| Leibniz’s Law | Necessarily, |
Many British idealists espoused a form of radical holism according to which the nature of every object depends on every property of every other object. According to this view, no actual object could have existed were any other actual object different.
This was one of the aspects of idealism which Moore, Russell, and other like-minded philosophers were inclined to reject. We are discussing this question not just because it is an interesting metaphysical issue, but also because it provides a good case study for the usefulness of the kind of method of solving philosophical problems via logical analysis with which we are familiar from our discussion of Russell’s solutions to the problem of negative existentials and the other puzzles to do with definite descriptions.
But we will begin by getting clear on what radical holism amounts to, and why McTaggart, and perhaps Bradley, seems to have thought that it was true.
The most important sections of The Nature of Existence for our purposes will be the sections on ‘Derivative Characteristics’ and ‘Determination.’ Some of the main theses are as follows:
A background claim required by the argument. Every object stands in some relation to every object; every object stands in some relation to every change in every other object.
McTaggart writes,
“The occurrence of any relation involves the occurrence of a quality in each of its terms -- the quality of being a term of that relation.” (§85)
The distinction between relations and relational qualities, and why standing in any relation involves having at least one relational quality.
In §108, McTaggart says the following about the properties of a thing and its nature:
“If now we enquire what A is, a complete answer must be given by giving the nature of A, and this consists of its qualities. X, Y , and Z are taken as a complete list of these, and thus the nature of A is X, Y , Z. Let us suppose any of the qualities altered, either by addition or subtraction or substitution, so that the complete list would be represented by W, X, Y , Z, or by X, Y , or by W, X, Y . Thus the nature of the substance which had such qualities would be different from the nature of A. Therefore the substance in question could not be A.”
The conclusion is that an object’s being the object that it is depends on each of its qualities. Why would McTaggart thinks this? Leibniz’s law: the indiscernibility of identicals.
| Leibniz’s Law | Necessarily, |
The idea that difference in properties implies numerical distinctness. The connection between this and the idea of a change in nature through the idea that an essential property of an object -- one which is a part of its nature -- is one without which that object would not be the object that it is. McTaggart’s thought here is that every property of an object is essential to it.
So far we have laid out three theses which McTaggart seems to endorse in this passage, and given arguments for each. But if we put these three theses together, we get a valid argument for radical holism:
| 1. | For any two objects x and y, a difference in the qualities of x implies a difference in the relations in which y stands. |
| 2. | For any object, a difference in the relations in which that object stands implies a difference in that object’s qualities. |
| 3. | For any objects x and y, a difference between the qualities of x and y implies that x and y have different natures. |
| C. | For any two objects x and y, a difference in the qualities of x implies a difference in the nature of y. |
Since to say that the nature of an object changes is just to say that the object ceases to be the object that it is, the conclusion of this argument appears to be another way of stating radical holism: the nature of every object depends on every property of every other object. No object could be what it is without every other object being just the way it is.
One way to express this conclusion is to say that no relations are external. The distinction between internal and external relations and properties is just another way of talking about the distinction between essential and accidental properties, or between these properties without which a thing would not be what it is, and properties without which a thing could still be what it is.
Moore thinks that radical holism is clearly false. His strategy for showing it to be false is reminiscent of Russell’s strategy for solving the problem of negative existentials: he thinks that by paying close attention to the logical forms of sentences involved in stating the problem, we can see that the arguments for radical holism are fallacious, and remove any plausibility that the thesis might have seemed to have.
Moore spends the first part of the article clarifying the nature of the thesis that all relations are internal. He concedes the point that all relations are associated with (at least one) relational property, and grants that the holding of a relation between two objects cannot be analyzed in terms of the existence of the objects and the relation, but claims that neither of these claims exhaust what proponents of radical holism mean when the say that all relations are internal.
Moore states his view about what proponents of this thesis do mean when he says:
“I want to suggest, then, that one thing which is always implied by the dogma that, ‘All relations are internal,’ is that, in the case of every relational property, it can truly be asserted of any term x which has that property, that any term which had not had it would necessarily have been different from x.” (47)
(Here Moore is following McTaggart and Bradley in using ‘term’ to express what we might more naturally express by ‘object.’)
But he claims that this thesis is ambiguous, and that the key to understanding the weakness of the thesis lies in seeing this. He points out two phrases in the thesis which need more clarification:
1. ‘is necessary.’ Moore says that to say that to say that there is a necessary connection between an object’s having a pair of properties is to say that it follows from the fact that an object has one that it also has the other. As an example, he uses the properties of being a right angle and being an angle, and says that it follows from the fact that something is a right angle that it is also an angle. What, you might ask, does ‘follow from’ mean here? A good answer, though not one that Moore gives, is that one claim follows from another just in case it could not be the case that the latter is true without the former being true as well. In general, to say that a certain claim is necessary is to say that it could not be false, or that, no matter how the world had turned out, it would not have been false.
2. ‘is different from.’ Moore distinguishes two senses in which two things can be different from each other: either by being simply numerically distinct, or by being qualitatively distinct. Two things are numerically distinct when they are, well, two separate things. But you might think that things can be numerically distinct without being in any strong sense qualitatively distinct. (Imagine two mass-produced paper clips which are in every intrinsic way exactly the same.) But if two things are qualitatively distinct, they must also be numerically distinct. Hence you might think that it follows from the fact that x and y are qualitatively distinct than x and y are also numerically distinct, but not the other way around. (Moore seems to think this.)
This ambiguity in ‘is different from’ gives us two interpretations of what the denier of external relations could be saying. On the one hand, she might be saying that
In the case of every relational property, it can truly be asserted of any term x which has that property, that any term which had not had it would necessarily have been numerically different from x.
Alternatively, she might be saying that
In the case of every relational property, it can truly be asserted of any term x which has that property, that any term which had not had it would necessarily have been qualitatively different from x.
Moore thinks that his opponents believe both of these theses. But his argument focuses only on showing that the first of the above versions is false. And there is a good reason for this. As we have seen, the second formulation implies the first; so if the first is false, so is the second. Hence if Moore’s argument is successful, that will be enough to discredit both theses. (From here on, you can read ‘different from’ as ‘distinct from’ or ‘numerically different from.’)
Moore claims that some relational properties are internal, in the above sense, and some external:
“...it is quite easy to point out some relational properties which are certainly internal in this sense. Let us take as an example the relational property which we assert to belong to a visual sense datum, when we say of it that it has another visual sense datum as a spatial part: the assertion, for instance, with regard to a colored patch half of which is red and half yellow: “This whole patch contains this patch” (where “this patch” is a proper name for the red half). It is here, I think, quite plain that, in a perfectly clear and intelligible sense, we can say that any whole, which had not contained that red patch, could not have been identical with the whole in question ...[But] it seems quite clear that, though the whole could not have existed without having the red patch for a part, the red patch might perfectly well have existed without being part of that particular whole. ...Yet this ...is one of the things which the dogma of internal relations denies. ...And in saying this it obviously flies in the face of common sense. It seems quite obvious that in the case of many relational properties which things have, the fact that they have them is a mere matter of fact: that the things in question might have existed without having them.” (50-51)
The importance of the distinction between things are true as a mere matter of fact and things which are true necessarily, or as a matter of the essence of things.
So much for Moore’s denial of the ‘dogma of internal relations’; how does he respond to the argument that we discussed above?
Moore is willing to concede the first and second premises of the argument outlined above. His concerns are with the third premise. He thinks that it is ambiguous. One one reading, he thinks, the argument is valid but the premise false; on the other reading, the premise is true, but the argument invalid. Either way, he thinks, the argument fails.
Moore makes this point on pp. 51-2:
“What I am maintaining is the commonsense view, which seems obviously
true, that it may be true that A has in fact got 
, and yet also true that
A might have existed without having . And I say that this is equivalent to
saying that it might be true that A has , and yet not true that from the
proposition that a thing has not got it follows that that thing is other than
- numerically different from it. And one reason why this is disputed is, I
think, simply because it is in fact true that if A has , and x has not, it does
follow that x is other than A.”
Moore continues:
“These two propositions, the one which I admit to be true (1) that if A has
, and x has not, it does follow that x is other than A, and the one which I
maintain to be false (2) that if A has , then from the proposition with regard
to any term x that it has not got , it follows that x is other than A are, I
think, easily confused with one another. ...
By far the most important point in connexion with the dogma of internal relations seems to be simply to see clearly the difference between these two propositions (1) and (2), and that (2) does not follow from (1). If this is not understood, nothing in connexion with the dogma can, I think, be understood.”
Moore thinks that premise (3) of our argument for radical holism is ambiguous between the following:
| (1) | If A is |
| (2) | If A is |
This is important because, as we have seen, (1) seems obviously to be true. Moore is claiming that (2) expresses the claim of radical holism, and that we cannot deduce it from (1).
To get clearer on the difference between these propositions, remember that we can capture the intended sense of ‘x follows from y’ as ‘x is a necessary consequence of y’ or, equivalently, ‘necessarily, if x then y.’ Using this reformulation, (1) and (2) are as follows:
| (1*) | Necessarily ((A is |
| (2*) | A is |
Is Moore right that (2) does not follow from (1)? How can we show this? How would you formulate the claim that a certain property is essential, or internal, to an object?
If it is true that (2) does not follow from (1), does this show that the argument above for radical holism fails?
In this article, Moore provides some considerations which he thinks count against radical holism, but does not provide any kind of alternative metaphysical picture. You might wonder what we could use to replace the metaphysical thesis that the essence of every individual thing is bound up with every property of every other existing thing.
One alternative view is that of logical atomism, which Moore’s colleague Russell did much to defend. According to this view, the appearance that the world consists of a large number of different, independent, atomic things is correct; and we can discover the nature of these atomic things and facts via the method of logical analysis. (Hence ‘logical atomism.’) This is a view we will be discussing at length in a few weeks.
In an Appendix to a later edition of Appearance and Reality, Bradley gave the following response to opponents of the denial of external relations:
“And it is not hard, perhaps, at this point to dispense with a fallacy which seems somewhat common. You may take, it is said, some terms, A, B, and C, and may place them in various relations, X, Y , and Z, and through all they remain still A, B, and C. And this, it is urged, proves that A, B, and C exist, or may exist, free from all relations or at least independently. My character, for example, may be compared with that of another man, or, having first lived to the north of him, I may change to the south; and to neither of us need it make a difference, and therefore we both are unaffected and so independent. But an answer to this fallacy seems even obvious. What is proved is that a certain character may, as such and in respect of that character, exist indifferently in various relations. But what is not proved at all is that this character could exist independent and naked.” (from Note B to Appearance and Reality, “Appearance and Quality”)
The difference between the claim that an object’s nature may be independent of the relations in which it stands, and the claim that an object could exist without standing in any relations.
