last revised October 11th, 2004.Most of Loux's discussion in chapter 5 focuses on propositions. He follows his normal practice of proposing a deliberately extravagant realist doctrine and then examining, and faulting, alternatives to it. Towards the end he moves on to other issues, which we shall deal with later. For now, however, I want also to touch on the ontology of mathematics, since that may seem to give us the most difficult cases of abstract objects.
For a lively and sceptical discussion of abstract objects, see Rosen in the SEP 'Abstract Objects'.
Loux says that propositions, as a kind of abstract object, are typically introduced for the following reasons:
While these reasons all involve our thinking or speaking, a realist about propositions is not going to think that propositions amount to no more than our thinking. Rather
Frege ascribes to senses and thoughts objective existence. In his mind, they are objects every bit as real as tables and chairs. Their existence is not dependent on language or the mind. Instead, they are said to exist in a timeless "third realm" of sense, existing apart from both the mental and the physical. Frege concludes this because, although senses are obviously not physical entities, their existence likewise does not depend on any one person's psychology. A thought, for example, has a truth-value regardless of whether or not anyone believes it and even whether or not anyone has grasped it at all. Moreover, senses are interpersonal. Different people are able to grasp the same senses and same thoughts and communicate them, and it is even possible for expressions in different languages to express the same sense or thought. Frege concludes that they are abstract objects, incapable of full causal interaction with the physical world. They are actual only in the very limited sense that they can have an effect on those who grasp them, but are themselves incapable of being changed or acted upon. They are neither created by our uses of language or acts of thinking, nor destroyed by their cessation.
Loux mentions various issues about which defenders of propositions differ, but we need not take these up. Instead let us turn to nominalist alternatives. These are already familar in outline since they echo the metalinguistic strategies of nominalism more generally.
Loux concludes this section by reporting one of Russell's attempts to get by without propositions, the 'multiple relation' theory of belief. Instead of the traditional account (a dyadic relation between a person and a proposition) Russell's account of belief took it to be a polyadic relation involving an ordered set (e.g. 'Othello believes that Desdemona loves Cassio' is taken to be a relation between Othello, Loving, Desdemona, and Cassio, in that order). He claims that though Loving is a relation, it is not a relation when existing in the belief-complex. If, however, in the real world Loving does relate Desdemona and Cassio then Othello's belief is true, if not, not.
Loux observes that Russell did not give us a complete theory, so it is difficult to know exactly what to make of it. The idea of relations ceasing to be relations inside a belief-complex is mysterious. Russell also has to allow that belief is of various 'adicities' - in our example it is a four-place relation, but it is three-place when John believes that grass is green. Many people think that this breaks up a unified concept into completely separate items, but it is not obvious to me that it does - we are happy to say that the relativity of simultaneity proposed by Einstein shows that what we took to be two-place spatial relations are really three-place, but not for that reason utterly distinct.
The traditional proposition theorist thinks that for a thought to have the content it has is for a person to be related appropriately to a proposition. Loux raises the manifold problems posed by Putnam's arguments about the world-dependence of what we mean. Putnam's 'twin-earth' stories are meant to show that the content of what a person thinks depends, in part at least, on the physical environment in which she exists. So it is not contributed by a relation to an abstract object.
Loux usually takes universals and propositions to be abstract and takes this to mean that they are not in space-time and not in causal relations with things that are in space-time.
I think it is worth noting some very different thoughts that invoke abstraction. One appeals to a psychological process of selective attention, and the ignoring of certain features of things - abstracting certain features away from their surroundings. When we do this, there is no reason to suppose that the results are in some supersensible or eternal realm. They are in space-time; it's just that we are ignoring their surroundings.
Another kind of thought is of the abstract as the opposite of the concrete where this does involve being in space-time and in causal connection with other things. See Rosen for most of the features people have taken this sort of abstraction to involve.
Yet another idea of what makes for abstraction is that of ontological dependence. This is the idea that Lowe makes central in his discussion of abstract and concrete.
© Ed Brandon, 2004.
last revised October 11th, 2004.
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