GeniusNZ2 comments on Hand vs. Fingers - Less Wrong
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A non reductionist might talk about X where X is specifically defined as 'stuff that cannot be reduced'. The reductionist hears the term X and starts to argue how it can be reduced. Point is that the non-reductionist is fundamentally talking about something different.
the solution is that one can use a on reductionist framework to consider the issue (with an associated shift in definitions of words etc) and one can use a reductionist framework or one can take a position somwhere in the middle. In my opinion the reductionist one is more useful - but if the objective is to "understand the non reducible nature of the soul" (trying to be extreme) or anything along those lines then I guess non reduction might be a way to go.
Similarly, to a non-reductionist a world which is identical but with no qualia is an interesting topic and is conceivable - to a reductionist it may be 'inconceivable'. Just a different definition of the fairly flexible thing 'conceivability'.
mtraven creates a good example,
it would seem mt doesn't seem to care about reductionism. Effectively saying it achieves nothing. On the other side a reductionist would wonder what he was going to achieve via analysis of mind without any sort of reduction.
Similarly we have a semantic debate about if hands without fingers are possible - well to some people it is and some it isn't depending on how they define hands - and whether that should or should not be the case is a pragmatic matter.
So in a fairly pure form you could have a person who denies that 2 is reducible to 1+1 and that 2 can exist without 1 - because he understands the concept in that way. Another person may say thats 2 is only 1+1 and that there is nothing theoretically interesting in the change entailed by having (1+1) appear everywhere that 2 is now.