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The kinds of theories that are reducible to each other

In Discussion on February 16, 2010 by Lynn Chiu

After a very pleasant evening chatting with Leo and Josh, I’ve finally clarified what’s been bothering me with the readings this week, particularly Waters’. Upon reading the blog afterwards, I realized that Todd might be touching something on similar lines. However, since this is a separate issue in itself, I decided to post an independent article.

The issue is about what makes theories “higher-level” than a “lower-level” one, such that we can debate whether they are reducible to each other or not. Some theories reside in domains that are obviously in nested hierarchical relation to each other, such as social psychology theories versus cognitive neuroscience theories. These obviously induce the question of whether they can be reduced to each other. Others, are in the same domain, such as Newtonian physics versus the Special Relativity Theory, and thus do not bring about the question of reducibility but which is right or wrong.

However, within the same domain, there seems to still exist theories that treat with topics that are relatively “macro” and “micro”. The topic of our focus today is Classical Mendelian Genetics (CMG) versus molecular biology (MB) (or sometimes molecular genetics). They both belong in the biology domain, but the former talks about patterns that are at a more macro-scale than those of the latter. The question then becomes, is there a genuine difference in level between CMG and MB such that there is an issue of reducibility?

I think there are three possibilities.

The first is that CMG and MB are genuinely different levels of explanation, with the targets of their investigation phenomena happening at different but simultaneously occurring levels. In this case, the two would be reducible in the formal Nagel’s sense of theoretical reduction.

The second is that CMG and MB are two theories that aim to describe the same level of phenomena but are constructed on different assumptions (set of axioms) and laws. In this case, it is not proper to say that the two are reducible to each other but that one is right and the other is wrong.

The third is that CMG and MB are theories that are both useful, that they correctly grasp patterns in the world. Therefore, the two are informally reducible in the sense that the patterns that are usefully described in one can be usefully described in the other.

I think we need to be clear about what we think about the two theories such that we find it meaningful to discuss whether they are reducible to each other or not, and in what sense reducible.

My oversimplifying opinion is that Todd seems to be aiming for (2), while Josh is for (3). Waters on the other hand, seems to set out to do (1), but I only see him providing evidence for (3).

As for myself, I’m thinking more that (2) is actually the case. But an explanation of my own views would make this post wayyyy too long. I’ll put in the comments later!

Looking forward to your comments!

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2 Responses to “The kinds of theories that are reducible to each other”

  1. Lynn, I like the three possibilities you propose. I am interested in (3). How do we understand this informal reductionism? You say that informal reduction means “the patterns that are usefully described in one can be usefully described in the other”. It seems to mean that the underlying pattern makes the reduction possible. In this sense, any theories that can use the same model are informally reduced to each other. But I think this is not what you mean. Can you flesh out (3)?

    As for Waters’ article, I only see him to argue for (1). Why do you think that he only provides evidence for (3)? How do we distinguish (1) from (3)?

  2. Hi Wenwen,

    Thanks a lot for the comment! I will need to go back to the paper to answer your second question more sophistically, so I will answer your first one first for the time being.
    Now that we have the language of models/analogy/isomorphism, etc. under our belt, I think I can flesh out this option more fruitfully. And since this might be relevant to the idealization talks we’re having today, I decided to make a new post about this issue. So please refer to my latest post as my reply to you. I’ll reply to your second question under this post.

    Lynn

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