kp@uts.amdahl.com (Ken Presting) (03/20/90)
In article <2540@quiche.cs.mcgill.ca> utility@quiche.cs.mcgill.ca (Ronald BODKIN) writes: >I am still troubled by the "ontological status" of these universals; i.e. >concepts are somehow implemented in a system (quite right), . . . This is not exactly what I have in mind, or at least you have formulated your statement in a way that could lead to confusion. It's not the concepts themselves of any given abstraction that are implemented, it's the structure of an abstract system as a whole that is implemented. We verify that a real system does implement some abstraction by comparing a description of the real system (in an independent descriptive vocabulary) with the assertions in the abstract formal system. If there is a homomorphism of logical structure, then the semantics of the independent descriptive language can be used to define a semantics for the vocabulary of the abstraction. Wrt this new semantics, the terms of the abstraction denote parts or properties of the implementation. >what exactly are these concepts. I find it hard to exactly describe what >is annoying me about this. Platonism can be modified to assert that these >structures are somehow "real", while Aristotleanism can be modified to >assert that they are real but only exist in implementations/embeddings. Concepts, in my view, have a role *only* in thinking. The role of concepts in thinking is similar to the role of predicates in logic and dialectic. But it is very important that thinking can lead to false conclusions, which prevents any attempt to explain or even describe thinking simply as an implementation of logic. The relation between thought and action also complicates the picture - logic alone would not be enough. We need a concept of "practical reason" (R. C. Jeffrey's _The Logic of Decision_ is preferred by Donald Davidson for this purpose, and I follow him on this). The relation of logic to thinking is *normative*. Logic tells us how we SHOULD think, not how we DO think. What happens when we try to find a homomorphism of logical structure between an abstract account of logic and human psychology? We can't quite find one - there are some things that people do that don't make perfect sense, even when they try hard. Since human beings are natural phenomena, there is little to be gained by criticising the "implementation". (Scare quotes, because there is no "implementor") This raises a very serious issue. Terms like "inference", "assertion", and "truth" are part of the abstraction we use to describe logic. But if there is no homomorphism of logical structure between an abstraction of logic and human behavior or psychology, then it is difficult to see what the reference of such terms might be. Implementationism provides an account of reference across abstractions only when a homomorphism can actually be found. For now, I just want to point out that implementationism has this limitation, and leave open how the problem is to be solved. The solution is based on the concept of "interpretation", which is not to hard to define logically, but has a very complex psychological implementation. (and leads to some very controversial issues) >In some sense, the question can be placed as, concepts are some kind of >well-founded abstraction, but what exactly is the nature of such >abstraction? I'd say that the term "concept" is part of a *completely unfounded* abstraction! Logic, mathematics, the theory of algorithms, and any formal theory, can be studied without specifying any model or semantics at all. This gets back to the issue of "formal symbol manipulation", which I think is the most complicated part of human behavior. For example, it seems to me that mathematicians need not suppose, as Penrose does, that their theories have some real model in a Platonic heaven. I think it is sufficient that the theories have the possibility of having a model (ie are consistent). But then it is hard for me to explain what mathematics is about, and whether it is true. This does not worry me much, because nobody has an uncontroversial explanation of mathematical knowledge. What does worry me is how to explain why human behavior includes so much formal symbol manipulation. There is plenty of controversy on this issue also, but I think there should be more! > Ron >p.s. I first followed up to talk.philosophy.misc, but I guess no one in >comp.ai reads that. (I do read that group, but if anything is cross-posted to comp.ai, my .newsrc shows it to me there first. I'll rearrange the group listing, to encourage myself to put philosophy elsewhere. Sci.philosophy.tech is probably the best place to discuss reduction vs. implementation.) Thanks for bringing this up, Ron. I sort of ducked the question of ontology for abstract theories, but I think that's the only way to handle it :-). Ken Presting