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Russell and Negative Facts
September 22, 2004
In Lecture III of his The Philosophy of Logical Atomism1, Russell discusses the problem of negative facts. Although he admits of a “certain repugnance” regarding the existence of negative facts, he claims that are indeed negative facts, and proceeds to counter an argument there are no such facts by Raphael Demos. I use this interaction between the views of Demos and Russell as the ground for a defense of the existence of negative facts. It seems that we have three main potential views that explain negative propositions. First, we can say that there are negative facts that ground the truth of these propositions. Second, we can offer an alternative view, namely, “incompatibility” (as Demos does) to explain negation by sticking to positive facts alone. Third, we may say there is nothing to which negative propositions correspond, that is, negation rests on a simple absence of a positive fact. In what follows, I hope to raise serious doubts about option two (incompatibility) and reduce option three (absence, or non-existent facts) to option one (negative facts). After doing so, I will offer an account of negative facts that relies on negative exemplification, a view that squares well with Russell’s ontology of logical atomism. I believe that, at the very least, if one is to accept Russell’s theory of truth, namely, that what grounds the truth of propositions is their correspondence to facts, then one is committed to negative facts.
The Challenge from Demos
Demos points out three aspects of negative propositions before providing an explanation for them. First, a negative proposition is objective and does rely on a cognitive subject, that is, to say ‘Gore is not president’ is not a mere expression of my disbelief in the proposition that Gore is president. Russell agrees with this. Second, that one cannot take a negative proposition at its face value since to do so would require one to include “a new class of negative facts.”2 Demos maintains that to do so would be bizarre since there are no such things as negative facts that one meets in experience. Thus any “knowledge of a negative nature seems to be derived form perception of a positive kind.”3 Demos claims that an interpretation of a special kinftnref3d is needed when considering negative propositions. Although Russell is also uneasy about negative facts because one does not have direct acquaintance with them, he does not agree that negative propositions are derived in some way from positive ones, but rather that we have to admit the existence of negative facts (I will say more on this below). The third point raised by Demos is that ‘not’ applies to the whole proposition not just the predicate. So ‘This is not-red’ is wrong to say, rather one must say ‘Not: this is red’ if one strict with language. Russell does not “entirely agree with”4 and I take it that he means that while makes a good point that is rather unnoticed about negative propositions, this cannot be applied to all negative propositions. This part of the discussion, however, is rather mysterious, and Russell himself is not clear about where is disagreement really lies.
Demos proposes the “contrariety” or “incompatibility” view to account for negative propositions. On this view, if I say “Bush is not in Washington” really means that I believe the opposite to “Bush is in Washington.” My saying “Bush is not at home” is really an ambiguous way of saying that, for instance, “Bush is in Crawford,” that is, there really is some positive proposition that makes “Bush is not in Washington” true. The positive proposition “Bush is in Crawford” is incompatible with the proposition “Bush is in Washington” thus, “Bush is in Crawford” accounts for the truth of “Bush is not in Washington.” It is not the case that there is a negative fact that makes the proposition “Bush is not in Washington” true. Although positive propositions are made true by positive facts (the fact that Bush is in Crawford, makes that proposition true), negative propositions are not made true in the same form, that is, they are not made true by negative facts.5
Russell’s Response
Russell has three main objections which are interrelated. First, Demos’ view, which he takes to be the best counter to the notion that there are negative facts6, introduces “incompatibility” as “fundamental and an objective fact, which is not so very much simpler than allowing negative facts.”7 If one says ‘There is not a hippopotamus in this room’, there is some way in which this statement is made true by a fact. On Demos’ view there is a positive incompatible fact, or multiple facts, which makes this proposition true. To Russell it seems much easier to allow the negative fact that there is no hippopotamus in this room than to list all the positive facts necessary to make the negative proposition true. It “cannot be merely that every part of this room is filled with something that is not a hippopotamus . . . we have been trying to avoid both negative facts and molecular facts, and all this succeeds in doing is to substitute molecular facts for negative facts.”8 The molecular fact here expressed is the disjunct of all the positive statements regarding the things that are in the room. This brings molecular facts into the ontology, something the logical atomist Russell wishes to avoid. Thus he thinks that allowing for negative facts (atomic) in one’s ontology is better. Although one may not be acquainted with negative facts, one is also not acquainted with disjunctive facts; one does not encounter something in the world which is represented by ‘or’ either.
Russell’s second complaint with regard to Demos’ account is that even if one tries to take incompatibility as a fundamental objective fact, this “incompatibility is not between facts but between propositions.”9 ‘P’ being incompatible with ‘q’ meftnref9ans that either ‘p’ or ‘q’ must be false, or perhaps they both are. But this incompatibility is clearly between the propositions, not the facts. For Demos’ to explain negatives this way he has to take as “fundamental fact something involving propositions as opposed to facts. It is quite clear that propositions are not what you might call ‘real’. If you were making an inventory of the world, propositions would not come in.”10 Demos would then need to give real ontological status to propositions, something that he would not want to do, and something that would clearly not be as simple as allowing negative facts.
Related to this is Russell’s third objection. Trying to avoid negative facts puts one in a tough position when one tries to determine what it is that actually corresponds to negative propositions. The truth or falsity of any proposition is only determined by facts. This is a core commitment of Russell’s view. So when you take a false proposition, ‘Gore is president’ it is false because of a real fact, namely the negative fact that Gore is not president, otherwise it will be very difficult to account for the falsity of ‘Gore is president’.11 The incompatibility view of Demos, according to Russell, forces one to admit that incompatibility is an objective fact in the world (thus allowing for disjunctive facts in the world), and it also forces one to account for truth in terms of propositions alone, not facts, and this is very problematic due to the correspondence theory of truth that Russell holds. Russell has one principle for truth, that only facts, as non-linguistic features in the world, make their corresponding propositions true or false. The incompatibility view, although an effort to avoid the “certain repugnance” of allowing for negative facts, amounts to a relation between propositions
More Problems with the Incompatibility View
Some other commentators have come to Russell’s defense.12 Brownstein, in particular, attacks the incompatibility view. Take the two sentences, “Bush is president” and “Gore is president.” The first sentence corresponds to the fact that Bush is president, and does so truly. The second sentence corresponds to the fact that Gore is not president, and do so falsely. But there is no cross correspondence, that is, “Gore is president” does not correspond in any way to the fact that Bush is president, and “Bush is president” does not correspond in any way to the fact that Gore is not president. The sentence “Gore is not president” corresponds truly to the fact---a negative one---that Gore is not president. “Bush is not president” corresponds falsely to the fact---a positive one---that Bush is president. Here, keeping with Russell’s account of facts and propositions, each fact---one positive and one negative---corresponds to two propositions.
On the incompatibility view, more facts would be required to bring in the actual opposition. “Gore is not president” is not just made false by the positive fact that Bush is President because additional facts are needed such as the fact that there can be only one president, and the fact that Gore and Bush are not the same person. One must turn to experience to learn these extra facts.
Absence of a Fact versus Negative Facts
Another avenue one could take to account for negative propositions is to claim that such propositions refer to nothing, or an absence of any fact whatsoever.13 The negative propositions does not correspond to anything in the world. This view seems to also fall into the trap of tying truth to propositions for as Oaklander and Miracchi claim, the sentence, ‘This is red does not exist’ can be altered to ‘It is false that this is red,’ and this statement of absence does not require a negative fact to ground the absence of this fact. Rather the absence “can be treated as a feature of the ‘language’ without ontological significance, since it implies nothing more than that a certain positive sentence does not correspond to anything.”14 So this view requires either positing some sort of objective fact (one would think either incompatibility of negativity) or one must account for absence by claiming the absence is just a feature of the language. This view does not square with Russell’s view of truth, namely, that the truth of propositions is determined by non-linguistic features of the world. If one accepts Russell’s theory of truth-makers, one should reject this account of absence.
I will turn to Russell himself to see what he says about absence. In fact, he claims that the absence of a fact just is the same as positing a negative fact. He writes in “On Propositions” that:
If A loves B, it may be said, that is a good substantial fact; while if A does not love B,
that merely expresses the absence of a fact composed of A and loving and B, and by no means involves the
actual existence of a negative fact. But the absence of a fact is itself a negative fact; it is the fact
there is not such a fact as A loving B. Thus, we cannot escape from negative facts in this way.15
Absence just means that there is no such fact as A loving B in the world. This is not a matter of a proposition that does not correspond to anything, but rather the fact that A does not love B. On Russell’s view there must be a fact that grounds the truth or falsity of propositions. Either absence of a fact is to be taken as the same as a negative fact, or it is just a feature of language. If it is the latter, then, for Russell, it cannot be the ground for the truth of the proposition that ‘A does not love B’.
Hochberg16 has also claimed that absence of a positive fact entails negative facts. Say that the world contains two things: a white square and a black square. There are thus four positive sentences: W(a), B(b), S(a), S(b). From these sentences there is no way to infer ‘~ W(b)’.17 There is an asymmetry between positive propositions and negative propositions if one claims that the fact that makes ‘B(b)’ true is also the same fact that makes ‘~ W(b)’ true since this is different then the sense in which one fact makes ‘W(a) true and ‘~ Wa’ false.18
Hochberg claims, as Russell does, that the pair “positive fact and negative fact” accomplishes the same thing that “presence and absence” would do. Hochberg still has questions about just how to ground the truth of sentences such as ~ W(b) ontologically19, as does Brownstein. Brownstein thinks that this question may have been answered differently by Russell and Wittgenstein and this explains why Russell thought there were negative facts, and why Wittgenstein did not. He admits that there is some conjecture here because both are not necessarily clear about the issue of negative facts.20 It is to the view of negative exemplification that I turn next.21 I believe this account explains negative facts and sticks with the fundamental tenets of logical atomism.
Negative Exemplification
What is the precise character of negative facts? Following Hochberg and Brownstein22, let me outline four major theories of the character of negative facts. Let ‘W’ denote the quality white, and both ‘a’ and ‘b’ be color spots. Suppose that ‘a’ bears the exemplification tie to W. Thus a’s exemplifying W is a positive fact. Therefore three possible formulations of negative facts are:
- A negative fact consists of W, b, and some third element that is negative, as well as a tie of exemplification.
- A negative fact consists of b, the tie of exemplification, and a negative quality.
- A negative fact consists of W, b, and the tie of negative exemplification.
- A negative fact consists of b, some quality other than W and the “absence” of W.23
Note that (2) and (4) only complicate positive facts. (2) proposes that there are
non-white qualities, thus there are both negative and positive qualities in the world. (4) is merely the “absence” view already discussed above which seems to imply that the proposition does not refer to anything, that is, there is an absence of qualities altogether. This seems to be the same as (2) since it seems to be the same as a negative quality such as non-white.24 The presence of the quality non-white and the absence of white seem to be the exact same thing. So, let us say that there is a negative fact which involves b and the negative quality ~ W. It would seem that we posit ~ W because we fail to notice the presence of W. We thus only introduce the quality ~ W because of the quality W. We introduce a pair of qualities, namely two complements, all the time. So when we do not notice not-white we must admit white as well. One then has the problem of imaginary or non-colors. Since I fail to notice not-yerne exemplified by any color spot, do I also have to admit the quality yerne?
Let us turn our attention to (1) and (3) then. It seems that we should dismiss (1) since there is one tie of exemplification that serves two roles, one negative and one positive, so that the same tie of exemplification accounts for both white and not-white. (3) is the view that there is a spot b, the quality white, and a tie of negative exemplification. There are two possible states of affairs into which these parts may be assembled.25 The spot may have the quality (white) or not. Brownstein introduces an informative analogy regarding the third view. Suppose you have two circles of the same diameter C 1 and C 2 which can be arranged in two different fundamental ways. Either the circles are placed in perfect coincidence or they are placed so that at least one point on C 1 does not coincide with C 2. In either case there is some determinate spatial relation between these circles.
Just as is the case with circles in spatial relations, so it is for colors. The object b must stand in some determinate relation. Either b is white or it is not white. Brownstein notes:
Just as the difference between the circumstance in which [C] 1 coincides perfectly with [C] 2 and the circumstances in which [C]1 and [C]2 do not coincide perfectly is a difference in the relations by which [C] 1 and [C] 2 are related, so it seems reasonable to suggest, the difference between b’s being white and b’s not being white is a difference in the “relations” or ties by which b and white are tied.26
So b is related somehow to white. There are two ways b may be related to white---negatively or positively---and this is determined by the tie of exemplification, or a tie of negative exemplification. If b can enter into one state of affairs, it can also relate to the other state of affairs.
The difference between Russell and Wittgenstein, according to Brownstein, may lie in how each conceived of the actual character of negative facts. While Wittgenstein may have believed that a negative fact must contain some negative element, perhaps Russell viewed negative facts as involving negative exemplification.27
Thus there is no element that we are acquainted with in experience, but the way things are exemplified. Negative facts involve negative exemplification and represent one possible state of affairs. This would dispel Halbasch’s concern that since “not” is just like “or” and “and” in that they are “particles” then Russell is inconsistent in allowing negative facts and not disjunctive and conjunctive facts.28 There is no element or particle that makes for a negation, rather it is the way a quality is exemplified that determines a positive or negative state of affairs regarding some object (such as a color spot).
Footnotes