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The Theory of Abstract Objects

by Edward N. Zalta

Introduction
The theory in question is presented by Zalta in a very concise HTML introduction to which the reader is referred ( ). The technical details are presented at length in Principia Metaphysica, available in various electronic formats through links from Zalta's introduction. The purpose of these notes is not to summarise or to criticise Zalta's writings, but to provide in as few words as possible a clear account of how Zalta's view of metaphysics differs from that advocated in Factasia.

**Introduction**
The theory in question is presented by Zalta in a very concise HTML introduction to which the reader is referred ( ). The technical details are presented at length in Principia Metaphysica, available in various electronic formats through links from Zalta's introduction.	The purpose of these notes is not to summarise or to criticise Zalta's writings, but to provide in as few words as possible a clear account of how Zalta's view of metaphysics differs from that advocated in Factasia.

Summary
Zalta Zalta takes Metaphysics to be concerned with providing a framework in which science (and other things?) can be conducted. This framework consists of a logic extending classical logic to distinguish between abstract and concrete objects and certain amount of development of theory about these objects. He seems to apply this primarily to the formalisation of the kinds of theory which previous philosophers have undertaken as metaphysics. There doesn't seem to be much about science. Factasia Factasia is primarily concerned with metaphysics as a stage in the formulation of scientific theories. I am in this concerned to produce an account of metaphysics which supports the formalisation of existing science, without expecting either the science or the mathematics it uses to need substantial modification on account of the metaphysics. In Factasia, logic, abstract ontology and mathematics are in place before metaphysics begins. Metaphysics can be conducted as an entirely abstract theoretical study of certain possible structures for the concrete universe or parts of it, in which case it is, like mathematics, a branch of applied logic. The purpose of metaphysics is, however, to undertake certain work preliminary to the formulation of scientific theories. Once a metaphysic is incorporated into a scientific model then the claim that this model is a true model is synthetic. Metaphysics by itself, however, makes no synthetic claims.

**Summary**
Zalta Zalta takes Metaphysics to be concerned with providing a framework in which science (and other things?) can be conducted. This framework consists of a logic extending classical logic to distinguish between abstract and concrete objects and certain amount of development of theory about these objects. He seems to apply this primarily to the formalisation of the kinds of theory which previous philosophers have undertaken as metaphysics. There doesn't seem to be much about science.	Factasia Factasia is primarily concerned with metaphysics as a stage in the formulation of scientific theories. I am in this concerned to produce an account of metaphysics which supports the formalisation of existing science, without expecting either the science or the mathematics it uses to need substantial modification on account of the metaphysics. In Factasia, logic, abstract ontology and mathematics are in place before metaphysics begins. Metaphysics can be conducted as an entirely abstract theoretical study of certain possible structures for the concrete universe or parts of it, in which case it is, like mathematics, a branch of applied logic. The purpose of metaphysics is, however, to undertake certain work preliminary to the formulation of scientific theories. Once a metaphysic is incorporated into a scientific model then the claim that this model is a true model is synthetic. Metaphysics by itself, however, makes no synthetic claims.

The Objectives of Metaphysics
Zalta's Objective Factasia Attitude

1. To describe the logic underlying thought and reasoning by extending classical propositional, predicate, and modal logic. In Factasia, logic, including abstract ontology, and the mathematics necessary for science, are pre-requisite to metaphysics, not a part of it. Taking classical set theory to be adequate (if not ideal) for the mathematics needed by science, factasian metaphysics works within that context.

2. To describe the laws governing universal entities such as properties, relations, and propositions. To the extent that such entities are required for logic or mathematics then they are considered in Factasia to be a part of logic or mathematics, and for these purposes set theory suffices (though other alternatives may be equally acceptable). If universal entities are needed for science then their theory would be a part of metaphysics, but, Factasian metaphysics works by conservative means within an abstract ontology provided by logic, so in effect everything is made out of sets.

3. To identify theoretical mathematical objects and relations as well as the natural mathematical objects such as natural numbers and natural sets. As far as Factasia is concerned this is mathematics not metaphysics, and is pre-requisite to metaphysics. More important than this arbitrary choice of scope for metaphysics, Factasia rests broadly content with modern "classical" foundations for mathematics. The metaphysician can work from alternative logical and mathematical bases, but since we allege universality of set theory the reasons would be pragmatic rather than fundamental.

5. To systematize our modal thoughts about possible (actual, necessary) objects, states of affairs, situations and worlds. I guess this must be metaphysics, but I can't really see how it bears upon science. "Possible worlds" is a point at which metaphysics feeds back into the notion of logical truth and suggests to me that I should perhaps consider logic to be a part of metaphysics rather than a pre-requisite to it. However, it doesn't suggest it strongly enough for me to actually do it. So the Factasia position is that there is some of this which is logic, and some which is metaphysics, and they have to be worked out to fit together. I'm sticking to set theory (or HOST) for the logic. The possible worlds figure in the account of how set theory relates to (captures) the notion of logical truth. Modal logics are for reasoning about necessity, but do not provide a basis for establishing the full range of necessary truths. Set theory (+conservative extensions) provides a formalisation of the necessary truths, if you want to reason about necessity this can be done within this framework (if you like, by embedding a modal logic).

6. To account for the deviant logic propositional attitude reports, explain the informativeness of identity statements, and give a general account of the objective and cognitive content of natural language. I'm not sure that any of this belongs in my conception of Metaphysics. I guess the main issue in relation to advocacy of set theory is "how does set theory cope with the problems which provoke in ordinary language the use a referentially opaque constructs". I think I would deal with this in the arguments for the universality of set theory, and so it would come under philosophy of logic. This doesn't actually give an account of these things it just argues that the account, if you must have one (and its not clear that you need it for science) can be constructed in the context of set theory (if it can be constructed at all).

7. To axiomatize the philosophical objects postulated by other philosophers. I believe that these are pretty irrelevant to the conduct of science, but if you think of it as a thought experiment about how science might have developed if scientists had taken these philosophers seriously then I would have to accept it as metaphysics. This is handy since otherwise I would have excluded from metaphysics pretty much all the metaphysics which has been done in the past. (which is still more generous than many have been in this century) If you were serious about using this for science then it would still be advisable to do it in something like set theory.

**The Objectives of Metaphysics**
Zalta's Objective	Factasia Attitude
1. To describe the logic underlying thought and reasoning by extending classical propositional, predicate, and modal logic.	In Factasia, logic, including abstract ontology, and the mathematics necessary for science, are pre-requisite to metaphysics, not a part of it. Taking classical set theory to be adequate (if not ideal) for the mathematics needed by science, factasian metaphysics works within that context.
2. To describe the laws governing universal entities such as properties, relations, and propositions.	To the extent that such entities are required for logic or mathematics then they are considered in Factasia to be a part of logic or mathematics, and for these purposes set theory suffices (though other alternatives may be equally acceptable). If universal entities are needed for science then their theory would be a part of metaphysics, but, Factasian metaphysics works by conservative means within an abstract ontology provided by logic, so in effect everything is made out of sets.
3. To identify theoretical mathematical objects and relations as well as the natural mathematical objects such as natural numbers and natural sets.	As far as Factasia is concerned this is mathematics not metaphysics, and is pre-requisite to metaphysics. More important than this arbitrary choice of scope for metaphysics, Factasia rests broadly content with modern "classical" foundations for mathematics. The metaphysician can work from alternative logical and mathematical bases, but since we allege universality of set theory the reasons would be pragmatic rather than fundamental.
5. To systematize our modal thoughts about possible (actual, necessary) objects, states of affairs, situations and worlds.	I guess this must be metaphysics, but I can't really see how it bears upon science. "Possible worlds" is a point at which metaphysics feeds back into the notion of logical truth and suggests to me that I should perhaps consider logic to be a part of metaphysics rather than a pre-requisite to it. However, it doesn't suggest it strongly enough for me to actually do it. So the Factasia position is that there is some of this which is logic, and some which is metaphysics, and they have to be worked out to fit together. I'm sticking to set theory (or HOST) for the logic. The possible worlds figure in the account of how set theory relates to (captures) the notion of logical truth. Modal logics are for reasoning about necessity, but do not provide a basis for establishing the full range of necessary truths. Set theory (+conservative extensions) provides a formalisation of the necessary truths, if you want to reason about necessity this can be done within this framework (if you like, by embedding a modal logic).
6. To account for the deviant logic propositional attitude reports, explain the informativeness of identity statements, and give a general account of the objective and cognitive content of natural language.	I'm not sure that any of this belongs in my conception of Metaphysics. I guess the main issue in relation to advocacy of set theory is "how does set theory cope with the problems which provoke in ordinary language the use a referentially opaque constructs". I think I would deal with this in the arguments for the universality of set theory, and so it would come under philosophy of logic. This doesn't actually give an account of these things it just argues that the account, if you must have one (and its not clear that you need it for science) can be constructed in the context of set theory (if it can be constructed at all).
7. To axiomatize the philosophical objects postulated by other philosophers.	I believe that these are pretty irrelevant to the conduct of science, but if you think of it as a thought experiment about how science might have developed if scientists had taken these philosophers seriously then I would have to accept it as metaphysics. This is handy since otherwise I would have excluded from metaphysics pretty much all the metaphysics which has been done in the past. (which is still more generous than many have been in this century) If you were serious about using this for science then it would still be advisable to do it in something like set theory.

created 1998/10/30 modified 1998/10/31