is the axiomatic/ZFC approach). Boolos and Parsons have a couple of nice papers on this worth checking out.– Hunan RostomyanMay 22, 2014 at 17:06
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@HunanRostomyan: Does this have any relation to structural realism vs. scientific formalism?– GeremiaMay 23, 2014 at 2:28
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@Geremia It might. What do you think?– Hunan RostomyanMay 23, 2014 at 4:33
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@HunanRostomyan: "constructive approach to explication" → scientific formalism. "axiomatic approach to explication" → scientific realism. ?– GeremiaMay 23, 2014 at 5:30
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@Geremia I had the opposite pairing, but sure. You just have to narrow the definitions down to the essentials and see if you get anywhere. Could lead to an interesting research paper if there is indeed an interesting connection.– Hunan RostomyanMay 23, 2014 at 5:40
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I think conception of something generally refers to those things that we abstract from approved writings or sometimes through unreliable source which might not be authentic.That might be a reason , we sometimes realize that we are understanding that particular thing differently than what it really is.Conception of something depends on our way of understanding that something and setting it in our mind.
Meanwhile, theory of something is proved, reliable ,authentic, practised writings which is outcome of long term rational analysing and processing of different hypothesises .Theory of something might be universal as well.Its one of the major sources of gaining conception of that thing.
Making conception of a thing is a lot easier than making it recognised as a theory.