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Part II of the kinds of theories that are reducible to each other

In Discussion on February 25, 2010 by Lynn Chiu

Wenwen’s comment on my other post about the kinds of theories that can be reduced to each other induced me to post a part II. This is primarily due to its relation with the topic of this week–model idealization.

In that post, I puzzled over the kinds of theories that can be reduced to each other. My understanding of Nagelian formal reduction of a higher-level theory, a lower-level theory and bridging laws (of the terms and laws specified in the two theories) does not include specifications on what kind of models can be plugged into the higher and lower levels. Anything goes, it seems like, as long as there can be bridging laws. But what kinds of theories allow bridging laws? What kind of bridging laws?

Maybe this is a question Nagel already answered, so please inform and enlighten me if you know.

My discussion below relies on the assumption that theories are idealizations of the target phenomenon. This is arguable, so please attack this point if you don’t feel comfortable with this.

Following Weisberg’s distinction between different representational ideals, the higher and lower level theories may be models that are aiming for different goals: completeness, primary causations (1-causal), predictions (Maxout), simplicity (qualitative matches between the model and the target) or generality (application range). Depending on what the models are for, what the bridging laws capture would be dramatically different. I will discuss the first four because generality concerns the actual/possible range of future applications, which is not my focus here.

completeness: if they are both providing completeness models, then they are both introducing distortions that will be removed eventually. Therefore, the bridging laws are basically linking the same entities and the same laws, though accounted for differently by the two formal systems because of  their particular distortions.

1-causal: If they are both providing 1-causal models and both accurate, then if reduction is possible, the higher-level causation links can be explained by the real causal links at the lower level.

This is very different from how higher/lower level theories would look like if their purpose is to achieve predictions or qualitative similarity with the target phenomenon. These models are not concerned with getting the actual causal links “right”. It is possible that the models match the surface phenomenon and predict really well, but are not structurally isomorphic to the causal structure of the phenomenon at all.

Therefore, there are two ways reduction could go:

(1) the bridging laws demonstrate how they the two models parallel in prediction

(2) since the “surface phenomenon” is different at different levels, the bridging laws might be showing how the phenomenon matches each other at the different levels via their descriptive models, respectively.

So…depending on what models one is talking about, the “reductions” mean completely different things!!!!

If you buy my argument, looking back to the relation between Classical Mendelian Genetics (CMG) and the achievements of molecular genetics (MG), what kind of reduction does Waters, etc. have in mind?

I have the feeling that the general consensus is models that are for 1-causation. However, is this what CMG and MG really aim to do? Suppose they are both aiming for determining the core causal connections. Next, we have to figure out whether we’re discussing this question because  (1) CMG and MG are accurate in predicting and describing the surface phenomenon or because (2) CMG and MG posit laws and entities that are real.

If the former, then even if they actually are 1-causal models, we are not reducing them for what they actually are but for what they achieve as prediction and/or simplicity models. If this is so, we are applying the wrong sort of reduction to these models.

If the latter, well, that has to be PROVEN. If one of them is wrong (ex. there are no genes), then even if they are accurate in their descriptions and predictions, reduction cannot be done at all!!! This was what I think was lacking in the papers we read last week. They did not show that the assumptions and posited entities/laws of CMG were still correct but seemed to only rely on the CMG’s accurate descriptions of the phenomenon.

Whew!

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2 Responses to “Part II of the kinds of theories that are reducible to each other”

  1. I think Lynn’s point brings up two conflicting views regarding science and scientific method that often appear to be overlooked in the literature we have been examining. Weisberg’s work largely treats models as part of the process of scientific exploration and growing understanding. In this sense models provide only partial representation of observable phenomena and have the required tradeoffs.

    Lynn has, on the other hand, posited that theories are models, and this may not be the case. The debates over reductionism at times assume that the current theories are correct. In this case a theory with a model like appearance would be a law and if really ‘correct’ correspond to at least some aspect of explaining phenomena. Is this a model then or an ‘accurate’ representation of reality? As it looks like a model, then let us say it is close enough to accept Lynn’s point.

    So, if we move on the reductionist point of view, true completeness would not introduce distortion as there would be no idealization, if reduction is theoretically possible (and despite my objections to the arguments against reduction in other posts- I don’t believe everything will ultimately be reducible, but for very different reasons). Thus the theory that looks like a model that will emerge will be all encompassing. Ultimately the reductionist project would absorb one-causal theories into the totality by reduction, if they were ‘true’ theories and not merely exploratory models.

    Since the ideas of completeness and one-causal appear to relate to models that have not quite reached the levels of theories ripe for actual reduction (as incompletely understanding and incorrect or inadequate hypothesis would expected to be irreducible) I’m not quite getting my head about the second half of your piece where you now apply these to reduction. I’m going to mediate on this more. But I think there is a theoretical difficulty in applying models to theories in the same way that it is mistaken to apply models to reality in any isomorphic way.

    Except for reduction to work, one likely has to get to that isomorphic representation of reality that is similar to a model. Perhaps more evidence reduction is ultimately impossible, if we suppose the process of science will never end and all theories will we replaced by others over the infinite horizon, never achieving a perfect representation.

  2. Lynn,

    I like the way you relate reductionism and minimal idealization, whose representational ideal is 1-causal. In this way, the topics we discussed in two diffrent weeks have some internnections.

    Todd raised a good point: are the reducing theory and the reduced theory models? Weisberg said that eolutionary models are mathematical structure + interpretations. Say we focus on Classical Mendelian Genetics (CMG) and Molecular Genetics (MG). I will say that they both try to explain the same phenomenon. And if CMG can be reduced to MG, then their models have similar structures (the most straightforward way would be isomorphism, but not necessary.

    I do think that the cases we talk about in this class are mostly about the same target phenomenon and about explanatory reductionism. For example, Putnam’s case is about how to explain why the peg passes through the square hole but not the round hole. Same with CMG and and MG.

    Thus, I am inclined to say that the option (1) you laid out is correct. But I think the focus is explanation rather than prediction (I may be wrong). And explanatory reductionism isn’t concerned about ontological reductionism (I learnt this term from Andre’s comments on Todd’s post). It seems that what you mean by ‘the right sort of reduction’ is ontological reduction.

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